TEST BANK for Thinking Mathematically, 8th edition by Robert Blitzer by ACADEMIAMILL

Blitzer, Thinking Mathematically, 8e Chapter 1 Test Item File SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find a counterexample to show that the statement is false. 1) No women have sat on the bench of the U.S. Supreme Court. Objective: (1.1) Understand and Use Inductive Reasoning

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) If a number is multiplied by itself, the result is greater than 0. A) The number is 0.

B) The number is 0.1.

C) The number is 1.

D) The number is

Objective: (1.1) Understand and Use Inductive Reasoning

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 3) All U.S. presidents have been one-term presidents. Objective: (1.1) Understand and Use Inductive Reasoning

4) All actors are Academy Award winners. Objective: (1.1) Understand and Use Inductive Reasoning

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify a pattern in the list of numbers. Then use this pattern to find the next number. 5) 2, 9, 16, 23, 30, ___ A) 37 B) 32 C) 44

D) 36

Objective: (1.1) Understand and Use Inductive Reasoning

6) 1, 12, 1, 18, 1, 24, 1, _____ A) 36

B) 30

C) 1

D) 32

C) 0

D) 2

C) -3,375

D) 3,375

C) -1/32

D) -1/64

Objective: (1.1) Understand and Use Inductive Reasoning

7) 31, 26, 21, 16, 11 A) 6

B) 5

Objective: (1.1) Understand and Use Inductive Reasoning

8) 3, -15, 75, -375, 1,875 A) 9,375

B) -9,375

Objective: (1.1) Understand and Use Inductive Reasoning

9) 1, -

1 1 1 1 , ,- , 8 16 2 4

A) 1/32

B) 1/64

Objective: (1.1) Understand and Use Inductive Reasoning

1 . 2

10) 1, 5, 2, 10, 4, 20 A) 30

B) 8

C) 6

D) 40

Objective: (1.1) Understand and Use Inductive Reasoning

Identify a pattern in the sequence of figures. Then use the pattern to find the next figure in the sequence. 11)

________________ C)

Objective: (1.1) Understand and Use Inductive Reasoning

12)

Objective: (1.1) Understand and Use Inductive Reasoning

The problem describes procedures that are to be applied to numbers. Repeat the procedure for four numbers of your choice. Write a conjecture that relates the result of the process to the original number selected. 13) Select a number. Multiply the number by 16. Add 16 to the product. Divide this sum by 8. Subtract 2 from the quotient. A) The result is one more than the original number. B) The result is one more than double the original number. C) The result is double the original number. D) The result is the original number. Objective: (1.1) Understand and Use Inductive Reasoning

Use inductive reasoning to predict the next line in the pattern. Then perform the arithmetic to determine whether your conjecture is correct. 14) 60 - 9 = 51 600 - 89 = 511 6,000 - 789 = 5,211

A) 60,000 - 6,789 = 593,211 C) 60,000 - 6,789 = 53,211

B) 6,000 - 6,789 = 53,211 D) 600,000 - 6,789 = 53,211

Objective: (1.1) Understand and Use Inductive Reasoning

15) 96 - 94 + 92 - 90 = 97 - 95 + 93 - 91 106 - 104 + 102 - 100 = 107 - 105 + 103 - 101 A) 116 + 114 - 112 - 110 = 117 + 115 - 113 + 111 C) 116 - 114 - 112 + 110 = 117 - 115 + 113 - 111

B) 116 + 114 - 112 + 110 = 117 + 115 - 113 + 111 D) 116 - 114 + 112 - 110 = 117 - 115 + 113 - 111

Objective: (1.1) Understand and Use Inductive Reasoning

16) 2 x 4 = 3 × 5 - 7 4 x 6 = 5 × 7 - 11 A) 6 × 8 = 7 × 9 + 13

B) 6 × 8 = 7 × 9 - 13

C) 6 × 8 = 7 × 9 - 15

D) 6 × 8 = 9 × 11 - 15

Objective: (1.1) Understand and Use Inductive Reasoning

17) 3 × 3 = 9 33 × 33 = 1,089 333 × 333 = 110,889 A) 3,333 × 3,333 = 112,889 C) 3,333 × 3,333 = 111,889

B) 3,333 × 3,333 = 11,108,889 D) 333 × 3,333 = 11,108,889

Objective: (1.1) Understand and Use Inductive Reasoning

18) 20 × 21 = 22 × 23 - (20 + 21 + 22 + 23) 21 × 22 = 23 × 24 - (21 + 22 + 23 + 24) A) 23 × 24 = 25 × 26 - (23 + 24 + 25 + 26) C) 23 × 24 = 25 × 26 - (22 + 21 + 20 + 19)

B) 22 × 23 = 24 × 25 - (20 + 21 + 22 + 23 + 24 + 25) D) 22 × 23 = 24 × 25 - (22 + 23 + 24 + 25)

Objective: (1.1) Understand and Use Inductive Reasoning

19) (1 × 9) - 9 = 0 (21 × 9) - 9 = 180 (321 × 9) - 9 = 2,880 A) (4321 × 9) - 9 = 3,879 C) (4321 × 9) - 9 = 28,880

B) (4321 × 9) - 9 = 38,880 D) (432 × 9) - 9 = 38,880

Objective: (1.1) Understand and Use Inductive Reasoning

20) (4 × 1) × (2 × 1) = 8 (4 × 10) × (2 × 2) = 160 (4 × 100) × (2 × 3) = 2,400 A) (4 × 1000) × (2 × 4) = 36,000 C) (4 × 1000) × (2 × 4) = 32,000

B) (4 × 1000) × (2 × 4) = 28,000 D) (4 × 1000) × (2 × 4) = 3,200

Objective: (1.1) Understand and Use Inductive Reasoning

21) 37,037 × 3 = 111,111 37,037 × 6 = 222,222 37,037 × 9 = 333,333 37,037 × 12 = 444,444 A) 111,111 × 15 = 1,666,665 C) 37,037 × 18 = 666,666

B) 37,037 × 13 = 481,481 D) 37,037 × 15 = 555,555

Objective: (1.1) Understand and Use Inductive Reasoning

1 1 1 = 13 2 3

22)

1 1 1 1 + = 13 9 2 9 1 1 1 1 1 = 1+ + 27 3 9 27 2 1 1 1 1 1 1 = 1+ + + 81 3 9 27 81 2

1 1 1 1 1 1 1 = 1+ + + + 729 3 9 27 81 729 2

1 1 1 1 1 1 1 = 1+ + + + 243 3 9 27 81 243 3

1 1 1 1 1 1 1 + + + + = 1243 3 9 27 81 243 2

1 1 1 1 1 1 1 + + + + = 1162 3 9 27 81 162 2

Objective: (1.1) Understand and Use Inductive Reasoning

23)

8(5) = 10(5 - 1) 8(5) + 8(25) = 10(25 - 1) 8(5) + 8(25) + 8(125) = 10(125 - 1) 8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)

A) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 8(3125 - 1) B) 8(5) + 8(25) + 8(125) + 8(625) + 8(1250) = 10(1250 - 1) C) 8(5) + 8(25) + 8(125) + 8(625) + 8(5000) = 10(5000 - 1) D) 8(5) + 8(25) + 8(125) + 8(625) + 8(3125) = 10(3125 - 1) Objective: (1.1) Understand and Use Inductive Reasoning

The following table relates an adult's body weight, in pounds, to his or her dosage of a certain medication, in milligrams. 24) Weight 100 125 150 175 200 225 Dosage 20 25 30 a. Use inductive reasoning to fill in the missing portions of the table. b. What would be the dosage of a person who weighs 375 pounds?

A) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 95 115

B) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 39 40

b. 80 mg

b. 70 mg

C) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 35 35

D) a. Weight 100 125 150 175 200 225 Dosage 20 25 30 35 40 45

b. 65 mg

b. 75 mg

Objective: (1.1) Understand and Use Inductive Reasoning

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem using inductive reasoning. 25) Write the next three "square" figurate numbers.

Objective: (1.1) Understand and Use Inductive Reasoning

26) Write the next three "triangular" figurate numbers.

Objective: (1.1) Understand and Use Inductive Reasoning

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which reasoning process is shown in the following example? 27) We examine the genetic blueprints of 100 people. No two individuals from this group of people have identical genetic blueprints. We conclude that for all people, no two people have identical genetic blueprints. A) reasoning by counterexample B) deductive reasoning C) theoretical reasoning D) inductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning

28) If Mary goes to the mall, she gets ice cream. Mary did not get ice cream. We conclude Mary did not go to the mall. A) inductive reasoning B) reasoning by counterexample C) theoretical reasoning D) deductive reasoning Objective: (1.1) Understand and Use Deductive Reasoning

The problem describes procedures that are to be applied to numbers. Represent the original number as n and use deductive reasoning to prove a conjecture that relates the result of the process to the number n. 29) Select a number. Multiply the number by 24. Add 24 to the product. Divide this sum by 12. Subtract two from the quotient. 24n + 24 24n + 24 - 2 = 2n + 2 - 2 = 2n -2=n+1-2=n-1 A) B) 12 24

24n + 24 -1=n+1-1=n 24

24n + 12 - 2 = 2n + 1 - 2 = 2n - 1 12

Objective: (1.1) Understand and Use Deductive Reasoning

Solve the problem. 30) Study the pattern, or trend, shown by the data. Then select the expression that best describes the number of tickets sold, in thousands, n years after Year 1.

A) 2.5 - 0.2n

B) 2.5 - 1.02n

C) 2.5 + 0.2n

D) 2.5 + 1.02n

Objective: (1.1) Understand and Use Deductive Reasoning

Round the number to the given place value. 31) In the past year, a company spent $693,749,312 on advertising. Round the advertising figure to the nearest hundred thousand. A) $693,800,000 B) $700,000,000 C) $693,700,000 D) $600,000,000 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

32) A publishing company sold 16,267,591 books last year. Round the number of books sold to the nearest ten million. A) 16,270,000 B) 20,000,000 C) 16,000,000 D) 10,000,000 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

33) In a town in Nebraska, the average consumption of soft drinks per day per elementary school student is 14.189 ounces. Round this value to the nearest tenth. A) 14.2 ounces B) 15 ounces C) 14.3 ounces D) 14.1 ounces Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

34) According to his ultra-precise scale, Jeremy gained 3.558 pounds in a three-month period. Round this amount to the nearest hundredth. A) 3.57 pounds B) 0.56 pounds C) 4 pounds D) 3.56 pounds Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

35) In a laboratory course in veterinary biology, fleas gathered from Alexander, a volunteered pet dog, averaged 0.168209 inch in length. Round this amount to the nearest thousandth. A) 0.169 inch B) 0.168 inch C) 1 inch D) 0.167 inch Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

Solve the problem with estimation, but do not use a calculator. Use rounding to make the resulting calculations simple. 36) Estimate the cost to buy a refrigerator for $999, a stove for $459, and a dishwasher for $349. A) $1,800 B) $1,600 C) $1,900 D) $1,700 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

37) Estimate the cost of 101 shirts at $19.95 each. A) $1995 B) $2000

C) $2,014.95

D) $200

Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

38) If a person earns $29.90 per hour, estimate that person's annual salary. A) $70,000 B) $60,000 C) $50,000

D) $40,000

Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

39) Find an estimate of A) 36

0.245 × 72 . 0.538

B) 144

C) 9

D) 18

Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

40) Estimate the number of seconds in a day. A) 3,600 seconds B) 72,000 seconds

C) 1,400 seconds

D) 600,000 seconds

Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

41) If a person earns $19,500 per year, estimate that person's hourly salary. A) $10 B) $50 C) $100

D) $40

Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

42) You rented an apartment for $815 per month for 4 years. What is the total amount you paid in rent? A) $9600 B) $4,800 C) $38,400 D) $3,200 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

43) You spend $40.24 for a meal. If you want to leave a 15% tip, estimate the amount of the tip. A) $4 B) $6 C) $10 D) $8 Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 44) Four people share the use of a cable modem service that costs $49.95 a month. Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

45) If Jessica can type 48 words per minute, estimate the number of words she can type in one hour. Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The map shows main roads between various towns in a certain county. Use the map to answer the question. 46)

90 a. Estimate the distance from State City to Capitol Park. b. If a vehicle travels at an average of 30 miles per hour, estimate the traveling time from State City to Capitol Park. A) a. 360 miles B) a. 180 miles C) a. 270 miles D) a. 90 miles b. 12 hours b. 6 hours b. 9 hours b. 3 hours Objective: (1.2) Use Estimation Techniques to Arrive at an Approximate Answer to a Problem

The circle graph shows the number of times a group of survey respondents watched the news in the past week. Use the chart to answer the question.

47) If the number of respondents in the study was approximately 44,779, estimate how many stated that they watched the news 5-6 times in the last week. A) 8000 respondents B) 12,000 respondents C) 6000 respondents D) 10,000 respondents Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

The bar graph below represents various colors of cars sold. Use the graph to answer the question(s).

48) Estimate the number of tan cars sold. A) 30,000 B) 35,000

C) 40,000

D) 25,000

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

49) Estimate the number of white cars sold. A) 50,000 B) 47,000

C) 40,000

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

D) 52,000

50) Which color sold over 50,000 cars? A) White B) Tan

C) Silver

D) Red

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

51) Which color sold under 20,000 cars? A) White B) Black

C) Tan

D) Yellow

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

52) Estimate how many more black cars were sold than silver cars. A) 21,000 B) 11,000 C) 14,000

D) 31,000

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

53) Estimate how many more white cars were sold than tan cars. A) 22,000 B) 17,000 C) 7,000

D) 27,000

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

The bar graph shows the percentages of health clubs in a large city that offer the service listed on the left. Use the graph to answer the question.

54) Estimate the percentage of health clubs in this city that offer Pilates. A) 19% B) 26% C) 29%

D) 23%

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

55) Which services are offered at at least 20% of this city's health clubs and at most 45% of the clubs? A) massage, Pilates and nutritional counseling B) Pilates and nutritional counseling C) Pilates, nutritional counseling, and body fat testing D) massage, Pilates, nutritional counseling, and body fat testing Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

The bar graph shows the amount of scholarship money available to student athletes at State University in four consecutive years. Use the graph to answer the question.

56) Estimate the amount of scholarship money available to female student athletes at State University in year 1. A) $16,000 B) $11,000 C) $1,900 D) $7,000 Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

The line graph below shows the price of a stock over the course of the day. Use the graph to answer the question(s). 10 9 8 7 Stock Price 6 (in dollars) 5 4 3 2 1 9AM 10AM 11AM 12PM 1PM

2PM

3PM

4PM

57) At what time was the stock price highest? A) 12 PM B) 2 PM

5PM 6PM

C) 9 AM

D) 1 PM

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

58) At what time was the stock price the lowest? A) 6 PM B) 10 AM

C) 1 PM

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

D) 9 AM

The line graph shows the pollution rate for a certain lake over six decades. Use the graph to answer the question.

59) Find an estimate for the pollution rate of the lake at the beginning of decade 6. A) 2.5% B) 3% C) 1.5%

D) 1%

Objective: (1.2) Apply Estimation Techniques to Information Given by Graphs

The bar-graph shows the average living expenses of an undergraduate student. Provide an appropriate response.

60) Estimate the yearly increase in living expenses. A) $750 B) $500

C) $450

D) $650

Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables

61) Write a mathematical model that estimates the average living expenses, E, of an undergraduate student for x years after 2000. A) E = 5000 + 750x B) E = 5000 + 450x C) E = 5000 + 500x D) E = 5000 + 650x Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables

62) Use a mathematical model to predict the average living expenses of an undergraduate student in 2015 A) $12,500 B) $11,750 C) $14,750 D) $16,250 Objective: (1.2) Develop Mathematical Models that Estimate Relationships Between Variables

State the necessary piece of information that is missing which prevents you from solving the problem. 63) A car traveled at an average rate of 55 miles per hour and then reduced its speed to 49 miles per hour for the rest of the trip. If the trip took 4 hours, determine how long the car traveled at each rate. A) the destination B) the time of day C) the time at each rate D) the distance of the trip Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

Solve the problem. Then identify the piece of information that is unnecessary to solve the problem. 64) A rental car company that rents cars for local-only use charges $30 plus $0.30 for each mile the rental car is driven. If a customer gives the rental attendant $100 for a charge of $54, how many miles did the customer drive? A) 40 miles unnecessary information: the $54 charge B) 79 miles unnecessary information: the $0.30 per-mile charge C) 180 miles unnecessary information: the $30 flat charge D) 80 miles unnecessary information: giving $100 to attendant Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

Use the four-step method in problem solving to solve the problem. 65) City A has an elevation of 3,189 feet above sea level while city B has an elevation of 77 feet below sea level. How much higher is City A than City B? A) -3,012 feet B) -3,112 feet C) 3,266 feet D) 3,366 feet Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

66) Ashley owns 16 acres of land which she rents to a timber grower for $3,886 per acre per year. Her property taxes are $776 per acre per year. How much profit does she make on the land each year? A) $49,760 B) $62,952 C) $74,592 D) $61,400 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

67) At the beginning of the year, the odometer on an SUV read 37,587 miles. At the end of the year, it read 51,847 miles. If the car averaged 23 miles per gallon, how many gallons of gasoline did it use during the year? A) 620 gallons B) 14,260 gallons C) 62 gallons D) 327,980 gallons Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

68) A couch sells for $820. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $400 down and $60 a month for 12 months. How much is saved by paying the total amount at the time of purchase? A) $960 B) $300 C) $100 D) $30 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

69) CD's were purchased at $55 per dozen and sold at $40 for four CD's. Find the profit on 7 dozen CD's. A) $15 B) $65 C) $105 D) $455 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

70) A college cafeteria pays student cashiers $7.50 per hour. Cashiers earn an additional $1.70 per hour for each hour worked over 35 hours per week. A cashier worked 37 hours one week and 42 hours the second week. How much did this cashier earn in this two-week period? A) $726.80 B) $607.80 C) $592.50 D) $540.30 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

71) A car rents for $230 per week plus $0.25 per mile. Find the rental cost for a three-week trip of 700 miles. A) $175.00 B) $865.00 C) $1,215.00 D) $405.00 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

72) An accountant receives a salary of $261,500 per year. During the year, he plans to spend $91,000 on his mortgage, $58,000 on food, $32,000 on clothing, $43,000 on household expenses, and $29,000 on other expenses. With the money that is left, he expects to buy as many shares of stock at $250 per share as possible. How many shares will he be able to buy? A) 33 shares B) 34 shares C) 31 shares D) 36 shares Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

73) Andrea decided to rollerblade to her mother's house. Six blocks from her home, one of the wheels on her skate broke, and she had to walk the remaining eight blocks to her mother's. She could not repair her skate and had to walk all the way back home. How many more blocks did Andrea walk than she skated? A) 14 blocks B) 22 blocks C) 16 blocks D) 28 blocks Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

74) A store received 200 containers of milk to be sold by February 1. Each container cost the store $0.81 and sold for $1.57. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1. If 180 containers were sold by February 1, how much profit did the store make? A) $120.60 B) $130.60 C) $145.80 D) $136.80 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

Solve the problem using the strategy of making a list or using a diagram. 75) How many matches will be required to determine the champion in a single-elimination tennis tournament that starts with 58 players? A) 58 matches B) 48 matches C) 57 matches D) 29 matches Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

76) A coin is tossed four times. How many ways can it come up heads 3 times and tails once? A) 4 B) 2 C) 3 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

D) 1

Solve the problem using the strategy of your choice. 77) Can you place the digits 1 through 9 into a 3 x 3 square so that each row, column, and diagonal add up to the same total? Four digits have been inserted. ( ) 1 ( ) 3 ( )( ) 4 ( ) 2 A) B) C) D) 8 1 9 8 1 6 6 1 8 8 1 7 3 5 7 3 5 7 3 5 7 3 5 6 4 6 2 4 9 2 4 9 2 4 9 2 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 78) Some numbers in the printing of a division problem have become illegible. They are designated below by *. Fill in the blanks. 1 * * * * 5 * * * 3 6 * 7 2 * * * * ** * * * 0 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 79) Three people have telephone prefixes whose three digits have the same sum. One of the prefixes is 448. None of the prefixes contains a digit that is in one of the other prefixes. None of the prefixes has a first digit of 6 or 1. One of the prefixes begins with 5. Another ends with 2. What is the prefix that ends with 2? A) 372 B) 772 C) 962 D) 592 Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

80) Find the number of squares in the figure.

A) 30

B) 55

C) 26

Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

D) 25

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. This exercise involves problems encountered in everyday life. Write seven or more short solutions that might be effective in solving the problem. 81) Your younger brother has just graduated college. You allow him to live in your house, rent-free, under the condition that he does all the household chores. However, after two months of living with you, your brother has not done any chores. What actions can you take to remedy this situation? Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

Solve the problem. 82) A certain Internet provider charges $16.95 for 150 hours of online usage per month and $0.95 for each additional hour. If Marc was online for 200 hours last month, what was his bill for that month? Objective: (1.3) Solve Problems Using the Organization of the Four-Step Problem-Solving Process

Answer Key Testname: UNTITLED1

1) Answers may vary. Sandra Day O'Connor is one possible answer. 2) A 3) Answers may vary. Sample answer: George Washington was elected to two terms. 4) Answers may vary. Sample answer: Actor Jim Carrey is not an Academy Award winner. 5) A 6) B 7) A 8) B 9) C 10) B 11) D 12) A 13) C 14) C 15) D 16) C 17) B 18) D 19) B 20) C 21) D 22) C 23) D 24) D 25) 16, 25, 36 26) 10, 15, 21 27) D 28) D 29) A 30) A 31) C 32) B 33) A 34) D 35) B 36) A 37) B 38) B 39) A

40) B 41) A 42) C 43) B 44) $50 ÷ 4 = $12.50 45) 50 × 60 = 3000 46) C 47) A 48) A 49) B 50) D 51) D 52) A 53) B 54) D 55) B 56) D 57) D 58) D 59) C 60) D 61) D 62) C 63) D 64) D 65) C 66) A 67) A 68) B 69) D 70) B 71) B 72) B 73) C 74) B 75) C 76) A 77) B 148 78) 36 5328 36

81) Answers may vary. Possible answers may include: 1. I could kick my brother out of my house. 2. I could start charging my brother rent. 3. I could make a list or schedule of chores that I want him to perform, in hopes of motivating him. 4. I could offer my brother an additional incentive for each chore he performs. 5. I could relentlessly follow my brother around the house to ensure that he performs his chores. 6. I can throw out the agreement completely and allow him to live in my house for free. 7. I could hire a maid and make my brother pay for it. 8. I could change all the locks on the doors. 82) $64.45

172 144 288 288 0

79) B 80) B 17

Blitzer, Thinking Mathematically, 8e Chapter 2 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the collection is not well defined and therefore not a set. 1) The collection of frogs and toads currently in tanks at a nature center A) well defined; set B) not well defined; not a set Objective: (2.1) Determine Whether the Collections are Well Defined or Not

2) The collection of beautiful oil paintings currently on display at an art gallery A) well defined; set B) not well defined; not a set Objective: (2.1) Determine Whether the Collections are Well Defined or Not

Write a word description of the set. 3) {January, February, March, April, May, June, July, August, September, October, November, December} A) seasons of the year B) days of the year C) days of the week D) months of the year Objective: (2.1) Use Three Methods to Represent Sets

4) {2, 4, 6, 8, ..., 100} A) odd numbers from 2 to 100 C) even numbers from 2 to 100

B) numbers from 2 to 100 D) all even numbers

Objective: (2.1) Use Three Methods to Represent Sets

5) {March, May} A) the set of months in the year C) the set of months that begin with M

B) the set of months in the Spring D) the set of months that are warm

Objective: (2.1) Use Three Methods to Represent Sets

6) {10, 11, 12, 13, ...} A) the set of natural numbers less than 14 C) the set of natural numbers

B) the set of two-digit natural numbers D) the set of natural numbers greater than 9

Objective: (2.1) Use Three Methods to Represent Sets

Express the set using the roster method. 7) the set of natural numbers less than or equal to 7 A) {0, 1, 2, 3, . . . , 6} B) {1, 2, 3, . . . , 7}

C) {1, 2, 3, . . . , 6}

D) {0, 1, 2, 3, . . . , 7}

C) {2, 4, 6, . . . , 14}

D) {1, 3, 5, . . . , 15}

C) {10,11,12,...}

D) {10,11,12}

Objective: (2.1) Use Roster Method

8) the set of odd natural numbers less than 15 A) {1, 3, 5, . . . , 13} B) {0, 1, 3, 5, . . . , 13} Objective: (2.1) Use Roster Method

9) {x | x % N and x is greater than 9} A) {9,10,11,...} B) {10,12,14,...} Objective: (2.1) Use Roster Method

10) {x | x % N and x lies between 0 and 4} A) {1, 2, 3, 4} B) {0, 1, 2, 3}

C) {0, 1, 2, 3, 4}

Objective: (2.1) Use Roster Method

List the elements in the set. 11) The set of the days of the week A) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} B) {Saturday, Sunday} C) {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} D) {Tuesday, Thursday} Objective: (2.1) Use Roster Method

Determine if the set is the empty set. 12) {0, +} A) Yes, it is the empty set.

B) No, it is not the empty set.

Objective: (2.1) Define and Recognize the Empty Set

13) {x|x is a living U.S. president born after 1700} A) Yes, it is the empty set.

B) No, it is not the empty set.

Objective: (2.1) Define and Recognize the Empty Set

14) {x|x is the number of living U.S presidents born before 1700} A) Yes, it is the empty set. B) No, it is not the empty set. Objective: (2.1) Define and Recognize the Empty Set

15) {x|x is a day of the week whose name begins with the letter Y} A) Yes, it is the empty set. B) No, it is not the empty set. Objective: (2.1) Define and Recognize the Empty Set

16) {x|x < 2 and x > 6} A) Yes, it is the empty set.

B) No, it is not the empty set.

Objective: (2.1) Define and Recognize the Empty Set

17) {x|x % Ν and 10 < x < 14} A) Yes, it is the empty set.

B) No, it is not the empty set.

Objective: (2.1) Define and Recognize the Empty Set

18) {x|x is a number less than 6 or greater than 10} A) Yes, it is the empty set.

B) No, it is not the empty set.

Objective: (2.1) Define and Recognize the Empty Set

Determine whether the statement is true or false. 19) 9 % {1, 3, 5, 7, 9} A) True

B) False

Objective: (2.1) Use the Symbols % and '

D) {1, 2, 3}

20) 7 % {1, 2, 3, ..., 15} A) True

B) False

Objective: (2.1) Use the Symbols % and '

21) 19 % {2, 4, 6, ..., 20} A) True

B) False

Objective: (2.1) Use the Symbols % and '

22) 14 ' {1, 2, 3, ..., 10} A) True

B) False

Objective: (2.1) Use the Symbols % and '

23) 11 ' {1, 2, 3, ..., 40} A) True

B) False

Objective: (2.1) Use the Symbols % and '

24) 3 ' {x|x % N and x is odd} A) True

B) False

Objective: (2.1) Use the Symbols % and '

25) 22 ' {x|x % N and 15 < x K 25} A) True

B) False

Objective: (2.1) Use the Symbols % and '

26) -5 ' N A) True

B) False

Objective: (2.1) Use the Symbols % and '

Find the cardinal number for the set. 27) {33, 35, 37, 39, 41} A) 4

B) 33

C) 6

D) 5

C) 60

D) 30

C) 3

D) 1

Objective: (2.1) Find the Cardinal Number for Each Set

28) {10, 12, 14, . . . , 68} A) 20

B) 15

Objective: (2.1) Find the Cardinal Number for Each Set

29) {x | x is a day of the week that begins with the letter N} A) 0 B) 2 Objective: (2.1) Find the Cardinal Number for Each Set

30) Determine the cardinal number of the set {x | x is a letter of the alphabet} A) 25 B) 26 C) 30

D) 23

Objective: (2.1) Find the Cardinal Number for Each Set

31) D = {seven} A) 1

B) 7

C) 0

Objective: (2.1) Find the Cardinal Number for Each Set

D) 5

32) B = {x|x % N and 1 K x < 9} A) 7

B) 9

C) 8

D) 10

C) 9

D) 16

Objective: (2.1) Find the Cardinal Number for Each Set

33) C = {x|x K 4 and x L 12} A) 0

B) 8

Objective: (2.1) Find the Cardinal Number for Each Set

Are the sets equivalent? 34) A is the set of residents age 45 or older living in the United States B is the set of residents age 45 or older registered to vote in the United States A) Yes B) No Objective: (2.1) Recognize Equivalent Sets

35) A = {11, 12, 13, 14, 15} B = {10, 11, 12, 13, 14} A) Yes

B) No

Objective: (2.1) Recognize Equivalent Sets

36) A = {13, 15, 17, 19, 21} B = {14, 16, 18, 20, 22} A) Yes

B) No

Objective: (2.1) Recognize Equivalent Sets

37) A = {11, 12, 12, 13, 13, 13, 14, 14, 14, 14} B = {14, 13, 12, 11} A) Yes

B) No

Objective: (2.1) Recognize Equivalent Sets

38) A = {Larry, Moe, Curly. Shemp} B = {Posh, Sporty, Baby, Scary} A) Yes

B) No

Objective: (2.1) Recognize Equivalent Sets

Are the sets equal? 39) {p, q, r, s} = {q, s, r, p} A) Yes

B) No

Objective: (2.1) Recognize Equal Sets

40) {20, 22, 24, 26, 28} = {22, 24, 26, 28} A) Yes

B) No

Objective: (2.1) Recognize Equal Sets

41) {7, 7, 11, 11, 16} = {7, 11, 16} A) Yes

B) No

Objective: (2.1) Recognize Equal Sets

42) A is the set of residents age 53 or older living in the United States B is the set of residents age 53 or older registered to vote in the United States A) Yes B) No Objective: (2.1) Recognize Equal Sets

43) A = {20, 21, 22, 23, 24} B = {19, 20, 21, 22, 23} A) Yes

B) No

Objective: (2.1) Recognize Equal Sets

44) A = {21, 23, 25, 27, 29} B = {22, 24, 26, 28, 30} A) Yes

B) No

Objective: (2.1) Recognize Equal Sets

45) A = {14, 15, 15, 16, 16, 16, 17, 17, 17, 17} B = {17, 16, 15, 14} A) Yes

B) No

Objective: (2.1) Recognize Equal Sets

Determine whether the set is finite or infinite. 46) {x | x % N and x L 100} A) Finite

B) Infinite

Objective: (2.1) Distinguish Between Finite and Infinite sets

47) {x | x % N and x K 1,000} A) Finite

B) Infinite

Objective: (2.1) Distinguish Between Finite and Infinite sets

48) The set of natural numbers less than 50 A) Finite

B) Infinite

Objective: (2.1) Distinguish Between Finite and Infinite sets

49) The set of natural numbers less than 1 A) Finite

B) Infinite

Objective: (2.1) Distinguish Between Finite and Infinite sets

Express the set using set-builder notation. Use inequality notation to express the condition x must meet in order to be a member of the set. 50) A = {14, 15, 16, 17, 18,...} A) {x | x % N and x K 14} B) {x | x % N and x L 14} C) {x | x % N and x > 14} D) {x | x % N and x L 18} Objective: (2.1) Apply Set Notation to Sets of Natural Numbers

51) A = {600, 601, 602, . . ., 6,000} A) {x | x % N and 600 K x K 6,000} C) {x | x % N and x L 600 }

B) {x | 600 < x < 6,000} D) {x | x % N and x K 6,000}

Objective: (2.1) Apply Set Notation to Sets of Natural Numbers

The bar graph shows the percentage of adults that use the Internet for specific tasks. Use the graph to represent the given set using the roster method. 52)

34 29

25 18 13

the set of tasks in which usage exceeds 23% A) {e-mail, information searches} C) {e-mail, information searches, news}

B) {e-mail, information searches, news, job} D) {job, school}

Objective: (2.1) Solve Applications

53)

33 28

24 17 12 {x | x is a task in which usage lies between 14% and 32%} A) {news, job} C) {email, information searches, news, job, school} Objective: (2.1) Solve Applications

B) {information searches, news, job} D) {news}

The line graph shows the percentage of obese adults in a certain city by age. Based on the information in the graph, represent the set using the roster method. 54)

30 25 20 15 10 5

{x | x is an age at which 20% of adults in city X are obese} A) {30} B) {40}

C) {60}

Objective: (2.1) Solve Applications

Write 5 or * in the blank so that the resulting statement is true. 55) {4, 6, 8} {3, 4, 5, 6, 8} A) 5

B) *

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

56) {3, 40, 45} A) 5

{9, 40, 45, 55} B) *

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

57) {red, blue, green} _____ {blue, green, yellow, black} A) 5

B) *

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

58) {x | x is a tree} _____ {x | x is a spruce tree} A) 5

B) *

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

59) {c, a, n, d, i, d, a, t, e} _____ {a, c, d, e, i, t, a, n, d} A) 5

B) *

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

60)

8 3 11 7 , _____ , 11 7 8 3

A) 5

B) *

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

D) {50}

Use 5, *, 2, or both 2 and 5 to make a true statement. 61) {a, b} {z, a, y, b, x, c} A) * B) 2 and 5

C) 2

D) 5

C) 5

D) 2 and *

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

62) {6, 7, 8} A) *

{6, 7, 8} B) 2

Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

63) {x | x is a male who is registered with Selective Service} _____ {x | x is a male who is in the Army} A) 2 B) 5 and 2 C) * D) 5 Objective: (2.2) Recognize Subsets and Use the Notation 2, 5

Determine whether the statement is true or false. 64) Alice 5 {Bob, Carol, Ted, Alice} A) True

B) False

Objective: (2.2) Determine Whether Each statement is True or False

65) {Ted} 5 {Bob, Carol, Ted, Alice} A) True

B) False

Objective: (2.2) Determine Whether Each statement is True or False

66) +5 {France, Germany, Switzerland} A) True

B) False

Objective: (2.2) Determine Whether Each statement is True or False

67) {2, 9} * {9, 2} A) True

B) False

Objective: (2.2) Determine Whether Each statement is True or False

68) {1} * + A) True

B) False

Objective: (2.2) Determine Whether Each statement is True or False

List all the subsets of the given set. 69) {Siamese, domestic shorthair} A) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, B) {Siamese, domestic shorthair}, {Siamese}, {domestic shorthair}, { } C) {Siamese, domestic shorthair}, {domestic shorthair}, { } D) {Siamese}, {domestic shorthair}, { } Objective: (2.2) Determine the Number of Subsets of a Set

70) {12} A) {12}

B) { }

C) {0}, {12}, { }

Objective: (2.2) Determine the Number of Subsets of a Set

D) {12}, { }

71) + A) +

B) no subsets

C) { }, {0}

D) {+}

Objective: (2.2) Determine the Number of Subsets of a Set

Calculate the number of subsets and the number of proper subsets for the set. 1 1 1 1 , , , 72) 6 7 8 9 A) 15; 14

B) 14; 15

C) 15; 16

D) 16; 15

C) 64; 63

D) 63; 64

C) 510; 511

D) 511; 512

C) 16; 15

D) 8; 7

C) 64; 65

D) 128; 127

Objective: (2.2) Determine the Number of Subsets of a Set

73) {1, 3, 5, 7, 9, 11} A) 63; 62

B) 62; 63

Objective: (2.2) Determine the Number of Subsets of a Set

74) the set of natural numbers less than 10 A) 512; 511 B) 511; 510 Objective: (2.2) Determine the Number of Subsets of a Set

75) the set of words describing the colors on a stoplight A) 15; 16 B) 7; 8 Objective: (2.2) Determine the Number of Subsets of a Set

76) {x | x is a day of the week} A) 127; 126

B) 128; 129

Objective: (2.2) Determine the Number of Subsets of a Set

Provide an appropriate response. 77) If set A is equivalent to the set of natural numbers, then n(A) < E0 . A) True

B) False

Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets

78) If set A is equivalent to the set of odd natural numbers, then n(A) = E0 . A) True

B) False

Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets

79) The set {1, 2, 3, ..., 100} has 2 100 proper subsets. A) True

B) False

Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets

80) {x|x % N and 45 < x < 70} 5 {x|x % N and 45 K x K 70} A) True

B) False

Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets

81) +* {+ } A) True

B) False

Objective: (2.2) Apply Concepts of Subsets and Equivalent Sets to Infinite Sets

Consider below the branching tree diagram based on the number per 3000 American adults.

Let T = the set of Americans who like classical music R = the set of Republicans who like classical music D = the set of Democrats who like classical music I = the set of Independents who like classical music Determine whether the statement is true or false. 82) R % T A) True

B) False

Objective: (2.2) Solve Applications

83) D 2 T A) True

B) False

Objective: (2.2) Solve Applications

84) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music W 2T A) True B) False Objective: (2.2) Solve Applications

85) Let M = the set of Democratic men who like classical music W = the set of Democratic women who like classical music If x %D, then x %M. A) True B) False Objective: (2.2) Solve Applications

86) Let M = the set of Republican men who like classical music W = the set of Republican women who like classical music If x %W, then x %R. A) True B) False Objective: (2.2) Solve Applications

87) If x %R, then x'I. A) True

B) False

Objective: (2.2) Solve Applications

88) Let M = the set of Independent men who like classical music W = the set of Independent women who like classical music The set of elements in M and W combined is equal to set I. A) True B) False Objective: (2.2) Solve Applications

Use the formula for the number of subsets of a set with n elements to solve the problem. 89) Pasta comes with tomato sauce and can be ordered with some, all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli, shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for ordering pasta with tomato sauce? A) 128 B) 255 C) 127 D) 256 Objective: (2.2) Solve Applications

90) A village has 4 fire engines. If a radio dispatcher receives a call, depending on the nature of the situation, no engines, one engine, two engines, three engines, or all four engines can be sent to a fire. How many options does the dispatcher have for sending the fire engines to the scene of the caller? A) 15 B) 8 C) 7 D) 16 Objective: (2.2) Solve Applications

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Describe a universal set U that includes all elements in the given sets. Answers may vary. 91) A = {Copeland, Gershwin, Bernstein} B = {Strauss, Mendlssohn} Objective: (2.3) Understand the Meaning of a Universal Set

92) A = {fruit juice, coffee} B = {tea, spring water} Objective: (2.3) Understand the Meaning of a Universal Set

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set. 93) A = {2, 4, b, d} A) {1, 5, a, c, e} B) {1, 5, a, e} C) {1, 2, 4, 5, a, b, c, d, e} D) {1, 3, 5, a, c, e} Objective: (2.3) Understand the Meaning of a Universal Set

Let U = {21, 22, 23, ..., 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, ..., 39}, and D = {22, 24, 26, 28, ..., 40}. Use the roster method to write the following set. 94) A' A) A' = {21, 22, 23, . . . , 40} B) A' = {26, 28, 30, . . . , 40} C) A' = {27, 29, 31, . . . , 39} D) A' = {26, 27, 28, . . . , 40} Objective: (2.3) Understand the Meaning of a Universal Set

Let U = {21, 22, 23, 24, ...}, A = {21, 22, 23, 24, ..., 40}, B = {21, 22, 23, 24, ..., 50}, C = {22, 24, 26, 28, ...}, and D = {21, 23, 25, 27, ...}. Use the roster method to write the following set. 95) C' A) C' = {21, 23, 25, 27, ..., 39} B) C' = {21, 22, 23, 24, ...} C) C' = {21, 23, 25, 27, ...} D) C' = {22, 24, 26, 28, ...} Objective: (2.3) Understand the Meaning of a Universal Set

Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 96) (A 1 B)' A) {r, t, v, x} B) {s, u, w}

C) {r, s, t, u, v, w, x, z}

D) {t, v, x}

C) {s, u, w}

D) {q, s, t, u, v, w, x, y}

C) {q, s, u, v, w, x, y, z}

D) {w, y}

Objective: (2.3) Perform Operations with Sets

97) A' 1 B A) {r, s, t, u, v, w, x, z}

B) {q, r, s, t, v, x, y, z}

Objective: (2.3) Perform Operations with Sets

98) C' 1 A' A) {q, r, s, t, u, v, x, z}

B) {s, t}

Objective: (2.3) Perform Operations with Sets

99) B 1 C A) {q, s, u, w, y} C) {q, s, v, w, x, y, z}

B) {v, w, x, y, z} D) {q, r, s, t, u, v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

100) C 1 + A) {v, w, x, y, z}

B) {q, s, y, z}

C) { }

D) {q, s, u, w, y}

Objective: (2.3) Perform Operations with Sets

101) B 1 U A) {q, s, y, z} C) {q, r, s, t, u, v, w, x, y, z}

B) {q, s, u, w, y} D) {v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

102) A . B' A) {u, w}

B) {r, s, t, u, v, w, x, z}

C) {t, v, x}

D) {q, s, t, u, v, w, x, y}

C) {r, s, t, u, v, w, x, z}

D) {t, v, x}

C) {t, v, x}

D) {q, s, t, u, v, w, x, y}

Objective: (2.3) Perform Operations with Sets

103) (A 1 B)' A) {s, u, w}

B) {r, t, v, x}

Objective: (2.3) Perform Operations with Sets

104) (A . B)' A) {r, t, u, v, w, x, z}

B) {s, u, w}

Objective: (2.3) Perform Operations with Sets

105) A' 1 B A) {q, r, s, t, v, x, y, z}

B) {r, s, t, u, v, w, x, z}

C) {q, s, t, u, v, w, x, y}

D) {s, u, w}

C) {w, y}

D) {q, r, s, t, u, v, x, z}

C) {w, y}

D) {r, t}

C) {q, s, u, w, y, z}

D) {q, s, y}

Objective: (2.3) Perform Operations with Sets

106) C' 1 A' A) {s, t}

B) {q, s, u, v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

107) C' . A' A) {q, r, s, t, u, v, x, z}

B) {q, s, u, v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

108) A . B A) {r, t, u, v, w, x, z}

B) {v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

109) B 1 C A) {v, w, x, y, z} C) {q, s, u, w, y}

B) {q, s, v, w, x, y, z} D) {q, r, s, t, u, v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

110) A' A) {r, t, v, x, z} C) {q, r, s, t, u, v, w, x, y, z}

B) {s, u, w, y} D) {q, s, y, z}

Objective: (2.3) Perform Operations with Sets

111) (A . C)' A) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z}

B) {w, y} D) {q, r, s, t, u, v, x, z}

Objective: (2.3) Perform Operations with Sets

112) C 1 + A) {q, s, u, w, y}

B) {q, s, y, z}

C) {v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

113) B 1 U A) {q, r, s, t, u, v, w, x, y, z} C) {q, s, y, z}

B) {q, s, u, w, y} D) {v, w, x, y, z}

Objective: (2.3) Perform Operations with Sets

D) { }

Use the Venn diagram to determine the set or cardinality. 114) A

A) {12, 15, 16}

B) {11, 13, 14, 17}

C) {11, 12, 13}

D) {13, 17}

Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets

115) B

A) {12, 13, 15, 16, 17}

B) {14, 16, 17}

C) {11, 14}

Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets

116) U

A) {12, 15, 16} C) {11, 12, 13, 14, 15, 16, 17, 18, 19}

B) {13, 17} D) {11, 14}

Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets

D) {13, 17}

117) A . B

A) {%, @, &, one, six}

B) {@, &}

C) {%, one, six}

D) {77, 95}

Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets

118) n(A 1 B)

A) 5

B) {%, @, &, one, six}

C) 2

D) {@, &}

Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets

119) n(1) - n(B)

A) {%, 77, 95}

B) 4

C) 3

D) {%, @, &, 77, 95}

Objective: (2.3) Use Venn Diagrams to Visualize Relationships Between Two Sets

Use the formula for the cardinal number of the union of two sets to solve the problem. 120) Set A contains 4 elements, set B contains 9 elements, and 2 elements are common to sets A and B. How many elements are in A 1 B? A) 11 B) 13 C) 12 D) 10 Objective: (2.3) Use the Formula for n(A 1 B)

121) Set A contains 8 letters and 12 numbers. Set B contains 12 letters and 8 numbers. Two letters and 5 numbers are common to both sets A and B. Find the number of elements in set A or set B. A) 40 B) 33 C) 27 D) 47 Objective: (2.3) Use the Formula for n(A 1 B)

122) Set A contains 35 elements and set B contains 22 elements. If there are 40 elements in (A 1 B) then how many elements are in (A . B)? A) 13 B) 8 C) 17 D) 5 Objective: (2.3) Use the Formula for n(A 1 B)

In the exercise below, let U = {x|x % N and x < 10} A = {x|x is an odd natural number and x < 10} B = {x|x is an even natural number and x < 10} C = {x|x % N and 3 < x < 5} Find the set. 123) A 1 B A) {1, 3, 5, 7, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9}

B) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} D) B or {2, 4, 6, 8}

Objective: (2.3) Find Each of the Given Sets

124) B . U A) U or {1, 2, 3, 4, 5, 6, 7, 8, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B) B or {2, 4, 6, 8} D) B or {2, 4, 6, 8, 10}

Objective: (2.3) Find Each of the Given Sets

125) B . C' A) B or {2, 4, 6, 8, 10}

B) C or {4}

C) B or {2, 4, 6, 8}

Objective: (2.3) Find Each of the Given Sets

126) (A . C)' A) {1, 3, 4, 5, 7, 9} C) U or {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B) {1, 2, 3, 5, 6, 7, 8, 9} D) U or {1, 2, 3, 4, 5, 6, 7, 8, 9}

Objective: (2.3) Find Each of the Given Sets

Use the Venn diagram to list the elements of the set in roster form. 127)

A 1B A) {11, 12, 13, 14, 15, 16, 17, 18, 19} C) {13, 17}

B) {11, 12, 14, 15, 16} D) {11, 12, 13, 14, 15, 16, 17}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

D) {2, 6, 8}

128)

A .B A) {13, 17} C) {11, 12, 13, 14, 15, 16, 17}

B) {11, 12, 13, 14, 15, 16, 17, 18, 19} D) {11, 12, 14, 15, 16}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

129)

A) {12, 15, 16, 18, 19}

B) {11, 13, 14, 17}

C) {11, 14, 18, 19}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

130)

A) {11, 14} C) {12, 15, 16, 18, 19}

B) {11, 14, 18, 19} D) {11, 13, 14, 17, 18, 19}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

D) {12, 15, 16}

131)

(A . B)' A) {11, 12, 14, 15, 16, 18, 19} C) {13, 17}

B) {11, 12, 14, 15, 16} D) {18, 19}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

132)

(A 1 B)' A) {11, 12, 14, 15, 16} C) {13, 17}

B) {11, 12, 13, 14, 15, 16, 17} D) {18, 19}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

133)

A' . B A) {11, 13, 14, 17, 18, 19} C) {11, 14}

B) {12, 15, 16} D) {12, 15, 16, 18, 19}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

Use the Venn diagram to list the elements of the set in roster form.

134) The set of students who studied Sunday A) {Kenneth, Miguel, Kavita} C) {Sam, Sophia, Kenneth, Miguel, Kavita}

B) {Kenneth, Miguel, Kavita, Vijay} D) {Sam, Sophia}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

135) The set of students who studied Saturday or Sunday A) {Karen, Charly, Vijay} B) {Sam, Sophia} C) {Karen, Charley, Sam, Sophia, Kenneth, Miguel, Kavita, Vijay} D) {Karen, Charley, Sam, Sophia, Kenneth, Miguel, Kavita} Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

136) The set of students who studied Sunday and not Saturday A) {Kenneth, Miguel, Kavita, Vijay} C) {Sam, Sophia}

B) {Karen, Charly} D) {Kenneth, Miguel, Kavita}

Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

137) The set of students who studied neither Saturday nor Sunday A) {Vijay} B) {U, Vijay} C) {} D) {Vijay, Karen, Charly} Objective: (2.3) Determine Sets Involving Set Operations from a Venn Diagram

The bar graph shows the percentage of adults that prefer to do certain activities during the weekdays or weekends.

Use the information in the graph to place the indicated activity in the correct region of the Venn diagram below.

138) Cleaning A) II

B) I

C) IV

D) III

B) III

C) I

D) II

B) I

C) III

D) IV

B) II

C) III

D) I

Objective: (2.3) Solve Applications

139) Exercising A) IV Objective: (2.3) Solve Applications

140) Shopping A) II Objective: (2.3) Solve Applications

141) Reading A) IV Objective: (2.3) Solve Applications

Use the following definition to place the indicated natural number in the correct region of the Venn diagram. A palindromic number is a natural number whose value does not change if its digits are reversed. U = the set of natural numbers A = the set of palindromic numbers B = the set of odd numbers

142) 160

160

Objective: (2.3) Understanding Palindromic Number

143) 1,840

1,840

Objective: (2.3) Understanding Palindromic Number

144) 175

175

Objective: (2.3) Understanding Palindromic Number

145) 258

258

258 Objective: (2.3) Understanding Palindromic Number

Many children do not have access to computers at home. School has an equalizing effect. Family income is a strong factor in access. Use the information in the graph to write the set in the exercise in roster form or express the set as +.

146) {x | x is home access by more than 34% of the students} . {x | x is school access by less than 73% of the students} A) {$75,000 or more} B) {$50,000 to $74,999} C) {$25,000 to $49,999} D) {Less than $25,000} Objective: (2.3) Solve Apps: Venn Diagram

147) the set of home access by more than 80% of the students and school access by less than 70% of the students} A) {$50,000 to $74,999} B) {$50,000 to $74,999, $75,000 or more} C) {Less than $25,000} D) + Objective: (2.3) Solve Apps: Venn Diagram

Solve the problem. 148) Let U = the set of the days of the week, A = {Monday, Tuesday, Wednesday, Thursday, Friday} and B = {Friday, Saturday, Sunday}. Find (A . B)'. A) {Saturday, Sunday} B) {Friday} C) {Monday, Tuesday, Wednesday, Thursday, Saturday, Sunday} D) + Objective: (2.3) Solve Apps: Venn Diagram

149) {x | x is home access by more than 34% of the students} 1 {x | x is school access by less than 81% of the students} A) {$50,000 to $74,999, $75,000 or more} B) {Less than $25,000, $75,000 or more} C) {$25,000 to $49,999, $50,000 to $74,999} D) {Less than $25,000, $25,000 to $49,999} Objective: (2.3) Solve Apps: Venn Diagram

150) the set of home access by more than 80% of the students or school access by less than 87% of the students} A) {Less than $25,000, $25,000 to $49,999, $50,000 to $74,999} B) {$50,000 to $74,999, $75,000 or more} C) {Less than $25,000, $25,000 to $49,999} D) {$25,000 to $49,999, $50,000 to $74,999, $75,000 or more} Objective: (2.3) Solve Apps: Venn Diagram

Use sets to solve the problem. 151) Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans, and 17 like both red and green jelly beans. How many of the students surveyed like neither red nor green jelly beans? A) 17 B) 13 C) 12 D) 8 Objective: (2.3) Solve Apps: Venn Diagram

152) Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own no cats? A) 15 B) 10 C) 27 D) 22 Objective: (2.3) Solve Apps: Venn Diagram

153) Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support both Moore and Allen, and 250 support only Moore. How many residents support Allen? A) 400 B) 250 C) 100 D) 150 Objective: (2.3) Solve Apps: Venn Diagram

Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set. 154) A 1 (B . C) A) {q, y, z} B) {q, s, u, w, y, z}

C) {q, w, y}

D) {q, r, w, y, z}

C) {q, s, u, w, y, z}

D) {q, s, w, y}

C) {q, s, u, w, y, z}

D) {q, s, u, w, y}

C) {q, s, w, y}

D) {q, s, u, w, y}

C) {r, t, z}

D) {q, r, s}

C) {r, s, t, y, z}

D) {q, s, u, v, x, y}

C) {s, t}

D) {v, z}

Objective: (2.4) Perform Set Operations with Three Sets

155) A . (B 1 C) A) {q, y, z}

B) {q, r, w, y, z}

Objective: (2.4) Perform Set Operations with Three Sets

156) (A 1 B) . (A 1 C) A) {r, t, v, x}

B) {q, s, w, y}

Objective: (2.4) Perform Set Operations with Three Sets

157) (A . B) 1 (A . C) A) {r, t, u, v, x, z}

B) {q, s, v, w, y}

Objective: (2.4) Perform Set Operations with Three Sets

158) A' . (B 1 C') A) {q, s, u, v, x, y}

B) {q, r, s, t, z}

Objective: (2.4) Perform Set Operations with Three Sets

159) (A' . B) 1 (A' . C') A) {q, r, t, y, z}

B) {r, t, z}

Objective: (2.4) Perform Set Operations with Three Sets

160) (A 1 B 1 C)' A) {q, s}

B) {r, t}

Objective: (2.4) Perform Set Operations with Three Sets

161) (A . B . C)' A) {q, s, u, w, z} C) {q, r, s, t, u, v, w, x, z}

B) {r, t, v, x} D) +

Objective: (2.4) Perform Set Operations with Three Sets

162) (A 1 B)' . C A) {q, v, x}

B) {v, x}

C) {r, w}

D) {s, u, v, z}

C) {u}

D) {w}

Objective: (2.4) Perform Set Operations with Three Sets

163) (B 1 C)' . A A) {v}

B) +

Objective: (2.4) Perform Set Operations with Three Sets

Use the Venn diagram shown to answer the question.

164) Which regions represent set E? A) VIII B) II, III, V, VI

C) III

D) I, IV, VII

Objective: (2.4) Use Venn Diagrams with Three Sets

165) Which regions represent set D 1 F? A) I, II, IV, V, VI, VII C) VIII

B) I, II, IV, V, VI, VII, VIII D) III

Objective: (2.4) Use Venn Diagrams with Three Sets

166) Which regions represent set D . E? A) IV, V B) II, V

C) I, III, IV, VI

D) VIII

C) II, III, V, VI

D) I, IV, VII, VIII

Objective: (2.4) Use Venn Diagrams with Three Sets

167) Which regions represent set E'? A) II, V, VI B) VIII Objective: (2.4) Use Venn Diagrams with Three Sets

Construct a Venn diagram illustrating the given sets. 168) A = [4, 5, 6, 7, 8, 9], B = [3, 4, 5, 6, 10], C = [2, 3, 4, 5, 9], U = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Objective: (2.4) Use Venn Diagrams with Three Sets

Use set notation to identify the shaded region. 169)

A) B - A

B) A .B

C) B . A

D) A - B

C) A 1 B

D) A .B

Objective: (2.4) Use Venn Diagrams with Three Sets

170)

A) A - B

B) A . B

Objective: (2.4) Use Venn Diagrams with Three Sets

171)

A) (A . B)'

B) B . A'

C) A' . B

D) A' 1 B

C) (A 1 B) . C'

D) (A 1 B) 1 C'

C) B . (A . C)'

D) A . B . C

C) A 1 C

D) B' . (A 1 C)

Objective: (2.4) Use Venn Diagrams with Three Sets

172)

A) (A 1 B 1 C)'

B) (A . B) 1 C'

Objective: (2.4) Use Venn Diagrams with Three Sets

173)

A) B' . (A 1 B)

B) A' . C' . B

Objective: (2.4) Use Venn Diagrams with Three Sets

174)

A) (C . B') 1 A

B) (A 1 C) . B'

Objective: (2.4) Use Venn Diagrams with Three Sets

The chart shows the most common causes of death in certain areas of the United States. Most Common Causes of Death in U.S. Region A Region B Region C 1. heart disease 1. heart disease 1. heart disease 2. cerebrovascular 2. cerebrovascular 2. cerebrovascular 3. COPD 3. COPD 3. COPD 4. pneumonia 4. accidents 4. accidents 5. accidents 5. pneumonia 5. liver disease Use the Venn diagram to indicate in which region each cause should be placed.

175) liver disease A) V

B) VII

C) VI

D) IV

C) V

D) II

C) II

D) VI

Objective: (2.4) Use Venn Diagrams with Three Sets

176) pneumonia A) VI

B) IV

Objective: (2.4) Use Venn Diagrams with Three Sets

177) heart disease A) V

B) IV

Objective: (2.4) Use Venn Diagrams with Three Sets

Use the following information to construct a Venn Diagram that illustrates the given sets.

178) U = the set of members of the bookclub shown in the chart A = the set of members of the bookclub who read at least 25 books B = the set of members of the bookclub who suggested 5 or less books C = the set of members of the bookclub who have been members for less than 7 years Members of the bookclub Carla Marge Sandy Laura Kim Peter Jim Ann Paul

Numbers of books read 21 25 5 42 42 32 44 24 17

Numbers of books suggested 7 2 1 15 12 8 5 1 4

Years of membership 6 7 3 9 9 8 7 7 5

Objective: (2.4) Use Venn Diagrams with Three Sets

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Venn diagram shown below to solve the problem.

179) a) Which regions are represented by A . B'? b) Which regions are represented by (A' 1 B)'? c) Based on parts a) and b), what can you conclude about the relationship between A . B' and (A' 1 B)'? Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

180) a) Which regions are represented by (A' . B)'? b) Which regions are represented by A . B'? c) Based on parts a) and b), what can you conclude about the relationship between (A' . B)' and A . B'? Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

181) a) Which regions are represented by (A 1 B')'? b) Which regions are represented by A' . B? c) Based on parts a) and b), what can you conclude about the relationship between (A 1 B')' and A' . B? Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

182) a) Which regions are represented by (A' 1 B)'? b) Which regions are represented by A' . B? c) Based on parts a) and b), what can you conclude about the relationship between (A' 1 B)' and A' . B? Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

183) Show that (A' . B)' = A 1 B'. Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

Use the Venn diagram shown below to solve the problem.

184) a) Which regions are represented by (A . B) 1 C? b) Which regions are represented by (A 1 C) . (A 1 B)? c) Based on parts a) and b), what can you conclude about the relationship between (A . B) 1 C and (A 1 C) . (A 1 B)? Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

185) a) Which regions are represented by B 1 (A . C)? b) Which regions are represented by (A 1 B) . (B 1 C)? c) Based on parts a) and b), what can you conclude about the relationship between B 1 (A . C) and (A 1 B) . (B 1 C)? Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

186) Show that B 1 (A . C) = (A 1 B) . (B 1 C). Objective: (2.4) Use Venn Diagrams to Prove Equality of Sets

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the accompanying Venn diagram that shows the number of elements in regions I through IV to answer the question. 187)

8 18

17 9

How many elements belong to set A? A) 26 B) 8

C) 17

Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

D) 18

188)

9 18

17 10

How many elements belong to set B? A) 26 B) 35

C) 17

D) 27

C) 15

D) 8

C) 12

D) 7

Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

189)

8 15

14 9

How many elements belong to set A but not set B? A) 14 B) 9 Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

190)

6 12

11 7

How many elements belong to set B but not set A? A) 6 B) 11 Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

191)

7 17

16 8

How many elements belong to set A or set B? A) 7 B) 40

C) 48

D) 33

C) 6

D) 29

C) 12

D) 9

Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

192)

6 15

14 7

How many elements belong to set A and set B? A) 35 B) 7 Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

193)

8 13

12 9

How many elements belong to neither set A nor set B? A) 13 B) 8 Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

194)

9 16

15 10

How many elements are there in the universal set? A) 40 B) +

C) 31

D) 50

Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

Use the given cardinalities to determine the number of elements in the specific region. 195) n(U) = 235, n(A) = 80, n(B) = 100, n(C) = 86, n(A . B) = 35, n(A . C) = 38, n(B . C) = 34, n(A . B . C) = 18 Find III.

A) 46

B) 50

C) 49

Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

D) 30

196) n(U) = 191, n(A) = 64, n(B) = 84, n(C) = 66, n(A . B) = 27, n(A . C) = 30, n(B . C) = 26, n(A . B . C) = 14 Find VIII.

A) 74

B) 0

C) 46

D) 64

Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

197) n(U) = 85, n(A) = 61, n(B) = 42, n(C) = 40, n(A . B) = 26, , n(A . C) = 23, n(B . C) = 21, n(A . B . C) = 12 Find VI.

A) 9

B) 11

C) 8

D) 10

Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

Use a Venn diagram to answer the question. 198) At East Zone University (EZU) there are 672 students taking College Algebra or Calculus. 270 are taking College Algebra, 455 are taking Calculus, and 53 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus? A) 402 B) 217 C) 619 D) 164 Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

199) At East Zone University (EZU) there are 586 students taking College Algebra or Calculus. 438 are taking College Algebra, 182 are taking Calculus, and 34 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra? A) 370 B) 148 C) 552 D) 404 Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

200) A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with the following results: 90 were interested in an interview show and a documentary, but not reruns; 12 were interested in an interview show and reruns, but not a documentary; 42 were interested in reruns but not documentaries or interviews; 72 were interested in an interview show but not a documentary; 30 were interested in a documentary and reruns; 18 were interested in an interview show and reruns; 24 were interested in none of the three. How many are interested in exactly one kind of show? A) 144 B) 154 C) 124 D) 134 Objective: (2.5) Use Venn Diagrams to Visualize a Survey's Results

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. A pollster conducting a telephone poll asked three questions: 1. Are you religious? 2. Have you spent time with a person convicted of a crime? 3. Are you in favor of the death penalty? Solve the problem. 201) Construct a Venn Diagram with three circles that can assist the pollster in tabulating the responses to the three questions.

Objective: (2.5) Use Survey Results to Complete Venn Diagrams and Answer Questions about the Survey

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 202) Write the letter b in every region of the diagram that represents all religious persons polled who are not in favored of death penalty.

Objective: (2.5) Use Survey Results to Complete Venn Diagrams and Answer Questions about the Survey

203) Write the letter c in every region of the diagram that represents the people polled who do not consider themselves religious, who have not spent time with a person convicted with a crime, and who are in favor of the death penalty.

Objective: (2.5) Use Survey Results to Complete Venn Diagrams and Answer Questions about the Survey

Solve the problem. 204) A pollster conducting a telephone poll asked two questions: 1. Would you like to live to be 100 years old, if it was possible? 2. Do you have confidence that medical science will find cures for major diseases during your lifetime? Construct a Venn diagram that allows the respondents to the poll to be identified by whether or not they want to live to be 100 and whether or not they believe cures for major diseases will be found.

Write the letter q in the region of the diagram that identifies those would like to live to be 100 who believe cures will be found.

Write the letter t in the region of the diagram that identifies those would not like to live to be 100 who believe cures will be found. Write the letter v in the region of the diagram that identifies those would not like to live to be 100 who believe cures will not be found. A) B)

Objective: (2.5) Use Survey Results to Complete Venn Diagrams and Answer Questions about the Survey

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 205) A pollster conducting a telephone poll asked three questions: 1. Are you a registered voter? 2. Do you currently have any children in grades kindergarten through 12th grade? 3. Would you support a tax increase to build a new school? Construct a Venn diagram with three circles that can assist the pollster in tabulating the responses to the three questions.

Write the letter h in the region of the diagram that identifies all registered voters polled who do not have children in school and who do not support a tax increase. Write the letter j in the region of the diagram that identifies people who are not registered to vote, who do not have children in school, and who do not support a tax increase. Write the letter k in the region of the diagram that identifies all registered voters polled who have children in school, and who do not support a tax increase. Objective: (2.5) Use Survey Results to Complete Venn Diagrams and Answer Questions about the Survey

206) There are 777,859 physicians in the United States. 177,030 are women. 33,947 physicians have cardiology as their specialty. 6,817 women physicians specialize in cardiology. Identify the Venn diagram in which U is the set of all physicians, W is the set of all women physicians, and C is the set of all U.S. physicians specializing in cardiology. Fill in each of the four regions of the Venn diagram with the number of physicians who belong to that region.

Use your Venn diagram to answer the questions. How many physicians in the United States are there who are men specializing in cardiology? How many male physicians in the United States do not specialize in cardiology? Objective: (2.5) Use Survey Results to Complete Venn Diagrams and Answer Questions about the Survey

Answer Key Testname: 02-BLITZER_TM8E_TEST_ITEM_FILE

1) A 2) B 3) D 4) C 5) C 6) D 7) B 8) A 9) C 10) D 11) C 12) B 13) B 14) B 15) A 16) A 17) B 18) B 19) A 20) A 21) B 22) A 23) B 24) B 25) B 26) A 27) D 28) D 29) A 30) B 31) A 32) C 33) A 34) B 35) A 36) A 37) A 38) A 39) A 40) B 41) A 42) B 43) B 44) B 45) A 46) B 47) A 48) A 49) A 50) B

51) A 52) C 53) B 54) D 55) A 56) B 57) B 58) B 59) A 60) B 61) B 62) C 63) C 64) B 65) A 66) A 67) B 68) A 69) B 70) D 71) A 72) D 73) C 74) A 75) D 76) D 77) B 78) A 79) B 80) A 81) B 82) B 83) A 84) A 85) B 86) A 87) A 88) A 89) D 90) D 91) Answers may vary. One possible answer is: U = the set of all famous composers. 92) Answers may vary. One possible answer is: U = the set of all non-carbonated beverages. 93) A

94) D 95) C 96) A 97) B 98) A 99) C 100) A 101) C 102) A 103) B 104) A 105) A 106) D 107) D 108) D 109) B 110) A 111) D 112) C 113) A 114) B 115) A 116) C 117) B 118) A 119) C 120) A 121) B 122) C 123) C 124) B 125) D 126) D 127) D 128) A 129) A 130) B 131) A 132) D 133) B 134) C 135) D 136) D 137) A 138) D 139) C 140) A 141) B 142) A 143) B 44

144) C 145) C 146) D 147) D 148) C 149) D 150) B 151) D 152) D 153) B 154) B 155) D 156) C 157) C 158) C 159) B 160) B 161) C 162) B 163) C 164) B 165) A 166) B 167) D 168) C 169) C 170) D 171) D 172) D 173) B 174) A 175) B 176) D 177) A 178) D b) I c) 179) a) I They are equal. 180) a) I, II, and IV b) I c) They are not equal. b) III c) 181) a) III They are equal. b) III c) 182) a) I They are not equal.

Answer Key Testname: 02-BLITZER_TM8E_TEST_ITEM_FILE

183) A' = III, IV B = II, III (A' . B) = III (A' . B)' = I, II, IV

202) A 203) A 204) C 205)

A = I, II B' = I, IV A 1 B' = I, II, IV 184) a) II, IV, V, VI, and VII b) I, II, IV, V, and VI c) They are not equal. b) II - VI 185) a) II - VI c) They are equal. 186) (A . C) = IV, V B = II, III, V, VI B 1 (A . C) = II, III, IV, V, VI

206)

(A 1 B) = I, II, III, IV, V, VI (B 1 C) = II, III, IV, V, VI, VII (A 1 B) . (B 1 C) = II, III, IV, V, VI 187) A 188) A 189) C 190) B 191) B 192) C 193) D 194) D 195) C 196) C 197) A 198) B 199) B 200) A 201)

27,130 male physicians in the United States specialize in cardiology. 573,699 male physicians in the United States do not specialize in cardiology.

Blitzer, Thinking Mathematically, 8e Chapter 3 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the sentence is a statement. 1) The orbit of Venus lies completely within the orbit of Jupiter. A) statement B) not a statement Objective: (3.1) Identify English Sentences that are Statements

2) Does Rose always act like that when she's unhappy? A) statement

B) not a statement

Objective: (3.1) Identify English Sentences that are Statements

3) Pick up a paper on the way home. A) not a statement

B) statement

Objective: (3.1) Identify English Sentences that are Statements

4) This test is too hard. A) not a statement

B) statement

Objective: (3.1) Identify English Sentences that are Statements

5) Do you like this color? A) statement

B) not a statement

Objective: (3.1) Identify English Sentences that are Statements

6) No professional hockey player has ever gone on to become a news announcer. A) statement B) not a statement Objective: (3.1) Identify English Sentences that are Statements

7) 6 + 7 = 14 A) not a statement

B) statement

Objective: (3.1) Identify English Sentences that are Statements

8) 0.6 = .06 A) not a statement

B) statement

Objective: (3.1) Identify English Sentences that are Statements

Provide an appropriate response. 9) In symbolic logic, we use A) numbers

to represent statements.

B) operation symbols

C) lowercase letters

Objective: (3.1) Express Statements Using Symbols

Form the negation of the statement. 10) Today is June 9 A) It is not true that today is June 10. C) Today is not June 9.

B) Today is not June 10. D) Yesterday was not June 7.

Objective: (3.1) Form the Negation of a Statement

D) uppercase letters

11) Copenhagen is not the capital of Iran. A) It is true that Copenhagen is not the capital of Iran. B) It is not true that Iran is not the capital of Copenhagen. C) It is not true that Copenhagen is not the capital of Iran. D) It is true that Iran is not the capital of Copenhagen. Objective: (3.1) Form the Negation of a Statement

Let p, q, r, and s represent the following statements: p: One plays hard. q: One is a guitar player. r: The commute to work is not long. s: It is not true that the car is working. Express the following statement symbolically. 12) One does not play hard. A) ~p B) ~q

C) q

D) p

C) p

D) q

C) ~r

D) s

C) r

D) s

Objective: (3.1) Express Negations Using Symbols

13) One is not a guitar player. A) ~p

B) ~q

Objective: (3.1) Express Negations Using Symbols

14) The commute to work is long. A) ~s

B) r

Objective: (3.1) Express Negations Using Symbols

15) The car is working. A) ~s

B) ~r

Objective: (3.1) Express Negations Using Symbols

Express the symbolic statement ~p in words. 16) p: Lake Winnipesaukee is one of the Great Lakes. A) It is not true that Lake Winnipesaukee is not one of the Great Lakes B) It is true that Lake Winnipesaukee is one of the Great Lakes. C) Lake Winnipesaukee is truly one of the Great Lakes. D) Lake Winnipesaukee is not one of the Great Lakes. Objective: (3.1) Translate a Negation Represented by Symbols into English

17) p: The Pilgrims did not land in Tahiti. A) The Pilgrims almost landed in Tahiti. C) It is not true that the Pilgrims landed in Tahiti.

B) The Pilgrims landed in Tahiti. D) The Pilgrims landed on Plymouth Rock.

Objective: (3.1) Translate a Negation Represented by Symbols into English

18) p: Vitamin C helps the immune system. A) Vitamin C may help the immune system. B) Vitamin A helps the immune system. C) It is true that Vitamin C helps the immune system. D) Vitamin C does not help the immune system. Objective: (3.1) Translate a Negation Represented by Symbols into English

19) p: The refrigerator is not working. A) It is not true that the refrigerator is working. C) The refrigerator is almost working.

B) The oven is working. D) The refrigerator is working.

Objective: (3.1) Translate a Negation Represented by Symbols into English

Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning. 20) All robins are birds. A) All birds are not robins. B) At least one robin is a bird. C) Some birds are not robins. D) There are no robins that are not birds. Objective: (3.1) Express Quantified Statements in Two Ways

21) Some buildings are garages. A) No buildings are garages. C) There exists at least one garage that is a building.

B) All garages are buildings. D) At least one building is a garage.

Objective: (3.1) Express Quantified Statements in Two Ways

22) Some violinists are not humans. A) All violinists are not humans. C) All violinists are humans.

B) Some humans are not violinists. D) Not all violinists are humans.

Objective: (3.1) Express Quantified Statements in Two Ways

23) No politicians have told a lie. A) All politicians have not told a lie. C) Some politicians have told a lie.

B) All politicians have told a lie. D) At least one politician has told a lie.

Objective: (3.1) Express Quantified Statements in Two Ways

Write the negation of the quantified statement. (The negation should begin with "all," "some," or "no.") 24) All uncles are males. A) Some males are not uncles. B) All males are not uncles. C) Some uncles are not males. D) No uncles are not males. Objective: (3.1) Write Negations of Quantified Statements

25) Some flowers are daffodils. A) Not all flowers are daffodils. C) No flowers are daffodils.

B) No daffodils are flowers. D) All daffodils are flowers.

Objective: (3.1) Write Negations of Quantified Statements

26) Some petunias are not flowers. A) All petunias are flowers. C) No petunias are flowers.

B) All petunias are not flowers. D) All flowers are petunias.

Objective: (3.1) Write Negations of Quantified Statements

27) No medicines have made people well. A) Some medicines have made people well. C) All medicines have made people well.

B) Some medicines have not made people well. D) All medicines have not made people well.

Objective: (3.1) Write Negations of Quantified Statements

28) All athletes are famous. A) Some athletes are famous. C) Some athletes are not famous.

B) All athletes are not famous. D) All athletes are somewhat famous.

Objective: (3.1) Write Negations of Quantified Statements

Choose the correct conclusion. 29) As a special promotion, the Green Thumb organic foods chain said that everyone who came to one of their stores between noon and 1 p.m. on January 4 would be offered a free loaf of 23-grain bread. They did not keep this promise. Therefore, between noon and 1 p.m. on January 4: A) The Green Thumb chain ran out of 23-grain bread. B) No one who came to a Green Thumb store was offered a free loaf of 23-grain bread. C) At least one person who came to a Green Thumb store was not offered a free loaf of 23-grain bread. D) At least one person who came to a Green Thumb store was offered a free loaf of 23-grain bread. Objective: (3.1) Write Negations of Quantified Statements

30) In a statement to the press, a representative of a tobacco company stated "In our years of research, we never discovered a link between cancer and smoking." That statement was later found to be false. Therefore, in their years of research: A) The tobacco company always discovered a link between cancer and smoking. B) The tobacco company sometimes did not discover a link between cancer and smoking. C) The tobacco company never discovered a link between cancer and smoking. D) The tobacco company sometimes discovered a link between cancer and smoking. Objective: (3.1) Write Negations of Quantified Statements

Express the symbolic statement ~p in words. 31) p: Not all people like football. A) Some people do not like football. C) All people like football.

B) All people do not like football. D) Some people like football.

Objective: (3.1) Write Negations of Quantified Statements

32) p: Everyone is asleep. A) Nobody is asleep. C) Everyone is awake.

B) Nobody is awake. D) Not everyone is asleep.

Objective: (3.1) Write Negations of Quantified Statements

33) p: Some athletes are musicians. A) All athletes are musicians. C) No athlete is a musician.

B) Not all athletes are musicians. D) Some athletes are not musicians.

Objective: (3.1) Write Negations of Quantified Statements

34) p: No fifth graders play soccer. A) All fifth graders play soccer. C) Not all fifth graders play soccer.

B) No fifth grader does not play soccer. D) At least one fifth grader plays soccer.

Objective: (3.1) Write Negations of Quantified Statements

35) p: Some people don't like walking. A) Nobody likes walking. C) Everyone likes walking.

B) Some people don't like driving. D) Some people like walking.

Objective: (3.1) Write Negations of Quantified Statements

Given that p and q each represents a simple statement, write the indicated compound statement in its symbolic form. 36) p: Tosca is an opera. q: Carmen is an opera. Tosca is an opera and Carmen is an opera. A) p q B) p ,q C) p "q D) p "~ q Objective: (3.2) Express Compound Statements in Symbolic Form

37) p: 1984 is a novel. q: Persuasion is a novel. 1984 is a novel and Persuasion is not a novel. A) p ,~ q B) p "q

C) p "~ q

D) p ~ q

C) p "q

D) p ,q

C) p ,~ q

D) p , q

C) p ,q

D) p q

C) p ~ q

D) ~ p ~ q

Objective: (3.2) Express Compound Statements in Symbolic Form

38) p: She drives at 80 mph. q: She gets a speeding ticket. She drives at 80 mph or she gets a speeding ticket. A) p ,~ q B) p q Objective: (3.2) Express Compound Statements in Symbolic Form

39) p: They set the alarm. q: They get up on time. They set the alarm or they do not get up on time. A) p "~ q B) p ~ q Objective: (3.2) Express Compound Statements in Symbolic Form

40) p: This is a hammer. q: This is a tool. If this is a hammer, then this is a tool. A) p q B) p "q Objective: (3.2) Express Compound Statements in Symbolic Form

41) p: This is a brontosaurus. q: This is a dinosaur. If this is not a brontosaurus, then this is not a dinosaur. A) ~ q ~ p B) ~ p "~ q Objective: (3.2) Express Compound Statements in Symbolic Form

42) p: You can get lunch here. q: It is between noon and 2 o'clock. You can get lunch here if and only if it is between noon and 2 o'clock. A) p q B) p "q C) q p

D) p q

Objective: (3.2) Express Compound Statements in Symbolic Form

43) p: Manuel is Carmen's brother. q: Carmen is Manuel's sister. Manuel is not Carmen's brother if and only if Carmen is not Manuel's sister. A) ~ p ~ q B) ~ p "~ q C) ~ p ~ q Objective: (3.2) Express Compound Statements in Symbolic Form

D) p ~ q

44) p: The outside humidity is low. q: The central humidifier is running. r: The air in the house is getting dry. The outside humidity is low and the central humidifier is running, or the air in the house is getting dry. A) p " (q , r) B) (p " q) ~ r C) (p " q) ,r D) p " q ,r Objective: (3.2) Express Compound Statements in Symbolic Form

45) p: The outside humidity is low. q: The central humidifier is running. r: The air in the house is getting dry. If the outside humidity is low, then the central humidifier is running or the air in the house is not getting dry. A) p (q , r) B) p (q ,~ r) C) p (q ,~ r) D) p (q "~ r) Objective: (3.2) Express Compound Statements in Symbolic Form

46) p: The outside humidity is high. q: The basement dehumidifier is running. r: The basement is getting moldy. If the outside humidity is high or the basement dehumidifier is not running, then the basement is getting moldy. A) (p , q) r B) (p "~ q) r C) (p ,~ q) r D) (~p ,~ q) r Objective: (3.2) Express Compound Statements in Symbolic Form

47) p: The outside humidity is high. q: The basement dehumidifier is running. r: The basement is getting moldy. It is not the case that if the basement is getting moldy, then the basement dehumidifier is not running. A) ~ r ~ q B) ~ (r ~ q) C) ~ (r "~ q) D) ~ (r q) Objective: (3.2) Express Compound Statements in Symbolic Form

48) p: The outside humidity is high. q: The basement dehumidifier is running. r: The basement is getting moldy. The basement is getting moldy, if and only if the outside humidity is high and the basement dehumidifier is not running. A) (p " q) r B) r (p " q) C) r (p "~ q) D) (r p) "~ q Objective: (3.2) Express Compound Statements in Symbolic Form

49) p: The outside humidity is low. q: The central humidifier is running. r: The air in the house is getting dry. If the central humidifier is running, then the outside humidity is low if and only if the air in the house is getting dry. A) (q p) r B) q (p " r) C) p (q r) D) q (p r) Objective: (3.2) Express Compound Statements in Symbolic Form

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. List the simple statements contained in the quotation and assign each one a letter. Then rewrite the compound statement in symbolic form. 50) "If the air is mellow and the sky is clear, then birds nest quietly and the night is at peace." (Unattributed) Objective: (3.2) Express Compound Statements in Symbolic Form

51) "If he does that, I will scream, but if he doesn't, I won't." Objective: (3.2) Express Compound Statements in Symbolic Form

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Given that p and q each represents a simple statement, write the indicated symbolic statement in words. 52) p: Emilio dislikes Laura q: Laura dislikes Emilio ~ (p " q) A) It is not true that Emilio dislikes Laura and Laura dislikes Emilio. B) Emilio does not dislike Laura, but Laura dislikes Emilio. C) Emilio dislikes Laura and Laura dislikes Emilio. D) Emilio dislikes Laura but Laura does not dislike Emilio. Objective: (3.2) Express Symbolic Statements with Parentheses in English

53) p: Emilio dislikes Laura q: Laura dislikes Emilio ~ p "q A) Emilio does not dislike Laura, or Laura dislikes Emilio. B) Emilio and Laura do not dislike each other. C) It is not true that Emilio dislikes Laura and Laura dislikes Emilio. D) Emilio does not dislike Laura, but Laura dislikes Emilio. Objective: (3.2) Express Symbolic Statements with Parentheses in English

54) p: Bob respects Linda q: Linda respects Bob ~ (q ,p) A) It is not true that Linda respects Bob and that Bob respects Linda. B) If Linda does not respect Bob, then Bob respects Linda. C) It is not true that Linda respects Bob or that Bob respects Linda. D) Linda does not respect Bob or Bob respects Linda. Objective: (3.2) Express Symbolic Statements with Parentheses in English

55) p: Darren dislikes Zoe q: Zoe dislikes Darren ~ q ,p A) Zoe does not dislike Darren, but Darren dislikes Zoe. B) It is not true that Zoe dislikes Darren or that Darren dislikes Zoe. C) Zoe does not dislike Darren, or Darren dislikes Zoe. D) Zoe and Darren do not dislike each other. Objective: (3.2) Express Symbolic Statements with Parentheses in English

56) p: Darren admires Vanessa q: Vanessa admires Darren ~ p "~ q A) It is not true that Darren and Vanessa do not admire each other. B) Either Darren admires Darren or Vanessa admires Darren. C) If Darren admires Vanessa, then Vanessa admires Darren. D) Darren and Vanessa do not admire each other. Objective: (3.2) Express Symbolic Statements with Parentheses in English

57) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. (p " q) r A) We will visit Aunt Tillie if and only if the car has been repaired and the kids are home. B) If the car has been repaired and the kids are home, we will visit Aunt Tillie. C) If the car has been repaired, we will visit Aunt Tillie even if the kids are not home. D) If the car has been repaired or the kids are home, we will visit Aunt Tillie. Objective: (3.2) Express Symbolic Statements with Parentheses in English

58) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. p " (q r) A) The car has been repaired, and we will visit Aunt Tillie if the kids are home. B) If the car has been repaired or the kids are home, we will visit Aunt Tillie. C) If the car has been repaired, we will visit Aunt Tillie if the kids are home. D) The car has been repaired and the kids are home, so we will visit Aunt Tillie. Objective: (3.2) Express Symbolic Statements with Parentheses in English

59) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. ~ r (~ p ,~ q) A) We will not visit Aunt Tillie if and only if the car has not been repaired or the kids are not home. B) If we visit Aunt Tillie, then the car has been repaired or the kids are home. C) If we will not visit Aunt Tillie, then the car has not been repaired and the kids are not home. D) If we will not visit Aunt Tillie, then the car has not been repaired or the kids are not home. Objective: (3.2) Express Symbolic Statements with Parentheses in English

60) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. (~ r ~ q) ,p A) We will not visit Aunt Tillie if and only if the kids are not home and the car has been repaired. B) If we will not visit Aunt Tillie then the kids are not home, and the car has been repaired. C) If the kids are not at home then we will not visit Aunt Tillie, or the car has been repaired. D) If we will not visit Aunt Tillie then the kids are not home, or the car has been repaired. Objective: (3.2) Express Symbolic Statements with Parentheses in English

61) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. r (p " q) A) We will visit Aunt Tillie if and only if the car has been repaired or the kids are home. B) We will visit Aunt Tillie if and only if the car has been repaired and the kids are home. C) If the car has been repaired and the kids are home, then we will visit Aunt Tillie. D) If the car has been repaired, then we will visit Aunt Tillie if the kids are home. Objective: (3.2) Express Symbolic Statements with Parentheses in English

62) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. (p q) "r A) If the car has been repaired then the kids are home, and we will visit Aunt Tillie. B) We will visit Aunt Tillie if and only if the car has been repaired and the kids are home. C) The car has been repaired if and only if the kids are home, and we will visit Aunt Tillie. D) If the car has been repaired or the kids are home, we will visit Aunt Tillie. Objective: (3.2) Express Symbolic Statements with Parentheses in English

63) p: The car has been repaired. q: The kids are home. r: We will visit Aunt Tillie. ~ r ~ (p " q) A) We will not visit Aunt Tillie if and only if the car has not been repaired and the kids are not home. B) If we will not visit Aunt Tillie then it is not true that the car has been repaired, and the kids are home. C) If we will not visit Aunt Tillie, then the statement that the car has been repaired and the kids are home is not true. D) If we will not visit Aunt Tillie, then the statement that the car has been repaired or the kids are home is not true. Objective: (3.2) Express Symbolic Statements with Parentheses in English

64) p: The refrigerator is working. q: The milk is warm. ~ p "q A) If the milk is warm, then the refrigerator is not working. B) The refrigerator is working and the milk is warm. C) The refrigerator is not working if and only if the milk is warm. D) The refrigerator is not working and the milk is warm. Objective: (3.2) Express Symbolic Statements with Parentheses in English

65) p: The air freshener is working. q: The basement is smelly. p ,~ q A) If the air freshener is not working, then the basement is smelly. B) If the air freshener is working, then the basement is not smelly. C) The air freshener is working or the basement is not smelly. D) The air freshener is not working or the basement is smelly. Objective: (3.2) Express Symbolic Statements with Parentheses in English

66) p: The refrigerator is working. q: The milk is warm. p ~ q A) Either the refrigerator is working or the milk is warm. B) The refrigerator is working if and only if the milk is not warm. C) If the refrigerator is not working then the milk is warm. D) If the refrigerator is working then the milk is not warm. Objective: (3.2) Express Symbolic Statements with Parentheses in English

67) p: The fan is working. q: The bedroom is stuffy. p ~ q A) The fan is working if and only if the bedroom is not stuffy. B) The fan is not working if and only if the bedroom is not stuffy. C) The fan is working and the bedroom is not stuffy. D) If the fan is working, then the bedroom is not stuffy. Objective: (3.2) Express Symbolic Statements with Parentheses in English

Let p, q, and r represent the following simple statements: p: There is a blizzard outside. q: We do not have to go to school. r: We go sledding. First place parenthesis as needed before and after the most dominant connective and then translate the symbolic statement into English.

68) ~r ~p ,~q A) If we do not go sledding, then there is not a blizzard outside or we have to go to school. B) If we go sledding then there is a blizzard outside, and we do not have to go to school. C) If we go sledding, then there is a blizzard outside or we do not have to go to school. D) If we do not go sledding then there is not a blizzard outside, or we have to go to school. Objective: (3.2) Use the Dominance of Connectives

69) ~p r ,q A) If there is a blizzard outside, then we go sledding or we do not have to go to school. B) If there is not a blizzard outside, then we go sledding or we do not have to go to school. C) If there is not a blizzard outside, then we go sledding and we do not have to go to school. D) If there is a blizzard outside, then we go sledding and we do not have to go to school. Objective: (3.2) Use the Dominance of Connectives

70) r p "q A) We go sledding if there is a blizzard outside, and we do not have to go to school. B) If we go sledding then, there is a blizzard outside and we do not have to go to school. C) We go sledding if and only if there is a blizzard outside and we do not have to go to school. D) We go sledding if and only if there is a blizzard outside, and we do not have to go to school. Objective: (3.2) Use the Dominance of Connectives

Write the compound statement in symbolic form. Let letters assigned to the simple statements represent English sentences that are not negated. Use the dominance of connectives to show grouping symbols (parentheses) in symbolic statements. 71) If I like the song or the DJ is entertaining then I do not change the station. A) p , (q r) B) (p , q) r C) p , (q ~r) D) (p , q) ~r Objective: (3.2) Use the Dominance of Connectives

72) I change the station if and only if it's not true that both I like the song and the DJ is entertaining. A) r (~p " q) B) (r ~p) "q C) r ~(p " q) D) r ~(p , q) Objective: (3.2) Use the Dominance of Connectives

73) If I like the song I do not change the station if and only if the DJ is entertaining. A) (p r) q B) (p ~r) q C) p ( r q)

D) p (~r q)

Objective: (3.2) Use the Dominance of Connectives

74) If I do not like the song and I change the station then the DJ is not entertaining or I look for a CD to play. A) [~p " (r ~q)] , s B) (~p " r) (~q , s) C) (p "~r) (q ,~s) D) ~p " [(r ~q) , s] Objective: (3.2) Use the Dominance of Connectives

Use grouping symbols to clarify the meaning of the symbolic statement. 75) p , q p q "~p A) [(p , q) p] (q "~p) B) (p , q) [(p q) "~p] C) (p , q) (p q) "~p D) p , (q p) (q "~p) Objective: (3.2) Use the Dominance of Connectives

76) p r " q p ,r A) [(p r) " q] (p , r) C) (p r) " [q (p , r)]

B) p [(r " q) (p , r)] D) [p (r " q)] (p , r)

Objective: (3.2) Use the Dominance of Connectives

Write the statement in symbolic form to determine the truth value for the statement. 77) Berlin is a city and Sweden is a country. A) True B) False Objective: (3.3) Use the Definitions of Negation, Conjunction, and Disjunction

78) 6 + 3 = 9 and 2 is an odd number. A) False

B) True

Objective: (3.3) Use the Definitions of Negation, Conjunction, and Disjunction

79) 4 × 3 = 12 or Spanish is a language. A) True

B) False

Objective: (3.3) Use the Definitions of Negation, Conjunction, and Disjunction

80) All musicians are from the United States or some professional baseball players drive a sports car. A) True B) False Objective: (3.3) Use the Definitions of Negation, Conjunction, and Disjunction

In a small town shopping mall last December, market researchers recorded the top five gifts that children requested while visiting "Santa." The bar graph below shows the number of children who requested each gift. Use the information given by the graph to determine the truth value of the statement. 81)

More than 90 children requested books and more children requested dolls than board games. A) True B) False Objective: (3.3) Use the Definitions of Negation, Conjunction, and Disjunction

Complete the truth table by filling in the required columns. 82) ~ p , p p ~ p ~ p ,p T F A) p ~ p ~ p ,p T F T F F F

C) p ~ p ~ p ,p T F F F T F

D) p ~ p ~ p ,p T T T F F T

p ~ p ~ p ,p T F T F T T

Objective: (3.3) Construct Truth Tables

83) p "~ q p q ~ q p "~ q T T T F F T F F A) p q ~ q p "~ q T T F F T F T T F T F F F F T T

C) p q ~ q p "~ q T T F T T F T T F T F F F F T F

Objective: (3.3) Construct Truth Tables

D) p q ~ q p "~ q T T F F T F T T F T F F F F T F

p q ~ q p "~ q T T F F T F T T F T T F F F T F

84) ~ (p " q) p q p "q ~ (p " q) T T T F F T F F A) p q p "q ~ (p " q) T T T F T F F T F T F T F F F F

p q p "q ~ (p " q) T T T T T F F F F T F F F F F F

p q p "q ~ (p " q) T T T F T F F T F T F T F F T F

p q p "q ~ (p " q) T T T F T F F T F T F T F F F T

Objective: (3.3) Construct Truth Tables

85) ~ p ,~ q p q ~ p ~ q ~ p ,~ q T T T F F T F F A) p q ~ p ~ q ~ p ,~ q T T F F F T F F T F F T T F F F F T T T

p q ~ p ~ q ~ p ,~ q T T F F F T F F T T F T T F T F F T T T

p q ~ p ~ q ~ p ,~ q T T F F T T F F T F F T T F F F F T T F

p q ~ p ~ q ~ p ,~ q T T F F F T F F F T F T T T T F F T F T

Objective: (3.3) Construct Truth Tables

Construct a truth table for the statement. 86) ~r "~p A) r p (~r "~p) B) r T T F F

T F T F

T F F T

T T F F

(~r "~p)

C) r p (~r "~p)

T F T F

F F F T

T T F F

r , (r "~r)

C) r

T F T F

D) r p (~r "~p)

F T T T

T T F F

r , (r "~r)

D) r

T F T F

F F F F

Objective: (3.3) Construct Truth Tables

87) r , (r "~r) A) r

r , (r "~r)

T F

B) r

F F

T F

T T

T F

r , (r "~r)

T F

F T

Objective: (3.3) Construct Truth Tables

88) (q "p) , (~q "~p) A) q

(q "p) , (~q "~p)

B) q

(q "p) , (~q "~p)

T T F F C) q

T F T F p

T F F T (q "p) , (~q "~p)

T F

F T

F F

D) q

(q "p) , (~q "~p)

T T F F

T F T F

F F T T

T T F F

T F T F

T T T F

C) r

~(~(r ,p))

T F

F T

T F

Objective: (3.3) Construct Truth Tables

89) ~(~(r ,p)) A) r

~(~(r ,p))

T T F F

T F T F

F F F T

B) r

~(~(r ,p))

T T F F

T F T F

T T F F

Objective: (3.3) Construct Truth Tables

90) ~(r , t) "~(t "r) A) r

~(r , t) "~(t "r)

B) r

~(r , t) "~(t "r)

T T F F C) r

T F T F t

F F F F ~(r , t) "~(t "r)

T T F F D) r

T F T F t

F F T F ~(r , t) "~(t "r)

T T F F

T F T F

F T T F

T T F F

T F T F

F F F T

Objective: (3.3) Construct Truth Tables

D) r

~(~(r ,p))

T T F F

T F T F

T T T F

91) ~(p , q) "~ p A) p q p ,q ~(p , q) ~ p ~(p , q) "~ p T T T F F F T F T F F F F T T T T T F F F T T T

B) p q p ,q ~(p , q) ~ p ~(p , q) "~ p T T T F F F T F T F F F F T T F T T F F F T T T

D) p q p "q ~(p , q) ~ p ~(p " q) "~ p T T T F F F T F F T F F F T F T T T F F T F T F

p q p ,q ~(p , q) ~ p ~(p , q) "~ p T T T F F F T F T F F F F T T F T F F F F T T T

Objective: (3.3) Construct Truth Tables

92) ~q , (~p , q) A) q p ~q , (~p , q)

B) q

~q , (~p , q)

T T F F C) q

T F T F p

F F T T ~q , (~p , q)

T T F F D) q

T F T F p

T T T T ~q , (~p , q)

T T F F

T F T F

T F T T

T T F F

T F T F

F T T T

Objective: (3.3) Construct Truth Tables

93) r ,~(c "s) A) r

r ,~(c "s)

B) r

r ,~(c "s)

T T T T F F F F C) r

T T F F T T F F c

T F T F T F T F s

T T T T F T T T r ,~(c "s)

T T T T F F F F D) r

T T F F T T F F c

T F T F T F T F s

T F F T F T T F r ,~(c "s)

T T T T F F F F

T T F F T T F F

T F T F T F T F

F T T F F T T F

T T T T F F F F

T T F F T T F F

T F T F T F T F

T T T T F T T F

Objective: (3.3) Construct Truth Tables

94) (p "~s) "q A) p s

(p "~s) "q

B) p

(p "~s) "q

T T T T F F F F C) p

T T F F T T F F s

T F T F T F T F q

F F F F F T T F (p "~s) "q

T T T T F F F F D) p

T T F F T T F F s

T F T F T F T F q

F F F F F T T T (p "~s) "q

T T T T F F F F

T T F F T T F F

T F T F T F T F

T T T F F T T T

T T T T F F F F

T T F F T T F F

T F T F T F T F

F F T F F F F F

Objective: (3.3) Construct Truth Tables

95) ~((w "q) ,t) A) w

~((w "q) ,t)

B) w

~((w "q) ,t)

T T T T F F F F C) w

T T F F T T F F q

T F T F T F T F t

T T T F T F F F ~((w "q) ,t)

T T T T F F F F D) w

T T F F T T F F q

T F T F T F T F t

T F T F T F F T ~((w "q) ,t)

T T T T F F F F

T T F F T T F F

T F T F T F T F

T T T T F F F F

T T F F T T F F

T F T F T F T F

F F F T F T F T

T F T F T F T F

Objective: (3.3) Construct Truth Tables

96) t , (t "~t) A) t T F

t , (t "~t) F F

B) t T F

t , (t "~t)

C) t

T T

T F

Objective: (3.3) Construct Truth Tables

t , (t "~t) T F

D) t T F

t , (t "~t) F T

97) (p "s) , (~p "~s) A) p

(p "s) , (~p "~s)

B) p

(p "s) , (~p "~s)

T T F F C) p

T F T F s

F F T T (p "s) , (~p "~s)

T F

F T

F F

D) p

(p "s) , (~p "~s)

T T F F

T F T F

T F F T

T T F F

T F T F

T T T F

Objective: (3.3) Construct Truth Tables

98) (s "q) " (~q , t) A) s

(s "q) " (~q , t)

B) s

(s "q) " (~q , t)

T T T T F F F F C) s

T T F F T T F F q

T F T F T F T F t

F T T T T F T T (s "q) " (~q , t)

T T T T F F F F D) s

T T F F T T F F q

T F T F T F T F t

F T T F T F F T (s "q) " (~q , t)

T T T T F F F F

T T F F T T F F

T F T F T F T F

T T T T T F T T

T T T T F F F F

T T F F T T F F

T F T F T F T F

T F F F F F F F

Objective: (3.3) Construct Truth Tables

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. 99) p "q A) True B) False Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

100) ~p ,q A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

101) p " (q ,p) A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

102) p , ~q A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

103) ~(p , ~q) A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

104) [(~p "~q) ,~q] A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

105) ~[~p , (~q " p)] A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

106) ~[(~p "~q) ,~q] A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. 107) ~p , (q "~r) A) True B) False Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

108) (p "~q) "r A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

109) ~[(~p " q) , r] A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

110) ~(p " q) " (r , ~q) A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

111) ~(~p "~q) , (~r , ~p) A) True

B) False

Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

Use the information in the graphs to determine the truth value of the compound statement.

112) It is not true that in Year 1, 53.6% of declared majors were liberal arts and 40.3% were science. A) True B) False Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

113) It is not true that in Year 1, 41.7% of declared majors were science or 4.3% were undecided. A) True B) False Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

114) From Year 1 though Year 3, the percentage of science majors increased or the percentage of liberal arts majors increased, and those who where undecided did not decrease. A) True B) False Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

115) From Year 1 though Year 3, the percentage of liberal arts majors decreased, but the percentage of science majors did not increase, and those who where undecided decreased. A) True B) False Objective: (3.3) Determine the Truth Value of a Compound Statement for a Specific Case

Provide an appropriate response. 116) A conditional statement is false only when the the

, the statement before the connective, is true and

, the statement after the connective, is false.

A) implication; tautology C) tautology; implication

B) consequent; antecedent D) antecedent; consequent

Objective: (3.4) Understand the Logic Behind the Definition of the Conditional

Construct a truth table for the statement. 117) ~ p ~ q A) p q ~ p ~ q ~ p ~ q T T F T T T F F F T F T T T T F F T F F

B) p q ~ p ~ q ~ p ~ q T T F F F T F F T T F T T F F F F T T T

D) p q ~ p ~ q ~ p ~ q T T F F T T F F T T F T T F F F F T T T

p q ~ p ~ q ~ p ~ q T T F F T T F F T F F T T F F F F T T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

118) ~(q ~ p) A) p q ~ p q ~ p ~(q ~ p) T T F F T T F F T F F T T T F F F T T F

B) p q ~ p q ~ p ~(q ~ p) T T F T F T F F F T F T T F T F F T F T

D) p q ~ p q ~ p ~(q ~ p) T T F F T T F F T F F T T T T F F T T F

p q ~ p q ~ p ~(q ~ p) T T F F T T F F F T F T T T F F F T T F

Objective: (3.4) Construct Truth Tables for Conditional Statements

119) (p " q) (p , q) A) p q p "q p ,q (p " q) (p , q) T T T T T T F F T T F T F T T F F F F F

B) p q p "q p ,q (p " q) (p , q) T T T T T T F F T T F T F T T F F F F T

D) p q p "q p ,q (p " q) (p , q) T T T T T T F T F F F T T F F F F F F T

p q p "q p ,q (p " q) (p , q) T T T T T T F F T T F T F T T F F T F F

Objective: (3.4) Construct Truth Tables for Conditional Statements

120) (q p) "~ q A) p q q p ~ q (q p) "~ q T T T F F T F F T F F T T F F F T T F F

B) p q q p ~ q (q p) "~ q T T T F F T F T T T F T F F T F T T F F

D) p q q p ~ q (q p) "~ q T T T F T T F T T T F T F F T F T T F F

p q q p ~ q (q p) "~ q T T T F F T F T T T F T F F F F F T T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

121) ~q (~q "p) A) q

~q (~q "p)

B) q

~q (~q "p)

T T F F C) q

T F T F p

F F T F ~q (~q "p)

T T F F D) q

T F T F p

T F T F ~q (~q "p)

T T F F

T F T F

T T T F

T T F F

T F T F

T T T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

122) (r ~p) (r "~p) A) r

(r ~p) (r "~p)

B) r

(r ~p) (r "~p)

T T F F C) r

T F T F p

T T F F

T F F T p

F F F T

(r ~p) (r "~p)

T T F F D) r

(r ~p) (r "~p)

T T F F

T F T F

T T F T

T T F F

T F T F

F T T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

123) (p q) (~p , q) A) p

(p q) (~p , q)

B) p

(p q) (~p , q)

T T F F C) p

T F T F q

F T F F (p q) (~p , q)

T T F F D) p

T F T F q

T T T T (p q) (~p , q)

T T F F

T F T F

T T F F

T F T F

T F T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

124) ~(p q) (p "~q) A) p

~(p q) (p "~q)

B) p

~(p q) (p "~q)

T T F F C) p

T F T F q

T F T T ~(p q) (p "~q)

T T F F D) p

T F T F q

T T T T ~(p q) (p "~q)

T T F F

T F T F

T T F F

T F T F

T F F F

T F F T

Objective: (3.4) Construct Truth Tables for Conditional Statements

125) (~p , ~q) ~(q "p) A) p

(~p , ~q) ~(q "p)

B) p

(~p , ~q) ~(q "p)

T T F F C) p

T F T F q

T T T F (~p , ~q) ~(q "p)

T T F F D) p

T F T F q

T F F T (~p , ~q) ~(q "p)

T T F F

T F T F

T T F F

T F T F

T T T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

F F F F

126) ~(p "q) ~(p ,q) A) p

~(p "q) ~(p ,q)

B) p

~(p "q) ~(p ,q)

T T F F C) p

T F T F q

T T T T ~(p "q) ~(p ,q)

T T F F D) p

T F T F q

T F F T ~(p "q) ~(p ,q)

T T F F

T F T F

T T F F

T F T F

B) p

(~p q) (q ~r)

T T T T F F F F D) p

T T F F T T F F q

T F T F T F T F r

T T T T T T F F (~p q) (q ~r)

T T T T F F F F

T T F F T T F F

T F T F T F T F

F F T T F F F F

F F F T

F T T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

127) (~p q) (q ~r) A) p q r (~p q) (q ~r) T T T T F F F F C) p

T T F F T T F F q

T F T F T F T F r

T T T T F F F F

T T F F T T F F

T F T F T F T F

F T T T F T T T (~p q) (q ~r) F T F T F T F T

Objective: (3.4) Construct Truth Tables for Conditional Statements

128) ~(p "q) (p (~w "q)) A) p

~(p "q) (p (~w "q))

B) p

~(p "q) (p (~w "q))

T T T T F F F F

T T F F T T F F

T F T F T F T F

T T F F T T T T

T T T T F F F F

T T F F T T F F

T F T F T F T F

T F T F T T T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

129) q ~r A) q

q ~r

B) q

q ~r

C) q

q ~r

D) q

q ~r

T T F F

T F T F

F T T T

T T F F

T F T F

F F T T

T T F F

T F T F

T T F F

T F T F

T F T T

Objective: (3.4) Construct Truth Tables for Conditional Statements

Construct a truth table for the given statement and then determine if the statement is a tautology. 130) [ (p ~ q) , q ] p A) p q ~ q p ~ q (p ~ q) ,q [ (p ~ q) ,q ] p T T F F F T Is not a tautology. T F T T T T F T F F T F F F T T T F B) p q ~ q p ~ q (p ~ q) ,q [ (p ~ q) ,q ] p T T F F T T Is not a tautology. T F T T T T F T F T T F F F T T T F

C) p q ~ q p ~ q (p ~ q) ,q [ (p ~ q) ,q ] p T T F F T T Is a tautology. T F T T T T F T F T T F F F T T T F

D) p q ~ q p ~ q (p ~ q) ,q [ (p ~ q) ,q ] p T T F F T T Is a tautology. T F T T T T F T F T T T F F T T T T Objective: (3.4) Construct Truth Tables for Conditional Statements

131) [ (p ~ q) " q ] ~ p A) p q ~ q p ~ q (p ~ q) "q ~ p [ (p ~ q) " q ] ~ p T T F T T F T Is a tautology. T F T F F F T F T F F F T T F F T F F T T B) p q ~ q p ~ q (p ~ q) "q ~ p [ (p ~ q) " q ] ~ p T T F F F F F Is not a tautology. T F T T F F F F T F T T T T F F T T F T T

C) p q ~ q p ~ q (p ~ q) "q ~ p [ (p ~ q) " q ] ~ p T T F F F F T Is a tautology. T F T T T F T F T F T F T T F F T T F T T

D) p q ~ q p ~ q (p ~ q) "q ~ p [ (p ~ q) " q ] ~ p T T F F F F T Is a tautology. T F T T F F T F T F T T T T F F T T F T T Objective: (3.4) Construct Truth Tables for Conditional Statements

132) [ (p "~ q) "~ p ] ~ q A) p q ~ q p "~ q ~ p T T F F F T F T T F F T F F T F F T F T

(p "~ q) "~ p [ (p "~ q) "~ p ] ~ q F T Is not a tautology. F T F T F T

B) p q ~ q p "~ q ~ p T T F F F T F T T F F T F F T F F T F T

(p "~ q) "~ p [ (p "~ q) "~ p ] ~ q F T Is a tautology. F T F T F T

p q ~ q p "~ q ~ p T T F F F T F T T F F T F F T F F T F T

(p "~ q) "~ p [ (p "~ q) "~ p ] ~ q F F Is not a tautology. F F F F F F

p q ~ q p "~ q ~ p T T F F F T F T T F F T F F T F F T F T

(p "~ q) "~ p [ (p "~ q) "~ p ] ~ q F T Is not a tautology. F F F T F F

Objective: (3.4) Construct Truth Tables for Conditional Statements

133) ( ~ p , q) (p q) A) p q ~ p ~ p ,q p q ( ~ p , q) (p q) T T F T T T Is not a tautology. T F F T F F F T T T T T F F T F T F B) p q ~ p ~ p ,q p q ( ~ p , q) (p q) T T F T T T Is not a tautology. T F F F F T F T T T F F F F T T F F

C) p q ~ p ~ p ,q p q ( ~ p , q) (p q) T T F T T T Is a tautology. T F F F F T F T T T T T F F T T T T

D) p q ~ p ~ p ,q p q ( ~ p , q) (p q) T T F T T T Is not a tautology. T F F F F F F T T T T T F F T T T T Objective: (3.4) Construct Truth Tables for Conditional Statements

134) ( ~ p " q) " (~ p , q) A) p q ~ p ~ p "q ~ p ,q ( ~ p " q) " (~ p , q) T T F F T T Is not a tautology. T F F F F F F T T T T T F F T F T T B) p q ~ p ~ p "q ~ p ,q ( ~ p " q) " (~ p , q) T T F F F F Is not a tautology. T F F F F F F T T T T T F F T F F F

C) p q ~ p ~ p "q ~ p ,q ( ~ p " q) " (~ p , q) T T F F T F Is not a tautology. T F F F F F F T T T T T F F T F T F

D) p q ~ p ~ p "q ~ p ,q ( ~ p " q) " (~ p , q) T T F F T T Is a tautology. T F F F F T F T T T T T F F T F T T Objective: (3.4) Construct Truth Tables for Conditional Statements

Provide an appropriate response. 135) The biconditional statement p q can be written symbolically as A) (p q) , (q p)

B) (p q) " (~q ~p)

Objective: (3.4) Understand the Definition of the Biconditional

C) (p q) , (~p ~q)

D) (p q) " (q p)

Construct a truth table for the given statement. 136) ~ p ~ q A) p q ~ p ~ q ~ p ~ q T T F F T T F F T T F T T F T F F T T T

B) p q ~ p ~ q ~ p ~ q T T F F T T F F T F F T T F F F F T T T

D) p q ~ p ~ q ~ p ~ q T T F F T T F F T F F T T F T F F T T T

p q ~ p ~ q ~ p ~ q T T F T F T F F T F F T T F F F F T T T

Objective: (3.4) Construct Truth Tables for Biconditional Statements

137) ~ (p ~ q) A) p q ~ q p ~ q ~ (p ~ q) T T F F T T F T T F F T F T F F F T T F

B) p q ~ q p ~ q ~ (p ~ q) T T F T F T F T F T F T F F T F F T T F

D) p q ~ q p ~ q ~ (p ~ q) T T F F T T F T T T F T F T T F F T F T

p q ~ q p ~ q ~ (p ~ q) T T F F T T F T T F F T F T F F F T F T

Objective: (3.4) Construct Truth Tables for Biconditional Statements

138) (p q) ~ q A) p q p q T T T T F F F T F F F T

B) ~ q (p q) ~ q F F T T F T T T

p q p q T T T T F F F T F F F T

~ q (p q) ~ q F F T F F T T T

p q p q T T T T F F F T F F F T

~ q (p q) ~ q F T T F F F T F

D) p q p q T T T T F F F T T F F T

~ q (p q) ~ q F F T T F F T T

Objective: (3.4) Construct Truth Tables for Biconditional Statements

139) (p ~ q) ( ~q ~ p) A) p q ~ q p ~ q ~ p ~q ~ p (p ~ q) ( ~q ~ p) T T F F F T F T F T T F F F F T F T T T T F F T F T T F B) p q ~ q p ~ q ~ p ~q ~ p (p ~ q) ( ~q ~ p) T T F F F T T T F T T F F T F T F T T T T F F T F T T T

C) p q ~ q p ~ q ~ p ~q ~ p (p ~ q) ( ~q ~ p) T T F F F T T T F T T F F F F T F T T F F F F T F T T T

D) p q ~ q p ~ q ~ p ~q ~ p (p ~ q) ( ~q ~ p) T T F F F T T T F T T F F F F T F T T T T F F T F T T T Objective: (3.4) Construct Truth Tables for Biconditional Statements

140) [ (p " q) " (p q) ] (p , q ) A) p q p "q p q (p " q) " (p q) T T T T T T F F F F F T F T T F F F T T

p ,q [ (p " q) " (p q) ] (p , q ) T T T F T T F T

B) p q p "q p q T T T T T F F F F T F T F F F T

(p " q) " (p q) T F F F

p ,q [ (p " q) " (p q) ] (p , q ) T T T F T F F T

p q p "q p q T T T T T T F F F T F T F F F T

(p " q) " (p q) T F T F

p ,q [ (p " q) " (p q) ] (p , q ) T T F F T F F F

p q p "q p q T T T T T F F F F T F T F F F T

(p " q) " (p q) T F F F

p ,q [ (p " q) " (p q) ] (p , q ) T T F T F T F T

Objective: (3.4) Construct Truth Tables for Biconditional Statements

Construct a truth table for the statement. Then determine if the statement is a tautology. 141) ~(~p " q) (p "~ q) A) p q ~p ~p "q ~( ~p " q) ~ q p "~ q ~( ~p " q) (p "~ q) T T F F T F T T T F F F T T T T F T T T F F F T F F T F T T T T Is a tautology. B) p q ~p ~p "q ~( ~p " q) ~ q p "~ q ~( ~p " q) (p "~ q) T T F F T F F F T F F F T T T T F T T T F F F T F F T F T T F T Is not a tautology.

C) p q ~p ~p "q ~( ~p " q) ~ q p "~ q ~( ~p " q) (p "~ q) T T F F T F F F T F F F T T T T F T T T F F F T F F T F T T F F Is not a tautology.

D) p q ~p ~p "q ~( ~p " q) ~ q p "~ q ~( ~p " q) (p "~ q) T T F F T F F T T F F F T T T T F T T T F F F T F F T F T T F T Is a tautology. Objective: (3.4) Construct Truth Tables for Biconditional Statements

142) (p q) (~ q ~ p) A) p q p q ~ q ~ p ~ q ~ p (p q) (~ q ~ p) T T T F F T T Is not a tautology. T F F T F F T F T F F T T F F F T T T T T B) p q p q ~ q ~ p ~ q ~ p (p q) (~ q ~ p) T T T F F T F Is not a tautology. T F F T F F T F T T F T T T F F T T T T T

C) p q p q ~ q ~ p ~ q ~ p (p q) (~ q ~ p) T T T F F F T Is a tautology. T F F T F F T F T F F T T T F F T T F T T

D) p q p q ~ q ~ p ~ q ~ p (p q) (~ q ~ p) T T T F F T T Is a tautology. T F F T F F T F T T F T T T F F T T T T T Objective: (3.4) Construct Truth Tables for Biconditional Statements

143) (q p) (~ p , q) A) p q q p ~ p ~ p ,q (q p) (~ p , q) T T T F T T Is not a tautology. T F T F F F F T F T T F F F T T T T B) p q q p ~ p ~ p ,q (q p) (~ p , q) T T T F T T Is a tautology. T F F F F T F T T T T T F F T T T T

C) p q q p ~ p ~ p ,q (q p) (~ p , q) T T T T T F Is not a tautology. T F T F F F F T F T T F F F F T T T

D) p q q p ~ p ~ p ,q (q p) (~ p , q) T T T F T T Is not a tautology. T F T F F F F T F T T T F F T T T T Objective: (3.4) Construct Truth Tables for Biconditional Statements

144) (p q) [ (q p) , (p ~ q) ] A) p q p q q p ~ q p ~ q (q p) , (p ~ q) (p q) [ (q p) , (p ~ q) ] T T T T F F F T T F F F T T T F F T T F F F T F F F T T T T T T Is not a tautology. B) p q p q q p ~ q p ~ q (q p) , (p ~ q) (p q) [ (q p) , (p ~ q) ] T T T T F F F T T F F F T T T T F T F F F T T T F F T T T T T T Is a tautology.

C) p q p q q p ~ q p ~ q (q p) , (p ~ q) (p q) [ (q p) , (p ~ q) ] T T T T F F T T T F F F T T T F F T F F F T T F F F T T T T T T Is a tautology.

D) p q p q q p ~ q p ~ q (q p) , (p ~ q) (p q) [ (q p) , (p ~ q) ] T T T T F F T T T F F T T T T F F T F F F T T F F F T T T T T T Is not a tautology. Objective: (3.4) Construct Truth Tables for Biconditional Statements

In a small town shopping mall, market researchers recorded the number of children who requested video games while visiting "Santa." The bar graph below shows the results for five consecutive years. Use the information given by the graph to determine the truth value of the statement. 145)

If there was a decrease in the number of children at this mall requesting video games from Year 3 to Year 4, then more than 85 children at this mall requested computer games in Year 5. A) True B) False Objective: (3.4) Determine the Truth Value of a Compound Statement for a Specific Case

The table shows ice cream cone sales at an ice cream shop. Let p and q represent the following statements: p: Vanilla is the best-selling flavor. q: Chocolate chip outsold strawberry by 13,000 cones. Ice Cream Sold One Year Sales in Thousands Flavor of Cones chocolate 33 vanilla 31 chocolate chip 27 strawberry 14 coffee 8 butterscotch 5 146) Write the symbolic statement below in words. Then use the table to determine the truth value of the statement. ~ q ~ p A) If chocolate chip did not out sell strawberry by 13,000 cones, then vanilla was not the best-selling flavor. Truth value: False B) If chocolate chip did not out sell strawberry by 13,000 cones, then vanilla was not the best-selling flavor. Truth value: True C) If chocolate chip out sold strawberry by 13,000 cones, then vanilla was not the best-selling flavor. Truth value: True D) If chocolate chip did not out sell strawberry by 13,000 cones, then vanilla was the best-selling flavor. Truth value: True Objective: (3.4) Determine the Truth Value of a Compound Statement for a Specific Case

Use a truth table to determine whether the two statements are equivalent. 147) ~p " ~q and ~(p , q) A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

148) ~p ,~q and ~(p " q) A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

149) q " ~p and ~p ~q A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

150) ~(~q) and q A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

151) q p and ~q , p A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

152) ~q " p and ~q p A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

153) q p and ~p ~q A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

154) ~(q p) and q "~p A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

155) p q and ~q ~p A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

156) q p and p q A) Yes

B) No

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

Use a truth table to show that p q and ~ p , q are equivalent. Then use the result to write a statement that is equivalent to the statement shown. 157) If the garden is not watered every day, the flowers wilt. A) p q p q ~ p ~ p ,q T T T F T T F F F F F T T T T F F T T T Either the garden is not watered every day, or the flowers don't wilt.

B) p q p q ~ p ~ p ,q T T T F T T F F F F F T T T T F F T T T The flowers do not wilt if and only if the garden is not watered every day.

C) p q p q ~ p ~ p ,q T T T F T T F F F F F T T T T F F T T T The flowers wilt if the garden is not watered every day.

D) p q p q ~ p ~ p ,q T T T F T T F F F F F T T T T F F T T T Either the garden is watered every day, or the flowers wilt. Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

Select the statement that is equivalent to the given statement. 158) I ate a cucumber or a candy bar. A) If I ate a cucumber, then I ate a candy bar. B) If I did not a cucumber, then I did not eat a candy bar. C) If I ate a cucumber, then I did not eat a candy bar. D) If I did not eat a cucumber, then I ate a candy bar. Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

Select the statement that is NOT equivalent to the given statement. 159) It is not true that Giselle and Gerry are both chefs. A) Giselle is not a chef and Gerry is not a chef. C) Giselle is not a chef or Gerry is not a chef.

B) If Giselle is a chef, then Gerry is not a chef. D) If Gerry is a chef, then Giselle is not a chef.

Objective: (3.5) Use a Truth Table to Show That Statements are Equivalent

Write the contrapositive of the statement. 160) If I am in the city of Fligaroo, then I am on the planet Plochus. A) If I am not on the planet Plochus, then I am not in the city of Fligaroo. B) If I am not on the planet Plochus, then I am in the city of Fligaroo. C) If I am not in the city of Fligaroo, then I am not on the planet Plochus. D) If I am not in the city of Fligaroo, then I am on the planet Plochus. Objective: (3.5) Write the Contrapositive for a Conditional Statement

161) If the electricity is out, then I cannot use the computer. A) If I can use the computer, then the electricity is not out. B) If the electricity is not out, then I can use the computer. C) If I cannot use the computer, then the electricity is out. D) If the electricity is not out, then I cannot use the computer. Objective: (3.5) Write the Contrapositive for a Conditional Statement

162) If he is not working in Malaysia, then he is vacationing in Japan. A) If he is working in Malaysia, then he is not vacationing in Japan. B) If he is vacationing in Malaysia, then he is not working in Japan. C) If he is not vacationing in Japan, then he is working in Malaysia. D) If he is not vacationing in Malaysia, then he is working in Japan. Objective: (3.5) Write the Contrapositive for a Conditional Statement

163) If the news report is accurate, then house prices are rising. A) If the news report is not accurate, then it is misleading. B) If house prices are not rising, then the news report is accurate. C) If house prices are not rising, then the news report is not accurate. D) If the news report is not accurate, then house prices are not rising. Objective: (3.5) Write the Contrapositive for a Conditional Statement

Write the converse and inverse of the statement. 164) If you eat too much, then you get fat. A) converse: If you get fat, then you are eating too much. inverse: If you don't eat too much, you don't get fat. B) converse: If you get fat, then you are eating too much. inverse: If you don't get fat, then you are eating too much. C) converse: If you get fat, then you are eating too much. inverse: If you don't get fat, then you are not eating too much. D) converse: If you don't eat too much, you don't get fat. inverse: If you get fat, then you are eating too much. Objective: (3.5) Write the Converse and Inverse of a Conditional Statement

165) If you are running on the beach, then you are not dancing. A) converse: If you are dancing, then you are not running on the beach. inverse: If you are not running on the beach, then you are dancing B) converse: If you are not running on the beach, then you are dancing inverse: If you are not dancing, then you are running on the beach. C) converse: If you are not dancing, then you are running on the beach. inverse: If you are not running on the beach, then you are dancing D) converse: If you are not dancing, then you are running on the beach. inverse: If you are running on the beach, then you are not dancing Objective: (3.5) Write the Converse and Inverse of a Conditional Statement

166) If it is winter, then some people go skiing. A) converse: If some people do not go skiing, then it is not winter inverse: If it is not winter, then everyone goes skiing. B) converse: If some people go skiing, then it is winter inverse: If it is not winter, then everyone goes skiing. C) converse: If some people do not go skiing, then it is not winter inverse: If it is not winter, then no one goes skiing. D) converse: If some people go skiing, then it is winter inverse: If it is not winter, then no one goes skiing. Objective: (3.5) Write the Converse and Inverse of a Conditional Statement

167) If Nathan performs in New York, then he performs in the United States. A) converse: If Nathan performs in the United States, then he performs in New York. inverse: If Nathan does not perform in New York, then he does not perform in the United States. B) converse: If Nathan does not perform in the United States, then he does not perform in New York. inverse: If Nathan does not perform in New York, then he performs in the United States. C) converse: If Nathan does not perform in the United States, then he does not perform in New York. inverse: If Nathan does not perform in New York, then he does not perform in the United States. D) converse: If Nathan performs in the United States, then he performs in New York. inverse: If Nathan does not perform in New York, then he performs in the United States Objective: (3.5) Write the Converse and Inverse of a Conditional Statement

Write the negation of the conditional statement. 168) If I am in Seoul, then I am in Korea. A) If I am not in Seoul, then I am not in Korea. C) If I am in Seoul, then I am not in Korea.

B) I am not in Seoul and I am in Korea. D) I am in Seoul and I am not in Korea.

Objective: (3.6) Write the Negation of a Conditional Statement

169) If it is pink, then it is not a clam. A) It is pink and it is not a clam. C) It is not pink and it is not a clam.

B) It is not pink and it is a clam. D) It is pink and it is a clam.

Objective: (3.6) Write the Negation of a Conditional Statement

170) If she can't take out the trash, I will. A) If she can take out the trash, I can't. C) She can't take out the trash, I can't.

B) She can take out the trash, and I can't. D) She can't take out the trash, and I won't.

Objective: (3.6) Write the Negation of a Conditional Statement

171) If there is an earthquake, then all policemen are on call. A) There is an earthquake and no policemen are on call. B) There is not an earthquake and some policemen are not on call. C) If there is an earthquake, then some policemen are not on call. D) There is an earthquake and some policemen are not on call. Objective: (3.6) Write the Negation of a Conditional Statement

172) If I get a high-paying job, then I can pay off all my bills. A) I get a high-paying job and I cannot pay off all my bills. B) I don't get a high-paying job and cannot pay off all my bills. C) I don't get a high-paying job and can pay off all my bills. D) I get a high-paying job and can pay off all my bills. Objective: (3.6) Write the Negation of a Conditional Statement

Use the De Morgan law that states: ~(p " q) is equivalent to ~ p ,~ q to write an equivalent English statement for the statement. 173) It is not true that condors and rabbits are both birds. A) rabbits are not birds, but condors are. C) Neither condors nor rabbits are birds.

B) condors are birds or rabbits are birds. D) condors are not birds or rabbits are not birds.

Objective: (3.6) Use De Morgan’s Laws

174) It is not the case that a gun and a nose are both weapons. A) A gun is not a weapon or a nose is not a weapon. B) A gun is not a weapon and a nose is not a weapon. C) guns are not noses. D) A gun is a weapon but a nose is not. Objective: (3.6) Use De Morgan’s Laws

175) It is not true that Kentucky and Luxemburg are both cities. A) Kentucky is not a city or Luxemburg is not a city. B) It is true that Kentucky and Luxemburg are both cities. C) Kentucky is not a city and Luxemburg is not a city. D) If Kentucky is a city, then Luxemburg is not a city. Objective: (3.6) Use De Morgan’s Laws

176) It is not true that Napoleon Bonaparte was a drummer or a bartender. A) Napoleon Bonaparte was either a drummer or a bartender. B) It is not true that Napoleon Bonaparte was not a drummer or not a bartender. C) Napoleon Bonaparte was not a drummer or was not a bartender. D) Napoleon Bonaparte was neither a drummer or a bartender. Objective: (3.6) Use De Morgan’s Laws

Use De Morgan's laws to write a negation of the statement. 177) Roger or Emil will attend the game. A) Roger will not attend the game and Emil will not attend the game. B) Roger or Emil will not attend the game. C) Roger and Emil will attend the game. D) Roger will not attend the game and Emil will attend the game. Objective: (3.6) Use De Morgan’s Laws

178) Cats are lazy or dogs aren't friendly. A) Cats aren't lazy or dogs are friendly. C) Cats aren't lazy or dogs aren't friendly.

B) Cats aren't lazy and dogs are friendly. D) Cats are lazy and dogs are friendly.

Objective: (3.6) Use De Morgan’s Laws

179) She is not older than 21 and he is older than 21. A) It is not true that she is older than 21 or he is not older than 21. B) She is older than 21 or he is not older than 21. C) She is older than 21 or he is not younger than 21. D) She is older than 21 but he is not older than 21. Objective: (3.6) Use De Morgan’s Laws

180) A man runs across the street and he does not get hit by a car. A) A man runs across the street or he gets hit by a car. B) A man does not run across the street or he gets hit by a car. C) A man runs across the street and he gets hit by a car. D) A man does not run across the street or he does not get hit by a car. Objective: (3.6) Use De Morgan’s Laws

Determine which, if any, of the three given statements are equivalent. 181) a. It is not true that I do not exercise daily and I stay healthy. b. I do not exercise daily and I stay healthy. c. I exercise daily or I do not stay healthy. A) b and c B) a and c C) none

D) a and b

Objective: (3.6) Use De Morgan’s Laws

182) a. If she does not misplace her keys or forgets her phone, then she will get locked out. b. If she misplaces her keys and does not forget her phone then she will not get locked out. c. If she did not get locked out, then she misplaced her keys or did not forget her phone. A) a and b B) b and c C) a and c D) none Objective: (3.6) Use De Morgan’s Laws

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. 183) p q ~p NNNN 0~ q A) p q p q ~ p (p q) "~ p ~ q [ (p q) "~ p ] ~ q T T T F T F T The argument is valid. T F F F F T T F T F T T F T F F F T T T T

B) p q p q ~ p (p q) "~ p ~ q [ (p q) "~ p ] ~ q T T T F F F T The argument is invalid. T F F F F T T F T T T T F F F F T T T T T

C) p q p q ~ p (p q) "~ p ~ q [ (p q) "~ p ] ~ q T T T F F F T The argument is valid. T F F F F T T F T F T F F T F F F T F T T

D) p q p q ~ p (p q) "~ p ~ q [ (p q) "~ p ] ~ q T T T F F F T The argument is invalid. T F F F T T T F T T T T F F F F T T T T T Objective: (3.7) Use Truth Tables to Determine Validity

184) (p q) " (q p) q NNNN 0p ,q A) p q p q q p [ (p q) " (q p) ] p ,q [ [(p q) " (q p) ] " q ] (p ,q) T T T T T F T T F F T F F T F T T F F F T F F T T T T F Argument is invalid.

B) p q p q q p [ (p q) " (q p) ] p ,q [ [( p q) " (q p) ] " q ] (p ,q) T T T T T T T T F F T F F T F T T F F F T F F T T T F F Argument is invalid.

C) p q p q q p [ (p q) " (q p) ] p ,q [ [(p q) " (q p) ] " q ] (p ,q) T T T T T T T T F F T F T T F T T F F T T F F T T T F F Argument is valid.

D) p q p q q p [ (p q) " (q p) ] p ,q [ [( p q) " (q p) ] " q ] (p ,q) T T T T T T T T F F T F T T F T T F F T T F F T T T F T Argument is valid. Objective: (3.7) Use Truth Tables to Determine Validity

185) q p p r NNNN 0r q A) p q r q p p r (q p) " (p r) r q [(q p) " (p r)] (r q) T T T T T T T T T T F T F F T T T F T T T T F F T F F T F F T T F T T F T F T T F T F F T F T T F F T T T T F F F F F T T T T T Symbolic argument is invalid.

B) p q r q p p r (q p) " (p r) r q [(q p) " (p r)] " (r q) T T T T T T T T T T F T F F T F T F T T T T F F T F F T F F T F F T T F T F T F F T F F T F T F F F T T T T F F F F F T T T T T Symbolic argument is invalid.

C) p q r q p p r (q p) " (p r) r q [(q p) " (p r)] (r q) T T T T T T T T T T F T F F T T T F T T T F T T T F F T F F T T F T T F T F T T F T F F T F T T F F T T T F T T F F F T T T T T Symbolic argument is valid.

D) p q r q p p r (q p) " (p r) r q [(q p) " (p r)] (r q) T T T T T T T T T T F T F F T T T F T T T F T T T F F T F F T T F T T F T F T T F T F F T F T T F F T T T F T T F F F T T F T T Symbolic argument is valid.

Objective: (3.7) Use Truth Tables to Determine Validity

186) ~ p "q q r NNNN 0p "r A) p q r ~ p ~ p "q q r (~ p " q) " (q r) p "r [(~ p " q) " (q r)] (p "r) T T T F F T F T T T T F F F F F F T T F T F F F F T T T F F F F T F F T F T T T T T T F F F T F T T F F F T F F T T F F F F T F F F T F T F F T Symbolic argument is invalid.

B) p q r ~ p ~ p "q q r (~ p " q) " (q r) p "r [(~ p " q) " (q r)] (p "r) T T T F F T F T T T T F F F F F F T T F T F F F F T T T F F F F T F F T F T T T T T T T T F T F T T F F F T F F T T F F F F T F F F T F T F T T Symbolic argument is valid.

C) p q r ~ p ~ p "q q r (~ p " q) " (q r) p "r [(~ p " q) " (q r)] (p "r) T T T F F T F T T T T F F F F F F T T F T F F F F T T T F F F F T F F T F T T T T T T T T F T F T T F F F T F F T T F F F F T F F F T F T F F T Symbolic argument is valid.

D) p q r ~ p ~ p "q q r (~ p " q) " (q r) p "r [(~ p " q) " (q r)] (p "r) T T T F F T F T F T T F F F F F F F T F T F F F F T F T F F F F T F F F F T T T T T T F F F T F T T F F F F F F T T F F F F F F F F T F T F F F Symbolic argument is invalid. Objective: (3.7) Use Truth Tables to Determine Validity

187) p q p r NNNN 0~ r q A) p q r p q p r (p q) " (p r) ~ r ~ r q [(p q) " (p r)] (~ r q) T T T T T T F T T T T F T F F T T F T F T F T F F T F T F F F F F T F F F T T F T F F T F F T F F T F T T F F F T T T T F T T F F F T T T T F F Symbolic argument is invalid.

B) p q r p q p r (p q) " (p r) ~ r ~ r q [(p q) " (p r)] (~ r q) T T T T T T F T T T T F T F F T T T T F T F T F F T T T F F F F F T F T F T T F T F F T T F T F F T F T T T F F T T T T F T T F F F T T T T F F Symbolic argument is invalid.

C) p q r p q p r (p q) " (p r) ~ r ~ r q [(p q) " (p r)] (~ r q) T T T T T T F T T T T F T F F T T T T F T F T F F T T T F F F F F T F T F T T F T F F T F F T F F T F T T T F F T T T T F T T F F F T T T T F F Symbolic argument is invalid.

D) p q r p q p r (p q) " (p r) ~ r ~ r q [(p q) " (p r)] (~ r q) T T T T T T F T T T T F T F F T T T T F T F T F F T T T F F F F F T F T F T T F T F F T T F T F F T F T T T F F T T T T F T T F F F T T T T F T Symbolic argument is valid. Objective: (3.7) Use Truth Tables to Determine Validity

188) p q q 0p A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

189) p q ~p 0~q A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

190) p ,q ~(p , q) 0~q A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

191) p ,q q 0p A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

192) p q ~q 0~p A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

193) ~p q ~q p 0p ,q A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

194) ~q "~p p , ~q 0~q A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

195) p ~q q ~p 0p ,q A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

196) (p q) " (q r) p 0r

A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

197) (~p " q) (q , r) ~q , r 0p ,q A) Valid

B) Invalid

Objective: (3.7) Use Truth Tables to Determine Validity

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Translate the argument into symbolic form. Then use a truth table to determine whether the argument is valid or invalid. (Ignore differences in past, present, and future tense.) 198) If it is Tuesday, I do not work late. I work late. 0It is not Tuesday. Objective: (3.7) Use Truth Tables to Determine Validity

199) If Emilio and Rodrigo both cook, then the meal is tasty. Emilio cooked and the meal was not tasty. 0Rodrigo did not cook. Objective: (3.7) Use Truth Tables to Determine Validity

200) There must be a cease-fire or there is fighting. There is fighting. 0There is no cease-fire. Objective: (3.7) Use Truth Tables to Determine Validity

201) If every student passes the quiz, then no review sessions are needed. Some students do not pass the quiz. 0Some review sessions are needed. Objective: (3.7) Use Truth Tables to Determine Validity

202) If it is July or August, then I am living at the beach I am not living at the beach. 0It is neither July nor August. Objective: (3.7) Use Truth Tables to Determine Validity

203) If this is Germany or Austria, then the signs are in German. The signs are in German. 0This is Germany or Austria Objective: (3.7) Use Truth Tables to Determine Validity

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the passage in the form of an argument using the following simple statements: p: The "diamond" is a fake. q: Peter will be unhappy for weeks. The argument's conclusion should be: The diamond must not have been a fake. Determine if the argument is valid or invalid. 204) Peter bought a "diamond" from a street vendor. I was sure it was a fake and that it would make Peter miserable for weeks. But I saw him a few days later. He had got the "diamond" appraised and looked quite happy.......

A) p q ~q NNNN 0~ p The argument is valid. C) p q ~q NNNN 0~ p The argument is invalid.

B) p q ~q NNNN 0 p The argument is invalid. D) p q ~q NNNN 0~ p The argument is valid.

Objective: (3.7) Use Truth Tables to Determine Validity

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Draw a valid conclusion from the given premises. 205) If a person cares about society, then that person does volunteer work. Sharon does not do volunteer work. Therefore.... Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

206) Lonni's math professor said to his class, "After the last session, we will go out for a beer or we will have dinner at Chez Louis." The professor and his class did not go out for a beer. Therefore.... Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

207) If all students passed the course, there are no students who will repeat the course. Some students will repeat the course. Therefore.... Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

208) If I work in the garden, my back gets sore. If my back gets sore, I take a hot bath Therefore.... Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 209) If I get robbed, I will go to court. I got robbed. Therefore.... A) I will go to court. C) I will not get robbed in court.

B) I will get robbed in court. D) I will not go to court.

Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

210) It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime. Therefore.... A) The squirrels are scurrying. B) Squirrels do not scurry during the day. C) The squirrels are not scurrying. D) Squirrels do not scurry at night. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

211) All birds have wings. None of my pets are birds. All animals with wings can flap them. Therefore.... A) All birds can flap their wings. B) All my pets can flap their wings. C) None of my pets can flap their wings. D) No birds can flap their wings. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

212) Every man with a mind can think. A distracted man can't think. A man who is not distracted can apply himself. Therefore.... A) Every distracted man can apply himself. B) Every man who can apply himself has a mind. C) Every man with a mind can apply himself. D) Every man with a mind is distracted. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

213) All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat. Therefore.... A) Any dead fish can dream. B) All fish have a heartbeat. C) All live animals can dream. D) Any dead animal has no heartbeat. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

214) If it's not Saturday, then Dad will shave. If Dad has whiskers, then he did not shave. If it's Saturday, then Dad will take us to the game. Therefore.... A) If Dad shaves, then it's not Saturday. B) If Dad has whiskers, then he will take us to the game. C) If Dad did not shave, then he has whiskers. D) If Dad takes us to the game, then he has whiskers. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

215) If you pay your taxes, then you are a good citizen. People who do not pay their taxes did not receive a tax bill. If it is April, then you will receive a tax bill. It is April. Therefore.... A) You did not receive a tax bill. B) You are a good citizen. C) You did not pay your taxes. D) You are not a good citizen. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

216) Students who watch television while doing homework jeopardize their grades. Students with grades in jeopardy get grounded. Being grounded includes being barred from watching television. Therefore.... A) Students who watch TV will be grounded. B) Students who are grounded watch TV while doing homework. C) Students who watch TV will be barred from watching TV. D) Students who watch TV while doing homework will not be allowed to watch TV. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

217) Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents. Therefore.... A) People who smile have accidents. B) Careful drivers have accidents. C) Careful drivers are happy. D) People who smile are alert. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

218) Hard workers sweat. Sweat brings on a chill. Anyone who doesn't have a cold never felt a chill. Anyone who works doesn't have a cold. Therefore.... A) Anyone who sweats works hard. B) Hard workers don't go to work. C) Hard workers don't get colds. D) Anyone who has a cold works hard. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Translate the argument into symbolic form, then use the table below to determine whether the argument is valid or invalid. Indicate valid/invalid and identify the type of answer. VALID ARGUMENTS Contrapositive Direct Reasoning Reasoning p q p q ~q p NNNN NNNN 0~ p 0q

Disjunctive Reasoning p ,q p ,q ~p ~q NNNN NNNN 0q 0p

Transitive Reasoning p q q r NNNN 0p q 0~ r ~ p

INVALID ARGUMENTS Fallacy Fallacy of the of the Converse Inverse p q p q ~p q NNNN NNNN 0~ q 0p

Misuse of Disjunctive Reasoning p ,q p ,q p q NNNN NNNN 0~ q 0~ p

Misuse of Transitive Reasoning p q q r NNNN 0 r p 0~ p ~ r

219) If Fred studies hard, then he gets a good grade. Fred got a good grade. 0He studies hard. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

220) We will lower the drinking age or we will require three photo IDs. We will not require three photo IDs. 0We will lower the drinking age. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

221) If I take a taxi, I will get to the museum faster. If I get to the museum faster, I will have more time to enjoy the paintings. 0If I take a taxi, I will have more time to enjoy the paintings. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

222) If he wants to come, he will say so. If he says so, then he will come. 0If he comes, that means he wants to. Objective: (3.7) Recognize and Use Forms of Valid and Invalid Arguments

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use an Euler diagram to determine whether the argument is valid or invalid. 223) All doctors have studied chemistry. All surgeons are doctors. Therefore, all surgeons have studied chemistry. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

224) All dogs like food. All pets like food. Therefore, all dogs are pets. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

225) All birds have feathers. No mammal has feathers. Therefore, no mammals are birds. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

226) All insects have six legs. No spiders are insects. Therefore, no spiders have six legs. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

227) All dogs are animals. Some animals are pets. Therefore, some dogs are pets. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

228) All wrestlers are strong. Some wrestlers are smart. Therefore, some strong people are smart. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

229) All rock stars are performers. Mauricio is a rock star. Therefore, Mauricio is a performer. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

230) All rock stars are performers. Meg is a performer. Therefore, Meg is a rock star. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

231) Some people enjoy walking. Some people enjoy swimming. Therefore, some people who enjoy walking enjoy swimming. A) valid B) invalid Objective: (3.8) Use Euler Diagrams to Determine Validity

232) All horses whinny. Some horses are brown. Therefore, all brown horses whinny. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

233) No cheap CDs sound good. Some cheap CDs have red tags. Therefore, some CDs with red tags do not sound good. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

234) All multiples of 4 are multiples of 2. Eleven is not a multiple of 2. Therefore, eleven is not a multiple of 4. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

235) Not all that glitters is gold. My ring glitters. Therefore, My ring is not gold. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

236) All cats like fish. Henry does not like fish Therefore, Henry is not a cat. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

237) Some investments are risky. Real estate is an investment. Therefore, Real estate is risky. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

238) All businessmen wear suits. Aaron wears a suit. Therefore, Aaron is a businessman. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

239) Some TV shows are comedies. All comedies are hits. Therefore, Some TV shows are hits. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

240) Some cars are considered sporty. Some cars are safe at high speeds. Therefore, Some sports cars are safe at high speeds. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

241) All students who study get better grades. Roger is a student who studies. Therefore, Roger will get better grades. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

242) No even number is divisible by 5. 30 is an even number. Therefore, 30 is not divisible by 5. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

243) All tigers are felines. All felines are mammals. All mammals nurse their young. Therefore, All tigers nurse their young. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

244) All painters use paint. All painters use brushes. Some people who use paint are teachers. Therefore, Some painters are teachers. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

245) Eric is older than Camille. Camille is older than Todd. Therefore, Todd is younger than Eric. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

246) 8 is a real number. 64 is a real number. Therefore, 8 is A) valid

64.

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

247) A square is a parallelogram. A square has four sides. Therefore, A parallelogram has four sides. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

248)

18 is less than 18. 9 is less than 18. Therefore, 18 is less than 9. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

249) Rational numbers are real numbers. Integers are rational numbers. Therefore, integers are real numbers. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

250) All soda pops are carbonated. All diet colas are soda pops. Therefore, all diet colas are carbonated. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

251) All dogs have fur. All cats have fur. Therefore, a cat is not a dog. A) valid

B) invalid

Objective: (3.8) Use Euler Diagrams to Determine Validity

Answer Key Testname: 03-BLITZER_TM8E_TEST_ITEM_FILE

1) A 2) B 3) A 4) A 5) B 6) A 7) B 8) B 9) C 10) C 11) C 12) A 13) B 14) C 15) A 16) D 17) B 18) D 19) D 20) D 21) D 22) D 23) A 24) C 25) C 26) A 27) A 28) C 29) C 30) D 31) C 32) D 33) C 34) D 35) C 36) C 37) C 38) D 39) C 40) A 41) D 42) D 43) A 44) C 45) C 46) C 47) B 48) C 49) D

50) p: The air is mellow. q: The sky is clear. r: Birds nest quietly. s: The night is at peace. (p " q) (r " s) 51) p: He does that. q: I scream (p q) " (~ p ~ q) 52) A 53) D 54) C 55) C 56) D 57) B 58) A 59) D 60) D 61) B 62) C 63) C 64) D 65) C 66) D 67) A 68) A 69) B 70) C 71) D 72) C 73) B 74) B 75) A 76) B 77) A 78) A 79) A 80) A 81) A 82) D 83) C 84) D 85) B 86) B 87) C 88) A 89) D 90) D 91) D 92) B

93) A 94) D 95) C 96) C 97) C 98) D 99) B 100) B 101) A 102) A 103) B 104) A 105) B 106) B 107) B 108) B 109) A 110) A 111) A 112) A 113) B 114) A 115) B 116) D 117) C 118) A 119) B 120) D 121) C 122) A 123) B 124) B 125) C 126) B 127) A 128) A 129) A 130) B 131) D 132) B 133) C 134) C 135) D 136) B 137) D 138) A 139) D 140) B 141) C 142) D 59

143) A 144) D 145) A 146) B 147) A 148) A 149) B 150) A 151) A 152) B 153) A 154) A 155) A 156) B 157) D 158) D 159) A 160) A 161) A 162) C 163) C 164) A 165) C 166) D 167) A 168) D 169) D 170) D 171) D 172) A 173) D 174) A 175) A 176) D 177) A 178) B 179) B 180) B 181) B 182) D 183) B 184) D 185) A 186) A 187) B 188) B 189) B 190) A 191) B 192) A

Answer Key Testname: 03-BLITZER_TM8E_TEST_ITEM_FILE

193) A 194) A 195) B 196) A 197) B 198) p: It is Tuesday. q: I do not work late. p q ~q NNNN 0~ p

p q p q ~ q (p q) T T T F F T F F T F F T T F F F F T T T Argument is valid.

199) p: Emilio cooks. q: Rodrigo cooks. r: The meal is tasty. (p " q) r p "~ r NNNN 0~ q p q r p"q (p"q) r ~r TTT T T F TTF T F T TFT F T F TFF F T T FTT F T F FTF F T T FFT F T F FFF F T T Argument is valid.

200) p: There is a cease-fire. q: There is fighting.

202) p: It is July. q: It is August. r: I am living at the beach.

p ,q q NNNN 0~ p

(p , q) r ~r NNNN 0~ p "~ q

p q p ,q (p , q) "q ~ T T T T T F T F F T T T F F F F Argument is invalid.

201) p: Every student passes the quiz q: No review sessions are needed. p q ~p NNNN 0~ q

(p , q) ~r p q r p,q r TTT T T F TTF T F T TFT T T F TFF T F T FTT T T F FTF T F T FFT F T F FFF F T T Argument is valid.

203) p: This is Germany. q: This is Austria. r: The signs are in German.

p q p q ~ p (p q) T T T F F T F F F F F T T T T F F T T T Argument is invalid.

(p , q) r r NNNN 0p ,q p q r p ,q (p , q) r T T T T T T T F T F T F T T T T F F T F F T T T T F T F T F F F T F T F F F F T Argument is invalid.

204) A 205) ...Sharon does not care about so . 206) ....the professor and his class had dinner at Chez Louis. 60

207) ...some students did not pass t . 208) ...if I work in the garden, I take a hot bath. 209) A 210) A 211) A 212) C 213) B 214) B 215) B 216) D 217) A 218) B 219) invalid; Fallacy of the Converse 220) valid; Disjunctive Reasoning 221) valid; Transitive Reasoning 222) invalid; Misuse of Transitive Reasoning 223) A 224) B 225) A 226) B 227) B 228) A 229) A 230) B 231) B 232) A 233) A 234) A 235) B 236) A 237) B 238) B 239) A 240) B 241) A 242) A 243) A 244) B 245) A 246) B 247) B 248) B

Answer Key Testname: 03-BLITZER_TM8E_TEST_ITEM_FILE

249) A 250) A 251) B

Blitzer, Thinking Mathematically, 8e Chapter 4 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. 1) 6 2 A) 12

B) 64

C) 6

D) 36

C) 10

D) 49

C) 20

D) 25

C) 282,475,249

D) 70

C) (8 × 101 ) + (5 × 1)

D) (5 × 101 ) + (8 × 1)

Objective: (4.1) Evaluate an Exponential Expression

2) 7 3 A) 21

B) 343

Objective: (4.1) Evaluate an Exponential Expression

3) 5 4 A) 625

B) 125

Objective: (4.1) Evaluate an Exponential Expression

4) 107 A) 10,000,000

B) 17

Objective: (4.1) Evaluate an Exponential Expression

Write the Hindu-Arabic numeral in expanded form. 5) 85 A) (8 × 101 ) B) (8 × 102 ) + (5 × 10) Objective: (4.1) Write a Hindu-Arabic Numeral in Expanded Form

6) 271 A) (2 × 102 ) + (7 × 101 ) C) (2 × 102 ) + (7 × 101 ) + (1 × 1)

B) (2 × 101 ) + (7 × 1) + (1) D) (2 × 102 ) + (1 × 1)

Objective: (4.1) Write a Hindu-Arabic Numeral in Expanded Form

7) 6858 A) (6 × 103 ) + (8 × 102 ) + (8 × 1) C) (6 × 103 )

B) (6 × 103 ) + (8 × 102 ) + (5 × 101 ) + (8 × 1) D) (6 × 103 ) + (8 × 102 ) + (5 × 101 )

Objective: (4.1) Write a Hindu-Arabic Numeral in Expanded Form

8) 18121 A) (1 × 104 ) + (8 × 103 ) + (1 × 102 ) + (2 × 101 ) B) (1 × 104 ) + (8 × 103 ) + (1 × 102 ) C) (1 × 104 ) + (8 × 103 ) D) (1 × 104 ) + (8 × 103 ) + (1 × 102 ) + (2 × 101 ) + (1 × 1) Objective: (4.1) Write a Hindu-Arabic Numeral in Expanded Form

9) 530,007,008 A) (5 × 108 ) + (3 × 107 ) + ( 0 × 106 ) + ( 0 × 105 ) + ( 0 × 104 ) + (7 × 103 ) + ( 0 × 102 ) + ( 0 × 101 ) B) (5 × 108 ) + ( 0 × 106 ) + ( 0 × 105 ) + ( 0 × 104 ) + (7 × 103 ) + ( 0 × 102 ) + ( 0 × 101 ) + (8 × 1 ) C) (5 × 108 ) + (3 × 107 ) + ( 0 × 106 ) + ( 0 × 105 ) + ( 0 × 104 ) + ( 0 × 102 ) + ( 0 × 101 ) + (8 × 1 ) D) (5 × 108 ) + (3 × 107 ) + ( 0 × 106 ) + ( 0 × 105 ) + ( 0 × 104 ) + (7 × 103 ) + ( 0 × 102 ) + ( 0 × 101 ) + (8 × 1 ) Objective: (4.1) Write a Hindu-Arabic Numeral in Expanded Form

Express the expanded form as a Hindu-Arabic numeral. 10) (6 × 101 ) + (8 × 1) A) 140

B) 14

C) 48

D) 68

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

11) (6 × 102 ) + (7 × 101 ) + (9 × 1) A) 22

B) 378

C) 220

D) 679

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

12) (3 × 105 ) + (7 × 104 ) + (3 × 103 ) + (6 × 102 ) + (5 × 101 ) + (5 × 1) A) 373,655 B) 290 C) 29

D) 9,450

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

13) (8 × 106 ) + (5 × 105 ) + (1 × 104 ) + (1 × 103 ) + (3 × 102 ) + (1 × 101 ) + (8 × 1) A) 8,511,318 B) 960 C) 270

D) 27

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

14) (7 × 103 ) + (0 × 102 ) + (0 × 101 ) + (6 × 1) A) 76 B) 706

C) 42

D) 7006

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

15) (1 × 104 ) + (0 × 103 ) + (0 × 102 ) + (5 × 101) + (6 × 1) A) 156 B) 30

C) 1056

D) 10,056

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

16) (6 × 108 ) + (5 × 103 ) + (7 × 1) A) 600,005,007

B) 6,005,007

C) 60,005,007

D) 60,000,507

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

17) (9 × 108 ) + (5 × 104 ) + (2 × 1) A) 90,050,002

B) 900,050,002

C) 90,005,002

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

D) 9,005,002

If n is a natural number, then 10-n =

1 . Negative powers of 10 can be used to write the decimal part of Hindu-Arabic 10n

numerals in expanded form. Express the expanded form as a Hindu-Arabic numeral. 18) (9 × 1) + (3 × 10-1 )

A) 93

B) 12

C) 9.3

D) 0.27

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

19) (5 × 10-1 ) + (8 × 10-2 ) + (5 × 10-3 ) A) 0.180 B) 18

C) 5.85

D) 0.585

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

20) (1 × 10-1 ) + (6 × 10-3 ) + (5 × 10-5 ) + (7 × 10-7 ) + (3 × 10-8 ) + (3 × 10-9 ) A) 0.1065733 B) 0.10605070303 C) 0.165733

D) 0.106050733

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

21) (3 × 103 ) + (3 × 102 ) + (8 × 101 ) + (8 × 1) + (8 × 10-1 ) + (2 × 10-2 ) + (6 × 10-3 ) A) 33888.26 B) 338.8826 C) 3,388,826

D) 3388.826

Objective: (4.1) Express a Number's Expanded Form as a Hindu-Arabic Numeral

If the Babylonian numeral stands for one and the Babylonian numeral numeral as a Hindu-Arabic numeral.

stands for ten, then write the Babylonian

22) A) 32

B) 23

C) 5

D) 50

Objective: (4.1) Understand and Use the Babylonian Numeration System

23) A) 1203

B) 23

C) 203

D) 1262

Objective: (4.1) Understand and Use the Babylonian Numeration System

24) A) 903

B) 18

C) 11,523

D) 1083

Objective: (4.1) Understand and Use the Babylonian Numeration System

25) A) 2,416,271

B) 2,200,271

C) 3300

Objective: (4.1) Understand and Use the Babylonian Numeration System

Express the result of the addition as a Hindu-Arabic numeral in expanded form. + 26) 4 A) (4 × 10 ) + (1 × 103 ) + (6 × 102 ) + (5 × 101 ) + (7 × 1) B) (4 × 105 ) + (2 × 104 ) + (2 × 103 ) + (5 × 102 ) + (1 × 101 ) C) (4 × 105 ) + (1 × 104 ) + (6 × 103 ) + (5 × 102 ) + (7 × 101 ) D) (4 × 104 ) + (2 × 103 ) + (2 × 102 ) + (5 × 101 ) + (1 × 1) Objective: (4.1) Understand and Use the Babylonian Numeration System

D) 44

27)

+ 5 4 3 A) (1 × 10 ) + (1 × 10 ) + (4 × 10 ) + (8 × 102 ) + (1 × 101 ) + (7 × 1)

B) (4 × 104 ) + (8 × 103 ) + (9 × 102 ) + (7 × 101 ) + (3 × 1) C) (1 × 106 ) + (1 × 105 ) + (4 × 104 ) + (8 × 103 ) + (1 × 102 ) + (7 × 101 ) D) (4 × 105 ) + (8 × 104 ) + (9 × 103 ) + (7 × 102 ) + (3 × 101 ) Objective: (4.1) Understand and Use the Babylonian Numeration System

Use the table below to write the Mayan numeral as a Hindu-Arabic numeral.

28)

A) 14

B) 19

C) 10

D) 4

Objective: (4.1) Understand and Use the Mayan Numeration System

29)

A) 5046

B) 100,806

C) 5,406

D) 286

Objective: (4.1) Understand and Use the Mayan Numeration System

30)

A) 3048

B) 888

C) 24

Objective: (4.1) Understand and Use the Mayan Numeration System

D) 512

31)

A) 2168

B) 43,208

C) 128

D) 14

Objective: (4.1) Understand and Use the Mayan Numeration System

32)

A) 45,366

B) 18

C) 2286

D) 4326

Objective: (4.1) Understand and Use the Mayan Numeration System

Express the result of the addition as a Hindu-Arabic numeral in expanded form. 33)

A) (4 × 103 ) + (4 × 102 ) + (9 × 101 ) + (7 × 1) C) (4 × 103 ) + (5 × 102 ) + (0 × 101 ) + (7 × 1)

B) (4 × 104 ) + (5 × 103 ) + (0 × 102 ) + (7 × 101 ) D) (4 × 104 ) + (4 × 103 ) + (9 × 102 ) + (7 × 101 )

Objective: (4.1) Understand and Use the Mayan Numeration System

34)

A) (5 × 104 ) + (6 × 103 ) + (3 × 102 ) + (4 × 101 ) C) (5 × 103 ) + (6 × 102 ) + (2 × 101 ) + (9 × 1)

B) (5 × 103 ) + (6 × 102 ) + (3 × 101 ) + (4 × 1) D) (5 × 104 ) + (6 × 103 ) + (2 × 102 ) + (9 × 101 )

Objective: (4.1) Understand and Use the Mayan Numeration System

Convert the numeral to a numeral in base ten. 35) 77 eight A) 85

B) 504

C) 63

D) 112

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

36) 64,177 eight A) 513,416

B) 151

C) 200

D) 26,751

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

37) 24 five A) 14

B) 70

C) 30

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

D) 120

38) 231four A) 6

B) 21

C) 45

D) 24

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

39) 1101two A) 13

B) 6

C) 12

D) 22

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

40) 3205six A) 4325

B) 725

C) 125

D) 43

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

41) 3207nine A) 2943

B) 28,863

C) 2356

D) 268

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

42) 3095sixteen A) 12,437

B) 197

C) 49,520

D) 6320

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

43) 54012six A) 336

B) 32,472

C) 1106

D) 7352

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

44) 2301fifteen A) 7426

B) 496

C) 346

D) 3465

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

45) 101101two A) 113

B) 77

C) 45

D) 28

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

46) BAE4sixteen A) 47,844

B) 560

C) 44,004

D) 52,196

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

Break the binary sequence into groups of seven digits and write the word represented by the sequence. 47) 100001010001011000100 A) bad B) arm C) bed D) cue Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

48) 1001100100000110011011010000 A) damp B) swamp

C) lamp

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

D) map

49) 1001101100111110011111001110 A) soon B) moon

C) mend

D) mash

Objective: (4.2) Change Numerals in Bases Other Than Ten to Base Ten

Use divisions to convert the base ten numeral to a numeral in the given base. 50) 2,874 to base eight A) 4,527eight B) 5,427eight C) 4,572eight

D) 5,472eight

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

51) 2,874 to base seven A) 11,244seven

B) 11,224seven

C) 11,442seven

D) 11,422seven

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

52) 83 to base five A) 413five

B) 133five

C) 313five

D) 410five

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

53) 89 to base seven A) 152seven

B) 155seven

C) 66seven

D) 1520seven

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

54) 205 to base four A) 3301four

B) 3031four

C) 3331four

D) 331four

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

55) 125 to base three A) 1112three

B) 11121three

C) 1122three

D) 11122three

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

56) 295 to base six A) 2211six

B) 1211six

C) 1221six

D) 121six

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

57) 532 to base nine A) 648nine

B) 561nine

C) 551nine

D) 651nine

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

58) 1776 to base eight A) 3336eight

B) 3660eight

C) 3360eight

D) 3366eight

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

59) 359 to base two A) 101100111two

B) 101101011two

C) 101100101two

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

D) 101011111two

Convert the number to the indicated base. 60) 53six to base three A) 111three

B) 1120three

C) 1020three

D) 100three

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

61) 123five to base nine A) 42nine

B) 14nine

C) 38nine

D) 24nine

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

62) 303four to base eight A) 37eight

B) 51eight

C) 75eight

D) 63eight

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

63) 10101 two to base eight A) 816eight

B) 24 eight

C) 12 eight

D) 25 eight

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

64) 10001011 two to base eight A) 112 eight

B) 8816eight

C) 224 eight

D) 213 eight

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

65) 10111111000 two to base eight A) 824240 eight

B) 1330 eight

C) 2770 eight

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

Write the Hindu-Arabic numeral as a Babylonian numeral. 66) 5803 A) B) C) D) Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

67) 32,564 A) B) C) D) Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

D) 2660 eight

Write the Hindu-Arabic numeral as a Mayan numeral. 68) 8402 A) B)

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

69) 46,375 A)

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

Write the binary representation for the letter or word. 70) Q A) 1010010 B) 1010001

C) 1010100

D) 100100

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

71) R A) 1100101

B) 1010010

C) 1001010

D) 1010100

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

72) C A) 1110011

B) 1100001

C) 1000111

D) 1000011

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

73) Mexico A) 110110111001011011011100111000111111001101 C) 100110111011011101000110100111000111110011

B) 100110101001011111000110100111000111101111 D) 100110110001011011000100100110000111001111

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

74) Bob A) 100001011011111100010 C) 100001010011111000010

B) 100010110100010011101 D) 100001011011001100001

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

75) couch A) 11000111101101111010111100111101010 C) 10111001100110011011101111000110011

B) 11000111101111111010110001111101000 D) 11000111101111111010111000111101000

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

Use divisions to solve the problem. 76) Change 166 days to weeks and days. A) 24 weeks and 6 days C) 23 weeks and 5 days

B) 23 weeks and 7 days D) 16 weeks and 6 days

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

77) Change $9.38 to quarters, nickels , and pennies. A) 38 quarters, two nickels, and three pennies C) 36 quarters, six nickels, and three pennies

B) 37 quarters, one nickel, and three pennies D) 37 quarters, two nickels, and three pennies

Objective: (4.2) Change Base Ten Numerals to Numerals in Other Bases

Add in the indicated base. 78) 32four +12four

A) 110four

B) 210four

C) 220four

D) 120four

C) 1010two

D) 101two

C) 1420five

D) 1440five

C) 15740nine

D) 15750nine

C) 10102three

D) 20102three

Objective: (4.3) Add in Bases Other Than Ten

79) 110two + 11two

A) 1001two

B) 111two

Objective: (4.3) Add in Bases Other Than Ten

80) 342five +343five

A) 124five

B) 1240five

Objective: (4.3) Add in Bases Other Than Ten

81) 8765nine +5864 nine

A) 15840nine

B) 16740nine

Objective: (4.3) Add in Bases Other Than Ten

82) 2011three +1021 three

A) 10122three

B) 12102three

Objective: (4.3) Add in Bases Other Than Ten

83) 15432seven + 6504 seven

A) 26236seven

B) 25336seven

C) 25236seven

D) 25436seven

C) BADsixteen

D) BDDsixteen

C) 111111two

D) 11111two

C) 1101011two

D) 101011two

C) 3 four

D) 11four

C) 14five

D) 22five

C) 326eight

D) 436eight

Objective: (4.3) Add in Bases Other Than Ten

84) 64Asixteen +593sixteen

A) B9Dsixteen

B) BBDsixteen

Objective: (4.3) Add in Bases Other Than Ten

85) 10010two + 11010two + 10011two A) 111011two

B) 101111two

Objective: (4.3) Add in Bases Other Than Ten

86) 10111two + 11110two + 10110two A) 1001011two

B) 1011011two

Objective: (4.3) Add in Bases Other Than Ten

Subtract in the indicated base. 87) 22four - 13four

A) 12four

B) 13four

Objective: (4.3) Subtract in Bases Other Than Ten

88) 42five -13five

A) 12five

B) 24five

Objective: (4.3) Subtract in Bases Other Than Ten

89) 564eight - 236 eight

A) 362eight

B) 336eight

Objective: (4.3) Subtract in Bases Other Than Ten

90) 721nine - 473nine

A) 327nine

B) 227nine

C) 237nine

D) 238nine

C) 465seven

D) 646seven

C) 1111two

D) 111two

C) 1102three

D) 1002three

C) 33Esixteen

D) 32Dsixteen

C) 74eight

D) 53eight

C) 1 two

D) None of the above

Objective: (4.3) Subtract in Bases Other Than Ten

91) 653seven - 154seven

A) 466seven

B) 456seven

Objective: (4.3) Subtract in Bases Other Than Ten

92) 1101two - 110two

A) 1011two

B) 101two

Objective: (4.3) Subtract in Bases Other Than Ten

93) 2100three - 1021three

A) 1022three

B) 1012three

Objective: (4.3) Subtract in Bases Other Than Ten

94) 5B7sixteen -289sixteen

A) 32Esixteen

B) 32Fsixteen

Objective: (4.3) Subtract in Bases Other Than Ten

95) 247eight - 153eight A) 94eight

B) 76eight

Objective: (4.3) Subtract in Bases Other Than Ten

96) 101two - 11two A) 10two

B) 101two

Objective: (4.3) Subtract in Bases Other Than Ten

Multiply in the indicated base. 97) 34six × 5 six

A) 312six

B) 322six

C) 212six

D) 302six

C) 332five

D) 232five

C) 111two

D) 110two

C) 4404seven

D) 4040seven

C) 3435nine

D) 3445nine

C) 326eight

D) 3226eight

Objective: (4.3) Multiply in Bases Other Than Ten

98) 43five × 4five

A) 223five

B) 123five

Objective: (4.3) Multiply in Bases Other Than Ten

99) 10two × 1 two

A) 11two

B) 10two

Objective: (4.3) Multiply in Bases Other Than Ten

100) 453seven × 6 seven

A) 4444seven

B) 4044seven

Objective: (4.3) Multiply in Bases Other Than Ten

101) 432nine × 7 nine

A) 3345nine

B) 3343nine

Objective: (4.3) Multiply in Bases Other Than Ten

102) 536eight × 5 eight

A) 3326eight

B) 3236eight

Objective: (4.3) Multiply in Bases Other Than Ten

103) 32four ×13four

A) 1202four

B) 1222four

C) 1220four

D) 122four

C) 213five

D) 123five

C) 301five

D) 444five

C) 1010100two

D) 10101000two

C) 34623seven

D) 36432seven

C) 2AC4sixteen

D) 2814sixteen

C) 30four

D) 3 four

C) 30five

D) 3 five

C) 13five

D) 12five

Objective: (4.3) Multiply in Bases Other Than Ten

104) 43five × 3 five A) 234five

B) 112five

Objective: (4.3) Multiply in Bases Other Than Ten

105) 12five × 21five A) 323five

B) 302five

Objective: (4.3) Multiply in Bases Other Than Ten

106) 110two × 111two A) 101009two

B) 101010two

Objective: (4.3) Multiply in Bases Other Than Ten

107) 456seven × 55seven A) 25080seven

B) 35828seven

Objective: (4.3) Multiply in Bases Other Than Ten

108) E4sixteen × 2Dsixteen A) 2AD8sixteen

B) 2BC8sixteen

Objective: (4.3) Multiply in Bases Other Than Ten

Divide in the indicated base. 109) 3 four 210four A) 303four

B) 33four

Objective: (4.3) Divide in Bases Other Than Ten

110) 4 five 224five A) 31five

B) 32five

Objective: (4.3) Divide in Bases Other Than Ten

111) 4 five 112five A) 2 five

B) 5 five

Objective: (4.3) Divide in Bases Other Than Ten

The diagram shows two binary sequences about to be manipulated by passing through a microchip's series of gates. Provide the results of these computer manipulations, designated by ? in the diagram. 112) 11011 10001

A) 11011

00100

10001

01110

11011

10001

11011

10001

11011

00100

10001

01110

10001

11011

00100

Objective: (4.3) Base Two Computer Logic

113) 10011 11001

A) 10011

11001 10001

11001

10011

11001

10011

01100

11001

00110

10011

01100

11001

00110

11011

01110

00100

Objective: (4.3) Base Two Computer Logic

114) 11101

10101

A) 11101

10101 10101 10101

10101

11101

B) 11101

00010 10111 00010

10101

01010

C) 11101

00010 00000 00000

10101

01010

D) 11101

00010 10111 11111

10101

01010

Objective: (4.3) Base Two Computer Logic

115) 11011

10101

A) 11011 11111

10101 11111

10101

11111

B) 11011 11111

00000 01010

10101

01010

C) 11011 10001

01110 01110

10101

01010

D) 11011 10001

10101 10101

10101

10001

Objective: (4.3) Base Two Computer Logic

Write the Egyptian numeral as a Hindu-Arabic numeral using the table below. Hindu-Arabic Egyptian Numeral Numeral Description 1

Staff

Heel bone

100

Spiral

1000

Lotus blossom

10,000

Pointing finger

100,000

Tadpole

1,000,000

Astonished person

116)

A) 23,223

B) 2,030,223

C) 2,300,223

D) 2,003,223

C) 20,313

D) 2313

C) 13,420

D) 132,402

Objective: (4.4) Understand and Use the Egyptian System

117)

A) 230,130

B) 200,313

Objective: (4.4) Understand and Use the Egyptian System

118)

A) 132,042

B) 13,242

Objective: (4.4) Understand and Use the Egyptian System

Write the Hindu-Arabic numeral as an Egyptian numeral using the table below. Hindu-Arabic Egyptian Numeral Numeral Description 1

Staff

Heel bone

100

Spiral

1000

Lotus blossom

10,000

Pointing finger

100,000

Tadpole

1,000,000

Astonished person

119) 234 A)

Objective: (4.4) Understand and Use the Egyptian System

120) 1534 A)

Objective: (4.4) Understand and Use the Egyptian System

121) 32,457 A)

Objective: (4.4) Understand and Use the Egyptian System

122) 1,235,042 A)

Objective: (4.4) Understand and Use the Egyptian System

Write the numeral as a numeral in base five. 123) A) 122five

B) 442five

C) 13042five

D) 1022five

C) 434five

D) 114204five

Objective: (4.4) Understand and Use the Egyptian System

124) A) 3214five

B) 4304five

Objective: (4.4) Understand and Use the Egyptian System

Perform the subtraction without converting to Hindu-Arabic numerals. 125)

A) B) C) D) Objective: (4.4) Understand and Use the Egyptian System

126)

A) B) C) D) Objective: (4.4) Understand and Use the Egyptian System

Write the Roman numeral as a Hindu-Arabic numeral. 127) XIII A) 13 B) 30

C) 103

D) 53

C) 108

D) 18

C) 109

D) 1009

C) 154

D) 165

C) 15,131

D) 1831

Objective: (4.4) Understand and Use the Roman System

128) XVIII A) 48

B) 63

Objective: (4.4) Understand and Use the Roman System

129) MIX A) 1110

B) 910

Objective: (4.4) Understand and Use the Roman System

130) XLVI A) 54

B) 46

Objective: (4.4) Understand and Use the Roman System

131) MDCXXXI A) 1591

B) 1631

Objective: (4.4) Understand and Use the Roman System

132) MMDCLXVI A) 2,656

B) 2,566

C) 2,565

D) 2,666

C) LXII

D) XXXXII

C) CXXXIX

D) CXXLIX

C) IVDCCLVIII

D) IVDCCLVIII

C) 2101five

D) 276five

C) 1132five

D) 932five

Objective: (4.4) Understand and Use the Roman System

Write the Hindu-Arabic numeral as a Roman numeral. 133) 42 A) XLII B) LVVII Objective: (4.4) Understand and Use the Roman System

134) 139 A) CXXXVIIII

B) CXXLVIIII

Objective: (4.4) Understand and Use the Roman System

135) 4758 A) MMMMDCCLVIII

B) VIDCCLVIII

Objective: (4.4) Understand and Use the Roman System

Write the numeral as a numeral in base five. 136) CCLXXIV A) 2044five B) 274five Objective: (4.4) Understand and Use the Roman System

137) CMXXXII A) 14012five

B) 12212five

Objective: (4.4) Understand and Use the Roman System

Solve the problem. 138) After watching a DVD from the local rental store you decide to sit through the credits. You notice the copyright date expressed as MCMXCIV. When was the movie made? A) 2004 B) 1994 C) 2006 D) 1996 Objective: (4.4) Understand and Use the Roman System

Use the table below to write the traditional Chinese numeral as a Hindu-Arabic numeral. Hindu-Arabic Numerals 1

Traditional Chinese Numerals

2 3 4 5

100

1000

139)

A) 717

B) 17

C) 77

Objective: (4.4) Understand and Use the Traditional Chinese System

D) 37

140)

A) 417

B) 437

C) 413

D) 4137

Objective: (4.4) Understand and Use the Traditional Chinese System

141)

A) 261,637

B) 2637

C) 21,637

Objective: (4.4) Understand and Use the Traditional Chinese System

D) 2367

Use the table below to write the Hindu-Arabic numeral as a traditional Chinese numeral.

Hindu-Arabic Numerals 1

Traditional Chinese Numerals

2 3 4 5

100

1000

142) 52 A)

Objective: (4.4) Understand and Use the Traditional Chinese System

143) 358 A)

Objective: (4.4) Understand and Use the Traditional Chinese System

144) 8506 A)

Objective: (4.4) Understand and Use the Traditional Chinese System

Write the Ionic Greek numeral as a Hindu-Arabic numeral using the table below. Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek Numeral Numeral Numeral Numeral Numeral Numeral 1 α 20 κ 200 σ 2 β 30 λ 300 τ 3 γ 40 μ 400 υ 4 δ 50 ν 500 φ 5 ε 60 ξ 600 χ 6 70 ο 700 ψ 7 ζ 80 π 800 ω 8 η 90 Q 900 9 θ 100 ρ 10 ι

145) ια A) 21

B) 11

C) 1

D) 10

C) 84

D) 89

Objective: (4.4) Understand and Use the Ionic Greek System

146) πδ A) 44

B) 49

Objective: (4.4) Understand and Use the Ionic Greek System

147) τπδ A) 284

B) 483

C) 384

D) 482

C) 783

D) 733

C) 562

D) 762

Objective: (4.4) Understand and Use the Ionic Greek System

148) ψιγ A) 723

B) 713

Objective: (4.4) Understand and Use the Ionic Greek System

149) φξβ A) 672

B) 572

Objective: (4.4) Understand and Use the Ionic Greek System

Write the Hindu-Arabic numeral as an Ionic Greek numeral using the table below. Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek Hindu-Arabic Ionic Greek Numeral Numeral Numeral Numeral Numeral Numeral 1 α 20 κ 200 σ 2 β 30 λ 300 τ 3 γ 40 μ 400 υ 4 δ 50 ν 500 φ 5 ε 60 ξ 600 χ 6 70 ο 700 ψ 7 ζ 80 π 800 ω 8 η 90 Q 900 9 θ 100 ρ 10 ι

150) 52 A) νε

B) εβ

C) νβ

D) βε

C) τξβ

D) τβπ

C) ρκξ

D) ρκε

Objective: (4.4) Understand and Use the Ionic Greek System

151) 362 A) τνγ

B) τκβ

Objective: (4.4) Understand and Use the Ionic Greek System

152) 125 A) σκε

B) σλε

Objective: (4.4) Understand and Use the Ionic Greek System

Answer Key Testname: 04-BLITZER_TM8E_TEST_ITEM_FILE

1) D 2) B 3) A 4) A 5) C 6) C 7) B 8) D 9) D 10) D 11) D 12) A 13) A 14) D 15) D 16) A 17) B 18) C 19) D 20) D 21) D 22) B 23) D 24) C 25) A 26) A 27) B 28) A 29) A 30) A 31) B 32) A 33) C 34) C 35) C 36) D 37) A 38) C 39) A 40) B 41) C 42) A 43) D 44) A 45) C 46) A 47) C 48) C 49) B 50) D

51) A 52) C 53) B 54) B 55) D 56) B 57) D 58) C 59) A 60) C 61) A 62) D 63) D 64) D 65) C 66) A 67) B 68) D 69) A 70) B 71) B 72) D 73) D 74) A 75) D 76) C 77) D 78) A 79) A 80) B 81) C 82) C 83) C 84) D 85) C 86) A 87) C 88) B 89) C 90) C 91) A 92) D 93) D 94) A 95) C 96) A 97) D 98) C 99) B 100) B

101) A 102) A 103) A 104) A 105) B 106) B 107) D 108) D 109) C 110) A 111) C 112) A 113) D 114) B 115) C 116) B 117) B 118) D 119) B 120) A 121) C 122) D 123) B 124) A 125) D 126) B 127) A 128) D 129) D 130) B 131) B 132) D 133) A 134) C 135) C 136) A 137) B 138) B 139) C 140) B 141) B 142) D 143) B 144) D 145) B 146) C 147) C 148) B 149) C 150) C 29

151) C 152) D

Blitzer, Thinking Mathematically, 8e Chapter 5 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine if the number is divisible by 2, 3, 4, 5, 6, 8, 9, 10, and/or 12. 1) 792 A) 2, 3, 4, 8 B) 2, 3, 4 C) 2, 3, 6, 8

D) 2, 3, 4, 6, 8, 9,12

Objective: (5.1) Determine Divisibility

2) 196,601 A) 3

B) None

C) 3, 7

D) 3, 5

C) 4

D) 2

C) 2, 3, 4

D) 3, 4, 6

C) 10

D) 2, 5, 10

C) 3

D) 3, 9

C) 2, 5

D) 2, 4, 5, 10

C) 2, 3, 4, 6, 8 , 12

D) 2, 3, 4, 6

Objective: (5.1) Determine Divisibility

3) 4,898 A) 2, 3, 4

B) 3, 4

Objective: (5.1) Determine Divisibility

4) 18,318 A) 4, 5, 6

B) 2, 3, 6

Objective: (5.1) Determine Divisibility

5) 5,185 A) 5

B) 5, 10

Objective: (5.1) Determine Divisibility

6) 2,067 A) 9

B) 2, 3, 9

Objective: (5.1) Determine Divisibility

7) 61,060 A) 4, 5, 10

B) 4, 5

Objective: (5.1) Determine Divisibility

8) 1,597,812 A) 2, 3, 4, 6, 12

B) 2, 4, 6, 8

Objective: (5.1) Determine Divisibility

Use a calculator to determine if the statement is true or false. 9) 4 494,084 A) True

B) False

Objective: (5.1) Determine Divisibility

10) 4 | 274,034 A) True

B) False

Objective: (5.1) Determine Divisibility

11) 3 | 677,712 A) True

B) False

Objective: (5.1) Determine Divisibility

12) 9 | 866,376 A) True

B) False

Objective: (5.1) Determine Divisibility

13) 5 | 773,944 A) True

B) False

Objective: (5.1) Determine Divisibility

14) 5 | 3,385 A) True

B) False

Objective: (5.1) Determine Divisibility

15) 6 | 2,000,820 A) True

B) False

Objective: (5.1) Determine Divisibility

Determine all values of d that make the statement true. 16) 6 | 43,67d A) 7 B) 6

C) 4

D) 1

C) 2

D) 4

C) 4, 8

D) 0, 4, 8

C) 2 2 × 7

D) 7 2

Objective: (5.1) Determine Divisibility

17) 8 | 6,341,78d A) 6

B) 8

Objective: (5.1) Determine Divisibility

18) 4 | 264,668,38d A) 8

B) 0

Objective: (5.1) Determine Divisibility

Find the prime factorization of the composite number. 19) 28 A) 4 × 2

B) 4 × 7

Objective: (5.1) Write the Prime Factorization of a Composite Number

20) 252 A) 3 4 × 7

B) 2 3 × 3 2 × 7

C) 2 4 × 7

D) 2 2 × 3 2 × 7

Objective: (5.1) Write the Prime Factorization of a Composite Number

21) 267 A) 3 × 89

C) 3 2

B) 3 × 87

Objective: (5.1) Write the Prime Factorization of a Composite Number

D) 3 2 × 89

22) 1,065 A) 15 × 71

B) 5 2 × 71

C) 3 2 × 71

D) 3 × 5 × 71

Objective: (5.1) Write the Prime Factorization of a Composite Number

23) 24,975 A) 3 3 × 5 2 × 37

B) 3 2 × 5 3 × 37

C) 3 4 × 37

D) 5 4 × 37

Objective: (5.1) Write the Prime Factorization of a Composite Number

24) 325 A) 5 2 × 13

B) 2 × 5 × 13

C) 5 × 13

D) 10 × 13

Objective: (5.1) Write the Prime Factorization of a Composite Number

25) 7,600 A) 16 × 25 × 19

C) 2 2 × 102 × 19

B) 2 × 5 × 19

D) 2 4 × 5 2 × 19

Objective: (5.1) Write the Prime Factorization of a Composite Number

Find the greatest common divisor of the numbers. 26) 30, 270 A) 6 B) 30

C) 10

D) 15

Objective: (5.1) Find the Greatest Common Divisor of Two Numbers

27) 44, 135 A) 1

B) 55

C) 22

D) 6

Objective: (5.1) Find the Greatest Common Divisor of Two Numbers

28) 38 and 57 A) 57

B) 114

C) 38

D) 19

Objective: (5.1) Find the Greatest Common Divisor of Two Numbers

29) 332 and 830 A) 332

B) 1,660

C) 166

D) 830

Objective: (5.1) Find the Greatest Common Divisor of Two Numbers

30) 249 and 581 A) 581

B) 249

C) 1,743

D) 83

Objective: (5.1) Find the Greatest Common Divisor of Two Numbers

Solve the problem. 31) A store owner wishes to stack books into equal piles, each pile containing only one title. There are 36 books of one title and 84 books of another title in a shipment. What is the largest number of books that can be stacked in each pile? A) 36 B) 252 C) 12 D) 84 Objective: (5.1) Solve Problems Using the Greatest Common Divisor

32) A club has 42 male members and 35 female members. If the club is to have a contest, where there are all-male and all-female teams competing, what is the most members a team can have? All teams must be of equal size and everyone must be on a team. A) 7 B) 42 C) 35 D) 210 Objective: (5.1) Solve Problems Using the Greatest Common Divisor

33) A child has 18 quarters and 30 dimes. The child wishes to stack the coins so that each stack has the same number of coins, and each stack contains only one kind of coin. What is the largest number of coins that the child can place in each stack? A) 90 B) 18 C) 30 D) 6 Objective: (5.1) Solve Problems Using the Greatest Common Divisor

34) A museum curator collects fossils from two different periods. He has 800 from one period and 408 from a later period. He plans to arrange the fossils in display cases so that each case contains the same number of fossils. Also, each case must contain fossils from only one period. What is the largest number of fossils that can be placed in each case? A) 800 B) 8 C) 40,800 D) 408 Objective: (5.1) Solve Problems Using the Greatest Common Divisor

35) Anthony has 63 toy cars and 84 toy trucks. He wants to divide them into groups that contain the same number of vehicles. Also, each group must contain the same type of vehicle (car or truck). What is the largest number of toys that can be put into each group? A) 3 B) 9 C) 21 D) 7 Objective: (5.1) Solve Problems Using the Greatest Common Divisor

Find the least common multiple of the numbers. 36) 34 and 51 A) 867 B) 578

C) 1,734

D) 102

C) 1,125

D) 450

C) 3,645

D) 945

C) 1,575

D) 18,900

C) 19,890

D) 8,775

C) 810,000

D) 22,500

Objective: (5.1) Find the Least Common Multiple of Two Numbers

37) 75 and 90 A) 6,750

B) 1,350

Objective: (5.1) Find the Least Common Multiple of Two Numbers

38) 135 and 189 A) 5,103

B) 25,515

Objective: (5.1) Find the Least Common Multiple of Two Numbers

39) 105 and 180 A) 1,260

B) 2,700

Objective: (5.1) Find the Least Common Multiple of Two Numbers

40) 510 and 585 A) 7,650

B) 298,350

Objective: (5.1) Find the Least Common Multiple of Two Numbers

41) 750 and 1,080 A) 27,000

B) 32,400

Objective: (5.1) Find the Least Common Multiple of Two Numbers

Solve the problem. 42) A course meets 5 times a week. One student misses class 2 days apart. A second student misses class 5 days apart. They were both absent on the second day of class. What is the next class day when both will be absent again? A) class 12 B) class 7 C) class 10 D) class 11 Objective: (5.1) Solve Problems Using the Least Common Multiple

43) A movie theater has two screens and shows its movie continuously. A 30 minute documentary is shown on one screen. A 120 minute feature is shown on the other screen. If both movies begin at noon, how many minutes will pass before both movies begin again at the same time? A) 120 minutes B) 240 minutes C) 150 minutes D) 10 minutes Objective: (5.1) Solve Problems Using the Least Common Multiple

44) Two toy cars race around a circular track (both go in the same direction). One car can travel around the track in 220 seconds. The other car travels around the track in 330 seconds. If both cars start from the same place, how long will it take for them to meet at the same place if they continue to race? A) 24,200 seconds B) 36,300 seconds C) 660 seconds D) 72,600 seconds Objective: (5.1) Solve Problems Using the Least Common Multiple

45) Two people are running around an oval track. They leave the starting point together. One completes the track every 52 minutes. The second completes the track every 65 minutes. How long will it take for them to both pass the starting point at the same time, if they both continue to run? A) 260 minutes B) 3,380 minutes C) 65 minutes D) 52 minutes Objective: (5.1) Solve Problems Using the Least Common Multiple

Solve. 46) A perfect number is a natural number that is equal to the sum of its factors, excluding the number itself. Determine whether or not the number 4 is perfect. A) Yes B) No Objective: (5.1) Demonstrate Additional Understanding and Skills

47) A prime number is an emirp if it becomes a different prime number when its digits are reversed. Determine whether or not the prime number 107 is an emirp. A) No B) Yes Objective: (5.1) Demonstrate Additional Understanding and Skills

48) A prime number p such that 2p + 1 is also a prime number is called a Germain prime, named after the German mathematician Sophie Germain (1776-1831), who made major contributions to number theory. Determine whether or not the prime number 89 is a Germain prime. A) Yes B) No Objective: (5.1) Demonstrate Additional Understanding and Skills

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Answer the question. 49) What is significant about the list {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,...} Objective: (5.1) Demonstrate Additional Understanding and Skills

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 50) Which of the following sets represents the set of integers? A) {0, 1, 2, 3, 4, 5 ...} C) {..., -3, -2, -1, 0, 1, 2, 3, ...}

B) {1, 2, 3, 4, 5, ...} D) {..., -3, -2, -1, 1, 2, 3, ...}

Objective: (5.2) Define the Integers

Graph the integer on the number line. 51) -6

Objective: (5.2) Graph Integers on a Number Line

52) -11

Objective: (5.2) Graph Integers on a Number Line

Insert < or > in the area between the integers to make the statement true. 53) -7 2 A) -7 < 2

B) -7 > 2

Objective: (5.2) Use the Symbols < and >

54) -71 A) -71 <

B) -71 >

Objective: (5.2) Use the Symbols < and >

55) -72

-25

A) -72 < -25

B) -72 > -25

Objective: (5.2) Use the Symbols < and >

56) -18

-2

A) -18 > -2

B) -18 < -2

Objective: (5.2) Use the Symbols < and >

57) -200

A) -200 < 0

B) -200 > 0

Objective: (5.2) Use the Symbols < and >

Find the absolute value. 58) |13| A) 26

B) 13

C) -13

D) 0

C) 0

D) 12

C) 8

D) -8

C) 1

D) -1

C) 61

D) -61

C) 50

D) 120

C) -6

C) -7

D) -31

C) -50

D) 50

C) 48

D) -10

Objective: (5.2) Find the Absolute Value of an Integer

59) |-6| A) 6

B) -6

Objective: (5.2) Find the Absolute Value of an Integer

60) |-800,000| A) -800,000

B) 800,000

Objective: (5.2) Find the Absolute Value of an Integer

Perform the indicated operation. 61) 6 + (-5) A) -11

B) 11

Objective: (5.2) Perform Operations with Integers

62) 1 + (-60) A) 59

B) -59

Objective: (5.2) Perform Operations with Integers

63) -85 + (-35) A) -50

B) -120

Objective: (5.2) Perform Operations with Integers

64) -42 + (+36) A) 6

B) -78

Objective: (5.2) Perform Operations with Integers

65) -12 - 19 A) 7

B) 31

Objective: (5.2) Perform Operations with Integers

66) 66 - (-16) A) -82

B) 82

Objective: (5.2) Perform Operations with Integers

67) -19 - (-29) A) -48

B) 10

Objective: (5.2) Perform Operations with Integers

68) 10 - 13 A) 3

B) -23

C) 23

D) -3

C) -23

D) 23

C) 11

D) -11

C) 0

D) -36

C) -220

D) 190

C) 2

D) -4

C) 117

D) 112

Objective: (5.2) Perform Operations with Integers

69) -5 + (-18) A) 13

B) -13

Objective: (5.2) Perform Operations with Integers

70) 7 - 18 A) -25

B) 25

Objective: (5.2) Perform Operations with Integers

Find the product. 71) 6(-6) A) 36

B) 12

Objective: (5.2) Perform Operations with Integers

72) (-19)(11) A) -209

B) -190

Objective: (5.2) Perform Operations with Integers

73) 0(-2) A) 0

B) -2

Objective: (5.2) Perform Operations with Integers

74) (-8)(-13) A) -112

B) 104

Objective: (5.2) Perform Operations with Integers

Evaluate the exponential expression. 75) -3 4 A) -81

B) 81

Objective: (5.2) Perform Operations with Integers

76) (-12)2 A) 144

B) -144

C) 24

D) -24

C) -8

D) -6

C) 8

Objective: (5.2) Perform Operations with Integers

77) (-2)3 A) 1

B) 8

Objective: (5.2) Perform Operations with Integers

78) (-1)8 A) 9

1 8

Objective: (5.2) Perform Operations with Integers

79) 5 2 A) -25

B) 10

C) 25

D) 7

C) 64

D) 7

C) -12

D) 81

Objective: (5.2) Perform Operations with Integers

80) 4 3 A) -64

B) 12

Objective: (5.2) Perform Operations with Integers

81) (-3)4 A)

B) -81

Objective: (5.2) Perform Operations with Integers

Find the quotient, or, if applicable, state that the expression is undefined. 12 82) -2 B) -6 D) The expression is undefined.

A) 2 C) 6 Objective: (5.2) Perform Operations with Integers

83)

0 -3

A) 0 C) -3

B) 3 D) The expression is undefined.

Objective: (5.2) Perform Operations with Integers

84)

12 0

A) 12 C) 0

B) 1 D) The expression is undefined.

Objective: (5.2) Perform Operations with Integers

85) (-30) ÷ (5) A) 5 C) -6

B) 6 D) The expression is undefined.

Objective: (5.2) Perform Operations with Integers

86) (-48) ÷ (-8) A) 6 C) -6

B) 8 D) The expression is undefined.

Objective: (5.2) Perform Operations with Integers

Use the order of operations to find the value of the expression. 87) + 4 · 9 A) 44 B) Objective: (5.2) Use the Order of Operations Agreement

88) 9 · 2 + (-7) · 2 A)

B) -5

C) 11

D) -45

C) 78

D) -48

D) 43

C) 5

C) 22

D) 32

C) -5

D) 2

C) 639

D) 81

C) 37

D) -19

C) -20

D) -40

C) -4

D) 8

C) 10

D) 0

Objective: (5.2) Use the Order of Operations Agreement

89) -9(-7) - 3(-5) A) -300

B) 48

Objective: (5.2) Use the Order of Operations Agreement

90) 4 - 5(-9) - 6 A)

B) 47

Objective: (5.2) Use the Order of Operations Agreement

91) 3 - 4(-9 + 4) A) 43

B) 55

Objective: (5.2) Use the Order of Operations Agreement

92) (2 - 4)(-6 - 10) A) 50

B) -8

Objective: (5.2) Use the Order of Operations Agreement

93) 7 - 2(8 - 6) - 8 A) 26

B) 3

Objective: (5.2) Use the Order of Operations Agreement

94) 3(-5)2 - 4(-3)2 A) 39

B) -6

Objective: (5.2) Use the Order of Operations Agreement

95) (2 + 1)3 - (4 - 2)3 A) -37

B) 19

Objective: (5.2) Use the Order of Operations Agreement

96) 7(5 - 3)3 - 2(6 - 4)3 A) 40

B) 20

Objective: (5.2) Use the Order of Operations Agreement

97) 4 2 - 8 ÷ 2 2 · 4 - 8 A) -6

B) 0

Objective: (5.2) Use the Order of Operations Agreement

98) 5 2 - 25 ÷ 5 · 2 + 10 A) 5

B) 25

Objective: (5.2) Use the Order of Operations Agreement

Solve the problem. 99) An experiment calls for cooling a mixture to -14°F, then increasing the temperature 80 degrees. What is the final temperature the experiment is to obtain? A) -94°F B) 94°F C) 66°F D) -66°F Objective: (5.2) Use the Order of Operations Agreement

100) A hill is at 534 feet above sea level, and a crater next to it is at 265 feet below sea level. What is the difference in height between the hill and the crater? A) 269 ft B) -799 ft C) -269 ft D) 799 ft Objective: (5.2) Use the Order of Operations Agreement

101) The temperature at the South pole was °F at 8 am. At 3 pm, it was -47°F. By how many degrees did the temperature drop? A) by -83°F B) by 83°F C) by -11°F D) by 11°F Objective: (5.2) Use the Order of Operations Agreement

Express the sentence as a single numerical expression. Then use the order of operations to simplify the expression. 102) Cube -5. Subtract this exponential expression from -50. A) B) 175 C) -75 D) -175 Objective: (5.2) Use the Order of Operations Agreement

103) Subtract 10 from 7. Multiply this difference by 3. Raise this product to the fourth power. A) 1,296 B) -6,561 C) -729

D) 6,561

Objective: (5.2) Use the Order of Operations Agreement

Solve the problem. 104) The bar graph shows the combined benefits /deficits of a company for six consecutive years.

-430

-394

-460 -511 -672 -798

Find the difference between the Year 2 combined amount and the Year 6 combined amount. A) $338,000 B) $404,000 C) -$338,000 D) -$404,000 Objective: (5.2) Use the Order of Operations Agreement

105) The bar graph shows the combined benefits /deficits of a company for six consecutive years.

-419

-395

-451 -511 -665 -807

By how much did the Year 6 combined amount exceed twice the Year 3 combined amount? A) -$95,000 B) $95,000 C) -$356,000 D) -$712,000 Objective: (5.2) Use the Order of Operations Agreement

106) The bar graph shows the combined benefits /deficits of a company for six consecutive years.

-426

-396

-453 -515 -678 -799

Find the average combined amount for Year 5 and Year 6. A) -$1,477,000 B) -$738,400

C) -$738,600

D) -$738,500

Objective: (5.2) Use the Order of Operations Agreement

Provide an appropriate response. 107) The set of rational numbers is the set of all numbers which can be expressed in the form are integers and

is not equal to 0.

A) a · b; a

a ;b b

Objective: (5.3) Define the Rational Numbers

a ;a b

, where a and b

D) a · b; b

Reduce the rational number to its lowest terms. 10 108) 12 A)

10 12

5 6

5 2

2 6

44 77

4 11

13 19

13 5

16 13

11 16

25 5

25 2

180 17

Objective: (5.3) Reduce Rational Numbers

109)

44 77

4 7

11 7

Objective: (5.3) Reduce Rational Numbers

110)

65 95

5 19

65 95

Objective: (5.3) Reduce Rational Numbers

111)

176 208

11 13

Objective: (5.3) Reduce Rational Numbers

Convert the mixed number to an improper fraction. 2 112) 5 5 A)

27 5

27 2

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

113) 18

10 17

316 10

476 10

316 17

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

114) -5

4 7

A) -

39 7

B) -

39 4

C) -

35 4

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

D) -

35 7

Convert the improper fraction to a mixed number. 22 115) 3 A) 7

1 3

C) 6

1 7

D) 8

1 3

D) 7

1 5

D) 6

1 2

D) 1

7 9

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

116)

36 5

A) 6

1 5

B) 7

1 7

C) 8

1 5

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

117)

15 2

A) 7

1 7

B) 7

1 2

C) 8

1 2

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

118)

16 9

A) 16

9 16

C) 16

16 9

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

119)

216 7

7 216

B) 216

7 216

216 7

D) 30

6 7

4 5

D) -7

4 5

C) 216

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

120) -

34 5

A) -6

4 7

B) -5

4 5

C) -6

Objective: (5.3) Convert Between Mixed Numbers and Improper Fractions

Express the rational number as a decimal. 15 121) 16 A) 0.9375

B) 0.9375

C) 0.9375

Objective: (5.3) Express Rational Numbers as Decimals

D) 0.9375

122)

7 20

A) 0.35

B) 0.355

C) 0.35

D) 0.35

C) 0.09

D) 0.09

C) 0.375

D) 0.125

C) 1.6

D) 0.8

C) 0.35

D) 0.7

C) 0.81

D) 0.181

C) 1.4

D) 1.14

Objective: (5.3) Express Rational Numbers as Decimals

123)

1 11

A) 0.09

B) 0.090

Objective: (5.3) Express Rational Numbers as Decimals

124)

3 8

A) 0.1375

B) 3.125

Objective: (5.3) Express Rational Numbers as Decimals

125)

4 5

A) 1

B) 0.1

Objective: (5.3) Express Rational Numbers as Decimals

126)

7 20

A) 3.2

B) 0.3

Objective: (5.3) Express Rational Numbers as Decimals

127)

9 11

A) 0.81

B) 0.181

Objective: (5.3) Express Rational Numbers as Decimals

128)

13 9

A) 1.14

B) 1.4

Objective: (5.3) Express Rational Numbers as Decimals

Express the rational number as a decimal. Then insert either < or > between the rational number to make the statement true. 4 5 129) 11 12

A) >

B) <

Objective: (5.3) Express Rational Numbers as Decimals

130)

24 37

23 36

A) >

B) <

Objective: (5.3) Express Rational Numbers as Decimals

131) -

5 6

1 3

A) >

B) <

Objective: (5.3) Express Rational Numbers as Decimals

Express the terminating decimal as a quotient of integers. If possible, reduce to lowest terms. 132) 0.1 1 1 1 A) B) C) 9 10 99

1 100

Objective: (5.3) Express Decimals in the Form a/b

133) 0.34 A)

17 5

34 9

17 50

34 99

267 500

178 333

2326 999

2326 9999

Objective: (5.3) Express Decimals in the Form a/b

134) 0.534 A)

178 3333

267 5000

Objective: (5.3) Express Decimals in the Form a/b

135) 0.2326 1163 A) 500

1163 5000

Objective: (5.3) Express Decimals in the Form a/b

Express the repeating decimal as a quotient of integers. If possible, reduce to lowest terms. 136) 0.1 A)

1 10

1 9

1 100

1 99

65 99

13 200

119 5000

119 500

Objective: (5.3) Express Decimals in the Form a/b

137) 0.65 A)

13 20

65 999

Objective: (5.3) Express Decimals in the Form a/b

138) 0.238 A)

238 9999

238 999

Objective: (5.3) Express Decimals in the Form a/b

Perform the indicated operation(s). Where possible, reduce the answer to lowest terms. 5 1 139) · 7 8 A)

2 5

56 5

7 40

5 56

6 5

Objective: (5.3) Multiply and Divide Rational Numbers

140) - 1 -

6 5

A) -

7 5

5 6

C) -

Objective: (5.3) Multiply and Divide Rational Numbers

141) 1

2 2 5 3 5

A) 9

B) 5

C) 8

D) 3

Objective: (5.3) Multiply and Divide Rational Numbers

142) -

2 1 9 12

A) -

1 36

B) -

1 7

1 54

2 21

16 35

7 120

21 8

2 9

Objective: (5.3) Multiply and Divide Rational Numbers

143)

6 7 ÷ 15 8

13 23

120 7

Objective: (5.3) Multiply and Divide Rational Numbers

144) -

7 8 ÷ 3 9

A) -

56 27

C) -

21 8

Objective: (5.3) Multiply and Divide Rational Numbers

145)

2 3 ÷ 15 5

A) -

2 25

B) -

2 9

Objective: (5.3) Multiply and Divide Rational Numbers

9 2

146) -

5 9 ÷ 6 10

A) -

3 4

B) -

27 25

25 27

27 25

2 9

4 81

4 7

56 45

Objective: (5.3) Multiply and Divide Rational Numbers

147)

1 3 + 9 9

4 9

B) 0

Objective: (5.3) Add and Subtract Rational Numbers

148)

4 4 + 5 9

8 45

1 6

Objective: (5.3) Add and Subtract Rational Numbers

149)

9 1 11 11

10 11

8 11

C) -

9 11

D) 0

Objective: (5.3) Add and Subtract Rational Numbers

150)

3 1 - 13 13

2 13

4 13

1 13

D) -

4 13

3 16

1 8

1 3

11 7

Objective: (5.3) Add and Subtract Rational Numbers

151)

2 1 8 8

1 4

1 2

Objective: (5.3) Add and Subtract Rational Numbers

152)

6 5 - 21 21

1 2

11 21

Objective: (5.3) Add and Subtract Rational Numbers

153)

5 6 25 22

7 25

7 550

1 550

1 25

9 88

D) 0

43 24

4 3

1 10

55 56

Objective: (5.3) Add and Subtract Rational Numbers

154)

1 1 8 ÷ 5 6 9

A) -

9 88

3 80

Objective: (5.3) Add and Subtract Rational Numbers

155)

1 1 1 1 + ÷ + 2 3 2 8

A) 2

31 24

Objective: (5.3) Add and Subtract Rational Numbers

Perform the indicated operations. If possible, reduce the answer to its lowest terms. 1 1 1 + · 156) 5 10 2 A)

3 20

3 40

3 5

Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers

157)

11 8 8 ÷ + 7 5 15

55 64

165 224

15 224

Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers

158)

5 1 2 2 ÷ 6 3 3 5

11 15

B) 1

5 6

C) 2

7 30

D) 12

Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers

159)

2 1 4 1 - ÷ 3 6 5 2

1 9

1 8

5 3

Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers

1 24

1 2

160)

1 4 2 1 + ÷ 4 5 3 6

10 21

10 63

14 5

32 63

Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers

161)

32 49 3 -5 7

1 5 7 4

1 4

B) -

1 4

C) -

9 4

D) -

9 2

Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers

Perform the indicated operations. Leave denominators in prime factorization form. 1 1 1 + 162) 4 2 3 2 2 · 112 2 · 5 · 11 2 · 5 A)

-4,671 3 2 · 5 4 · 112

5,009 4 2 · 5 3 · 112

-4,671 4 2 · 5 3 · 112

5,009 3 2 · 5 4 · 112

Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers

Find the rational number halfway between the two numbers in each pair. 1 1 163) and 2 4 A)

3 4

1 8

3 8

1 4

13 4

13 2

Objective: (5.3) Apply the Density Property of Rational Numbers

164) -

3 and -5 2

A) -

13 4

B) -

13 2

Objective: (5.3) Apply the Density Property of Rational Numbers

Solve the problem. 165) Of the 621 people polled about gardening, 207 replied that they plant a garden. What fractional part of those polled, expressed in lowest terms, plant a garden? 1 1 2 1 A) B) C) D) 3 2 3 4 Objective: (5.3) Solve Problems Involving Rational Numbers

166) Of the 500 urban residents polled about gardening, 108 replied that they plant a garden. What fractional part of those polled, expresses in lowest terms, plant a garden? 1 1 98 27 A) B) C) D) 500 125 125 5 Objective: (5.3) Solve Problems Involving Rational Numbers

167) Of the 300 suburban residents polled about gardening, garden? A) 180 residents

12 replied that they plant a garden. How many plant a 20

B) 300 residents

C) 60 residents

D) 15 residents

Objective: (5.3) Solve Problems Involving Rational Numbers

168) A recipe calls for A)

1 cup of butter. How much is needed to double the recipe? 4

2 c 3

1 c 8

1 c 6

1 c 2

Objective: (5.3) Solve Problems Involving Rational Numbers

169) A recipe calls for 7 ounces of unsweetened chocolate for 16 brownies. How much of unsweetened chocolate is needed to make 30 brownies? 7 56 105 oz oz oz A) B) 210 oz C) D) 16 15 8 Objective: (5.3) Solve Problems Involving Rational Numbers

170) A recipe calls for 1 1 A) 43 c 5

1 cups of sugar for 8 brownies. How much of sugar is needed to make 36 brownies? 5

B) 5

2 c 5

4 c 15

3 c 20

Objective: (5.3) Solve Problems Involving Rational Numbers

171) Jerry caught a fish that weighed 10

1 3 pounds. Pat caught a fish that weighed 7 pounds. How much more did 7 7

Jerry's fish weigh than Pat's fish? 5 4 A) 2 lb B) 2 lb 7 7

C) 17

5 lb 7

D) 16

5 lb 7

Objective: (5.3) Solve Problems Involving Rational Numbers

172) In most societies, men say they prefer women who are younger. In country A, the preferred age in a mate for men 4 6 is 14 years younger than self. In country B, the preferred age in a mate for men is 8 years younger than self. 7 7 What is the difference between the preferred age in a mate for men in country A and men in country B? 5 4 5 5 A) 22 yr B) 5 yr C) 5 yr D) 21 yr 7 7 7 7 Objective: (5.3) Solve Problems Involving Rational Numbers

173) A business is owned by three people. The first owns

7 1 of the business and the second owns of the business. 12 6

What fractional part of the business is owned by the third person? 1 1 3 A) B) C) 3 4 4 Objective: (5.3) Solve Problems Involving Rational Numbers

5 12

174) If a person walks A)

4 mi 13

3 1 mile, then jogs mile, what is the total distance covered? 8 5

23 mi 40

7 mi 40

1 mi 10

Objective: (5.3) Solve Problems Involving Rational Numbers

175) Some companies pay people extra when they work more than a regular 40-hour week. The overtime rate is often 1 3 1 , or , times the regular hourly rate. A clerical job pays $10 an hour and offers time and a half for hours worked 2 2 over 40. If a clerk works 44 hours during one week, what is the clerk's total pay before taxes? A) $460 B) $60 C) $440 D) $660 Objective: (5.3) Solve Problems Involving Rational Numbers

176) A will states that

2 1 of the estate is to be divided among the relatives. Of the remaining estate, goes to a certain 3 6

charity. What fractional part of the estate goes to the charity? 1 1 1 A) B) C) 9 6 18

11 18

Objective: (5.3) Solve Problems Involving Rational Numbers

177) On a map of Nature's Wonder Hiking Trails, 1 centimeter corresponds to 5 miles. Find the length of a trail 1 represented by a line that is 9 centimeters long on the map. 2 A)

10 mi 19

B) 484

1 mi 2

C) 1

9 mi 10

D) 47

1 mi 2

Objective: (5.3) Solve Problems Involving Rational Numbers

Provide an appropriate response. 178) Which of the following decimal numbers is an irrational number? Explain your answer. A) 1.73205080757... is irrational because it neither terminates nor repeats. B) 0.53 is irrational because it is a repeating decimal. C) 1.16 is irrational because it does not terminate. D) 0.0089372432 is irrational because it extends past the millionths place. Objective: (5.4) Define the Irrational Numbers

Evaluate the expression. 179) 16 A) 2

B) 4

C) 8

D) 16

Objective: (5.4) Simplify Square Roots

Use a calculator with a square root key to find a decimal approximation for the square root. Round the number displayed as indicated. 180) 888 to the nearest thousandth A) 888.000 B) 29.799 C) 29.796 D) 29.804 Objective: (5.4) Simplify Square Roots

181)

4,951 to the nearest hundredth A) 70.36 B) 70.4

C) 70.363

D) 70

C) 5.1

D) 15.9

Objective: (5.4) Simplify Square Roots

182)

9π to the nearest tenth A) 15.7

B) 5.3

Objective: (5.4) Simplify Square Roots

Simplify the square root. 183) 112 A) 10.583 C) 16 7

B) 4 7 D) This expression is already simplified.

Objective: (5.4) Simplify Square Roots

184)

72 A) 2 23 C) 3 8

B) 6 2 D) This expression is already simplified.

Objective: (5.4) Simplify Square Roots

185) 2 192 A) 4 12 C) 16 3

B) 4 48 D) This expression is already simplified.

Objective: (5.4) Simplify Square Roots

Perform the indicated operation. Simplify the answer when possible. 186) 3 · 2 A) 3 + 2 B) 6 C)

Objective: (5.4) Perform Operations with Square Roots

187)

7 · 16 A) 28

112

C) 4 7

D) 4

Objective: (5.4) Perform Operations with Square Roots

188)

5· 5 A) 2 5 · 12

B) 5

6 3

Objective: (5.4) Perform Operations with Square Roots

189)

6 3

A) 6

Objective: (5.4) Perform Operations with Square Roots

54 6

190)

B) 3 6

A) 6

3 6

D) 3

C) -1 19

C) 52 186

D) 9 3

C) 36

D) 6

C) 4 10

D) 2 10

C) 3 2

D) 8

C) 5 3

C) 14 3

D) 87

3 5

Objective: (5.4) Perform Operations with Square Roots

191) 17 19 + 18 19 A) -36 19

B) 35 19

Objective: (5.4) Perform Operations with Square Roots

3 + 3 75 + 6 108 A) 9 186

192)

B) 52 3

Objective: (5.4) Perform Operations with Square Roots

6+ 6 A) 2 6

193)

B) 72

Objective: (5.4) Perform Operations with Square Roots

194) 2 10 + 3 10 A) 5 10

B) 6 10

Objective: (5.4) Perform Operations with Square Roots

2+ 8 A) 4

195)

B) 5 2

Objective: (5.4) Perform Operations with Square Roots

27 - 12 A) 2 3

196)

Objective: (5.4) Perform Operations with Square Roots

197) 2 12 + 5 12 A) 399

B) 7 87

Objective: (5.4) Perform Operations with Square Roots

198)

1 5

12 +

1 15

1 10

2 5

2 15

Objective: (5.4) Perform Operations with Square Roots

199)

7 · 21 - 5 3 3 A)

B) -5(

21 + 3 7 )

Objective: (5.4) Perform Operations with Square Roots

C) 44 3

D) 7 3

200) 8 125 + 8 63 + 5 175 A) 191 5 + 197 7

B) 197 5 + 149 7

C) 37 5 + 49 7

D) 31 5 + 97 7

Objective: (5.4) Perform Operations with Square Roots

Solve the problem. 201) When an object is dropped to the ground from a height of h meters, the time it takes for the object to reach the h ground is given by the equation t = , where t is measured in seconds. If an object falls 19.6 meters before it 4.9 hits the ground, find the time it took for the object to fall. A) 5 sec B) 2 sec

C) 3 sec

D) 4 sec

Objective: (5.4) Perform Operations with Square Roots

202) The maximum number of volts, E, that can be placed across a resistor is given by the formula E = PR, where P is the number of watts of power that the resistor can absorb and R is the resistance of the resistor in ohms. Find E if P = 2 watts and R = 50 ohms. A) 10 V B) 20 V C) 100 V D) 5 V Objective: (5.4) Perform Operations with Square Roots

203) The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9 x + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 25 months of age and a child 16 months of age? A) 2.9 in. B) 14.5 in. C) 4.9 in. D) 43.1 in. Objective: (5.4) Perform Operations with Square Roots

204) The square root expression Rf 1 -

v 2 gives the aging rate of an astronaut relative to the aging rate of a friend on c

Earth, Rf, where v is the astronaut's speed and c is the speed of light. An astronaut is moving at 60% of the speed of light. Substitute 0.6c in the expression above. What is his aging rate, correct to two decimal places if necessary, relative to a friend on Earth? A) 0.8 B) 0.8Rf C) 0.63R f D) 1.17R f Objective: (5.4) Perform Operations with Square Roots

205) The square root expression Rf 1 -

v 2 gives the aging rate of an astronaut relative to the aging rate of a friend on c

Earth, Rf, where v is the astronaut's speed and c is the speed of light. An astronaut is moving at 70% of the speed of light. Substitute 0.7c in the expression above. If 50 weeks have passed for his friend, how long, to the nearest week, was he gone? A) 1 weeks B) 27 weeks C) 61 weeks D) 36 weeks Objective: (5.4) Perform Operations with Square Roots

Rationalize the denominator. 9 206) 7 A)

81 7 7

9 7 7

C) 58

Objective: (5.4) Rationalize Denominators

D) 9 7

207)

9 5

A) 9

9 5

C) 9 5

9 5 5

Objective: (5.4) Rationalize Denominators

208)

19 18

19 6

B) 57 2

19 6

3 5

15 5

8 4 35

46 4 35

8 15

D) 57 18

Objective: (5.4) Rationalize Denominators

209)

3 5

B) 3 5

A) 3

Objective: (5.4) Rationalize Denominators

Perform the indicated operation. Simplify the answer when possible. 36 100 + 210) 5 7 A)

23 4 6

92 4 35

Objective: (5.4) Rationalize Denominators

211)

3 + 5

5 3

8 3+

8 15 15

Objective: (5.4) Rationalize Denominators

List all numbers from the set that are natural numbers. 1 212) {-3, - , 0, 0.14, 15, 9.8, 9} 3 A) { 9} C) {-3,

B) {0,

D) {-3, -

Objective: (5.5) Recognize Subsets of the Real Numbers

1 , 0, 0.14, 9.8, 3

List all numbers from the set that are whole numbers. 1 213) {-8, - , 0, 0.14, 15, 9.8, 64} 8 A) {-8, C) {0,

1 , 0, 0.14, 9.8, 8

64}

B) { 64}

64}

D) {-8,

64}

Objective: (5.5) Recognize Subsets of the Real Numbers

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide a proper response. 214) Give an example of an integer that is not a natural number. Objective: (5.5) Recognize Subsets of the Real Numbers

215) Give an example of a rational number that is not a natural number. Objective: (5.5) Recognize Subsets of the Real Numbers

216) Give an example of a rational number that is a natural number. Objective: (5.5) Recognize Subsets of the Real Numbers

217) Give an example of a real number that is not a natural number. Objective: (5.5) Recognize Subsets of the Real Numbers

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Complete the statement to illustrate the commutative property. 218) 10 + (9 + 11) = 10 + (11 + ___ ) A) 20 B) 11

C) 9

D) 10

C) 3

D) 8

C) 4 and 8

D) 8 and 4

C) 4

D) -6

C) 4

D) 5

Objective: (5.5) Recognize Properties of Real Numbers

219) 3 · 2 = 2 · ___ A) 4

B) 5

Objective: (5.5) Recognize Properties of Real Numbers

Complete the statement to illustrate the associative property. 220) (8 + 6) + 4 = ___ + (6 + ___ ) A) 6 and 7 B) 3 and 9 Objective: (5.5) Recognize Properties of Real Numbers

Complete the statement to illustrate the distributive property. 221) 5 · (4 + 6) = 5 · 4 + 5 · ___ A) 5 B) 6 Objective: (5.5) Recognize Properties of Real Numbers

222) ___ · (3 + 4) = 5 · 3 + 5 · 4 A) 3

B) 10

Objective: (5.5) Recognize Properties of Real Numbers

Use the distributive property to simplify the radical expressions. 223) 8(9 + 5) A) 360 B) 8 5 + 72

C) 9 5

D) 72 5

C) 4 5

D) 3 5 + 3

C) 5

D) 3 3

Objective: (5.5) Recognize Properties of Real Numbers

224)

3( 15 + A) 18

B) 3 5

Objective: (5.5) Recognize Properties of Real Numbers

225)

3(2 + A) 6

B) 2 3 + 3

Objective: (5.5) Recognize Properties of Real Numbers

State the name of the property illustrated. 226) 12 · (3 + 6) = 12 · 3 + 12 · 6 A) distributive property of addition over multiplication B) associative property of addition C) distributive property of multiplication over addition D) associative property of multiplication Objective: (5.5) Recognize Properties of Real Numbers

227) 2(-5 + 7) = -10 + 14 A) commutative property of addition B) associative property of addition C) distributive property of multiplication over addition D) commutative property of multiplication Objective: (5.5) Recognize Properties of Real Numbers

228) -5(4 + 6) = -20 - 30 A) commutative property of multiplication B) distributive property of multiplication over addition C) commutative property of addition D) associative property of addition Objective: (5.5) Recognize Properties of Real Numbers

229) (7 3) · 7 = 7( 3 · 7) A) distributive property of multiplication over addition B) associative property of multiplication C) commutative property of multiplication D) associative property of addition Objective: (5.5) Recognize Properties of Real Numbers

Determine if the statement is true or false. Do not use a calculator. 230) 8(70 + 27) = 70 + 27(8) A) True Objective: (5.5) Recognize Properties of Real Numbers

B) False

231) 13(105 + 29) = 105(13) + 29(13) A) True

B) False

Objective: (5.5) Recognize Properties of Real Numbers

232) 120 · 12 + 35 · 12 = (120 + 35) · 12 A) True

B) False

Objective: (5.5) Recognize Properties of Real Numbers

233) 45 · 9 · 33 · 9 = (45 · 33) · 9 A) True

B) False

Objective: (5.5) Recognize Properties of Real Numbers

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Name the property used to go from step to step each time that (why?) occurs. 234) 7(x + 6) + 5x = (7x + 42) + 5x (why?) = (42 + 7x) + 5x (why?) = 42 + (7x + 5x) (why?) = 42 + (7 + 5)x (why?) = 42 + 12x (why?) = 12x + 42 Objective: (5.5) Recognize Properties of Real Numbers

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 235) A narcissic number is an n-digit number equal to the sum of each of its digits raised to the nth power. Determine if the real number 372 is narcissic. A) Yes B) No Objective: (5.5) Recognize Properties of Real Numbers

Name the kind of rotational symmetry shown in the figure. 236)

A) fourfold

B) sixfold

C) eightfold

Objective: (5.5) Apply Properties of Real Numbers to Clock Addition

D) onefold

237)

A) threefold

B) twofold

C) fourfold

D) onefold

Objective: (5.5) Apply Properties of Real Numbers to Clock Addition

Solve the problem. 238) Shown below is the table for clock addition in the 10-hour clock system.

Find the inverse of 9 in the 10-hour clock system. A) 11 B) 0

C) 1

D) 2

Objective: (5.5) Apply Properties of Real Numbers to Clock Addition

The tables show the operations 8and Pon the set {a, b, c, d, e}.

Replace x with a, b, c, d, or e to form a true statement. 239) x 8e = d A) a B) e

C) c

D) b

Objective: (5.5) Apply Properties of Real Numbers to Clock Addition

240) x P(a 8c) = e A) e

B) c

C) d

Objective: (5.5) Apply Properties of Real Numbers to Clock Addition

D) a

Use properties of exponents to simplify the expression. First, express the answer in exponential form. Then, evaluate the expression. 241) 3 2 · 3 7

A) 9 · 3; 27

B) 3 9 ; 19,683

C) 3 9 ; 2,196

D) 3 14; 4,782,969

C) 7 3 ; 343

D) 21; 21

C) 5 6 ; 15,625

D) 103 ; 250

C) 1 90; 0

D) 1 90; 1

C) 0

D) 1

Objective: (5.6) Use Properties of Exponents

242) 7 · 7 2 A) 7; 7

B) 7 2 ; 49

Objective: (5.6) Use Properties of Exponents

243) (5 2 )3 A) 5 5 ; 3,125

B) 152 ; 75

Objective: (5.6) Use Properties of Exponents

244) (1 9 )10 A) 1 19; 1

B) 1 90; 90

Objective: (5.6) Use Properties of Exponents

Use the zero and negative exponent rules to simplify the expression. 245) (8)0 A) -1

B) 8

Objective: (5.6) Use Properties of Exponents

246) 4 -5 A)

1 20

B) 1,024

1 1,024

D) -1,024

Objective: (5.6) Use Properties of Exponents

Use properties of exponents to simplify the expression. Express answer in exponential form. 247) 8 3 · 8 -5 A) -8 -2

B) -8 8

C) 8 -2

D) 8 -15

C) 3 -3

D) -3 · 3 2

C) -4 8

D) 4 -2

Objective: (5.6) Use Properties of Exponents

248) 3 -3 · 3 A) 3 -2

B) -3 2

Objective: (5.6) Use Properties of Exponents

249)

43 45

A) 4 -15

B) 4 2

Objective: (5.6) Use Properties of Exponents

250)

3 10 38

A) 3 18

B) 3 -2

C) 3 80

D) 3 2

Objective: (5.6) Use Properties of Exponents

Use properties of exponents to simplify the expression. Express answers in exponential form with positive exponents only. Assume that any variables in denominators are not equal to zero. -3 251) (x4 · x 3 ) 1 1 1 A) B) C) x21 D) x7 x21 x36 Objective: (5.6) Use Properties of Exponents

252)

x5 x2

-2

A) x6

1 x6

1 x14

D) x14

10x y6

D) 10xy5

-15x6 y7

-15x y7

5y4 x2

5x2 y4

1 8

Objective: (5.6) Use Properties of Exponents

253) (-5x2 y-4 )(-2x3 y2 ) A) 10x6y5

10x5 y2

Objective: (5.6) Use Properties of Exponents

254) (-3x4 y-4 )(5x3 y-2 ) A)

-15x y6

-15x7 y6

Objective: (5.6) Use Properties of Exponents

255)

10x2 y-6 2x4 y-10

y2 5x4

B) 5x2 y4

Objective: (5.6) Use Properties of Exponents

Perform the indicated operations. Express the answer as a fraction reduced to its lowest terms. 35 54 + 256) 37 55 A)

14 45

2 17

Objective: (5.6) Use Properties of Exponents

45 14

257)

25 35 24 38

55 27

53 27

29 54

D) -

53 27

Objective: (5.6) Use Properties of Exponents

Express the number in decimal notation. 258) 1.24 × 107 A) 1,240,000

B) 124,000,000

C) 86.8

D) 12,400,000

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

259) 3.78 × 10-4 A) 0.0000378

B) -378,000

C) 0.000378

D) 0.00378

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

260) 5.747 × 10-5 A) 0.000005747

B) 0.0005747

C) 0.00005747

D) -574,700

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

261) 2.628 × 10-6 A) 0.00002628

B) -2,628,000

C) 0.0000002628

D) 0.000002628

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

262) 8.0674 × 10-7 A) 0.000000080674

B) -806,740,000

C) 0.00000080674

D) 0.0000080674

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

263) 4 × 10 5 A) 0.00004

B) 4,000

C) 400,000

D) 200

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

264) 1 × 10 3 A) 30

B) 100

C) 1,000

D) 10,000

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

265) 9.4 × 10-1 A) 0.094

B) 0.94

C) 0.0094

D) -9.4

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

266) 3.91 × 10 -2 A) 0.391

C) -7.82

B) 0.00391

Objective: (5.6) Convert From Scientific Notation to Decimal Notation

D) 0.0391

Express the number in scientific notation. 267) 380,000 A) 3.8 × 10-4 B) 3.8 × 104

C) 3.8 × 105

D) 3.8 × 10-5

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

268) 0.000968 A) 9.68 × 10-4

C) 9.68 × 10-3

B) 9.68 × 104

D) 9.68 × 10-5

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

269) 0.0000065214 A) 6.5214 - 106

B) 6.5214 × 10-5

C) 6.5214 × 10-6

D) 6.5214 × 10-7

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

270) 0.000000625017 A) 6.25017 × 10-7

B) 6.25017 × 10-6

C) 6.25017 × 107

D) 6.25017 × 106

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

271) 220 A) 2.2 × 10 2

B) 22 × 10 2

C) 2.2 × 10 3

D) 22 × 10

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

272) 6,100 A) 61 × 10 4

B) 0.61 × 10 2

C) 6.1 × 10 3

D) 61 × 10 3

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

273) 780,000,000 A) 7.8 × 10 8

B) 7.8 × 10 7

C) 78 × 10 7

D) 7.8 × 10 9

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

274) 390,000,000,000 A) 39 × 10 10

B) 3.9 × 10 12

C) 39 × 10 11

D) 3.9 × 10 11

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

275) 0.043 A) 43 × 10 -4

B) 4.3 × 10 -2

C) 4.3 × 10 -1

D) 43 × 10 -3

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

276) 0.0021 A) 21 × 10 -4

B) 2.1 × 10 -4

C) 21 × 10 -1

D) 2.1 × 10 -3

Objective: (5.6) Convert from Decimal Notation to Scientific Notation

Perform the indicated operation and express the answer in decimal notation. 277) (5 x 104 ) x (4 x 102 ) A) 2,000,000

B) 200,000,000

C) 2,000,000,000

Objective: (5.6) Perform Computations Using Scientific Notation

D) 20,000,000

278)

21 × 108 7 × 106

A) 0.03

B) -0.03

C) 300

D) -300

C) -25,000

D) 25,000

Objective: (5.6) Perform Computations Using Scientific Notation

279)

4 × 102 16 × 10- 3

A) 0.0000025

B) -0.0000025

Objective: (5.6) Perform Computations Using Scientific Notation

280) (7 × 10 8 )(8 × 10 -6 ) A) 56,000,000,000,000,000 C) 5,600

B) 11,200 D) 0.56

Objective: (5.6) Perform Computations Using Scientific Notation

281) (3.5 × 10 7 )(8 × 10 -4 ) A) 28,000

B) 28

C) 280

D) 2,800

C) -1,800

D) -1,820,000

C) 0.00018

D) 0.0000000018

Objective: (5.6) Perform Computations Using Scientific Notation

282)

18 × 104 2 × 106

A) 0.09

B) 900

Objective: (5.6) Perform Computations Using Scientific Notation

283)

3.6 × 10-7 2 × 10-3

A) 18,000

B) 180,000,000,000

Objective: (5.6) Perform Computations Using Scientific Notation

Perform the indicated operation by first expressing each number in scientific notation. Write answer in scientific notation. 284) (260,000,000)(2,000,000,000) A) 5.2 × 1015 B) 5.2 × 1018 C) 5.2 × 1017 D) 5.2 × 1016 Objective: (5.6) Perform Computations Using Scientific Notation

285)

8,700,000 100

A) 8.7 × 105

B) 8.7 × 106

C) 8.7 × 103

D) 8.7 × 104

Objective: (5.6) Perform Computations Using Scientific Notation

Solve the problem. 286) In a certain year a state government collected $19 billion in taxes. If the state had 10,000,000 residents, what was the per capita tax burden, or the amount that each citizen of the state paid in taxes? Round to the nearest hundred dollars. A) $19,000 B) $190,000 C) $1,900 D) $190 Objective: (5.6) Solve Applied Problems Using Scientific Notation

287) In a state with a population of 3,000,000 the average citizen spends $6,000 on housing each year. What is the total spent on housing for the state? Express answer in scientific notation. A) $18 × 1011 B) $18 × 1010 C) $1.8 × 109 D) $1.8 × 1010 Objective: (5.6) Solve Applied Problems Using Scientific Notation

288) Approximately 4 × 103 employees of a certain company average $30,000 each year in salary. Write the total amount earned by all the employees of this company per year in scientific notation. A) $12 × 109 B) $1.2 × 109 C) $1.2 × 108 D) $12 × 108 Objective: (5.6) Solve Applied Problems Using Scientific Notation

289) The national debt of a small country is $787 billion and the population is 2,198,000. What is the amount of debt per person? Express the answer in scientific notation. A) $3.58 B) $3.58 × 105 C) $3.58 × 106 D) $35.80 Objective: (5.6) Solve Applied Problems Using Scientific Notation

290) The national debt of a country is $40 billion and the population is 5,590,000. What is the debt per person? Express the answer in decimal notation, rounded to the nearest whole number. A) $716 B) $124,992,400 C) $71,560 D) $7,156 Objective: (5.6) Solve Applied Problems Using Scientific Notation

291) The mass of one oxygen molecule is 5.3 × 10-23 gram. Find the mass of 3,000 molecules of oxygen. Express the answer in scientific notation. A) 1.59 × 10-18 g B) 1.59 × 10-21 g C) 1.59 × 10-20 g D) 1.59 × 10-19 g Objective: (5.6) Solve Applied Problems Using Scientific Notation

292) The world population of a certain species is evaluated at 5.8 × 1014. By some projections, this population will be 5 times more important in 30 years. Express the population at that time in scientific notation. A) 2.9 × 1015 B) 2.9 × 1045 C) 290 × 1014 D) 29 × 1015 Objective: (5.6) Solve Applied Problems Using Scientific Notation

Write the first six terms of the arithmetic sequence with the first term, a1 , and common difference, d.

293) a 1 = 4; d = 3 A) 7, 10, 13, 16, 19, 22

B) 4, 6, 8, 10, 12, 14

C) 4, 7, 10, 13, 16, 19

D) 0, 4, 7, 10, 13, 16

C) 8, 7, 6, 5, 4, 3

D) 7, 6, 5, 4, 3, 2

Objective: (5.7) Write Terms of an Arithmetic Sequence

294) a 1 = 8; d = -1 A) 9, 8, 7, 6, 5, 4

B) 8, 7, 5, 5, 4, 3

Objective: (5.7) Write Terms of an Arithmetic Sequence

295) a 1 = -27; d = 7 A) 1, -6, -13, -20, -27, -34 C) -13, -20, -27, -34, -41, -48

B) -27, -20, -13, -6, , D) -13, -6, , , ,

Objective: (5.7) Write Terms of an Arithmetic Sequence

296) a 1 = -600, d = 20 A) -580, -560, -540, -520, -500, -480 C) -600, -580, -560, -540, -520, -500

B) 200, 140, 80, 20, -40, -100 D) 140, 80, 20, -40, -100, -160

Objective: (5.7) Write Terms of an Arithmetic Sequence

297) a 1 = 300, d = -20 A) -170, -140, -110, -80, -50, -20 C) -200, -170, -140, -110, -80, -50

B) 280, 260, 240, 220, 200, 180 D) 300, 280, 260, 240, 220, 200

Objective: (5.7) Write Terms of an Arithmetic Sequence

298) a 1 =

1 1 ,d= 3 3

1 1 1 1 1 1 , , , , , 3 9 27 81 243 729

1 2 4 5 , , 1, , , 2 3 3 3 3

2 4 5 7 , 1, , , 2, 3 3 3 3

1 4 7 10 13 16 , , , , , 3 3 3 3 3 3

Objective: (5.7) Write Terms of an Arithmetic Sequence

299) a 1 =

1 3 ,d=4 4

3 3 3 3 3 3 , ,, ,,4096 256 1024 16 64 4

3 1 1 1 1 , , 0, - , - , 4 2 4 2 4

17 13 9 5 1 3 ,,- ,- ,- ,4 4 4 4 4 4

1 1 3 1 1 , , , 0, - , 2 4 4 2 4

Objective: (5.7) Write Terms of an Arithmetic Sequence

300) a 1 = 7.5, d = 0.4 A) 7.5, 7.9, 8.3, 8.7, 9.1, 9.5 C) 7.9, 8.3, 8.7, 9.1, 9.5, 9.9

B) 7.9, 15.4, 22.9, 30.4, 37.9, 45.4 D) 0.4, 7.9, 15.4, 22.9, 30.4, 37.9

Objective: (5.7) Write Terms of an Arithmetic Sequence

301) a 1 = 6.2, d = -0.25 B) -0.25, 5.95, 12.15, 18.35, 24.55, 30.75 D) 6.2, 5.95, 5.7, 5.45, 5.2, 4.95

A) 5.95, 5.7, 5.45, 5.2, 4.95, 4.7 C) 5.95, 12.15, 18.35, 24.55, 30.75, 36.95 Objective: (5.7) Write Terms of an Arithmetic Sequence

Find the indicated term for the arithmetic sequence with first term, a 1 , and common difference, d.

302) Find a 8 , when a 1 = -1, d = 5. A) -41

B) 34

C) 39

D) -36

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

303) Find a 10, when a 1 = -9, d = -8. A) -89

B) 81

C) 63

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

D) -81

304) Find a 8 , when a 1 = 6, d = 5. A) -34

B) -29

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

305) Find a 16, when a 1 = 4, d = - 2 B) - 26

D) - 28

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

306) Find a 300, where a 1 = -60 and d = 5. A) 1,445

B) 1,440

C) 1,555

D) 1,435

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

307) Find a 150, where a 1 = -12 and d = -0.6. A) -102

B) -77.4

C) -101.4

D) -552.6

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a 20, the 20th term of the sequence. 308) 2 , 6 , 10 , 14 , 18 , . . . A) a n = 2n - 4; a 20 = 36

B) a n = 4n - 2; a 20 = 78

C) a n = 2n - 1; a 20 = 39

D) a n = 4n - 1; a 20 = 79

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

309) 2 , 6 , 10 , 14 , 18 , . . . A) a n = 2n - 4; a 20 = 36

B) a n = 4n + 2; a 20 = 82

C) a n = 4n - 2; a 20 = 78

D) a n = n + 4; a 20 = 24

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

310) 18, 14 , 10, 6, . . . A) a n = 22 - 4n; a 20 = -58

B) a n = 18 - 4n; a 20 = -62

C) a n = 4n - 18; a20 = 62

D) a n = 4n - 22; a20 = 58

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

311) 22, 17 , 12, 7, . . . A) a n = -5n + 22; a 20 = -78

B) a n = 5n - 22; a20 = 78

C) a n = 5n - 27; a20 = 73

D) a n = -5n + 27; a 20 = -73

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

312) a 1 = -

1 4 ,d= 3 3

A) a n =

4 16 1 n - ; a 20 = 3 3 3

B) a n = -

1 79 4 n + ; a 20 = 3 3 3

C) a n =

5 1 n - ; a 20 = 5 3 3

D) a n = -

5 4 n + ; a 20 = - 25 3 3

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

313) a 1 = -2, d = 0.8 A) a n = -2n + 0.8; a 20 = -39.2

B) a n = -2n + 2.8; a 20 = -37.2

C) a n = 0.8n - 2; a 20 = 14

D) a n = 0.8n - 2.8; a 20 = 13.2

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

Determine whether the sequence is arithmetic or geometric. Then find the next two terms. 314) 16,23, 30, 37, . . . A) Geometric; 44, 51 B) Arithmetic; 44, 51 C) Arithmetic; 37, 44

D) Geometric; 37, 44

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

315) -5, -4, -3, -2, . . . A) Arithmetic; -1,

B) Geometric; -10, -5

C) Geometric; -1,

D) Arithmetic; 0, 1

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

316) 19, 0, -19, -38, . . . A) Arithmetic; -76, -95 C) Arithmetic; -57, -95

B) Geometric; -57, -76 D) Arithmetic; -57, -76

Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

Use the formula for the nth term of an arithmetic sequence to solve the problem. 317) During a certain year, a company has 143,646 employees. This number is then increased by 1,821 employees per year. How many employees will there be 8 years later? A) 14,568 B) 156,393 C) 158,214 D) 160,035 Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

318) Company A pays $25,000 yearly with raises of $1,700. Company B pays $30,000 yearly with raises of $1,200. Which company will pay more in year 8? How much more? A) Company B; $2000 B) Company B; $1500 C) Company A; $2000 D) Company A; $1500 Objective: (5.7) Use the Formula for the General Term of an Arithmetic Sequence

Write the first six terms of the geometric sequence with first term, a1 , and common ratio, r.

319) a 1 = 2; r = 3 A) 2, 5, 8, 11, 14, 17 C) 6, 18, 54, 162, 486, 1,458

B) 3, 6, 12, 24, 48, 96 D) 2, 6, 18, 54, 162, 486

Objective: (5.7) Write Terms of a Geometric Sequence

320) a 1 = -7; r = 5 A) -35, -175, -875, -4,375, -21,875, -109,375 C) -7, 35, -175, 875, -4,375, 30,625

B) -7, -2, , 8, 13, 18 D) -7, -35, -175, -875, -4,375, -21,875

Objective: (5.7) Write Terms of a Geometric Sequence

321) a 1 = 2,000, r = 1 A) 2,000, 2,001, 2,002, 2,003, 2,004, 2,005 C) 2,000, 4,000, 6,000, 8,000, 10,000, 12,000

B) 2,000, 2,000, 2,000, 2,000, 2,000, 2,000 D) 2,001, 2,002, 2,003, 2,004, 2,005, 2,006

Objective: (5.7) Write Terms of a Geometric Sequence

322) a 1 = -4, r = -3 A) -4, -12, -36, -108, -324, -972 C) -4, 12, -36, 108, -324, 972

B) -12, -36, -108, -324, -972, -2,916 D) 12, -36, 108, -324, 972, -2,916

Objective: (5.7) Write Terms of a Geometric Sequence

323) a 1 =

1 ,r=4 3

13 25 37 49 61 73 , , , , , 3 3 3 3 3 3

1 13 25 37 49 61 , , , , , 3 3 3 3 3 3

1 4 16 64 256 1024 , , , , , 3 3 3 3 3 3

4 16 64 256 1024 4096 , , , , , 3 3 3 3 3 3

Objective: (5.7) Write Terms of a Geometric Sequence

324) a 1 =

1 1 ,r= 5 3

1 1 1 1 1 1 , , , , , 3 15 75 375 1875 9375

16 17 6 19 4 7 , , , , , 15 15 5 15 3 5

1 1 1 1 1 1 , , , , , 15 75 375 1875 9375 46875

1 16 17 6 19 4 , , , , , 3 15 15 5 15 3

Objective: (5.7) Write Terms of a Geometric Sequence

325) a 1 = A)

1 , r = -3 6

243 27 81 3 9 1 , ,,- , ,2 2 2 2 2 2

B) -

27 81 3 9 1 1 , , ,- , ,2 2 2 2 6 2

81 9 27 1 3 1 ,,- , ,- , 2 2 2 2 2 6

D) -

91 73 55 37 19 1 ,,,,,6 6 6 6 6 6

C) -

Objective: (5.7) Write Terms of a Geometric Sequence

326) a 1 = -9,000, r =0.1 A) 900, 90, 9, 0.9, 0.09, 0.009 C) -9,000, -900, -90, -9, -0.9, -0.09

B) 9,000, 900, 90, 9, 0.9, 0.09 D) -900, -90, -9, -0.9, -0.09, -0.009

Objective: (5.7) Write Terms of a Geometric Sequence

Find the indicated term for the geometric sequence with first term, a1 , and common ratio, r.

327) Find a 5 , when a 1 = 9, r = 3. A) 81

B) 2,187

C) 729

D) 108

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

328) Find a 5 , when a 1 = 7, r = -5. A) -4,375

C) -21,875

B) 4,375

D) 625

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

329) Find a 500, when a 1 = 90, r = 1. A) 590

B) 589

C) 90

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

D) 45,000

330) Find a 6 , when a 1 = -2, r = -3. A) -20

B) -1,458

C) -17

D) 486

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

331) Find a 6 , when a 1 = 16, r = A)

1 . 2

1 2

37 2

C) 19

1 4

4 243

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

332) Find a 6 , when a 1 = 12, r = A) -

4 81

1 . 3

7 3

C) 10

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

333) Find a 8 , when a 1 = 1,000,000, r = 0.1. A) 1,000,000.7

B) 0.1

C) 1,000,000.8

D) 0.01

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

Determine whether the sequence is arithmetic or geometric. Then find the next two terms. 334) 0.25, 1, 4, 16, . . . A) Geometric; 4, 1 B) Arithmetic; 64, 256 C) Geometric; 64, 256 D) Geometric; -64, 256 Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

335) 12, 6, 3,

3 ,... 2

A) Arithmetic;

3 3 , 4 8

B) Geometric;

3 3 , 4 8

C) Geometric; 24, 48

D) Geometric; 6,

13 2

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

336) -4, 4, -4, 4, . . . A) Geometric; -4, 4

B) Geometric; -4, -4

C) Arithmetic; -4, 4

D) Geometric; 4, -4

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

337) 1,

3, 3, 3 3, . . . A) Geometric; 3, 9

B) Arithmetic; 9, 9 3

C) Geometric; 9 3, 9

D) Geometric; 9, 9 3

Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

Use the formula for the nth term of a geometric sequence to solve the problem. 338) You are offered a job that pays $35,000 for the first year with an annual increase of 4% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.04 times what it was in the previous year. What can you expect to earn in your seventh year on the job? Round answer to the nearest dollar. A) $46,058 B) $47,900 C) $44,286 D) $42,583 Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

Solve the problem. 339) The population of a town over a four year period is shown in the following table. Year 1 2 Population (in thousands) 1.02 1.04

3 1.06

4 1.08

Assume that the population can be modeled by a geometric sequence. Estimate the town's population for year 10. Round to two decimal places when calculating the common ratio, and the final answer. A) 1.20 thousand B) 1.22 thousand C) 1.27 thousand D) 1.24 thousand Objective: (5.7) Use the Formula for the General Term of a Geometric Sequence

Find the indicated sum. 340) -4, -1, 2, 5, 8, . . . ; S5 A) 80

B) 10

C) 38

D) -20

C) 5,117

D) 5,115

C) -88,565

D) -88,574

C) 120

D) 3,540

Objective: (5.7) Demonstrate Additional Understanding and Skills

341) 5, 10, 20, 40, 80, . . . ; S10 A) 5,095

B) 5,152

Objective: (5.7) Demonstrate Additional Understanding and Skills

342) 6, -18, 54, -162, 486, . . . ; S10 A) -88,578

B) -88,572

Objective: (5.7) Demonstrate Additional Understanding and Skills

343) 2, 4, 6, 8, . . . ; S59 A) 3,599

B) 3,545

Objective: (5.7) Demonstrate Additional Understanding and Skills

Solve. 344) Find 1 + 2 + 3 + 4 + . . . + 171, the sum of the first 171 natural numbers. A) 29,241 B) 29,412 C) 14,535

D) 14,706

Objective: (5.7) Demonstrate Additional Understanding and Skills

345) Find the sum of the first 59 terms of the arithmetic sequence: 2, 4, 6, 8, . . . A) 3,599 B) 3,540 C) 120 Objective: (5.7) Demonstrate Additional Understanding and Skills

D) 3,546

Answer Key Testname: 05-BLITZER_TM8E_TEST_ITEM_FILE

1) D 2) B 3) D 4) B 5) A 6) C 7) D 8) A 9) A 10) B 11) A 12) A 13) B 14) A 15) A 16) C 17) D 18) D 19) C 20) D 21) A 22) D 23) A 24) A 25) D 26) B 27) A 28) D 29) C 30) D 31) C 32) A 33) D 34) B 35) C 36) D 37) D 38) D 39) A 40) C 41) A 42) A 43) A 44) C 45) A 46) B 47) B 48) A 49) It is the list of the prime numbers.

50) C 51) B 52) A 53) A 54) A 55) A 56) B 57) A 58) B 59) A 60) B 61) C 62) B 63) B 64) C 65) D 66) B 67) B 68) D 69) C 70) D 71) D 72) A 73) A 74) B 75) A 76) A 77) C 78) D 79) C 80) C 81) D 82) B 83) A 84) D 85) C 86) A 87) A 88) A 89) C 90) D 91) D 92) D 93) C 94) A 95) B 96) A 97) B 98) B 99) C

100) D 101) B 102) A 103) D 104) B 105) B 106) D 107) B 108) B 109) A 110) C 111) B 112) A 113) C 114) A 115) A 116) D 117) B 118) D 119) D 120) C 121) A 122) A 123) A 124) C 125) D 126) C 127) C 128) B 129) B 130) A 131) B 132) B 133) C 134) C 135) B 136) B 137) C 138) B 139) D 140) D 141) A 142) C 143) C 144) C 145) B 146) D 147) A 148) D 149) B 43

150) B 151) D 152) B 153) B 154) B 155) D 156) A 157) B 158) C 159) A 160) A 161) C 162) C 163) C 164) A 165) A 166) D 167) A 168) D 169) D 170) B 171) A 172) C 173) B 174) B 175) A 176) C 177) D 178) A 179) B 180) B 181) A 182) B 183) B 184) B 185) C 186) D 187) C 188) B 189) C 190) D 191) B 192) B 193) A 194) C 195) C 196) B 197) C 198) C 199) A

Answer Key Testname: 05-BLITZER_TM8E_TEST_ITEM_FILE

200) C 201) B 202) A 203) A 204) B 205) D 206) B 207) D 208) C 209) D 210) D 211) B 212) A 213) C 214) Answers will vary. Any negative integer is a proper response. 215) Answers will vary. Any fraction or repeating or terminating decimal, excluding integers, would be a proper response. 216) Answers will vary. Any number that is a natural number will do. 217) Answers will vary. Any number that is an irrational number will do. 218) C 219) C 220) D 221) B 222) D 223) B 224) D 225) B 226) C 227) C 228) B 229) B 230) B 231) A 232) A 233) B

234) 7(x + 6) + 5x = (7x + 42) + 5x (Distributive property of multiplication over addition) = (42 + 7x) + 5x (Commutative property of addition) = 42 + (7x + 5x) (Associative property of addition) = 42 + (7 + 5)x (Distributive property of multiplication over addition) = 42 + 12x = 12x + 42 (Commutativ e property of addition) 235) B 236) C 237) D 238) C 239) B 240) B 241) B 242) C 243) C 244) D 245) D 246) C 247) C 248) A 249) D 250) D 251) B 252) B 253) B 254) B 255) C 256) A 257) B 258) D 259) C 260) C 261) D 262) C

263) C 264) C 265) B 266) D 267) C 268) A 269) C 270) A 271) A 272) C 273) A 274) D 275) B 276) D 277) D 278) C 279) D 280) C 281) A 282) A 283) C 284) C 285) D 286) C 287) D 288) C 289) B 290) D 291) D 292) A 293) C 294) C 295) B 296) C 297) D 298) B 299) D 300) A 301) D 302) B 303) D 304) D 305) B 306) D 307) C 308) B 309) C 310) A 311) D 312) C 44

313) D 314) B 315) A 316) D 317) C 318) B 319) D 320) D 321) B 322) C 323) C 324) A 325) B 326) C 327) C 328) B 329) C 330) D 331) A 332) A 333) B 334) C 335) B 336) A 337) D 338) C 339) B 340) B 341) D 342) B 343) D 344) D 345) B

Blitzer, Thinking Mathematically, 8e Chapter 6 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the algebraic expression for the given value(s) of the variable(s). 1) -5x - 1 ; x = -3 A) -14 B) -16 C) 16

D) 14

Objective: (6.1) Evaluate Algebraic Expressions

2) -3x2 + 7x - 8 ; x = -1 A) -12

B) -4

C) -18

D) 2

C) -84

D) -124

C) 14

C) -32y

D) 31

D) 8

C) 1

D) -1

C) -68

C) 11

D) 22

1 7

Objective: (6.1) Evaluate Algebraic Expressions

3) 2x2 + 2xy - 3y2 ; x = -4, y = 6 A) 340

B) -24

Objective: (6.1) Evaluate Algebraic Expressions

4) x2 + 5x ; x = 3 A) x2 + 15

Objective: (6.1) Evaluate Algebraic Expressions

5) 8xy ; x = -4, y = -1 A) 32

B) -32

Objective: (6.1) Evaluate Algebraic Expressions

6) x2 - 3x + y2 ; x = -1, y = -2 A) 2

B) 6

Objective: (6.1) Evaluate Algebraic Expressions

7) -x2 - 6xy + 2y2 ; x = -1, y = -3 A) -35 B) 35 Objective: (6.1) Evaluate Algebraic Expressions

8) x3 - 4x2 - 5 ; x = -3 A) -14

B) 58

Objective: (6.1) Evaluate Algebraic Expressions

9) (x + 4y)2 ; x = 3, y = 2 A) 121

B) 49

Objective: (6.1) Evaluate Algebraic Expressions

10)

x-2 ; x = -9 x-8

17 11

B) 7

Objective: (6.1) Evaluate Algebraic Expressions

11 17

11)

x-7 ; x = -2 -2x + 9

A) -

9 13

B) -

13 9

C) -

9 7

D) - 1

Objective: (6.1) Evaluate Algebraic Expressions

12)

x2 - 10x + 5 ; x = -3 x2 + 2x - 1

B) - 22

C) - 8

48 49

Objective: (6.1) Evaluate Algebraic Expressions

13)

a2 1 - a2

;a=7

A) -

49 48

C) -

49 50

Objective: (6.1) Evaluate Algebraic Expressions

14) 6y +

15 ; x = 5, y = 7 x

A) 45

B) 3

C) 9

D) 57

C) 54

D) 27

Objective: (6.1) Evaluate Algebraic Expressions

15)

2x + 11y ; x = 10, y = 8 x-6

A) -17

B) -27

Objective: (6.1) Evaluate Algebraic Expressions

Solve the problem. 16) Suppose that the cost of an item, excluding tax, is $2.25. The algebraic expression 2.25x describes the cost, in dollars, of purchasing x units of that item. Evaluate the algebraic expression when x = 70. A) $1,102.50 B) $157.50 C) $15.75 D) $1,575.00 Objective: (6.1) Use Mathematical Models

17) The formula P = 0.2x - 51 models the profit, P, in dollars, for a shoe shiner when he shines x pairs of shoes. Use the formula to find this shoe shiner's profit when he shines 500 pairs of shoes. A) -$49.00 B) $100 C) $449 D) $49 Objective: (6.1) Use Mathematical Models

18) A scientist performs an experiment to produce a compound by adding various amounts of a catalyst to a chemical reaction. Her data can be modeled by the formula A = 0.04c + 3.93, where A represents the amount of the compound, in grams, produced when c milligrams of the catalyst are added to the reaction. According to the formula, how much compound is produced when 400 milligrams of catalyst are added? A) 19.93 g B) 1,588.00 g C) 1,603.93 g D) 16.00 g Objective: (6.1) Use Mathematical Models

19) The formula W = 0.45g2 - 0.01g + 7.9 models the average weight, W, in ounces, for a mouse who is fed g grams per day of a special food. According to the formula, how much will a mouse weigh when it is fed 19 grams of the special food per day? If necessary, round answers to the nearest hundredth. A) 170.16 oz B) 170.34 oz C) 16.26 oz D) 312.36 oz Objective: (6.1) Use Mathematical Models

20) Forensic scientists use the lengths of certain bones to calculate the height of a person. When the femur (f), the bone from the knee to the hip socket is used, the following formula applies for men: h = 69.09 + 2.24f, where h is the height and f is the length of the femur. Find the height of a man with a femur measuring 61 centimeters. A) 130.09 cm B) 205.73 cm C) 3.61 cm D) 4,351.13 cm Objective: (6.1) Use Mathematical Models

21) The monthly cost of a certain texting plan is modeled by the formula C = 0.06n + 9.95, where C is in dollars and n is the number of texts sent in a month. Use the model to find and interpret the result whenn = 70. A) When n = 70, C = 4.20; It costs $4.20 to send 70 texts in a month using a certain texting plan. B) When n = 70, C = 14.15; It costs $14.15 to send 70 texts in a month using a certain texting plan. C) When n = 70, C = 16.95; It costs $16.95 to send 70 texts in a month using a certain texting plan. D) When n = 70, C = 13.15; It costs $13.15 to send 70 texts in a month using a certain texting plan. Objective: (6.1) Use Mathematical Models

22) P = 0.85x - 89 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes. Use the model to find and interpret the result when x = 600. A) When x = 600, P = 421; $421 is the profit the vendor makes from selling 600 pretzels. B) When x = 600, P = 511; $511 is the profit the vendor makes from selling 600 pretzels. C) When x = 510, P = 600; $600 is the profit the vendor makes from selling 510 pretzels. D) When x = 600, P = 600; $600 is the profit the vendor makes from selling 600 pretzels. Objective: (6.1) Use Mathematical Models

23) A rocket is 37 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 14 feet per second per second. The distance, in feet, between the rocket and the satellite is modeled by P = 7t2 + 37, where t is the number of seconds since the rocket started accelerating. Use the model to find and interpret the result when t = 5. A) When t = 72, P = 5; After 72 seconds, the distance between the rocket and the satellite is 5 feet. B) When t = 62, P = 5; After 62 seconds, the distance between the rocket and the satellite is 5 feet. C) When t = 5, P = 175; After 5 seconds, the distance between the rocket and the satellite is 175 feet. D) When t = 5, P = 212; After 5 seconds, the distance between the rocket and the satellite is 212 feet. Objective: (6.1) Use Mathematical Models

24) W = 0.56g2 - 0.03g + 9.8 models the average weight in ounces for a mouse who is fed g grams of a special food per day. Use the model to find and interpret the result when g = 14. A) When g = 14, P = 246.54; When a mouse is fed an average of 246.54 ounces of the special food per day, its weight will be at least 14 ounces. B) When g = 14, P = 119.14; When a mouse is fed 14 grams of the special food per day, its average weight is 119.14 ounces. C) When g = 14, P = 119.53; 14 mice gained an average of 119.53 ounces per day when fed the special food. D) When g = 14, P = 17.22; The average amount of the special food that 14 mice should be fed is 17.22 ounces. Objective: (6.1) Use Mathematical Models

25) State University has seen an increase in the number of students majoring in Native American Studies. The graph below shows the number of students with this major for the past six years.

200 160 120 80 40

Use the graph to estimate the number of Native American Studies Majors there were in year five. A) 210 students B) 120 students C) 130 students D) 180 students Objective: (6.1) Use Mathematical Models

26) The line graph shows the cost of inflation. What cost $10,000 in 1,985 would cost the amount shown by the graph in subsequent years.

40 35 30 25 20 15 10

$38,521 $22,521

1,990

1,995

2,000

2,005

2,010

Below are two mathematical models for the data shown in the graph. In each formula, C represents the cost x years after 1,990 of what cost $10,000 in 1,985. Model 1: C = 798x + 22,521 Model 2: C = -x2 + 820x + 23,017 (i) Use the graph to estimate the cost in 2,005, to the nearest thousand dollars, of what cost $10,000 in 1,985. (ii) Use model 1 to determine the cost in 2,005. How well does this describe your estimate from part (i)? (iii) Use model 2 to determine the cost in 2,005. How well does this describe your estimate from part (i)? A) (i) about $32,000; (ii) about $33,693, reasonably well; (iii) about $34,272, reasonably well B) (i) about $33,000; (ii) about $34,491, reasonably well; (iii) about $33,452, reasonably well C) (i) about $34,000; (ii) about $34,491, reasonably well; (iii) about $35,092, reasonably well D) (i) about $35,000; (ii) about $35,289, reasonably well; (iii) about $35,912, reasonably well Objective: (6.1) Use Mathematical Models

27) The line graph shows the cost of inflation. What cost $5,000 in 1,980 would cost the amount shown by the graph in subsequent years.

35 30 25 20 15 10 5

$33,521 $17,521

1,985

1,990

1,995

2,000

2,005

Below are two mathematical models for the data shown in the graph. In each formula, C represents the cost x years after 1,985 of what cost $5,000 in 1,980. Model 1: C = 798x + 17,521 Model 2: C = -x2 + 820x + 18,017 Which model is a better description for the cost in 2,005 of what cost $5,000 in 1,980? A) Model 1 B) Model 2 Objective: (6.1) Use Mathematical Models

An algebraic expression is given. Use the expression to answer the following questions. a) How many terms are there in the algebraic expression? b) What is the numerical coefficient of the first term? c) What is the constant term? d) Does the algebraic expression contain like terms? If so, what are the like terms? 28) 2x A) a) 1 B) a) 1 C) a) 1 b) 2 b) 2 b) 1 c) 2x c) none c) none d) no d) no d) no

D) a) 2 b) 2 c) none d) no

Objective: (6.1) Understand the Vocabulary of Algebraic Expressions

29) 8x + 2 A) a) 2 b) 8 c) 2 d) yes, 8x and 2

B) a) 1 b) 8 c) 2 d) no

C) a) 2 b) 2 c) 8x d) no

D) a) 2 b) 8 c) 2 d) no

Objective: (6.1) Understand the Vocabulary of Algebraic Expressions

30) x + 3 + 6x A) a) 2 b) 1 c) 3 d) yes, x and 6x

B) a) 3 b) 1 c) 3 d) yes, x and 6x

C) a) 3 b) 1 c) 3 d) no

Objective: (6.1) Understand the Vocabulary of Algebraic Expressions

D) a) 3 b) 6 c) 3 d) yes, x and 6x

31) 5y + 1 + 4x A) a) 3 b) 5 c) 1 d) yes, 5y and 4x

B) a) 3 b) 5 c) 1 d) no

C) a) 3 b) 4 c) 1 d) no

D) a) 2 b) 5 c) 1 d) no

Objective: (6.1) Understand the Vocabulary of Algebraic Expressions

Simplify the algebraic expression. 32) x + 3x A) x

B) 8x

C) 8 + x

D) x

C) 9x

D) x

C) -6x

D) 6x

C) 10a

D) 5a + 5

Objective: (6.1) Simplify Algebraic Expressions

33) 6x + 3x A) 9x2

B) -3x

Objective: (6.1) Simplify Algebraic Expressions

34) 8x - 2x A) 10x

B) -10x

Objective: (6.1) Simplify Algebraic Expressions

35) 8a + 5 - 3a A) -5a + 5

B) 11a + 5

Objective: (6.1) Simplify Algebraic Expressions

36) 26x2 - 26x2 A) x2

B) -52x2

C) 0

D) cannot be simplified

Objective: (6.1) Simplify Algebraic Expressions

37) 6y + 1 - 2y + 8 A) 4y + 9

B) 4y - 7

C) 8y + 9

D) 13y

C) 3x - 6x + 4y + 6y

D) 7xy

C) -3x + 7y + 19

D) 12xy + 19

C) x + y

D) xy

C) 54x

D) 13x + 8

Objective: (6.1) Simplify Algebraic Expressions

38) 3x + 4y - 6x + 6y A) 10x - 3y

B) -3x + 10y

Objective: (6.1) Simplify Algebraic Expressions

39) 3x + 5y + 10 + 6x - 2y + 9 A) 9x + 3y + 19

B) 9x + 7y + 19

Objective: (6.1) Simplify Algebraic Expressions

40) (x + y) A) x + 3y

B) x - 3y

Objective: (6.1) Simplify Algebraic Expressions

41) 6(7x + 2) A) 42x + 12

B) 42x + 2

Objective: (6.1) Simplify Algebraic Expressions

42) -3(10x + 7) A) -30x - 21

B) -51x

C) 7x + 4

D) -30x + 7

C) 40y + 28

D) -40y - 70

C) 4y + 1

D) 4y + 23

C) -16x - 36

D) 16x + 48

C) 20x - 40

D) 20x - 6

C) 18x - 15

D) -42x

C) -12x + 34

D) 12x + 34

C) -7x - 17

D) 28x - 9

x + 32

D) x + 96

Objective: (6.1) Simplify Algebraic Expressions

43) -5(8y + 7) - 7 A) -40y

B) -40y - 42

Objective: (6.1) Simplify Algebraic Expressions

44) (8y + 12) - (4y - 11) A) 12y + 23

B) 4y - 23

Objective: (6.1) Simplify Algebraic Expressions

45) -6(2x - 7) - 4x + 6 A) -16x + 48

B) 8x + 48

Objective: (6.1) Simplify Algebraic Expressions

46) 8(3x - 4) - 4(x - 2) A) 20x - 24

B) -8x - 24

Objective: (6.1) Simplify Algebraic Expressions

47) -6(2x + 5) + 3(10x + 5) A) -4x - 1

B) 18x + 5

Objective: (6.1) Simplify Algebraic Expressions

48) -4(2x - 7) - 4x + 6 A) -12x - 22

B) 4x + 34

Objective: (6.1) Simplify Algebraic Expressions

49) 3 - 4[4 - (7x + 1)] A) -7x - 9

B) 28x - 17

Objective: (6.1) Simplify Algebraic Expressions

50) 3[3(3x + 4) - 4(2x - 5)] A) x - 24

B) x + 27

Objective: (6.1) Simplify Algebraic Expressions

51) 5[3x2 + 4(-9 - x)] A) 15x2 + 20x - 180

B) 15x2 - 4x - 36

C) 15x2 - 20x - 180

D) 15x2 - 5x - 180

C) -18x2 + 7

Objective: (6.1) Simplify Algebraic Expressions

52) [-3x2 + (-4x2 + 1)] + [ (10x2 - (6 + 6x2 )) + 7x2 ] A) 4x2 - 5 B) -4x2 + 7 Objective: (6.1) Simplify Algebraic Expressions

x2 + 5

Write the English phrase as an algebraic expression. Let x represent the number. Simplify the expression, if possible. 53) The sum of a number and 104 A) 104 + x B) 104 - x C) 104x D) 104 Objective: (6.1) Simplify Algebraic Expressions

54) A number decreased by 20 A) 20 - x

B) 20

C) x - 20

D) 20x

C) 6 - x

D) 6x

C) 7 - x

D) 7 + x

C) 3x - 9

D) 3 - 9x

C) 3x + 4

D) 4x + 3

C) x + 4

C) 40 - x

D) x + 40

C) 19 - x

D) x + 19

C) x - 25

Objective: (6.1) Simplify Algebraic Expressions

55) 6 times a number A) 6 + x

6 x

Objective: (6.1) Simplify Algebraic Expressions

56) The product of 7 and a number A) 7x

7 x

Objective: (6.1) Simplify Algebraic Expressions

57) 9 less than 3 times a number A) 9x - 3

B) 9 - 3x

Objective: (6.1) Simplify Algebraic Expressions

58) 4 more than 3 times a number A) 3(4 + x)

B) 7x

Objective: (6.1) Simplify Algebraic Expressions

59) 4 more than a number A) x - 4

B) 4x

x 4

Objective: (6.1) Simplify Algebraic Expressions

60) 40 less than a number 40 A) x

B) x - 40

Objective: (6.1) Simplify Algebraic Expressions

61) A number subtracted from 19 A) x - 19

x 19

Objective: (6.1) Simplify Algebraic Expressions

62) The quotient of a number and 25 25 A) B) 25x x Objective: (6.1) Simplify Algebraic Expressions

x 25

63) The quotient of 68 and a number A) 68 - x

B) 68x

x 68

68 x

Objective: (6.1) Simplify Algebraic Expressions

64) 6 times a number increased by 11 A) 6x - 11 B) 6 + 11x

C) 6x · 11

D) 6x + 11

C) 3 - 7x

C) 8[x(-3)]; -24x

D) 8(x) + 3; -8x + 3

Objective: (6.1) Simplify Algebraic Expressions

65) Three times a number decreased by 7 A) 3x + 7

B) 3x - 7

3x 7

Objective: (6.1) Simplify Algebraic Expressions

Simplify the algebraic expression. 66) 8 times the product of a number and negative 3 A) 8[x(3)]; 24x B) 8(x) + (-3); 8x - 3 Objective: (6.1) Simplify Algebraic Expressions

67) 18 decreased by 4 times the sum of 1 and a number A) 18 - [4(1 + x)]; 14 - 4x C) 18 - [-4(1 + x)]; 22 + 4x

B) 18 - [-4(1 + x)]; 22 - 4x D) 18 - [4(1 + x)]; 4x - 14

Objective: (6.1) Simplify Algebraic Expressions

Solve and check the equation. 68) x - 20 = -3 A) {-23}

B) {23}

C) {-17}

D) {17}

C) {5}

D) {8}

Objective: (6.2) Solve Linear Equations

69)

x =4 2

A) {6}

B) {2}

Objective: (6.2) Solve Linear Equations

70) x = -16 A) {-2}

B) {1}

C) {

}

D) {-24}

Objective: (6.2) Solve Linear Equations

71) 6x - 10 = 32 A) {36}

B) {40}

C) {15}

D) {7}

C) 3

Objective: (6.2) Solve Linear Equations

72)

y + 7 = + 4y A) - 3

1 3

Objective: (6.2) Solve Linear Equations

7 8

73) 5x - (3x - 1) = 2 1 A) 8

1 2

1 8

C) -

B) {19}

C) {-1}

D) {1}

17 5

C) {4}

D) {-4}

B) { }

C) {8}

D) {10}

C) {-8}

D) {3}

C) {3}

D) {-31}

C) {-0.385}

D) {2.59}

C) {19}

D) {41}

C) {8.54}

D) {18.08}

C) {15}

D) {30}

C) {1,680}

D) {4,200}

1 2

Objective: (6.2) Solve Linear Equations

74) 3(2y - 3) = 5(y + 2) A) {4}

Objective: (6.2) Solve Linear Equations

75) 6 - 10x = -34 17 A) 5

Objective: (6.2) Solve Linear Equations

76) 8(2x - 10) - 6 = 8(x - 3) + (2) A) { }

Objective: (6.2) Solve Linear Equations

77) 5(3x + 3) + 2(3x + 1) = 4x - 17 A) {-2}

B) {-4}

Objective: (6.2) Solve Linear Equations

78) -9x + 1.2 = -22.2 - 1.2x A) {2.7}

B) {2.6}

Objective: (6.2) Solve Linear Equations

79) 1.4x - 3.4 = 0.7x - 1.58 A) {2.6}

B) {2.574}

Objective: (6.2) Solve Linear Equations

80) 0.7(x - 11) = 21 A) {45.714}

B) {32}

Objective: (6.2) Solve Linear Equations

81) 0.04 = 0.5x - 9 A) {-17.92}

B) {4.52}

Objective: (6.2) Solve Linear Equations

82) 0.80x - 0.40(20 + x) = 0.20(20) A) {40}

B) {20}

Objective: (6.2) Solve Linear Equations

83) 0.09y + 0.14(6,000 - y) = 0.45y A) {420}

B) {5,040}

Objective: (6.2) Solve Linear Equations

84) 7x - 8 + {6x - [8(x + 4) + 6]} = 6(x + 7) A) - 88

B) - 72

24 5

88 15

Objective: (6.2) Solve Linear Equations

Provide an appropriate response. 85) Evaluate x 2 - x for the value of x satisfying 10(x - 5) + 25 = 10x - 5(10 - x). A) 6

B) 20

C) 30

D) -4

Objective: (6.2) Solve Linear Equations

Solve the problem. 86) In one state, speeding fines are determined by the formula F = 10(x - 60) + 50, where F is the cost, in dollars, of the fine if a person is caught driving x miles per hour. If the fine comes to $110, how fast was the person driving? A) 76 mph B) 64 mph C) 68 mph D) 66 mph Objective: (6.2) Solve Linear Equations

87) Forensic scientists use the lengths of certain bones to calculate the height of a person. When the femur (f), the bone from the knee to the hip socket is used, the following formula applies for men: h = 69.09 + 2.24f, where h is the height and f is the length of the femur. Find the height of a man with a femur measuring 59 centimeters. A) 4,208.47 cm B) 4.50 cm C) 128.09 cm D) 201.25 cm Objective: (6.2) Solve Linear Equations

88) There is a formula that gives a correspondence between women's shoe sizes in the United States and those in Italy. The formula is S = 2(x + 12), where S is the size in Italy and x is the size in the United States. What would be the US size for an Italian size of 32? A) size 8 B) size 76 C) size 4 D) size 2 Objective: (6.2) Solve Linear Equations

89) In a computer simulation, growth in human populations threatens the population of a fictitious species, the striated perch, in North American waters. The bar graph shows the population of the striated perch for several years. The data can be modeled by P = - 0.15t + 4.9, where P is the population of that species, in millions, after t years. Use the formula to determine, to the nearest year, in what year there will be no more striated perch.

A) year 35

B) year 45

C) year 43

Objective: (6.2) Solve Linear Equations

D) year 33

Solve and check the equation. Begin your work by rewriting the equation without fractions. x x 32 90) + = 3 5 15 A) {3}

B) {4}

15 8

32 7

C) {4}

28 5

C) {15}

D) {16}

C) 6

D) -

Objective: (6.2) Solve Linear Equations Containing Fractions

91)

7 x x - = 3 3 4

A) {7}

B) {-4}

Objective: (6.2) Solve Linear Equations Containing Fractions

92)

7y y -7= -3 15 5

A) {17}

B) {13}

Objective: (6.2) Solve Linear Equations Containing Fractions

93)

5x x 9 -x= 4 28 7

9 2

B) - 6

9 2

Objective: (6.2) Solve Linear Equations Containing Fractions

Provide an appropriate response. 94) Evaluate x 2 - (xy - y) for x satisfying A) 3,295

x x - 8 = and y satisfying -2y - 10 = 5y + 25. 5 3

C) -300

B) 3,305

D) -60, -5

Objective: (6.2) Solve Linear Equations Containing Fractions

Solve the problem. 95) To convert a Fahrenheit temperature to Celsius, one formula to use is F =

9 C + 32, where F is the Fahrenheit 5

temperature (in degrees) and C is the Celsius temperature. What is the Celsius temperature (to the nearest degree) when Fahrenheit temperature is 68°? A) 129°C B) 34°C C) 20°C D) 154°C Objective: (6.2) Solve Linear Equations Containing Fractions

96) When you buy an item on which sales tax is charged, the total cost is calculated by the formula: T = P +

S P, 100

where T is the total cost, P is the item's price, and S is the sales tax rate (as a percent). If you pay $18.02 for an item priced at $17, what was the tax rate? A) 3% B) 8% C) 6% D) 7% Objective: (6.2) Solve Linear Equations Containing Fractions

97) The formula p = 15 +

5d describes the pressure of sea water, p, in pounds per square foot, at a depth of d feet 11

below the surface. If a diver was subjected to a pressure of 24 pounds per square foot, to what depth did she descend? At what depth is the pressure 182 pounds per square foot? A) 365.4ft; 365.4 ft B) 19.8 ft; 367.4 ft C) 397.4 ft; 397.4 ft D) 21.8 ft; 369.4 ft Objective: (6.2) Solve Linear Equations Containing Fractions

Solve the proportion. x 8 = 98) 45 15 A)

675 8

B) {32}

8 3

D) {24}

Objective: (6.2) Solve Proportions

99)

1 x = 2 19

1 38

19 2

C) {38}

D) {19}

15 2

C) {15}

D) {6}

B) {-126}

C) -

B) {3}

C) {-4}

D) {4}

14 5

C) {28}

D) -

Objective: (6.2) Solve Proportions

100)

2 3 = 5 x

3 2

Objective: (6.2) Solve Proportions

101) -

6 18 = 7 x

A) -

108 7

7 18

D) {-21}

Objective: (6.2) Solve Proportions

102)

y+ 6 y+ 8 = 3 6

A) {-12} Objective: (6.2) Solve Proportions

103)

x-2 2 = 2 5

A) 7

Objective: (6.2) Solve Proportions

6 5

Use a proportion to solve the problem. 104) It takes Emma 22 minutes to type and spell check 10 pages of a manuscript. Find how long it takes her to type and spell check 55 pages. Round answers to the nearest whole number if necessary. A) 1,210 min B) 22 min C) 25 min D) 121 min Objective: (6.2) Solve Problems Using Proportions

105) The ratio of a quarterback's completed passes to attempted passes is 4:7. If he attempted 35 passes, find how many passes he completed. Round to the nearest whole number if necessary. A) 7 passes B) 20 passes C) 5 passes D) 61 passes Objective: (6.2) Solve Problems Using Proportions

106) To estimate the number of people in Springfield, population 10,000, who have a swimming pool in their backyard, 250 people were interviewed. Of those polled, 117 had a swimming pool. How many people in the city might one expect to have a swimming pool? (Round to the nearest whole number, if necessary.) A) 468 people B) 21,368 people C) 3 people D) 4,680 people Objective: (6.2) Solve Problems Using Proportions

107) In a random sampling from a survey concerning music listening habits, 100 out of 140 at-home mothers preferred easy listening to heavy metal. Taking all the data from the survey, 280 at-home mothers expressed a preference for easy listening over heavy metal. How many at-home mothers would you estimate took part in the survey? A) 401 mothers B) 387 mothers C) 392 mothers D) 382 mothers Objective: (6.2) Solve Problems Using Proportions

108) The ratio of a basketball player's completed free throws to attempted free throws is 3 to 4. If she completed 6 free throws, find how many free throws she attempted. Round to the nearest whole number if necessary. A) 5 free throws B) 3 free throws C) 2 free throws D) 8 free throws Objective: (6.2) Solve Problems Using Proportions

109) On an architect's blueprint, 1 inch corresponds to 9 feet. If an exterior wall is 51 feet long, find how long the blueprint measurement should be. Write answer as a mixed number if necessary. 1 2 13 in. A) 38 in. B) 5 in. C) 51 in. D) 1 4 3 17 Objective: (6.2) Solve Problems Using Proportions

110) It is recommended that there be at least 9.8 square feet of floor space in a classroom for every student in the class. Find the minimum floor space that 15 students require. Round to the nearest tenth if necessary. A) 65.3 ft2 B) 153.1 ft2 C) 9.8 ft2 D) 147 ft2 Objective: (6.2) Solve Problems Using Proportions

111) It is recommended that there be at least 15.05 square feet of ground space in a garden for every newly planted shrub. A garden is 34.4' by 17.5'. Find the maximum number of shrubs the garden can accommodate. A) 172 shrubs B) 13 shrubs C) 2 shrubs D) 40 shrubs Objective: (6.2) Solve Problems Using Proportions

112) It is recommended that there be at least 19 square feet of work space for every person in a conference room. A certain conference room is 12' by 11'. Find the maximum number of people the room can accommodate. A) 17 people B) 27 people C) 6 people D) 7 people Objective: (6.2) Solve Problems Using Proportions

113) A bag of fertilizer covers 1,500 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 210 feet by 40 feet. A) 5 bags B) 56 bags C) 6 bags D) 560 bags Objective: (6.2) Solve Problems Using Proportions

114) Yearly homeowner property taxes are figured at a rate of $1.35 tax for every $100 of home value. Find the property taxes on a condominium valued at $247,000. A) $3335.85 B) $333.45 C) $2471.35 D) $3334.50 Objective: (6.2) Solve Problems Using Proportions

115) Andy is driving at a speed of 95 miles per hour. How many miles has he traveled after 24 minutes? A) 69 mi B) 71 mi C) 41 mi D) 38 mi Objective: (6.2) Solve Problems Using Proportions

Indicate whether the equation has no solution or is true for all real numbers. If neither is the case, solve for the variable. 116) 12x - 3(3 + 4x) = -9 4 A) + B) 3 C)

3 4

D) {x|x is a real number}

Objective: (6.2) Identity Equations with No Solution or Infinitely Many Solutions

117) 20x - 4(3 + 5x) = 12 3 A) 4

B) -

3 4

D) +

C) {x|x is a real number}

Objective: (6.2) Identity Equations with No Solution or Infinitely Many Solutions

118) 4(2x + 3) - 2 = 18x + 10 - 10x B) +

A) {x|x is a real number} C)

5 2

D) - 2

Objective: (6.2) Identity Equations with No Solution or Infinitely Many Solutions

119) 5(x - 4) - 4 = -4x + 9x - 28 1 A) 2

C) +

7 6

D) {x|x is a real number}

Objective: (6.2) Identity Equations with No Solution or Infinitely Many Solutions

120)

x x -3= 7 7

A) {0}

B) +

C) {x|x is a real number}

21 2

Objective: (6.2) Identity Equations with No Solution or Infinitely Many Solutions

121)

1 1 1 (8x - 12) = 6 x +4 2 4 3

A) {x|x is a real number} C) {0}

B) 1 D) +

Objective: (6.2) Identity Equations with No Solution or Infinitely Many Solutions

Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. 122) A number decreased by 229 is equal to 469. Find the number. A) 240 B) 698 C) -240 D) -698 Objective: (6.3) Use Linear Equations to Solve Problems

123) A number increased by 289 is equal to 763. Find the number. A) -474 B) -1,052 C) 1,052

D) 474

Objective: (6.3) Use Linear Equations to Solve Problems

124) The quotient of a number and 3 is 5. Find the number. 5 A) B) 3

3 5

D) 15

Objective: (6.3) Use Linear Equations to Solve Problems

125) If 3 times a number is added to -7, the result is equal to 10 times the number. Find the number. A) 2 B) 1 C) -2 D) -1 Objective: (6.3) Use Linear Equations to Solve Problems

126) Seven times the difference of 5 and a number yields 56. Find the number. A) 21 B) -3 C) 3

D) -21

Objective: (6.3) Use Linear Equations to Solve Problems

127) Ten less than five times a number is the same as seven times the number. Find the number. 1 1 A) B) -5 C) 5 D) 5 5 Objective: (6.3) Use Linear Equations to Solve Problems

128) The graph shows the number of people in Country A without health insurance from year 0 through year 3.

36.3 32.2 28.1 24

In year 0, there were 24 million people in Country A without health insurance. This number has increased at an average rate of 4.1 million people per year. In what year will the number of people without health insurance in Country A exceed the number in year 3 by 8.2 million? A) year 6 B) year 4 C) year 5 D) year 7 Objective: (6.3) Use Linear Equations to Solve Problems

129) The graph shows the number of people in Country A without health insurance from year 0 through year 3.

37.9 33.6 29.3 25

In year 0, there were 25 million people in Country A without health insurance. This number has increased at an average rate of 4.3 million people per year. In what year will the number of people in Country A without health insurance first reach 100 million? A) year 18 B) year 20 C) year 17 D) year 19 Objective: (6.3) Use Linear Equations to Solve Problems

Solve the equation for y. 130) 5x + y = 15 15 - x A) y = 5

B) y = 5x + 15

C) y = 15 - 5x

Objective: (6.3) Solve a Formula for a Variable

D) y = 3 - x

131) 15x + 7y = 18 18 15 xA) y = 7 7

B) y = 15x - 18

C) y =

18 15 x+ 7 7

D) y = -

18 15 x+ 7 7

C) y =

1 x-4 7

D) y =

4 1 x7 7

C) y = 3x + 4

D) y =

x 3

Objective: (6.3) Solve a Formula for a Variable

132) x = 7y + 4 A) y = x -

4 7

B) y = 7x - 4

Objective: (6.3) Solve a Formula for a Variable

133) -4x + 12y = 0 A) y = 3x

B) y = -3x

Objective: (6.3) Solve a Formula for a Variable

Solve the formula for the specified variable. 134) S = 2πrh + 2πr2 for h A) h = S - r

B) h =

S -1 2πr

C) h =

S - 2πr2 2πr

D) h = 2π(S - r)

C) h =

3B V

D) h =

Objective: (6.3) Solve a Formula for a Variable

135) V =

1 Bh for h 3

A) h =

B 3V

B) h =

V 3B

3V B

Objective: (6.3) Solve a Formula for a Variable

136) d = rt for t r A) t = d

B) t =

d r

C) t = d - r

D) t = dr

Objective: (6.3) Solve a Formula for a Variable

137) P = 2L + 2W for L P - 2W A) L = 2

B) L = P - 2W

C) L =

P-W 2

D) L = P - W

C) a =

A - hb 2h

D) a =

Objective: (6.3) Solve a Formula for a Variable

138) A =

1 h(a + b) for a 2

A) a =

hb - 2A h

B) a =

2A - hb h

Objective: (6.3) Solve a Formula for a Variable

2Ab - h h

139) I = Prt for t P-1 A) t = Ir

B) t =

I Pr

C) t =

P- I 1+r

D) t = P - Ir

C) x =

d(a + b) c

D) x =

c d(a + b)

C) x =

c + 2d ad

D) x =

b(c + d) ad

Objective: (6.3) Solve a Formula for a Variable

Solve the proportion for x. c d = 140) a+b x A) x =

c(a + b) d

B) x =

d c(a + b)

Objective: (6.3) Solve a Formula for a Variable

141)

ax - b c + d = b d

A) x =

b(c + 2d) ad

B) x =

ab(c + d) d

Objective: (6.3) Solve a Formula for a Variable

Graph the set of real numbers on a number line. 142) {x|x > 3}

Objective: (6.4) Graph Subsets of Real Numbers on a Number Line

143) {x|x < 5}

Objective: (6.4) Graph Subsets of Real Numbers on a Number Line

144) {x|x L 0}

Objective: (6.4) Graph Subsets of Real Numbers on a Number Line

145) {x|x K -5}

Objective: (6.4) Graph Subsets of Real Numbers on a Number Line

146) {x|-3 K x K }

Objective: (6.4) Graph Subsets of Real Numbers on a Number Line

147) {x|-2 < x < 2}

Objective: (6.4) Graph Subsets of Real Numbers on a Number Line

148) {x|-2 K x < }

Objective: (6.4) Graph Subsets of Real Numbers on a Number Line

Solve the inequality and graph the solution set. 149) -x < 3

A) {x|x < -3}

B) {x|x > 3}

C) {x|x < 3}

D) {x|x > -3}

Objective: (6.4) Solve Linear Inequalities

150) x + 4 < -7

A) {x x K -11}

B) {x x > -11}

C) {x x L -11}

D) {x x < -11}

Objective: (6.4) Solve Linear Inequalities

151) 2x + 6 < 24

A) {x | x > 9}

B) {x | x K 9}

C) {x | x < 9}

D) {x | x L 9}

Objective: (6.4) Solve Linear Inequalities

152) -4x + 6 L -5x - 4

A) {x x > -4}

B) {x x L -10}

C) {x x < -4}

D) {x x K -10}

Objective: (6.4) Solve Linear Inequalities

153)

y >5 2

A) {y y K 10}

B) {y y < 10}

C) {y y > 10}

D) {y y L 10}

Objective: (6.4) Solve Linear Inequalities

154) -7 <

y 5

A) {y y K -35}

B) {y y < -35}

C) {y y > -35}

D) {y y L -35}

Objective: (6.4) Solve Linear Inequalities

155)

1 x L5 3

A) {x|x L 15}

B) {x|x K

1 } 15

C) {x|x <

3 } 5

D) {x|x >

5 } 3

Objective: (6.4) Solve Linear Inequalities

156) 5x K 85

A) {x x K 17}

B) {x x > 17}

C) {x x < 17}

D) {x x L 17}

Objective: (6.4) Solve Linear Inequalities

157) -2x L 10

A) {x | x K -5}

B) {x | x L 5}

C) {x | x L -5}

D) {x | x K 5}

Objective: (6.4) Solve Linear Inequalities

158) 10x - 2 L 5x + 18

A) {x|x L 4}

B) {x|x K -4}

C) {x|x > 5}

D) {x|x L 5}

Objective: (6.4) Solve Linear Inequalities

159) x + 6 + 7x < 8 + 8x + 8

A) {x x > 11}

B) {x x < 11}

C) {x x < 5}

D) {x x > 5}

Objective: (6.4) Solve Linear Inequalities

160) 18x - 6 > 3(5x - 9)

A) {x x < -7}

B) {x x K -7}

C) {x x > -7}

D) {x x L -7}

Objective: (6.4) Solve Linear Inequalities

161) 6x - 3 < 7(x + 2)

A) {x|x >

}

B) {x|x < -11}

C) {x|x > -17}

D) {x|x <

}

Objective: (6.4) Solve Linear Inequalities

162) 9 - 8(x - 1) < 3(2 - 4x)

A) {x|x < -

11 } 2

B) {x|x > -

11 } 2

C) {x|x < -

11 } 4

D) {x|x > -

11 } 4

Objective: (6.4) Solve Linear Inequalities

163) -4(3y + 8) < -16y - 16

A) {y y < 4}

B) {y y L 4}

C) {y y > 4}

D) {y y K 4}

Objective: (6.4) Solve Linear Inequalities

164) -9x - 24 K -3(2x + 17)

A) {x x < 9}

B) {x x L 9}

C) {x x K 9}

D) {x x > 9}

Objective: (6.4) Solve Linear Inequalities

165)

x 1 x - K +1 7 5 4

A) x|x L -

56 5

B) x|x < -

56 5

C) x|x > -

56 5

D) x|x K -

56 5

Objective: (6.4) Solve Linear Inequalities

166)

x x L5 + 18 3

A) {x|x K 18}

B) {x|x L 18}

C) {x|x L -18}

D) {x|x > 18}

Objective: (6.4) Solve Linear Inequalities

167)

3 7 - x<2 4 8

A) x|x > -

6 7

B) x|x > -

10 7

C) x|x <

10 7

D) x|x < -

10 7

Objective: (6.4) Solve Linear Inequalities

168)

x x L +3 2 8

A) {x|x > 8}

B) {x|x L -8}

C) {x|x K 8}

D) {x|x L 8}

Objective: (6.4) Solve Linear Inequalities

169) -1 K 2x + 7 < 5 A) x|1 < x < 4

B) x|- 4 K x < - 1

C) x|1 K x < 4

D) x|- 4 K x < - 1

Objective: (6.4) Solve Linear Inequalities

Write an inequality with x isolated on the left side that is equivalent to the given inequality. 170) Ax + By < C; Assume A > 0 C - By C - By By - C A) x > B) x < C) x > A A A

D) x <

By - C A

D) x K

C - By A

Objective: (6.4) Solve Linear Inequalities

171) Ax + By L C; Assume A < 0 By - C A) x K A

B) x L

By - C A

C) x L

C - By A

Objective: (6.4) Solve Linear Inequalities

Use set-builder notation to describe all real numbers satisfying the given conditions. 172) A number increased by 9 is no more than four times the number. A) {x|x + 9 < 4x} or x|x > 3 B) {x|x + 9 < 4x} or x|x < 3 C) {x|x + 9 L 4x} or x|x K 3 D) {x|x + 9 K 4x} or x|x L 3 Objective: (6.4) Solve Linear Inequalities

5x - 6 L 26 2

or x|x L

64 5

D) x|

5x + 6 L 26 2

or x|x L 8

Objective: (6.4) Solve Linear Inequalities

Solve the problem. 174) The table below ranks the eight best professors at State College measured by the percentage of students who gave them a rating of "excellent" on a survey. Let x represent the percentage of students who gave a professor an "excellent" rating. Write the name or names of the professors described by the inequality 75.4% K x < 85.3%. Professor % of "excellent" rating Wu 91.3% Levan 88.0 Kallman 87.6 Diaz 85.5 Murphy 85.3 O'Brien 80.5 Davis 77.9 Isley 75.4 A) Diaz, Murphy, O'Brien, Davis, and Isley C) O'Brien, Davis, and Isley

B) Murphy, O'Brien, Davis, and Isley D) Wu, Levan, Kallman, Diaz, and Murphy

Objective: (6.4) Solve Applied Problems Using Linear Inequalities

175) Let x represent the speed of a bicycle in mph. Translate the following sentence into an inequality: "The speed of the bicycle exceeds 13 mph." A) x L 13 B) x < 13 C) x > 13 D) x K 13 Objective: (6.4) Solve Applied Problems Using Linear Inequalities

176) Claire has received scores of 85, 88, 87, and 85 on her algebra tests. What is the minimum score she must receive on the fifth test to have an overall test score average of at least 88? A) 96 B) 95 C) 93 D) 94 Objective: (6.4) Solve Applied Problems Using Linear Inequalities

177) When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.50. After that, each additional minute or portion of a minute of that call costs $0.40. Use an inequality to find the maximum number of minutes one can call long distance for $5.70. A) at most 2 minutes B) at most 11 minutes C) at most 14 minutes D) at most 8 minutes Objective: (6.4) Solve Applied Problems Using Linear Inequalities

178) Mary has been put in charge of buying soft drinks and chips for a party. If the soft drinks total $30 and chips are $3.89 per bag, how many bags can Mary buy if she wants to spend at most $100? A) 26 B) 18 C) 17 D) 25 Objective: (6.4) Solve Applied Problems Using Linear Inequalities

Use FOIL to find the product. 179) (x + 11)(x + 4) A) x2 + 14x + 44

B) x2 + 15x + 14

C) x2 + 44x + 15

D) x2 + 15x + 44

C) 3x2 - 17x - 28

D) x2 - 17x - 18

C) -6x2 - 26x - 26

D) x2 - 26x - 26

Objective: (6.5) Multiply Binomials Using the FOIL Method

180) (3x + 4)(x - 7) A) x2 - 28x - 17

B) 3x2 - 18x - 28

Objective: (6.5) Multiply Binomials Using the FOIL Method

181) (-4x + 5)(-2x + 4) A) -6x2 - 26x + 20

B) x2 - 26x + 20

Objective: (6.5) Multiply Binomials Using the FOIL Method

Factor the trinomial, or state that the trinomial is prime. Check your factorization using FOIL multiplication. 182) x2 - x - 56 A) (x + 8)(x - 7)

B) (x + 7)(x - 8)

C) (x + 1)(x - 56)

D) prime

B) (x - 9)(x + 1)

C) (x + 9)(x - 2)

D) prime

B) (x + 2)(x - 1)

C) (x - 2)(x - 1)

D) prime

B) (x - 40)(x + 1)

C) (x + 5)(x - 8)

D) prime

Objective: (6.5) Factor Trinomials

183) x2 + 7x - 18 A) (x - 9)(x + 2) Objective: (6.5) Factor Trinomials

184) x2 + 1x - 2 A) (x - 2)(x + 1) Objective: (6.5) Factor Trinomials

185) x2 - x - 40 A) (x - 5)(x + 8) Objective: (6.5) Factor Trinomials

186) 11x2 + 122x + 11 A) (11x - 1)(x - 11)

B) (11x + 1)(x + 11)

C) (11x + 11)(x + 1)

D) prime

B) (20x + 3)(x + 2)

C) (4x - 3)(5x - 2)

D) prime

B) (x - 4)(8x - 4)

C) (4x + 4)(2x + 4)

D) (4x - 4)(2x - 4)

B) (3x + 5)(x - 4)

C) (3x + 4)(x - 5)

D) prime

C) {-2, 9}

D) {-9, 2}

C) 4, -1

C) {7, 8}

D) {1, 56}

C) {-6, 2}

D) {6, -2}

Objective: (6.5) Factor Trinomials

187) 20x2 + 23x + 6 A) (4x + 3)(5x + 2) Objective: (6.5) Factor Trinomials

188) 8x2 - 24x + 16 A) (2x - 4)(4x + 4) Objective: (6.5) Factor Trinomials

189) 3x2 + 9x - 20 A) (3x - 5)(x + 4) Objective: (6.5) Factor Trinomials

Solve the equation using the zero-product principle. 190) (x - 2)(x + 9) = 0 A) {2, 9} B) {-9, -2, 2, 9} Objective: (6.5) Solve Quadratic Equations by Factoring

191) (8x - 2)(x + 1) = 0 A) 4, 1

B) 4, 0

1 , -1 4

Objective: (6.5) Solve Quadratic Equations by Factoring

Solve the quadratic equation by factoring. 192) x2 - x = 56 A) {-7, 8}

B) {-7, -8}

Objective: (6.5) Solve Quadratic Equations by Factoring

193) x2 + 4x - 12 = 0 A) {-6, 1}

B) {6, 2}

Objective: (6.5) Solve Quadratic Equations by Factoring

194) 2x2 - 7x - 9 = 0 9 , -1 A) 2

2 ,1 9

2 , -1 9

2 ,0 9

5 ,3 2

D) 0,

Objective: (6.5) Solve Quadratic Equations by Factoring

195) x(5x + 13) = 6 13 A) 0, 5

2 , -3 5

Objective: (6.5) Solve Quadratic Equations by Factoring

13 5

196) x2 - 16 = 15x A) {-4, 4}

B) {-4, -4}

C) {1, -16}

D) {-1, 16}

Objective: (6.5) Solve Quadratic Equations by Factoring

197) 6x2 + 23x + 20 = 0 4 5 ,A) 3 2

4 5 , 3 2

C) -

2 1 ,3 4

D) -

4 5 ,3 2

Objective: (6.5) Solve Quadratic Equations by Factoring

198) 56x2 + 56x = 0 A) {0}

B) - 1, 0

C) - 1, 56

D) - 1

Objective: (6.5) Solve Quadratic Equations by Factoring

199) 19x2 = 5x 19 ,0 } A) 5

B) -

19 ,0 5

5 ,0 19

C) 2, 3

1 , -3 2

C) {0}

D) 0,

C) -

Objective: (6.5) Solve Quadratic Equations by Factoring

200) x(4x + 10) = 6 5 A) 0, 2

B) 0,

5 2

Objective: (6.5) Solve Quadratic Equations by Factoring

201) 3x(x - 4) = 8x 2 - 13x 1 A) - , 0 5

B) {0, 5}

1 5

Objective: (6.5) Solve Quadratic Equations by Factoring

202) 7 - 7x = (4x + 9)(x - 1) A) {-4, 1}

C) 1, -

B) {-1, 4}

9 4

D) 1

Objective: (6.5) Solve Quadratic Equations by Factoring

203) 4x(x - 8) = (3x + 6)(x - 8) A) {6}

B) { , }

C) {-6}

D) {-8, -6}

C) {7, 9}

D) {-1, 0}

Objective: (6.5) Solve Quadratic Equations by Factoring

204)

x2 16 x+1=0 63 63

1 1 , 7 9

B) {6, 10}

Objective: (6.5) Solve Quadratic Equations by Factoring

Solve the equation by using the quadratic formula. 205) x2 + 5x - 66 = 0 A) {-11, 1}

B) {-11, 6}

D) {11, -6}

C) {11, 6}

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

206) x2 + 7x + 4 = 0 -7 - 33 -7 + 33 , A) 2 2 C)

33 7 + ,

33 2

-7 - 65 -7 + 65 , 2 2

-7 - 33 -7 + 33 , 14 14

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

207) 6x2 + 6x + 1 = 0 -3 - 3 -3 + 3 , A) 6 6 C)

-3 - 15 -3 + 15 , 6 6

-3 - 3 -3 + 3 , 12 12

-6 - 3 -6 + 3 , 6 6

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

208) x2 = 2 - 9x A) {-0.5 - 89 , -0.5 + C) {4.5 + 89}

B) {-4.5 - 89 , -4.5 + 89} D) {-4.5 - 1 89 , -4.5 + 1 89}

89}

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

209) 3x2 + x - 6 = 0 -1 - 73 -1 + 73 , A) 2 2 C)

-1 - 73 1 + 73 , 6 6

73 1 + ,

73 6

-1 - 73 -1 + 73 , 6 6

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

210) x2 + 28x + 196 = 0 A) {14}

B) {14 , 0}

C) {-14, 14}

D) {-14}

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

211) x2 - 22x + 121 = 0 A) {11}

B) {-11}

C) {-11, 0}

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

212) x2 + 14x + 26 = 0 A) {7 + 23} C) {-14 + 26}

B) {7 - 26, 7 + 26} D) {-7 - 23, -7 + 23}

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

D) {-11, 11}

213) 3x2 - 5x - 8 = 0 3 ,1 A) 8

3 , -1 8

3 ,0 8

8 , -1 3

2 7

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

214)

z2 z 2 = + -5 7 -35

A) -

2 ,1 7

B) -

2 , -1 7

C) -1,

2 7

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

215)

19 x2 =0 +x+ 12 12

A) {-6 - 17, -6 + C) {6 + 17}

B) {-12 + 19} D) {6 - 19, 6 +

17}

19}

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

216) (x - 5)(x - 1) = 8 A) {3 - 2 3, 3 + 2 3} C) {-3 - 2 3, -3 + 2 3}

B) {3 - 2 3} D) {-3 - 2 3}

Objective: (6.5) Solve Quadratic Equations Using the Quadratic Formula

Write an equation and then solve. 217) The product of two consecutive integers is 342. Find two pairs of integers that have this product. A) 18 and 19 B) -18, -17 and 18, 19 C) -18, -19 and 18, 19 D) -18 and -19 Objective: (6.5) Solve Problems Modeled by Quadratic Equations

218) Consider any unknown real number such that its square increased by four times the number is 2. Find the exact value of the number(s). A) 2 - 2 or 2 + 2 B) 2 - 6 or 2 + 6 C) -2 - 6 or -2 + 6 D) -2 - 2 or -2 + 2 Objective: (6.5) Solve Problems Modeled by Quadratic Equations

Solve the problem. 219) The formula P = 0.67x2 - 0.048x + 2 models the approximate population P, in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 44.496 thousand fish? A) 2,006 B) 2,004 C) 2,007 D) 2,005 Objective: (6.5) Solve Problems Modeled by Quadratic Equations

220) A ball is thrown upward with an initial velocity of 14 meters per second from a cliff that is 70 meters high. The height of the ball is given by the quadratic equation h = -4.9t2 + 14t + 90 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 20 meters from the ground. Round your answer to the nearest tenth of a second. A) 5.9 sec B) 5.5 sec C) 5.6 sec D) 6.0 sec Objective: (6.5) Solve Problems Modeled by Quadratic Equations

221) The number of milligrams of a certain compound, C, produced in a chemical reaction with temperature at x, in degrees Celsius, can be modeled by the formula C = 0.013x2 - 1.19x + 28.24. According to the formula, at what temperatures is the chemical reaction expected to produce 5 milligrams of the compound? Use a calculator and round answers to the nearest milligram. A) 62 ° C and 27 ° C B) 63 ° C and 28 ° C C) 62 ° C and 29 ° C D) 64 ° C and 27 ° C Objective: (6.5) Solve Problems Modeled by Quadratic Equations

222) The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups.

The number of fatal vehicle crashes per 100 million miles, N, for drivers of age x can be modeled by the formula N = 0.012x2 - 1.18x + 31.27. Using the formula, what age group(s) are expected to be involved in 3 fatal crashes per 100 million miles driven? Use a calculator and round to the nearest year. How well does the formula model the trend in the actual data shown in the bar graph? A) 73 year-olds; The formula models the trend in the data reasonably well. B) 25 year-olds ; The formula does not accurately model the data for ages expected to be involved in 3 fatal crashes per 100 million miles driven. C) 32 year-olds and 67 year-olds; The formula does not accurately model the data for ages expected to be involved in 3 fatal crashes per 100 million miles driven. D) 41 year-olds and 57 year-olds; The formula models the trend in the data reasonably well. Objective: (6.5) Solve Problems Modeled by Quadratic Equations

223) The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups.

The number of fatal vehicle crashes per 100 million miles, N, for drivers of age x can be modeled by the formula N = 0.012x2 - 1.18x + 31.25. Using the formula, what age group(s) are expected to be involved in 11 fatal crashes per 100 million miles driven? Use a calculator and round to the nearest year. How well does the formula model the trend in the actual data shown in the bar graph? A) 41 year-olds; The formula does not accurately model the data for ages expected to be involved in 11 fatal crashes per 100 million miles driven. B) 9 year-olds and 90 year-olds; The formula models the trend in the data reasonably well. C) 22 year-olds and 76 year-olds; The formula does not accurately model the data for ages expected to be involved in 11 fatal crashes per 100 million miles driven. D) 57 year-olds; The formula models the trend in the data reasonably well. Objective: (6.5) Solve Problems Modeled by Quadratic Equations

Answer Key Testname: 06-BLITZER_TM8E_TEST_ITEM_FILE

1) D 2) C 3) D 4) B 5) A 6) D 7) D 8) C 9) A 10) D 11) A 12) D 13) A 14) A 15) D 16) B 17) D 18) A 19) A 20) B 21) B 22) A 23) D 24) B 25) D 26) C 27) A 28) B 29) D 30) B 31) B 32) B 33) C 34) D 35) D 36) C 37) A 38) B 39) A 40) A 41) A 42) A 43) B 44) D 45) A 46) A 47) C 48) C 49) D 50) D

51) C 52) A 53) A 54) C 55) D 56) A 57) C 58) C 59) C 60) B 61) C 62) D 63) D 64) D 65) B 66) C 67) A 68) D 69) D 70) A 71) D 72) B 73) D 74) B 75) C 76) C 77) A 78) C 79) A 80) D 81) D 82) D 83) C 84) A 85) B 86) D 87) D 88) C 89) D 90) B 91) C 92) C 93) B 94) A 95) C 96) C 97) B 98) D 99) B 100) B

101) D 102) C 103) B 104) D 105) B 106) D 107) C 108) D 109) B 110) D 111) D 112) C 113) C 114) D 115) D 116) D 117) D 118) A 119) C 120) B 121) D 122) B 123) D 124) D 125) D 126) B 127) B 128) C 129) A 130) C 131) D 132) D 133) D 134) C 135) D 136) B 137) A 138) B 139) B 140) C 141) A 142) A 143) C 144) D 145) A 146) D 147) A 148) C 149) D 150) D 40

151) C 152) B 153) C 154) C 155) A 156) A 157) A 158) A 159) C 160) C 161) C 162) C 163) A 164) B 165) A 166) B 167) B 168) D 169) D 170) B 171) D 172) D 173) D 174) C 175) C 176) B 177) B 178) C 179) D 180) C 181) B 182) B 183) C 184) B 185) D 186) B 187) A 188) D 189) D 190) D 191) D 192) A 193) C 194) A 195) B 196) D 197) D 198) B 199) D 200) D

Answer Key Testname: 06-BLITZER_TM8E_TEST_ITEM_FILE

201) D 202) A 203) B 204) C 205) B 206) A 207) A 208) B 209) D 210) D 211) A 212) D 213) D 214) C 215) A 216) A 217) C 218) C 219) D 220) B 221) B 222) D 223) C

Blitzer, Thinking Mathematically, 8e Chapter 7 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Plot the point in the rectangular coordinate system. 1) (3, 1)

Objective: (7.1) Plot Points in the Rectangular Coordinate System

2) (-2, 3)

Objective: (7.1) Plot Points in the Rectangular Coordinate System

3) (5, -6)

Objective: (7.1) Plot Points in the Rectangular Coordinate System

4) (-6, -5)

Objective: (7.1) Plot Points in the Rectangular Coordinate System

5) (0, )

Objective: (7.1) Plot Points in the Rectangular Coordinate System

6) (-5, 0)

Objective: (7.1) Plot Points in the Rectangular Coordinate System

7) - 6, -

1 2

Objective: (7.1) Plot Points in the Rectangular Coordinate System

8) (-2.5, 1.5)

Objective: (7.1) Plot Points in the Rectangular Coordinate System

Graph the equation. Select integers for x, -3 K x K 3.

9) y = 4x - 6

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

10) y =

1 x-2 3

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

11) y = x2 + 3

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

12) y = x3 + 1

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

13) y = x

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

14) y = x + 3

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

Write the English sentence as an equation in two variables. Then graph the equation.

15) The y-value is two less than twice the x-value.

A) y = 2x - 2

B) y = x + 2

C) y = x - 2

D) y = 2x + 2

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

16) The y-value is one increased by the square of the x-value.

A) y = 1 + x2

B) y = -1 + x2

C) y = 1 - x2

D) y = 1 + 2x

Objective: (7.1) Graph Equations in the Rectangular Coordinate System

Evaluate the function at the given values of the variable. 17) f(x) = x - 6 a. f(-7) b. f(-9) A) , B) -1, -3

C) -13, -15

Objective: (7.1) Use Function Notation

D) -42, -54

18) f(x) = 5x - 2 A) , -60

a. f(7)

b. f(-6) B)

, -28

, -32

D) -70, 60

, -12

D) 7, 7

Objective: (7.1) Use Function Notation

19) f(x) = x2 + 6 A) 6, 6

a. f(1)

b. f(-1) B) ,

Objective: (7.1) Use Function Notation

a. f(9) 20) f(x) = 6x2 + 5 A) 2,921, 329

b. f(3) B) 491, 59

C) 113, 41

D) 540, 180

C) 1,262, 1,735

D) 212, 223

C) g(1) = 1; f(g(1)) = -5

D) g(1) = 9; f(g(1)) = 83

Objective: (7.1) Use Function Notation

21) f(x) = 7x2 + 6x + 7 A) , -113

a. f(5)

b. f(-6) B) 14,700, 21,168

Objective: (7.1) Use Function Notation

Provide an appropriate response. 22) Let f(x) = x2 + x - 7 and g(x) = 5x + 4. Find g(1) and f(g(1)). A) g(1) = 5; f(g(1)) = 23

B) g(1) = 9; f(g(1)) = 79

Objective: (7.1) Use Function Notation

23) Let f and g be defined by the following table: x -2 -1 0 1 2

f(x) -5 -1 4 0 4

g(x) -1 -6 0 -4 1

Find f(-2) + f(2) + [g(-1)]2 - f(0) ÷ g(2) · g(1)

A) 39

B) 53

1 2

D) 3

Objective: (7.1) Use Function Notation

24) The function f(x) = 0.81x + 168.3 models the cholesterol level of an American woman as a function of her age, x, in years. Use the function to find f(52). A) 7,088.796 B) 210.42 C) 221.11 D) 126.18 Objective: (7.1) Use Function Notation

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate f(x) for the given values for x. Then use the ordered pairs (x, f(x)) from your table to graph the function. 25) f(x) = x2 - 2 x f(x) -2 -1 0 1 2

Objective: (7.1) Graph Functions

26) f(x) = x + 2 x f(x) -2 -1 0 1 2

Objective: (7.1) Graph Functions

27) f(x) = (x - 2)2 x f(x) 0 1 2 3 4

Objective: (7.1) Graph Functions

28) f(x) = x3 - 2 x f(x) -2 -1 0 1 2

Objective: (7.1) Graph Functions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the vertical line test to determine if y is a function of x. 29)

A) Not a function

B) Function

Objective: (7.1) Use the Vertical Line Test

30)

A) Function

B) Not a function

Objective: (7.1) Use the Vertical Line Test

31)

A) Not a function

B) Function

Objective: (7.1) Use the Vertical Line Test

32)

A) Not a function

B) Function

Objective: (7.1) Use the Vertical Line Test

33)

A) Not a function

B) Function

Objective: (7.1) Use the Vertical Line Test

34)

A) Function

B) Not a function

Objective: (7.1) Use the Vertical Line Test

The figure shows the percentage of the U.S. population, f(x), made up of teachers as a function of time, x, where x is the number of years after 1900. Use the graph to solve the problem.

35) Use the graph to estimate f(20). A) 1.5% B) 2%

C) 1%

D) 20%

Objective: (7.1) Obtain Information About a Function from Its Graph

36) In which year did the percentage of teachers in the U.S. reach a minimum? A) 1900 B) 1970 C) 1990 Objective: (7.1) Obtain Information About a Function from Its Graph

D) 2,000

Provide an appropriate response. 37) State University has seen an increase in the number of students majoring in Native American Studies. The graph below shows the number of students with this major for the past six years.

1,000 800 600 400 200

Use the graph to write six ordered pairs that represent the number of Native American Studies majors for the years shown. Is this relation a function? A) {(1, 100), (2, 200), (3, 400), (4, 650), (5, 900), (6, 1,050)}; yes B) {(1, 100), (2, 200), (3, 400), (4, 650), (5, 900), (6, 1,050)}; no C) {(100, 1), (200, 2), (400, 3), (650, 4), (900, 5), (1,050, 6)}; no D) {(100, 1), (200, 2), (400, 3), (650, 4), (900, 5), (1,050, 6)}; yes Objective: (7.1) Obtain Information About a Function from Its Graph

38) The monthly cost of a certain texting plan is given by the function C(n) = 0.06n + 9.95, where C(n) is in dollars and n is the number of texts sent in a month. Find and interpret C(200) Monthly Cost of Texting Plan

A) 12.00; it costs $12.00 to send 200 texts in a month using a certain texting plan. B) 21.95; it costs $21.95 to send 200 texts in a month using a certain texting plan. C) 20.95; it costs $20.95 to send 200 texts in a month using a certain texting plan. D) 29.95; it costs $29.95 to send 200 texts in a month using a certain texting plan. Objective: (7.1) Obtain Information About a Function from Its Graph

39) The function P(x) = 0.35x - 71 models the relationship between the number of pretzels x that a certain vendor sells and the profit the vendor makes. Find and interpret P(600). Profit Made on Pretzel Sales

A) 210; $600 is the profit the vendor makes from selling 210 pretzels. B) 600; $600 is the profit the vendor makes from selling 600 pretzels. C) 139; $139 is the profit the vendor makes from selling 600 pretzels. D) 529; $529 is the profit the vendor makes from selling 600 pretzels. Objective: (7.1) Obtain Information About a Function from Its Graph

40) A rocket is 37 feet from a satellite when it begins accelerating away from the satellite at a constant rate of 10 feet per second per second. The distance, in feet, between the rocket and the satellite is given by the function P(t) = 5t2 + 37, where t is the number of seconds since the rocket started accelerating. Find and interpret P(9). Distance Between Rocket and Satellite

A) 442; after 9 seconds, the distance between the rocket and the satellite is 442 feet. B) 82; after 82 seconds, the distance between the rocket and the satellite is 9 feet. C) 118; after 118 seconds, the distance between the rocket and the satellite is 9 feet. D) 405; after 9 seconds, the distance between the rocket and the satellite is 405 feet. Objective: (7.1) Obtain Information About a Function from Its Graph

41) The function W(g) = 0.56g2 - 0.01g + 10.7 models the average weight in ounces for a mouse who is fed g grams of a special food per day. Use the function to find and interpret W(15). Average Weight of Mouse Fed Special Food

A) 136.55; when a mouse is fed 15 grams of the special food per day, its average weight is 136.55 ounces. B) 18.95; the average amount of the special food that 15 mice should be fed is 18.95 ounces. C) 136.69; 15 mice gained an average of 136.69 ounces per day when fed the special food. D) 286.35; when a mouse is fed an average of 286.35 ounces of the special food per day, its weight will be at least 15 ounces. Objective: (7.1) Obtain Information About a Function from Its Graph

42) The cost, in millions of dollars, for a company to manufacture x thousand automobiles is given by the function C(x) = 3x2 - 12x + 28. Find the number of automobiles that must be produced to minimize cost. Cost to Manufacture Automobiles

A) 2 thousand automobiles C) 4 thousand automobiles

B) 6 thousand automobiles D) 16 thousand automobiles

Objective: (7.1) Obtain Information About a Function from Its Graph

43) The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = -0.004x2 + 2.8x - 350. Find the number of pretzels that must be sold to maximize profit. Profit Made on Pretzel Sales

A) 200 pretzels

B) 350 pretzels

C) 700 pretzels

D) 100 pretzels

Objective: (7.1) Obtain Information About a Function from Its Graph

44) The function f(x) = 0.0036x2 - 0.48x + 36.12 models the median, or average, age, y, at which U.S. men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.) Median Age at Which U.S. Men First Married

A) 1967, 52.1 years old

B) 1953, 36 years old

C) 1967, 20.1 years old

Objective: (7.1) Obtain Information About a Function from Its Graph

D) 1936, 52.1 years old

45) An electronics company kept comparative statistics on two products, A and B. For years 0 to 8, the total number of Product A ever sold (in thousands) is given by the function A(x) = 75x + 240, where x is the number of years since year 0. For that same period, the total number of Product B ever sold (in thousands) is given by the function B(x) = -30x + 434, where x is the number of years since year 0. Interpret A(1.8) and B(1.8). Total Number of Product A and Product B Ever Sold

A) Product B sold 1.8 times as many as Product A. B) When 375,000 of Product A had been sold, Product B had sold 1.8 times as many. C) At some point between year 0 and year 8, both products had sold 1,800 each. D) At about 1.8 years (to the nearest tenth) from year 0, both products had sold the same amount. Objective: (7.1) Obtain Information About a Function from Its Graph

Use the x- and y-intercepts to graph the linear equation. 46) x + 2y = 4

Objective: (7.2) Use Intercepts to Graph a Linear Equation

47) 2x - 10y = 4

Objective: (7.2) Use Intercepts to Graph a Linear Equation

48) x - 5y = -10

Objective: (7.2) Use Intercepts to Graph a Linear Equation

49) 3x = y - 5

Objective: (7.2) Use Intercepts to Graph a Linear Equation

50) y - x = -2

Objective: (7.2) Use Intercepts to Graph a Linear Equation

Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical. 51) (2, 5), (3, 3) 1 8 A) - 2, falls B) - , falls C) 2, rises D) , rises 5 2 Objective: (7.2) Calculate Slope

52) ( , -9), ( , ) 5 , falls A) 13

5 , rises 13

13 , rises 5

D) -

13 , falls 5

D) -

33 , falls 7

Objective: (7.2) Calculate Slope

53) (-7, -4), (-7, -8) 6 A) , rises 7

B) -

C) 0, is horizontal

2 , falls 7

D) undefined, is vertical

Objective: (7.2) Calculate Slope

54) (-7, ), (-5, ) 1 , falls 2

A) 0, is horizontal

B) -

C) 3, rises

D) undefined, is vertical

Objective: (7.2) Calculate Slope

55) (11, -17), (4, 16) 1 , falls A) 15

C) -

, rises

Objective: (7.2) Calculate Slope

7 , falls 33

56) (7, 2), (-4, 6) 11 , falls A) 4

B) -

4 , falls 11

C) -

1 , falls 2

D) - 2, falls

Objective: (7.2) Calculate Slope

57) ( , 3), (-2, 3) A) 1, rises

B) 12, rises

C) 2, rises

D) 0, is horizontal

Objective: (7.2) Calculate Slope

Find the missing value so that the line containing the two points will have the required slope. 2 58) (3, 5) and (x, 3); m = 3 A)

1 6

B) -6

C) 6

D) 9

C) 0

D) -7

B) 15

D) 9

C) -9

D) -7

Objective: (7.2) Calculate Slope

59) (x, ) and (-9, -5); m = A) -9 Objective: (7.2) Calculate Slope

60) (5, 15) and (9, y); m = -

13 4

A) 0 Objective: (7.2) Calculate Slope

61) (-9, y), (0, -7); m = -

7 9

A) 0 Objective: (7.2) Calculate Slope

Provide an appropriate response. 62) Find the slope of the line passing through the pair of points or state that the slope is undefined. Assume that all variables represent positive real numbers. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (a + b, -c) and (a, a - c)

A) m = 0; horizontal C) m =

B) undefined slope; vertical

a ; rises b

D) m = -

a ; falls b

Objective: (7.2) Calculate Slope

63) Give the slope and the y-intercept of the line whose equation is given. Assume that B J 0. Ax - By = C C A A) m = ; b = B B

B) m = -

C A ;b= B B

C) m = -

Objective: (7.2) Calculate Slope

C A ;b=B B

D) m =

C A ;b= B B

64) Use the figure to make the requested lists. y = m 3 x + b3 y = m 2 x + b2

y = m 1 x + b1

y = m 4 x + b4 (i) List the slopes m 1 , m 2 , m 3 , and m 4 in order of decreasing size. (ii) List the y-intercepts b1 , b2 , b3 , and b4 in order of decreasing size.

A) (i) m 2 , m1 , m 3 , m 4 ;

B) (i) m 3 , m1 , m 2 , m 4 ;

C) (i) m 4 , m1 , m 3 , m 2 ;

D) (i) m 1 , m2 , m 3 , m 4 ;

(ii) b3 , b2 , b1 , b4

(ii) b4 , b2 , b1 , b3

(ii) b3 , b1 , b2 , b4

(ii) b4 , b3 , b1 , b2

Objective: (7.2) Calculate Slope

Graph the linear function using the slope and y-intercept. 65) y = x - 4

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

66) y =

1 x+2 5

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

67) y = -

1 x+5 2

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

68) y =

3 x+3 4

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

69) y =

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. In the following problem: a. Put the equation in slope-intercept form. b. Identify the slope and y-intercept. c. Graph the line. 70) 3y + x = 0

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

71) 6y = 5x

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

72) 4x + y = 3

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

73) 5x + 6y = 30

Objective: (7.2) Use the Slope and y-Intercept to Graph a Line

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the horizontal or vertical line. 38

74) x = -4

Objective: (7.2) Graph Horizontal or Vertical Lines

75) y = -5

Objective: (7.2) Graph Horizontal or Vertical Lines

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The graph shows that the cost of the average college mathematics textbook has been rising steadily since 1990.

76) a. What is the y-intercept? b. What is the slope? c. What is the equation of this line, in slope-intercept form? d. Predict the cost of an average college mathematics textbook in 2023. Objective: (7.2) Interpret Slope as a Rate of Change

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the slope of the line and write the slope as a rate of change. Don't forget to attach the proper units. 77) The graph shows the total cost y (in dollars) of owning and operating a mini-van where x is the number of miles driven.

A) $3.17 per mile C) cannot be determined

B) $0.32 per mile D) $25.00 per mile

Objective: (7.2) Use Slope and y-intercept to Model Data

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 78) For a certain film, an actor received a fixed salary plus a percentage of the film's profits. The linear function y = 0.10x + 5 describes his salary, y, in millions of dollars, as a function of the film's profits, x, also in millions of dollars. Find the slope and y-intercept of this function. What do they represent? Objective: (7.2) Use Slope and y-intercept to Model Data

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 79) When a tow truck is called, the cost of the service is given by the linear function y = 3x + 80, where y is in dollars and x is the number of miles the car is towed. Find and interpret the slope and y-intercept of the linear equation. A) m = 80; The number of miles the car is towed increases 80 miles for every dollar spent on the service. b = 3; The tow truck will tow the car 3 miles for no cost. B) m = 3; The number of miles the car is towed increases 3 miles for every dollar spent on the service. b = 80; The tow truck will tow the car 80 miles for no cost. C) m = 80; The cost of the service increases $80 every mile the car is towed. b = 3; The cost of the service is $3 if the car is not towed. D) m = 3; The cost of the service increases $3 every mile the car is towed. b = 80; The cost of the service is $80 if the car is not towed. Objective: (7.2) Use Slope and y-intercept to Model Data

80) The monthly cost of a certain texting plan is given by the function y = 0.05x + 14.95, where y is in dollars and x is the number of texts sent in a month. Find and interpret the slope and y-intercept of the linear equation. A) m = 0.05; The cost of the texting plan increases $0.05 for every text sent. b = 14.95; The cost of the texting plan is $14.95 if no texts are sent for the month. B) m = 14.95; The number of texts sent in a month increases 14.95 for every dollar spent. b = 0.05; The number of texts that can be sent when x = 0 is 0.05. C) m = 0.05; The number of texts sent in a month increases 0.05 for every dollar spent. b = 14.95; The number of texts that can be sent when x = 0 is 14.95. D) m = 14.95; The cost of the texting plan increases $14.95 for every text sent. b = 0.05; The cost of the texting plan is $0.05 if no texts are sent for the month. Objective: (7.2) Use Slope and y-intercept to Model Data

81) The amount of water in a leaky bucket is given by the linear function y = 117 - 3x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation. A) m = 117; The amount of water in the bucket decreases 117 ounces every minute. b = 3; At x = 0, the amount of water in the bucket was 3 ounces. B) m = 117; The amount of water in the bucket increases 117 ounces every minute. b = 3; At x = 0, the amount of water in the bucket was 3 ounces. C) m = -3; The amount of water in the bucket decreases 3 ounces every minute. b = 117; At x = 0, the amount of water in the bucket was 117 ounces. D) m = 3; The amount of water in the bucket increases 3 ounces every minute. b = 117; At x = 0 the amount of water in the bucket was 117 ounces. Objective: (7.2) Use Slope and y-intercept to Model Data

82) The altitude above sea level of an airplane just after taking off from an airport on a high plateau is given by the linear function y = 300x + 3,065, where y is in feet and x is the time in minutes since take-off. Find and interpret the slope and y-intercept. A) m = 300; The minutes since take-off increases 300 for every foot of altitude. b = 3,065; The minutes that the plane takes to get to the altitude of the airport from sea level. B) m = 3,065; The altitude of the airplane increases 3,065 feet every minute. b = 3,065; The altitude of the airport where the airplane took-off is 300 feet above sea level. C) m = 300; The altitude of the airplane increases 300 feet every minute. b = 3,065; The altitude of the airport where the airplane took-off is 3,065 feet above sea level. D) m = 3,065; The minutes since take-off increases 3,065 for every foot of altitude. b = 300; The minutes that the plane takes to get to the altitude of the airport from sea level. Objective: (7.2) Use Slope and y-intercept to Model Data

83) The speed of a ball dropped from a tower is given by the linear function y = 32x where y is in feet per second and x is the number of seconds since the ball was dropped. Find and interpret the slope and y-intercept of the linear equation. A) m = 32; The speed of the ball is 32 feet per second. b = 0; When the ball is dropped at x = 0, the ball has fallen 0 feet. B) m = 32; The speed of the ball increases 32 feet per second every second. There is no y-intercept to interpret. C) m = 0; The speed of the ball does not increase as time passes. b = 32; At time x = 0, the ball has fallen 32 feet. D) m = 32; The speed of the ball increases 32 feet per second every second. b = 0; The speed of the ball was 0 the moment it was dropped. Objective: (7.2) Use Slope and y-intercept to Model Data

84) The following bar graph shows the average annual income for single mothers over several years.

The linear function I(t) = 775.8t + 24,269 can be used to model the average annual income for single mothers as a function of t, where t represents the number of years since year 0. Interpret the slope. A) Average annual income decreased at a rate of $775.80 per year. B) Income increased by $775.80 from year 0 to year 5. C) Average annual income increased at a rate of $24,269 per year. D) Average annual income increased at a rate of $775.80 per year. Objective: (7.2) Use Slope and y-intercept to Model Data

85) The gas mileage, m, of a compact car is a linear function of the speed, s, at which the car is driven, for 40 K s K 90. For example, from the graph we see that the gas mileage for the compact car is 45 miles per gallon if the car is driven at a speed of 40 mph.

1 The linear function M = - s + 65 relates gas mileage, M, to speed, s. Interpret the slope. 2

A) When the car is not moving, the gas mileage is 65 miles per gallon. B) Between speeds of 40 and 90 mph, gas mileage decreases at a rate of 0.5 miles per gallon for each 1 mph increase in speed. C) Between speeds of 40 and 90 mph, speed decreases at a rate of 0.5 miles per hour for each 1 mpg increase in gas mileage. D) Between speeds of 40 and 90 mph, gas mileage increases at a rate of 0.5 miles per gallon for each 1 mph increase in speed. Objective: (7.2) Use Slope and y-intercept to Model Data

86) A vendor has learned that, by pricing caramel apples at $1.75, sales will reach 58 caramel apples per day. Raising the price to $2.50 will cause the sales to fall to 25 caramel apples per day. Let y be the number of caramel apples the vendor sells at x dollars each. The linear equation y = -44x + 135 models the number of caramel apples sold per day when the price is x dollars each. Interpret the slope. A) The number of caramel apples sold decreases at a rate of 135 per $1 increase in the price per item. B) The price of caramel apples decreases at a rate of $44 per item sold. C) The number of caramel apples sold increases at a rate of 44 per $1 increase in the price per item. D) The number of caramel apples sold decreases at a rate of 44 per $1 increase in the price per item. Objective: (7.2) Use Slope and y-intercept to Model Data

87) An investment is worth $3,992 in year 0. By year 4 it has grown to $6,168. Let I be the value of the investment in year x. The linear equation I = 544x + 3,992 models the value, I, of the investment on year x. Interpret the slope. A) The value of the investment is increasing at a rate of $544 per year. B) The value of the investment increased by $544 between year 0 and year 4. C) The value of the investment is decreasing at a rate of $544 each year. D) The value of the investment is increasing at a rate of $3,992 per year. Objective: (7.2) Use Slope and y-intercept to Model Data

88) A truck rental company rents a moving truck one day by charging $29 plus $0.09 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven 220 miles? A) C(x) = 0.09x - 29; -$9.20 B) C(x) = 29x + 0.09; $6,380.09 C) C(x) = 0.09x + 29; $30.98 D) C(x) = 0.09x + 29; $48.80 Objective: (7.2) Use Slope and y-intercept to Model Data

89) Linda needs to have her car towed. Little Town Auto charges a flat fee of $65 plus $3 per mile towed. Write a function expressing Linda's towing cost, c, in terms of miles towed, x. Find the cost of having a car towed 11 miles. A) c(x) = 3x + 65; B) c(x) = 3x; C) c(x) = 3 + 65; D) c(x) = 3x + 65; $88 $33 $68 $98 Objective: (7.2) Use Slope and y-intercept to Model Data

90) The following bar graph shows the average annual income for single mothers.

i) Determine a linear function that can be used to estimate the average yearly income for single mothers from year 0 through year 5. Let t represent the year. ii) Using the function from part i, determine the average yearly income for single mothers in year 1. iii) Assuming this trend continues, determine the average yearly income for single mothers in year 11. iv) Assuming this trend continues, in which year will the average yearly income for single mothers reach $36,000? A) i) I(t) = 770.8t + 24,269 B) i) I(t) = 775.8t + 24,269 ii) $25,039.80 ii) $25,044.80 iii) $32,747.80 iii) $32,802.80 iv) year 16 iv) year 16 C) i) I(t) = 775.8t + 24,269 D) i) I(t) = 775.8t + 24,269 ii) $25,820.60 ii) $25,044.80 iii) $32,802.80 iii) $32,802.80 iv) year 16 iv) year 17 Objective: (7.2) Use Slope and y-intercept to Model Data

91) The gas mileage, m, of a compact car is a linear function of the speed, s, at which the car is driven, for 40 K s K 90. For example, from the graph we see that the gas mileage for the compact car is 45 miles per gallon if the car is driven at a speed of 40 mph.

i) Using the two points on the graph, determine the function m(s) that can be used to approximate the graph. ii) Using the function from part i, estimate the gas mileage if the compact car is traveling 72 mph. If necessary, round to the nearest tenth. 1 1 A) i) m(s) = - s + 65 B) i) m(s) = s + 65 2 2

ii) 29 miles per gallon 1 C) i) m(s) = - s + 65 2

ii) 29 miles per gallon 1 D) i) m(s) = s + 65 2

ii) 101 miles per gallon

Objective: (7.2) Use Slope and y-intercept to Model Data

92) The graph shows that the cost of the average college mathematics textbook has been rising steadily since 1990.

Predict the cost of an average college mathematics textbook in 2025. A) $164 B) $361 C) $256 Objective: (7.2) Use Slope and y-intercept to Model Data

Determine whether the given ordered pair is a solution to the system. 93) ( , ) 2x + y = 3x + 2y = A) no B) yes Objective: (7.3) Decide Whether an Ordered Pair is a Solution of a Linear System

94) (-1, -4) 2x + y = 4x + 2y = A) no

B) yes

Objective: (7.3) Decide Whether an Ordered Pair is a Solution of a Linear System

95) (5, 8) 3x - 6y = -33 9y = 7x + 38 A) Yes

B) No

Objective: (7.3) Decide Whether an Ordered Pair is a Solution of a Linear System

D) $486

Solve the system by graphing. Check the coordinates of the intersection point in both equations. 96) 4x + y = -6 5x + 4y = 9

A) {(x, y) A4x + y = -6}

B) +

C) {(3, 6)}

D) {(-3, 6)}

C) {(1, 3)}

D) {(3, 1)}

Objective: (7.3) Solve Linear Systems by Graphing

97) 4x + 5y = 17 -2x + 4y = -2

A) {(x,y) 4x + 5y = 17}

B) +

Objective: (7.3) Solve Linear Systems by Graphing

98) y = x + 1 y = -x + 5

A) {(-1, 5)}

B) {(3, - 2)}

C) {(1, -5)}

D) {(2, 3)}

C) {(1, -2)}

D) {(-1, -4)}

Objective: (7.3) Solve Linear Systems by Graphing

99) y = x - 3 y = 4x - 6

A) {(0, -2)}

B) {(0, 2)}

Objective: (7.3) Solve Linear Systems by Graphing

100) y = -x - 5 2y - 5x = 4

A) {(0, -5)}

C) {(-2, -3)}

B) {(0, 2)}

D) {(-1, -1)}

Objective: (7.3) Solve Linear Systems by Graphing

Solve the system by the substitution method. Be sure to check all proposed solutions. 101) x + 7y = -4x + 8y = A) {(-3, 0)} B) {(0, 3)} C) {(1, 2)}

D) +

Objective: (7.3) Solve Linear Systems by Substitution

102) x + 2y = -7x + 3y = -56 A) {( , 0)}

B) {( , )}

C) {(-8, -1)}

D) +

C) {(3, 21)}

D) {(-4, 28)}

C) {(5, 18)}

D) {(7, 22)}

Objective: (7.3) Solve Linear Systems by Substitution

103) x + y = 24 y = 5x A) {(4, 20)}

B) {(5, 19)}

Objective: (7.3) Solve Linear Systems by Substitution

104) x + 5y = 106 y = 2x + 8 A) {(6, 20)}

B) {(-6, -4)}

Objective: (7.3) Solve Linear Systems by Substitution

Solve the system by the addition method. Be sure to check all proposed solutions. 105) x + y = 9 x-y=7 A) {( , )} B) {( , )} C) {(-8, 2)}

D) +

Objective: (7.3) Solve Linear Systems by Addition

106) x - 5y = -21 4x - 5y = -9 A) {(-5, 4)}

B) {( , )}

C) {( , )}

Objective: (7.3) Solve Linear Systems by Addition

D) +

107) x + 7y = -2x + 6y = A) {(-3, 6)}

B) {( , )}

C) {( , )}

D) +

Objective: (7.3) Solve Linear Systems by Addition

108) 3x = 7y + 5 -4x + 8y = 4 A) {(-8, -

7 )} 2

C) {(8,

B) {(5, 8)}

9 )} 2

D) {(-17, -8)}

Objective: (7.3) Solve Linear Systems by Addition

Solve by the method of your choice. Identify whether the system has no solution or infinitely many solutions, using set notation to express the solution set. 109) 2x + y = 8 y = 6 - 2x A) {(5, -2)} B) {(0, 8)} C) {(x, y) 2x + y = 8} D) + Objective: (7.3) Identify Systems That Do Not Have Exactly One Ordered-Pair Solution

110) 8x + y = 23 39 - 7 = 4y A) {(x, y) 8x + y = 23}

B) +

C) {1.875, 8}

D) {(14, 15)}

Objective: (7.3) Identify Systems That Do Not Have Exactly One Ordered-Pair Solution

111) 4x + y = 18 16x + 4y = 72 A) +

B) {(5, -2)}

C) {(x, y) 4x + y = 18}

Objective: (7.3) Identify Systems That Do Not Have Exactly One Ordered-Pair Solution

D) {(0, 18)}

Provide an appropriate response. 112) Use the graphs of the linear functions to solve the problem. Write the linear system whose solution set is

9 5 , 2 2

Express each equation in the system in slope-intercept form.

L1: x + 3y = 12 L2: x - 3y = -3 L3: x - y = 4

A) y = x + 4 1 y= x- 1 3

B) y = -

1 x+4 3

C) y = x - 4 1 y= x+ 1 3

y=x- 4

D) y = y=

1 x+4 3

1 x+1 3

Objective: (7.3) Solve Problems Using Systems Of Linear Equations

113) Solve the system for x and y, expressing either value in terms of a or b, if necessary. Assume that a J 0 and b J 0. -18ax + by = 1 -12ax + 3by = 45 1 17 1 19 1 17 1 19 , , A) - , B) C) D) - , a b a b a b a b Objective: (7.3) Solve Problems Using Systems Of Linear Equations

114) For the linear function f(x) = mx + b, f(9) = 8 and f(-27) = 20. Find m and b. 1 5 5 A) m = ; b = 10 B) m = ; b = 6 C) m = ; b = 3 3 9 9 Objective: (7.3) Solve Problems Using Systems Of Linear Equations

D) m = -

1 ; b = 11 3

115) The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells flat-screen TVs. Use the formulas shown to find R(300) - C(300). Describe what this means for the company.

A) 19,500; When the company produces and sells 300 flat-screen TVs, the profit is $19,500. B) -4,500; When the company produces and sells 300 flat-screen TVs, the loss is $4,500. C) 10,500; When the company produces and sells 300 flat-screen TVs, the profit is $10,500. D) -1,500; When the company produces and sells 300 flat-screen TVs, the loss is $1,500. Objective: (7.3) Solve Problems Using Systems Of Linear Equations

Let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. 116) One number is 4 less than a second number. Twice the second number is 1 less than 3 times the first. Find the two numbers. A) 10 and 14 B) -13 and -9 C) 9 and 13 D) 8 and 12 Objective: (7.3) Solve Problems Using Systems Of Linear Equations

117) The sum of five times a first number and eight times a second number is 56. If the second number is subtracted from twice the first number, the result is 14. Find the numbers. A) 10 and 1 B) 35 and 8 C) 8 and 2 D) 40 and 16 Objective: (7.3) Solve Problems Using Systems Of Linear Equations

118) Two numbers total 4, and their difference is 16. Find the two numbers. A) 3 and 1 B) 4 and 2 C) 2 and - 14

D) 10 and - 6

Objective: (7.3) Solve Problems Using Systems Of Linear Equations

119) One number is four more than a second number. Two times the first number is 12 more than four times the second number. A) 2 and - 2 B) 1 and - 3 C) 3 and - 1 D) - 10 and - 14 Objective: (7.3) Solve Problems Using Systems Of Linear Equations

120) The sum of two numbers is 20. If one number is subtracted from the other, their difference is 7. Find the numbers. A) 10.5 and 9.5 B) 13.5 and 6.5 C) 14.5 and 5.5 D) 12.5 and 7.5 Objective: (7.3) Solve Problems Using Systems Of Linear Equations

Solve the problem. 121) A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A charges $120 for the truck and $55 per hour for the movers. Company B charges $110 for the truck and $65 per hour for the movers. Create a cost equation for each company where y is the total cost and x is the number of hours of labor. Write a system of equations. A) 55y = 120x B) y = 55x + 120 C) 55y = x + 120 D) y = 120x + 55 65y = 110x y = 65x + 110 65y = x + 110 y = 110x + 65 Objective: (7.3) Solve Problems Using Systems Of Linear Equations

122) At Rhonda's diner, three loaded baked potatoes and four cheeseburgers provide 3,860 calories. One loaded baked potato and three cheeseburgers provide 2,170 calories. Find the calorie content of each item. A) A loaded baked potato has 590 calories, and a cheeseburger has 520 calories. B) A loaded baked potato has 560 calories, and a cheeseburger has 550 calories. C) A loaded baked potato has 620 calories, and a cheeseburger has 490 calories. D) A loaded baked potato has 580 calories, and a cheeseburger has 530 calories. Objective: (7.3) Solve Problems Using Systems Of Linear Equations

123) Devon purchased tickets to an air show for 4 adults and 2 children. The total cost was $110. The cost of a child's ticket was $5 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket. A) adult's ticket: $22; child's ticket: $17 B) adult's ticket: $19; child's ticket: $14 C) adult's ticket: $21; child's ticket: $16 D) adult's ticket: $20; child's ticket: $15 Objective: (7.3) Solve Problems Using Systems Of Linear Equations

124) Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 2 times as many dimes as nickels, and the value of the dimes is $1.35 more than the value of the nickels. How many nickels and dimes does Jamil have? A) 8 nickels and 16 dimes B) 9 nickels and 18 dimes C) 18 nickels and 9 dimes D) 10 nickels and 20 dimes Objective: (7.3) Solve Problems Using Systems Of Linear Equations

125) On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $6 each and a number of necklaces at $8 each. She wrote a check for $900 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase? A) 30 bracelets and 90 necklaces B) 25 bracelets and 95 necklaces C) 35 bracelets and 85 necklaces D) 40 bracelets and 80 necklaces Objective: (7.3) Solve Problems Using Systems Of Linear Equations

126) Julie and Eric row their boat (at a constant speed) 48 miles downstream for 6 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 8 hours. Find the rate of the current. A) 7 mph B) 2 mph C) 0.5 mph D) 1 mph Objective: (7.3) Solve Problems Using Systems Of Linear Equations

127) A barge takes 3 hours to move (at a constant rate) downstream for 27 miles, helped by a current of 3 miles per hour. If the barge's engines are set at the same pace, find the time of its return trip against the current. A) 6 hr B) 3 hr C) 54 hr D) 9 hr Objective: (7.3) Solve Problems Using Systems Of Linear Equations

128) Jimmy is a partner in an Internet-based coffee supplier.The company offers gourmet coffee beans for $13 per pound and regular coffee beans for $4 per pound. Jimmy is creating a medium-price product that will sell for $6 per pound.The first thing to go into the mixing bin was 18 pounds of the gourmet beans. How many pounds of the less expensive regular beans should be added? A) 65 lb B) 63 lb C) 64 lb D) 62 lb Objective: (7.3) Solve Problems Using Systems Of Linear Equations

129) Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 12 feet more than 4 times the width. He needs 84 feet of fencing to do the job. Find the length and width of the garden. 3 2 A) length: 36 ft; width: 6 ft B) length: 69 ft; width: 14 ft 5 5 C) length: 32 ft; width: 5 ft

D) length: 40 ft; width: 7 ft

Objective: (7.3) Solve Problems Using Systems Of Linear Equations

130) Northwest Molded molds plastic handles which cost $0.40 per handle to mold. The fixed cost to run the molding machine is $4,314 per week. If the company sells the handles for $2.40 each, how many handles must be molded and sold weekly to break even? A) 1,540 handles B) 2,157 handles C) 10,785 handles D) 1,438 handles Objective: (7.3) Solve Problems Using Systems Of Linear Equations

131) A lumber yard has fixed costs of $6,302.80 per day and variable costs of $0.14 per board-foot produced. Lumber sells for $1.54 per board-foot. How many board-feet must be produced and sold daily to break even? A) 3,751 board-feet B) 3,001 board-feet C) 45,020 board-feet D) 4,502 board-feet Objective: (7.3) Solve Problems Using Systems Of Linear Equations

132) Sybil is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $190 for materials and equipment rental plus $65 per hour for labor. Company B gave and estimate of $310 for materials and equipment rental plus $50 per hour for labor. Create a cost equation for each company where y is the total cost of the landscaping and x is the number of hours of labor. Determine how many hours of labor will be required for the two companies to cost the same. A) 11 hr B) 12 hr C) 8 hr D) 7 hr Objective: (7.3) Solve Problems Using Systems Of Linear Equations

133) Sue wants to plan a meal with 92 grams of fat and 2,230 calories. If hot dogs have 13 grams of fat and 145 calories each and if baked beans have 8 grams of fat and 330 calories per half-cup serving, how many hot dogs and servings of beans should she use? A) 8 hot dogs and 13 half-cup servings of baked beans B) 4 hot dogs and 5 half-cup servings of baked beans C) 13 hot dogs and 8 half-cup servings of baked beans D) 5 hot dogs and 4 half-cup servings of baked beans Objective: (7.3) Solve Problems Using Systems Of Linear Equations

134) A mother is choosing which baby foods to serve her infant. A jar of meat has 4 g of protein and 32 calories. A jar of vegetables has 2 g of protein and 16 calories. How much of each will she need to serve to get 6 g of protein and 106 calories? A) There is no such combination. B) 1.5 jars of meat and 2 jars of vegetables C) There are infinitely many such combinations. D) 2 jars of meat and 1.5 jars of vegetables Objective: (7.3) Solve Problems Using Systems Of Linear Equations

135) A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 7 slices of pizza and 5 soft drinks for $36.18. The second group bought 5 slices of pizza and 4 soft drinks for $26.64. How much does one slice of pizza cost? A) $3.34 per slice of pizza B) $2.36 per slice of pizza C) $1.86 per slice of pizza D) $3.84 per slice of pizza Objective: (7.3) Solve Problems Using Systems Of Linear Equations

136) Andrea Stinson scored 35 points in a recent basketball game without making any 3-point shots. She scored 23 times, making several free throws worth 1 point each and several field goals worth two points each. How many free throws did she make? How many 2-point field goals did she make? A) 9 free throws, 14 field goals B) 12 free throws, 11 field goals C) 13 free throws, 11 field goals D) 11 free throws, 12 field goals Objective: (7.3) Solve Problems Using Systems Of Linear Equations

137) Julio has found that his new car gets 39 miles per gallon on the highway and 32 miles per gallon in the city. He recently drove 426 miles on 12 gallons of gasoline. How many miles did he drive on the highway? How many miles did he drive in the city? A) 204 miles on the highway, 222 miles in the city B) 234 miles on the highway, 192 miles in the city C) 192 miles on the highway, 234 miles in the city D) 222 miles on the highway, 204 miles in the city Objective: (7.3) Solve Problems Using Systems Of Linear Equations

138) A textile company has specific dyeing and drying times for its different cloths. A roll of Cloth A requires 75 minutes of dyeing time and 50 minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing time and 25 minutes of drying time. The production division allocates 2,900 minutes of dyeing time and 1,700 minutes of drying time for the week. How many rolls of each cloth can be dyed and dried? A) 24 rolls of Cloth A, 20 rolls of Cloth B B) 29 rolls of Cloth A, 27 rolls of Cloth B C) 14 rolls of Cloth A, 37 rolls of Cloth B D) 9 rolls of Cloth A, 31 rolls of Cloth B Objective: (7.3) Solve Problems Using Systems Of Linear Equations

Graph the linear inequality. 139) x + y K 4

Objective: (7.4) Graph a Linear Inequality in Two Variables

140) 2x + 5y K 10

Objective: (7.4) Graph a Linear Inequality in Two Variables

141) x > -8

Objective: (7.4) Graph a Linear Inequality in Two Variables

142) y K -8

Objective: (7.4) Graph a Linear Inequality in Two Variables

143) y >

1 x 6

Objective: (7.4) Graph a Linear Inequality in Two Variables

144) y K 3x - 4

Objective: (7.4) Graph a Linear Inequality in Two Variables

145) y < -

1 x 2

Objective: (7.4) Graph a Linear Inequality in Two Variables

Write the sentence as an inequality in two variables. Then graph the inequality. 146) The y-variable is at least 1 more than the product of 4 and the x-variable.

A) y < 4x + 1

B) y K 4x + 1

C) y > 4x + 1

D) y L 4x + 1

Objective: (7.4) Graph a Linear Inequality in Two Variables

147) The y-variable is at most 4 less than the product of -3 and the x-variable.

A) y K -3x - 4

B) y L -3x - 4

C) y K -3x + 4

D) y < -3x - 4

Objective: (7.4) Graph a Linear Inequality in Two Variables

Solve the problem. 148) A boat has a capacity of 2,000 pounds. If a passenger averages 160 pounds, and a piece of cargo averages 50 pounds, write an inequality that describes when x passengers and y pieces of cargo will cause the boat to be overloaded. Graph the inequality. Because x and y must be positive, limit the graph to quadrant I only.

A) 160x + 50y L 2,000

B) 160x + 50y > 2,000

C) 160x + 50y < 2,000

D) 160x + 50y K 2,000

Objective: (7.4) Graph a Linear Inequality in Two Variables

149) Yvette has up to $5,000 to invest and has chosen to put her money into telecommunications and pharmaceuticals. The telecommunications investment is to be no more than 3 times the pharmaceuticals investment. Write a system of inequalities to describe the situation. Let x = amount to be invested in telecommunications and y = amount to be invested in pharmaceuticals. A) x + y = 5,000 B) x + y K 5,000 C) x + y = 5,000 D) x + y K 5,000 y L 3x 3x K y x K 3y x K 3y x L0 x L0 x L0 x L0 yL0 yL0 yL0 yL0 Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

150) Marcus is planting a section of garden with tomatoes and cucumbers. The available area of the section is 120 square feet. He wants the area planted with tomatoes to be more than 20% of the area planted with cucumbers. Write a system of inequalities to describe the situation. Let x = amount to be planted in tomatoes and y = amount to be planted in cucumbers. A) x + y = 120 B) x + y K 120 C) x + y K 120 D) x + y K 120 x L 0.20y x < 0.20y x > 20y x > 0.20y x L0 x L0 x L0 x L0 yL0 yL0 yL0 yL0 Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

151) Benjamin never has more than 18 hours free during the week. He is trying to make a weekly plan for dividing his free time between reading and working out. He wants to spend at least 6 hours per week reading. Write a system of inequalities to describe the situation. Let x = amount of time for reading and y = amount of time for working out. A) x + y K 18 B) x + y K 18 C) x + y K 18 D) x + y K 18 x L 6y x K 6y x L6 y L6 x L0 x L0 yL0 x L0 yL0 yL0 Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

152) Mrs. White wants to crochet beach hats and baby afghans for a church fund-raising bazaar. She needs 5 hours to make a hat and 2 hours to make an afghan and she has 10 hours available. Thus, 5x + 2y K 10, where x is the number of hats and y is the number of afghans. Can she make 9 hats and 3 afghans in the time allowed? A) No B) Yes Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

153) An office manager needs to buy new filing cabinets. Cabinet A takes up 8 square feet of floor space. Cabinet B takes up 9 square feet of floor space. The office has room for no more than 72 square feet of cabinets. Thus, 8x + 9y K 72, where x is the number of A cabinets and y is the number of B cabinets. Does the office have enough floor space for 10 A cabinets and 9 B cabinets? A) No B) Yes Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

154) The equation that represents the proper traffic control and emergency vehicle response availability in a small city is 2P + 3F K 23, where P is the number of police cars on active duty and F is the number of fire trucks that have left the firehouse in response to a call. In order to comply with staffing limitations, the equation 4P + 2F K 34 is appropriate. The number of police cars on active duty and the number of fire trucks that have left the firehouse in response to a call cannot be negative, so P L 0 and F L0. Graph the regions satisfying all the availability and staffing requirements, using the horizontal axis for P and the vertical axis for F. If 5 police cars are on active duty and 5 fire trucks have left the firehouse in response to a call, are all of the requirements satisfied?

; No

; Yes

; No

Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

155) A bakery plans to market a mixed assortment of its two most popular cookies: Chocolate Chip and Toffee Chunk. Their marketing analyst proposes that the new assortment be constrained by the inequality 3C + 4T K 31, where C is the number of Chocolate Chip cookies and T is the number of Toffee Chunk cookies. Their sales analyst suggests in order to offer a reasonably priced product the assortment should be constrained by the inequality 5C + 2T K 33. The number of each type of cookie cannot be negative, so C L 0 and T L 0. Graph the region satisfying all the requirements for the assortment using C as the horizontal axis and T as the vertical axis. Does the combination of 5 Chocolate Chip cookies and 4 Toffee Chunk cookies satisfy all of the requirements?

; No

; Yes

; No

Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 156) Charlene baby-sits for $10 per hour. She also works as a tutor for $12 per hour. Because of school, her parents only allow her to work 13 hours per week. How many hours can Charlene tutor and baby-sit and still make at least $75 per week? (a) Write a system of inequalities for this situation. (b) Graph the solution set.

Objective: (7.4) Use Mathematical Models Involving Linear Inequalities

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the system of inequalities. 69

157) x + 2y K 2 x + y L0

Objective: (7.4) Graph a System of Linear Inequalities

158) x - 2y K 2 x + y K0

Objective: (7.4) Graph a System of Linear Inequalities

159) x + 2y L 2 x - y K0

Objective: (7.4) Graph a System of Linear Inequalities

160) y > -5 x L -3

Objective: (7.4) Graph a System of Linear Inequalities

161) y L 3x - 3 x + y K3

Objective: (7.4) Graph a System of Linear Inequalities

162) y K 3x - 4 x + y L3

Objective: (7.4) Graph a System of Linear Inequalities

163) x + 2y > -4 y K2

Objective: (7.4) Graph a System of Linear Inequalities

164) 5x + 10y K 10 2x + y K 6

Objective: (7.4) Graph a System of Linear Inequalities

Write the sentences as a system of inequalities in two variables. Then graph the system.

165) The sum of the x-variable and the y-variable is at most -9. The y-variable added to the product of 4 and the x-variable does not exceed 16.

A) x + y L -9 4x + y L 16

B) x + y K -9 x + 4y K 16

C) x + y > -9 x + 4y > 16

D) x + y K -9 4x + y K 16

Objective: (7.4) Graph a System of Linear Inequalities

166) The sum of the x-variable and the y-variable is at least 4. The x-variable added to the product of 2 and the y-variable does not exceed -6.

A) x + y L 4 2x + y L -6

B) x + y K 4 x + 2y K -6

C) x + y L 4 x + 2y K -6

D) x + y K 4 2x + y K -6

Objective: (7.4) Graph a System of Linear Inequalities

Find the value of the objective function at each corner of the graphed region. Use this information to answer the question.

167) Objective Function z = x + 7y What is the maximum value of the objective function? A) 37 B) 30

C) 24

D) 18

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

168) Objective Function z = -x - 8y What is the maximum value of the objective function? A) -34 B) -42

C) -27

D) -20

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

169) Objective Function z = 7x + 8y What is the minimum value of the objective function? A) 96 B) 45

C) 0

D) 44

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

Find the value of the objective function at each corner of the graphed region. Use this information to answer the question. 170)

Objective Function z = 2x + y What is the maximum value of the objective function? A) 18 B) 1

C) 23

D) 28

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

171)

Objective Function z = x + 4y What is the maximum value of the objective function? A) 46 B) 50

C) 60

D) 38

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

172)

Objective Function z = x - 4y What is the minimum value of the objective function? A) -29 B) -50

C) -9

D) -38

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

173)

Objective Function z = 4x + 3y What is the maximum value of the objective function? A) 13 B) 29

C) 100

D) 27

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

174)

Objective Function z = 5x + 3y What is the minimum value of the objective function? A) 14 B) 30

C) 18

D) 0

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

Find the value of the objective function at each corner of the graphed region. What is the maximum value of the objective function? What is the minimum value of the objective function? 175) Objective Function z = 2x + 9y

A) maximum value: 85; minimum value: 64 C) maximum value: 85; minimum value: 11

B) maximum value: 30; minimum value: 11 D) maximum value: 64; minimum value: 30

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

176) Objective Function z = 70x + 80y

A) maximum value: 850; minimum value: 490 C) maximum value: 850; minimum value: 0

B) maximum value: 850; minimum value: 480 D) maximum value: 480; minimum value: 490

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. 177) Objective Function z = 24x + 12y Constraints 0 K x K 10 0 Ky K5 3x + 2y L 6

A) Maximum: 36; at (0, 3) C) Maximum: 240; at (10, 0)

B) Maximum: 60; at (0, 5) D) Maximum: 300; at (10, 5)

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

178) Objective Function Constraints

z = 18x - 22y 0 Kx K5 0 Ky K8 4x + 5y K 30 4x + 3y K 20

B) Maximum: -87.5; at (1.25, 5) D) Maximum: -132; at (0, 6)

A) Maximum: 90; at (5, 0) C) Maximum: 0; at (0, 0)

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

179) Objective Function Constraints

z = 6x + 6y x L0 0 Ky K5 2x + 3y L 12 2x + 3y K 20

B) Maximum: -24; at (4, 0) D) Maximum: 42; at (2, 5)

A) Maximum: 60; at (10, 0) C) Maximum: 36; at (6, 0)

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

180) Objective Function Constraints

z = 5x + 2y x L0 0 Ky K4 x - y K7 x + 2y K 10

A) Maximum: 42; at (8, 1) C) Maximum: 35; at (7, 0)

B) Maximum: 8; at (0, 4) D) Maximum: 18; at (2, 4)

Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

Write the objective function that describes the problem. 181) Mrs. White wants to crochet beach hats and baby afghans for a church fund-raising bazaar. She needs 6 hours to make a hat and 4 hours to make an afghan and she has 56 hours available. She wants to make no more than 12 items and no more than 9 afghans. The bazaar will sell the hats for $25 each and the afghans for $11 each. Let x equal the number of hats sold and y equal the number of afghans sold. A) z = 8x + 4y B) z = 4x + 8y C) z = 25x + 11y D) z = 11x + 25y Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

182) An office manager needs to buy new filing cabinets. Cabinet A costs $5, takes up 6 square feet of floor space, and holds 10 cubic feet of files. Cabinet B costs $8, takes up 8 square feet, and holds 13 cubic feet. He has only $67 to spend and the office has room for no more than 74 square feet of cabinets. Let x equal the number of cabinet A's bought and y equal the number of cabinet B's bought. A) z = 4x + 7y B) z = 13x + 10y C) z = 10x + 13y D) z = 7x + 4y Objective: (7.5) Write an Objective Function Describing a Quantity That Must Be Maximized or Minimized

Write a system of two inequalities that describe the constraints in the problem. 183) An office manager needs to buy new filing cabinets. Cabinet A costs $7, takes up 7 square feet of floor space, and holds 9 cubic feet of files. Cabinet B costs $11, takes up 9 square feet, and holds 14 cubic feet. He has only $114 to spend and the office has room for no more than 106 square feet of cabinets. Let x equal the number of cabinet A's bought and y equal the number of cabinet B's bought. A) 9y + 14x K 106, 106y + 114x K 9 B) 7x + 11y K 114, 7x + 9y K 106 C) 7y + 11x K 114, 7y + 9x K 106 D) 9x + 14y K 106, 106x + 114y K 9 Objective: (7.5) Use Inequalities to Describe Limitations in a Situation

Write a system of three inequalities that describe the constraints in the problem. 184) Mrs. White wants to crochet beach hats and baby afghans for a church fund-raising bazaar. She needs 5 hours to make a hat and 4 hours to make an afghan and she has 52 hours available. She wants to make no more than 12 items and no more than 9 afghans. The bazaar will sell the hats for $19 each and the afghans for $10 each. Let x equal the number of hats made and y equal the number of afghans made. A) 19x + 10y K 52, x + y K 12, y K 9 B) 19y + 10x K 52, x + y K 12, y K 9 C) 4x + 5y K 52, x + y K 12, y K 9 D) 5x + 4y K 52, x + y K 12, y K 9 Objective: (7.5) Use Inequalities to Describe Limitations in a Situation

185) An office manager is buying used filing cabinets. Small file cabinets cost $5 each and large file cabinets cost $9 each, and the manager cannot spend more than $90 on file cabinets. A small cabinet takes up 6 square feet of floor space and a large cabinet takes up 8 square feet, and the office has no more than 94 square feet of floor space available for file cabinets. The manager must buy at least 6 file cabinets in order to get free delivery. Let x = the number of small file cabinets bought and y = the number of large file cabinets bought. A) 5x + 9y K 90; 6x + 8y K 94; y L 6 B) 5x + 9y K 90; 8x + 6y K 94; x L 6 C) 5x + 9y K 90; 6x + 8y K 94; x + y K 6 D) 5x + 9y K 90; 6x + 8y K 94; x + y L 6 Objective: (7.5) Use Inequalities to Describe Limitations in a Situation

Use the two steps for solving a linear programming problem to solve the problem. 186) Mrs. White wants to crochet beach hats and baby afghans for a church fund-raising bazaar. She needs 8 hours to make a hat and 4 hours to make an afghan and she has 52 hours available. She wants to make no more than 10 items and no more than 8 afghans. The bazaar will sell the hats for $23 each and the afghans for $10 each. How many of each should she make to maximize the income for the bazaar? A) 5 hats and 5 afghans B) 7 hats and 3 afghans C) 8 hats and 2 afghans D) 3 hats and 7 afghans Objective: (7.5) Use Linear Programming to Solve Problems

187) An office manager needs to buy new filing cabinets. Cabinet A costs $4, takes up 7 square feet of floor space, and holds 7 cubic feet of files. Cabinet B costs $12, takes up 10 square feet, and holds 15 cubic feet. He has only $100 to spend and the office has room for no more than 109 square feet of cabinets. He wants to have at least one of each type of cabinet. How many of each can he buy to maximize storage capacity? A) 7 cabinet A and 6 cabinet B B) 13 cabinet A and 0 cabinet B C) 6 cabinet A and 7 cabinet B D) 0 cabinet A and 13 cabinet B Objective: (7.5) Use Linear Programming to Solve Problems

188) Bruce is bringing items to sell at a flea market, where he plans to sell televisions at $125 each and DVD players at $100 each. Due to space limitations he can only store at most 150 items for the day. However, because more people already own televisions, Bruce knows that the number of DVD sales must at least match the number of television sales. How many of each item should Bruce bring to the flea market to maximize his sales? A) 100 televisions and 50 DVD B) 25 televisions and 125 DVD C) 75 televisions and 75 DVD players D) 50 televisions and 100 DVD players Objective: (7.5) Use Linear Programming to Solve Problems

189) A candy company has 150 pounds of cashews and 200 pounds of peanuts which can be combined into two different mixes. The deluxe mix is half cashews and half peanuts and sells for $7 per pound. The economy mix is one-third cashews and two-thirds peanuts and sells for $5.00 per pound. How many pounds of each mix should be prepared for maximum revenue? A) 150 pounds of deluxe mix and 0 pounds of economy mix B) 300 pounds of deluxe mix and 100 pounds of economy mix C) 100 pounds of deluxe mix and 50 pounds of economy mix D) 200 pounds of deluxe mix and 150 pounds of economy mix Objective: (7.5) Use Linear Programming to Solve Problems

190) A doctor has told a sick patient to take vitamin pills. The patient needs at least 18 units of vitamin A, at least 6 units of vitamin B, and at least 24 units of vitamin C. The red vitamin pills cost 10¢ each and contain 6 units of A, 1 unit of B, and 3 units of C. The blue vitamin pills cost 20¢ each and contain 3 units of A, 1 unit of B, and 6 units of C. How many pills should the patient take each day to minimize costs? A) 4 red and 2 blue B) 5 red and 1 blue C) 2 red and 4 blue D) 6 red and 0 blue Objective: (7.5) Use Linear Programming to Solve Problems

191) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $30 and on an SST ring is $60? A) 0 VIP and 24 SST B) 12 VIP and 12 SST C) 8 VIP and 16 SST D) 16 VIP and 8 SST Objective: (7.5) Use Linear Programming to Solve Problems

192) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $50 and on an SST ring is $10? A) 24 VIP and 0 SST B) 20 VIP and 0 SST C) 20 VIP and 4 SST D) 24 VIP and 4 SST Objective: (7.5) Use Linear Programming to Solve Problems

193) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35? A) 16 VIP and 8 SST B) 14 VIP and 10 SST C) 12 VIP and 12 SST D) 18 VIP and 6 SST Objective: (7.5) Use Linear Programming to Solve Problems

194) Zach is planning to invest up to $40,000 in corporate and municipal bonds. The least he will invest in corporate bonds is $8,000 and he does not want to invest more than $25,000 in corporate bonds. He also does not want to invest more than $28,825 in municipal bonds. The interest is 8.7% on corporate bonds and 6% on municipal bonds. This is simple interest for one year. What is the maximum income? A) $11,275 B) $43,075 C) $18,075 D) $28,075 Objective: (7.5) Use Linear Programming to Solve Problems

195) A certain area of forest is populated by two species of animals, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as F1 and F2 . For one year, species A requires 1.45 units of F1 and 1.2 units of F2 . Species B requires 2.4 units of F1 and 1.9 units of F2 . The forest can normally supply at most 847 units of F1 and 489 units of F2 per year. What is the maximum total number of these animals that the forest can support? A) 337 animals

B) 184 animals

C) 407 animals

D) 921 animals

Objective: (7.5) Use Linear Programming to Solve Problems

196) Suppose an animal feed to be mixed from soybean meal and oats must contain at least 100 lb of protein, 20 lb of fat, and 9 lb of mineral ash. Each 100-lb sack of soybean meal costs $20 and contains 50 lb of protein, 10 lb of fat, and 8 lb of mineral ash. Each 100-lb sack of oats costs $10 and contains 20 lb of protein, 5 lb of fat, and 1 lb of mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum cost? A) 2 sacks of soybeans and 0 sacks of oats C) 1

B) 0 sacks of soybeans and 2 sacks of oats

3 9 sacks of soybeans and 1 sacks of oats 11 11

7 5 sacks of soybeans and sacks of oats 3 6

Objective: (7.5) Use Linear Programming to Solve Problems

197) Suppose an animal feed to be mixed from soybean meal and oats must contain at least 100 lb of protein, 20 lb of fat, and 12 lb of mineral ash. Each 100-lb sack of soybean meal costs $20 and contains 50 lb of protein, 10 lb of fat, and 8 lb of mineral ash. Each 100-lb sack of alfalfa costs $11 and contains 30 lb of protein, 8 lb of fat, and 3 lb of mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum cost? 18 20 sacks of soybeans and sacks of alfalfa A) 0 sacks of soybeans and 2 sacks of alfalfa B) 17 17 C)

2 20 sack of soybeans and sack of alfalfa 3 9

D) 2 sacks of soybeans and 0 sacks of alfalfa

Objective: (7.5) Use Linear Programming to Solve Problems

198) An airline with two types of airplanes, P1 and P2 , has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1 costs $10,000 to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost? A) 11 P1 planes and 7 P2 planes B) 5 P1 planes and 17 P2 planes

C) 9 P1 planes and 13 P2 planes

D) 7 P1 planes and 11 P2 planes

Objective: (7.5) Use Linear Programming to Solve Problems

199) An airline with two types of airplanes, P1 and P2 , has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane P1 costs $10,000 to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost? A) 9 P1 planes and 13 P2 planes B) 13 P1 planes and 9 P2 planes

C) 5 P1 planes and 22 P2 planes

D) 14 P1 planes and 7 P2 planes

Objective: (7.5) Use Linear Programming to Solve Problems

200) Suppose that Janine desires 46 grams of protein and 38 grams of dietary fiber daily. One serving of kidney beans has 8 grams of protein and 6 grams of dietary fiber. One serving of refried pinto beans has 6 grams of protein and 6 grams of dietary fiber. If a serving of kidney beans costs $0.45 and a serving of refried pinto beans costs $0.35, then how many servings of each should Janine eat to minimize cost and still meet her requirements? 1 A) 6 servings of kidney beans and no refried pinto beans 3 B) 7 C)

2 servings of refried pinto beans and no kidney beans 3

7 servings of refried pinto beans and 4 servings of kidney beans 3

D) 4 servings of refried pinto beans and

7 servings of kidney beans 3

Objective: (7.5) Use Linear Programming to Solve Problems

201) A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accommodate up to 45 staff members and needs at least 30 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost? A) 27 counselors and 18 aides B) 35 counselors and 10 aides C) 18 counselors and 12 aides D) 12 counselors and 18 aides Objective: (7.5) Use Linear Programming to Solve Problems

202) A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100. The camp can accommodate up to 35 staff members and needs at least 20 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost? A) 19 counselors and 23 aides B) 13 counselors and 16 aides C) 13 counselors and 17 aides D) 8 counselors and 12 aides Objective: (7.5) Use Linear Programming to Solve Problems

203) An automotive glass plant must be able to fill orders for 230 truck windshields, 350 auto windshields, and 310 RV windshields. Because the first shift crews are more experienced, they are each able to make 7 truck windshields, 12 auto windshields, and 9 RV windshields. The second shift crews are able to produce 4 truck windshields, 12 auto windshields, and 7 RV windshields. The more experienced first shift crews cost the company $360.00 per crew per shift and the second shift crews each cost $310.00 per shift. The company's facilities will handle at most 50 crews on each shift, and they must have at least 10 crews come in to keep the plant running. How many first shift and how many second shift crews should they schedule to minimize costs? A) 51 first shift crews and 17 second shift crews B) 43 first shift crews and 24 second shift crews C) 28 first shift crews and 10 second shift crews D) 37 first shift crews and 36 second shift crews Objective: (7.5) Use Linear Programming to Solve Problems

204) Wally's Warehouse sells trash compactors and microwaves. Wally has space for no more than 70 trash compactors and microwaves together. Trash compactors weigh 22 pounds and microwaves weigh 78 pounds. Wally is limited to a total of 8,700 pounds for these items. The profit on a microwave is $106 and on a compactor $82. How many of each should Wally stock to maximize profit potential? Let x represent the number of trash compactors and y represent the number of microwaves. A) 0 trash compactor(s) and 69 microwave(s) B) 70 trash compactor(s) and 1 microwave(s) C) 0 trash compactor(s) and 70 microwave(s) D) 1 trash compactor(s) and 69 microwave(s) Objective: (7.5) Use Linear Programming to Solve Problems

205) A chemical company must use a new process to reduce pollution. The old emits 2 g of sulphur and 5 g of lead per liter of chemical made. The new emits 1 g of sulphur and 4.6 g of lead per liter of chemical made. The company makes a profit per liter of 16¢ under the old and 29¢ under the new. No more than 14,328 g of sulphur and no more than 8,913 g of lead can be emitted daily. How many liters of chemical could be made under the old and under the new to maximize profits? Let x represent the number of liters produced under the old process and y represent the number of liters produced under the new process. A) 0 liter(s) under old process and 1,837 liter(s) under new process B) 6,196 liter(s) under old process and 1,837 liter(s) under new process C) 1,937 liter(s) under old process and 6,196 liter(s) under new process D) 0 liter(s) under old process and 1,937 liter(s) under new process Objective: (7.5) Use Linear Programming to Solve Problems

206) A breed of cattle needs at least 10 protein and 8 fat units per day. Feed type I provides 6 protein and 2 fat units at $4 per bag. Feed type II provides 2 protein and 3 fat units at $3 per bag. What mixture of Feed type I and Feed type II will fill the dietary needs at minimum cost? Let x represent the number of bags of Feed type I and y represent the number of bags of Feed type II. A) 1 bag Feed type I and 1 bag Feed type II B) 1 bag Feed type I and 2 bags Feed type II C) 0 bags Feed type I and 5 bags Feed type II D) 4 bags Feed type I and 0 bags Feed type II Objective: (7.5) Use Linear Programming to Solve Problems

Graph the exponential function whose equation is given. Start by using -2, -1, 0, 1, and 2 for x and finding the corresponding values for y. 207) f(x) = 2 x

Objective: (7.6) Graph Exponential Functions

208) f(x) =

1 x 4

Objective: (7.6) Graph Exponential Functions

209) y = 5 x + 2

Objective: (7.6) Graph Exponential Functions

210) y =

1 x-1 3

Objective: (7.6) Graph Exponential Functions

Use a calculator with a yx key or a ^ key to solve the problem. 211) The exponential function f(x) = 48.09(1.021)x describes the population of a certain country, y, in millions, in year x. a) Substitute 0 for x and, without using a calculator, find the country's population in year 0. b) Find the country's population in year 21 as predicted by this function. A) a) 48.09 million; b) 74.404 million B) a) 1 million; b) 77.562 million C) a) 1.021 million; b) 72.873 million D) a) 48.09 million; b) 75.966 million Objective: (7.6) Use Exponential Models

212) Research suggests that the probability of a certain fuse malfunctioning increases exponentially as the concentration of an impurity in the fuse increases. The probability is modeled by the function y = 5(257,938)x , where x is the impurity concentration, and y, given as a percent, is the probability of the fuse malfunctioning. Find the probability of the fuse malfunctioning for an impurity concentration of 0.11. Round to the nearest percent. A) 4% B) 31% C) 14% D) 20% Objective: (7.6) Use Exponential Models

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 213) The exponential function P = 7(1.03)x describes the price P, in dollars, of a movie ticket in a local cinema in year x, assuming a yearly inflation rate of 3%. What was the original ticket price (year 0)? What will the price be in year 9? Objective: (7.6) Use Exponential Models

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use a calculator with a ex key to solve the problem. 214) The function f(x) = 90e-0.3x + 10 models the percentage of information, f(x), that a particular person remembers x weeks after learning the information. a) Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b) Find the percentage of information that is remembered after 5 weeks. Round to the nearest thousandth of a percent. A) a) 50%; b) 413.352% B) a) 100%; b) 30.082% C) a) 90%; b) 20.082% D) a) 10%; b) 10.223% Objective: (7.6) Use Exponential Models

Objective: (7.6) Graph Logarithmic Functions

First, rewrite each equation in exponential form. Then, use a table of coordinates and the exponential form to graph the logarithmic function. Begin by selecting -2, -1, 0, 1 and 2 for y. Finally, based on your graph, describe the shape of a scatter plot that can be modeled by f(x) = log b x, 0 < b < 1.

216) y = log1/2 x

increasing

decreasing, although rate of decrease is slowing down

increasing, although rate of increase is slowing down

Objective: (7.6) Graph Logarithmic Functions

217) y = log1/5 x

decreasing, although rate of decrease is slowing down

increasing, although rate of increase is slowing down

increasing

decreasing, although rate of decrease is slowing down Objective: (7.6) Graph Logarithmic Functions

218) y = log1/8 x

decreasing, although rate of decrease is slowing down

increasing

increasing, although rate of increase is slowing down Objective: (7.6) Graph Logarithmic Functions

Solve the problem. Use a calculator with an LN or a LOG key. 219) The formula y = 1 + 1.5 ln(x + 1) models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball player has practiced for two hours. After 105 days of practice, what is the average number of consecutive free throws the basketball player makes? A) 11 consecutive free throws B) 8 consecutive free throws C) 12 consecutive free throws D) 9 consecutive free throws Objective: (7.6) Use Logarithmic Models

220) The long jump record, in feet, at a particular school can be modeled by f(x) = 18.2 + 2.5 ln(x + 1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 8 years after record started being kept? Round your answer to the nearest tenth. A) 23.1 ft B) 23.7 ft C) 23.4 ft D) 20.7 ft Objective: (7.6) Use Logarithmic Models

221) The population growth of an animal species is described by F(t) = 400 log(2t + 3) where t is the number of months since the species was introduced. Find the population of this species in an area 6 months after the species is introduced. A) 470 B) 240 C) 704 D) 74 Objective: (7.6) Use Logarithmic Models

222) The height in meters of girls of a certain tribe is approximated by h = 0.52 + 2 log

t where t is the girl's age in years 3

and 1 K t K 20. Estimate the height (to the nearest hundredth of a meter) of a girl of the tribe 4 years of age. A) 1.12 m B) 0.96 m C) 0.77 m D) 0.52 m Objective: (7.6) Use Logarithmic Models

223) In chemistry, the pH of a substance is defined by pH = -log [H+ ], where [H+ ] is the hydrogen ion concentration in moles per liter. Find the pH of a sample of lake water whose [H+ ] is 3.05 × 10-9 moles per liter. (Round to the nearest tenth.) A) 8.5

B) 7.3

C) 6.4

D) 10.1

Objective: (7.6) Use Logarithmic Models

224) An earthquake was recorded with an intensity which was 19,953 times more powerful than a reference level earthquake, or 19,953 · I0 . What is the magnitude of this earthquake on the Richter scale (rounded to the nearest tenth)? The magnitude on the Richter scale of an earthquake of intensity I is log10

A) 9.9

B) 3.3

C) 4.3

Objective: (7.6) Use Logarithmic Models

Determine if the parabola whose equation is given opens upward or downward. 225) y = x2 - 2x - 9 A) downward

B) upward

Objective: (7.6) Graph Quadratic Functions

226) y = -x2 + 2x - 5 A) upward

B) downward

Objective: (7.6) Graph Quadratic Functions

I . I0

D) 0.4

227) y = 4x2 + 2x - 1 A) downward

B) upward

Objective: (7.6) Graph Quadratic Functions

228) y = -3x2 - 2x - 3 A) downward

B) upward

Objective: (7.6) Graph Quadratic Functions

Find the x-intercepts for the parabola whose equation is given. If the x-intercepts are irrational, round your answers to the nearest tenth. 229) y = -x2 + 17x - 72

A) x-intercepts (8, 0) and (-9, 0) C) x-intercepts (8, 0) and (9, 0)

B) x-intercepts (-8, 0) and (-9, 0) D) No x-intercepts

Objective: (7.6) Graph Quadratic Functions

230) y = 2x2 - 10x - 72 A) x-intercepts (9, 0) and (4, 0) C) x-intercepts (-8, 0) and (-4.5, 0)

B) x-intercepts (9, 0) and (-4, 0) D) x-intercepts (-8, 0) and ( , 0)

Objective: (7.6) Graph Quadratic Functions

231) y = 2x2 - 32x + 126 A) x-intercepts (-7, 0) and (-9, 0) C) x-intercepts (-7, 0) and ( , 0)

B) x-intercepts (7, 0) and (-9, 0) D) x-intercepts (7, 0) and (9, 0)

Objective: (7.6) Graph Quadratic Functions

232) y = x2 + 4x - 7 A) x-intercept: (4, 0) C) x-intercepts: (-4, 0) and (3, 0)

B) x-intercepts: (-2 ± 3.3, 0) D) x-intercepts: none

Objective: (7.6) Graph Quadratic Functions

233) y = x2 - 5x + 1 A) x-intercepts:

5 ± 4.6 ,0 2

B) x-intercepts:

C) x-intercepts: none

-5 ± 4.6 ,0 2

D) x-intercepts: (-1, 0) and (5, 0)

Objective: (7.6) Graph Quadratic Functions

Find the y-intercepts for the parabola whose equation is given. If the y-intercepts are irrational, round your answers to the nearest tenth. 234) y = x2 - 5

A) y-intercept (0, 5)

B) y-intercept (0, 2.2)

C) No y-intercept

D) y-intercept (0, -5)

Objective: (7.6) Graph Quadratic Functions

235) y = x2 + 16x A) y-intercept (0, 16) C) y-intercept (0, 0)

B) y-intercepts (0, 0) and (-16, 0) D) No y-intercept

Objective: (7.6) Graph Quadratic Functions

100

236) y = -x2 + 5x - 6 A) y-intercept (0, -6)

B) y-intercept (0, 6)

C) y-intercept (0, -2)

D) y-intercept (0, 2)

C) y-intercept (0, -9)

D) y-intercept (0, 9)

C) y-intercept (0, 10)

D) y-intercept (0, -1)

C) No y-intercept

D) y-intercept (0, -7)

C) y-intercept (0, -5)

D) y-intercept (0, -1)

C) ( , -142)

D) ( , -44)

C) (-2, 0)

D) (-4, -4)

C) (2, 47)

D) (1, 22)

Objective: (7.6) Graph Quadratic Functions

237) y = 2x2 - 9x + 9 A) y-intercept (0, 1.5)

B) y-intercept (03)

Objective: (7.6) Graph Quadratic Functions

238) y = 2x2 - 8x - 10 A) y-intercept (0, -10)

B) y-intercept (0, 5)

Objective: (7.6) Graph Quadratic Functions

239) y = x2 + 4x - 7 A) y-intercept (0, -12)

B) y-intercept (0, 7)

Objective: (7.6) Graph Quadratic Functions

240) y = x2 - 5x + 1 A) y-intercept (0, 5)

B) y-intercept (0, 1)

Objective: (7.6) Graph Quadratic Functions

Find the vertex for the parabola whose equation is given. 241) y = x2 - 14x + 5 A) (-7, 152)

B) (-14, 397)

Objective: (7.6) Graph Quadratic Functions

242) y = -x2 - 4x - 4 A) ( , -16)

B) ( , -8)

Objective: (7.6) Graph Quadratic Functions

243) y = 5x2 + 10x + 7 A) (-1, )

B) (-2,

)

Objective: (7.6) Graph Quadratic Functions

244) y = x2 + 11x + 1 A) (

)

B) (-

117 11 ) ,4 2

C) (-

117 2 ) ,121 11

D) (

Objective: (7.6) Graph Quadratic Functions

245) y = x2 + 9x A) (-9, -81)

B) (-

81 9 ) ,4 2

C) (0, -9)

Objective: (7.6) Graph Quadratic Functions

Graph the parabola whose equation is given.

101

D) (0, 0)

367 ) 4

246) y = x2 + 8x + 7

Objective: (7.6) Graph Quadratic Functions

102

247) y = -x2 - 6x - 8

Objective: (7.6) Graph Quadratic Functions

103

248) y = x2 - 6x + 8

Objective: (7.6) Graph Quadratic Functions

104

249) y = -4x2 + 40x - 97

Objective: (7.6) Graph Quadratic Functions

105

250) f(x) = x2 - 4

Objective: (7.6) Graph Quadratic Functions

Solve the problem. 251) Fireworks are launched into the air. The quadratic function y = -13x2 + 181x + 4 models the fireworks' height, y, in feet, x seconds after they are launched. When should the fireworks explode so that they go off at the greatest height? What is that height? (Round answers the nearest hundredth.) A) -6.96 sec, 626.02 ft B) 676 sec, 4 ft C) 6.96 sec, 634.02 ft D) 4 sec, 181 ft Objective: (7.6) Use Quadratic Models

106

252) The quadratic function y = 0.0038x2 - 0.47x + 36.48 models the median, or average, age, y, at which U.S. men were first married x years after 1900. In which year was this average age at a minimum? (Round to the nearest year.) What was the average age at first marriage for that year? (Round to the nearest tenth.) A) 1962, 51 years old B) 1953, 36 years old C) 1962, 21.9 years old D) 1936, 51 years old Objective: (7.6) Use Quadratic Models

253) The cost, in millions of dollars, for a company to manufacture x thousand automobiles is given by the function C(x) = 3x2 - 18x + 63. Find the number of automobiles that must be produced to minimize cost. A) 6 thousand automobiles C) 3 thousand automobiles

B) 9 thousand automobiles D) 36 thousand automobiles

Objective: (7.6) Use Quadratic Models

254) The profit that the vendor makes per day by selling x pretzels is given by the function P(x) = -0.004x2 + 3.2x - 250. Find the number of pretzels that must be sold to maximize profit. A) 400 pretzels B) 800 pretzels C) 200 pretzels D) 100 pretzels Objective: (7.6) Use Quadratic Models

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 255) The equation y = -4x2 + 40x + 100 represents the total daily profit of big-screen TV sales. The variable y represents the total profit, in tens of dollars, of selling x big-screen TVs. How many big-screen TVs must be sold to achieve maximum daily profit? What is the maximum profit? Objective: (7.6) Use Quadratic Models

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. First, create a scatter plot for the data in the table. Then, use the shape of the scatter plot given to determine if the data are best modeled by a linear function, an exponential function, a logarithmic function, or a quadratic function. 256) x y 0.6 3 1.5 4.2 2.2 4 3 2.5 4 0.5 2.7 3 3.5 1.5 0 2

107

logarithmic function

quadratic function

exponential function

linear function

Objective: (7.6) Determine an Appropriate Function for Modeling Data

257) x 0.1 1 1.7 2.5 3.5 3.2

y 0.3 0.5 1 2 4 3

108

logarithmic function

exponential function

quadratic function linear function Objective: (7.6) Determine an Appropriate Function for Modeling Data

258) x 0.3 0.5 1 2 3 4

y 0.1 0.3 1 1.7 2.2 2.4

109

exponential function

logarithmic function

quadratic function

linear function

Objective: (7.6) Determine an Appropriate Function for Modeling Data

110

259) x 0 1 1.2 2 3.4 4.8 5

y 1 1.5 1.6 2 2.7 3.4 3.5

quadratic function

exponential function

linear function

logarithmic function

Objective: (7.6) Determine an Appropriate Function for Modeling Data

260) x y 0.05 4.1 0.4 3 1 2 2 1 3.5 0.2 4 0.15 5 0.1

111

exponential function

linear function

logarithmic function

quadratic function

Objective: (7.6) Determine an Appropriate Function for Modeling Data

112

Answer Key Testname: 07-BLITZER_TM8E_TEST_ITEM_FILE

1) A 2) C 3) D 4) A 5) C 6) C 7) C 8) C 9) C 10) A 11) D 12) D 13) A 14) C 15) A 16) A 17) C 18) C 19) D 20) B 21) D 22) D 23) B 24) B

25)

26) x f(x) -2 2 -1 -1 0 -2 1 -1 2 2

27) x f(x) -2 0 -1 1 0 2 1 3 2 4

113

x f(x) -1 9 0 4 1 1 2 0 3 1

Answer Key Testname: 07-BLITZER_TM8E_TEST_ITEM_FILE

28) x f(x) -2 -10 -1 -3 0 -2 1 -1 2 6

51) A 52) C 53) D 54) A 55) D 56) B 57) D 58) C 59) D 60) C 61) A 62) D 63) A 64) B 65) A 66) A 67) D 68) D 69) D 70) a. y = -

71) a. y =

5 x 6

b. slope =

73) a. y = 5 , 6

y-intercept = 0 c.

1 x 3

b. slope = -

72) a. y = -4x + 3 b. slope = -4, y-intercept = 3 c.

1 , 3

y-intercept = 0 c.

29) B 30) A 31) A 32) A 33) B 34) B 35) A 36) D 37) A 38) B 39) C 40) A 41) A 42) A 43) B 44) C 45) D 46) D 47) B 48) C 49) D 50) B 114

5 x+5 6

b. slope = -

5 , 6

y-intercept = 5 c.

74) D 75) D 76) a. 46 b. 6 c. y = 6x + 46 d. 244 77) B 78) The slope is 0.10, which means the actor received 10% of the film's profits in addition to his salary. The y-intercept is 5, which means the actor received 5 million dollars, regardless of the film's profits. 79) D 80) A 81) C 82) C 83) D 84) D 85) B 86) D 87) A 88) D 89) D 90) B

Answer Key Testname: 07-BLITZER_TM8E_TEST_ITEM_FILE

91) A 92) C 93) B 94) A 95) B 96) D 97) D 98) D 99) C 100) C 101) B 102) A 103) A 104) A 105) B 106) C 107) C 108) D 109) D 110) C 111) C 112) D 113) C 114) D 115) B 116) C 117) C 118) D 119) A 120) B 121) B 122) D 123) D 124) B 125) A 126) D 127) D 128) B 129) A 130) B 131) D 132) C 133) B 134) A 135) D 136) D 137) B 138) A 139) C 140) D

141) D 142) A 143) D 144) D 145) A 146) D 147) A 148) B 149) D 150) D 151) A 152) B 153) B 154) D 155) C 156) (a) x L0 y L0 10x + 12y L 75 x + y K 13

171) B 172) D 173) B 174) A 175) C 176) C 177) D 178) A 179) A 180) A 181) C 182) C 183) B 184) D 185) D 186) D 187) A 188) C 189) D 190) A 191) A 192) B 193) C 194) B 195) C 196) A 197) C 198) C 199) D 200) C 201) D 202) D 203) C 204) C 205) D 206) B 207) D 208) A 209) C 210) B 211) A 212) D 213) The original price was $7. The price of the ticket will be $9.13 in year 9. 214) B 215) B 216) C 217) A

(b)

157) B 158) C 159) B 160) C 161) A 162) D 163) D 164) A 165) D 166) C 167) A 168) D 169) D 170) C 115

218) B 219) B 220) B 221) A 222) C 223) A 224) C 225) B 226) B 227) B 228) A 229) C 230) B 231) D 232) B 233) A 234) D 235) C 236) A 237) D 238) A 239) D 240) B 241) D 242) C 243) A 244) B 245) B 246) B 247) B 248) B 249) D 250) D 251) C 252) C 253) C 254) A 255) 5 big-screen TVs must be sold to achieve a maximum profit of 2000 dollars. 256) B 257) B 258) B 259) C 260) B

Blitzer, Thinking Mathematically, 8e Chapter 8 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Express the fraction as a percent. 5 1) 8 A) 62.5%

B) 78.1%

C) 80%

D) 6.3%

C) 1.29 %

D) 77.5 %

C) 38%

D) 3.8%

C) 0.0947%

D) 0.947%

C) 0.48%

D) 0.0048%

C) 0.0405%

D) 0.2025%

C) 4.3%

D) 2,150%

C) 0.31

D) 3.1

C) -0.059

D) 0.051

C) 8.2

D) 0.82

Objective: (8.1) Express a Fraction as a Percent

31 40

A) 12.9 %

B) 7.75 %

Objective: (8.1) Express a Fraction as a Percent

Write the decimal as a percent. 3) 0.38 A) 0.038%

B) 380%

Objective: (8.1) Express a Decimal as a Percent

4) 0.947 A) 94.7%

B) 947%

Objective: (8.1) Express a Decimal as a Percent

5) 4.8 A) 48%

B) 480%

Objective: (8.1) Express a Decimal as a Percent

6) 0.00405 A) 0.405%

B) 0.000405%

Objective: (8.1) Express a Decimal as a Percent

7) 43 A) 0.43%

B) 4,300%

Objective: (8.1) Express a Decimal as a Percent

Express the percent as a decimal. 8) 31% A) 0.2

B) 0.031

Objective: (8.1) Express a Percent as a Decimal

9) 5.1% A) 0.51

B) 0.0051

Objective: (8.1) Express a Percent as a Decimal

10) 820% A) 8.21

B) 82

Objective: (8.1) Express a Percent as a Decimal

11) 3% A) 3

B) 30

C) 0.3

D) 0.03

C) 0.00625

D) 0.625

C) 0.0125

D) 1.37

C) 144

D) 90

Objective: (8.1) Express a Percent as a Decimal

12)

5 % 8

A) 6.25

B) 0.00063

Objective: (8.1) Express a Percent as a Decimal

1 13) 1 % 4

A) 1.25

B) 0.0137

Objective: (8.1) Express a Percent as a Decimal

Solve the problem. 14) 25% of 36 is what number? A) 14.4

B) 9

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

15) What number is 16% of 23? A) 368

B) 3.68

C) 0.368

D) 36.8

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

16) 23 is 4% of what number? A) 57.5

B) 575

C) 5,750

D) 92

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

17) 10% of what number is 91? A) 910

B) 9,100

C) 9.1

D) 91

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

18) 0.24 is 24% of what number? A) 0.1

B) 0.0576

C) 1

D) 0.01

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

19) 68 is what percent of 40? A) 170%

B) 1,700%

C) 1.7%

D) 17%

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

20) 16 is what percent of 50? A) 3,200%

B) 3.2%

C) 32%

D) 0.32%

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

21) 0.7 is 10% of what number? A) 70

B) 0.07

C) 7

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

D) 0.7

22) 150% of 2 is what number? A) 300

B) 0.3

C) 30

D) 3

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

1 23) 79.5 is 7 % of what number? 2

A) 1,060

B) 10,600

C) 106

D) 10.6

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

24) 215.6 is what percent of 88? A) 40.82%

B) 4.08%

C) 2.45%

D) 245%

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

25) What number is 21% of 20? A) 420

B) 4.2

C) 4,200

D) 42

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

26) What percent of 125 is 72.5? A) 58%

B) 580%

C) 0.58%

D) 5.8%

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

27) 130% of what number is 65? A) 16,900

B) 500

C) 169

D) 50

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

The circle graph shows the number of times a group of survey respondents watched the news in the past week. Use the chart to answer the question.

28) If the number of respondents in the study was approximately 37,000, how many stated that they watched the news 5-6 times in the last week? A) 1,258 respondents B) 666 respondents C) 6,660 respondents D) 12,580 respondents Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

Solve the problem. 29) Jeans with an original price of $62 are on sale at 30% off. What is the sale price of the jeans? (Round to the nearest cent, if necessary.) A) $43.40 B) $60.14 C) $18.60 D) $80.60 Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

30) As part of a fundraiser, a local charity has sold 7 raffle tickets, with a goal of selling 90 tickets. What percentage of the goal has been sold? (Round to the nearest tenth of a percent, if necessary.)" A) 128.6% B) 12.9% C) 7.8% D) 77.8% Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

31) Suppose that 9% of teachers at a university attended a conference. If 2,000 teachers are enrolled at the university, about how many teachers attended the conference? A) 18 teachers B) 1,800 teachers C) 180 teachers D) 18,000 teachers Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

32) Suppose that the luxury sales tax rate in a foreign country is 19%. A very wealthy socialite bought a diamond tiara for $134,000. How much tax does she pay? A) $255 B) $2,546 C) $7,053 D) $25,460 Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

33) The circle graph shows the total number of speeding tickets given out in one month in a 10-city area. What percent of the total tickets were given out in Burnside? Round to the nearest percent.

590

A) 0.12%

B) 14%

C) 0.14%

D) 12%

Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 34) A brand new video game system sells for $299. If the sales tax is 7%, how much is the tax on the system? How much is the total cost of the video game system? Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 35) A dress regularly sells for $123. The sale price is $95. Find the percent decrease of the sale price from the regular price. A) 77.2% B) 339.3% C) 22.8% D) 29.5% Objective: (8.1) Determine Percent Increase or Decrease

The graph shows the level of subsidized daycare spending in a foreign country for the period 1995-1999. Use the graph to answer the question. 36) Find the percent increase in daycare spending from 1,998 to 1,999. Round to the nearest percent.

A) 10%

B) 0.09%

C) 9%

D) 11%

Objective: (8.1) Determine Percent Increase or Decrease

Solve the problem. 37) Suppose that you invest $5,000 in a risky investment. At the end of the first year, the investment has decreased by 40% of its original value. At the end of the second year, the investment increases by 50% of the value it had at the end of the first year. Your investment consultant tells you that there must have been a 10% overall increase of the original $5,000 investment. Is this an accurate statement? If not, what is your actual percent gain or loss on the original $5,000 investment. Round to the nearest percent. A) A 10 % increase of the original investment is not correct. The true result is a gain of 9%. B) A 10 % increase of the original investment is not correct. The true result is a loss of 9%. C) A 10 % increase of the original investment is not correct. The true result is a loss of 10%. D) A 10 % increase of the original investment is correct. Objective: (8.1) Investigate Some of the Ways Percent Can Be Abused

38) The price of an item is reduced by 30% of its original price. A week later it is reduced by 20% of the reduced price. The cashier informs you that there has been a total reduction of 50%. Is the cashier using percentages correctly? If not, what is the actual percent reduction from the original price? A) The cashier is not using percentages correctly. The actual percent reduction from the original price is 56%. B) The cashier is not using percentages correctly. The actual percent reduction from the original price is 25%. C) The cashier is using percentages correctly. D) The cashier is not using percentages correctly. The actual percent reduction from the original price is 44%. Objective: (8.1) Investigate Some of the Ways Percent Can Be Abused

Find the gross income, the adjusted gross income, and the taxable income. 39) A taxpayer earned wages of $66,100, received $890 in interest from a savings account, and contributed $2,600 to a tax-deferred retirement plan. He was entitled to a personal exemption of $4050 and had deductions totaling $6,520. A) $69,590; $65,540; $59,020 B) $66,990; $64,390; $60,340 C) $66,990; $64,390; $53,820 D) $69,590; $65,540; $60,340 Objective: (8.2) Determine Gross Income, Adjustable Gross Income, and Taxable Income

Find the gross income, the adjusted gross income, and the taxable income. Base the taxable income on the greater of a standard deduction or an itemized deduction. 40) Suppose your friend earned wages of $93,950, received $1,310 in interest from a savings account, and contributed $6,500 to a tax-deferred retirement plan. She is entitled to a personal exemption of $4050 and a standard deduction of $6,300. The interest on her home mortgage was $4,700, she contributed $2,300 to charity, and she paid $1,375 in state taxes. A) $95,260; $88,760; $78,410 B) $101,760; $97,710; $89,335 C) $101,760; $97,710; $91,410 D) $95,260; $88,760; $76,335 Objective: (8.2) Determine Gross Income, Adjustable Gross Income, and Taxable Income

Use the table to calculate the tax owed. Round to the nearest cent. Table 8.1 2021 Marginal Tax Rates and Standard deductions

Tax Rate 10% 12% 22% 24% 32% 35% 37% Standard Deduction

Unmarried and paying more than half the cost of supporting a child or parent

Unmarried divorced, or Legally seperated

Married and each Partner files a separate tax return

Married and both partners file a single tax return

Single up to $9950 $9951 to $40,525 $40,526 to $86,375 $86,376 to $164,925 $164,926 to $209,425 $209,426 to $523,600 more than $523,600

Married Filing separately up to $9950 $9951 to $40,525 $40,526 to $86,375 $86,376 to $164,925 $164,926 to $209,425 $209,426 to $314,150 more than $314,150

Married Filing Jointly up to $19,900 $19,901 to $81,050 $81,050 to $172,750 $172,751 to $329,850 $329,850 to $418,850 $418,851 to $628,300 more than $628,300

Head of Household up to $14,200 $14,201 to $54,200 $54,201 to $86,350 $86,351 to $164,900 $164,901 to $209,400 $209,401 to $523,600 more than $523,600

$12,550

$25,100

$18,800

41) a married woman filing separately with a taxable income of $101,000 A) $11,241.00 B) $32,320.00 C) $30,093.00

D) $18,261.00

Objective: (8.2) Calculate Federal Income Tax

42) a single man with a taxable income of $28,000 and a $1,000 tax credit A) $854.00 B) $4,050.00 C) $3,161.00

D) $2,161.00

Objective: (8.2) Calculate Federal Income Tax

43) a married couple filing jointly with a taxable income of $800,000 and a $7,500 tax credit A) $221,588.50 B) $293,225.00 C) $232,522.50 Objective: (8.2) Calculate Federal Income Tax

D) $225,022.50

44) a head of household with a taxable income of $79,000 and a $6,500 tax credit A) $5,853.00 B) $5,176.00 C) $15,950.00

D) $11,676.00

Objective: (8.2) Calculate Federal Income Tax

45) Single female, no dependents Gross income: $35,000 Adjustments: $3000 Deductions: $2000 charitable contributions $2500 state taxes Tax credit: none A) $3053.00 B) $2108.00

C) $5870.00

D) $3247.00

C) $8685.00

D) $4240.00

Objective: (8.2) Calculate Federal Income Tax

46) Married couple filing jointly with two dependent children Gross income: $94,000 Adjustments: none Deductions: $12,000 mortgage interest $2500 property taxes $5000 charitable contributions Tax credit: $2000 A) $6285.00 B) $7870.00 Objective: (8.2) Calculate Federal Income Tax

Use the 2021 FICA tax rates in the table below to solve the problem. Round your answer to the nearest dollar. Table 8.2 2021 FICA Tax Rates Employee's Rates D 7.65% on first $142,800 of income

Matching Rates Paid by the Employer D 7.65% on first $142,800 paid in wages

Self-Employed Rates D 15.3% on first $142,800 of net profits

D 1.45% of income in excess of $142,800

D 1.45% of wages paid in excess of $142,800

D 2.9% of net profits in excess of $142,800

47) If you are not self-employed and earn $200,800, what are your FICA taxes? A) $23,530 B) $15,361 C) $6,508

D) $11,765

Objective: (8.2) Calculate FICA Taxes

48) If you are self-employed and earn $150,800, what are your FICA taxes? A) $11,040 B) $5,365 C) 23,072 Objective: (8.2) Calculate FICA Taxes

D) $22,080

Use the tables below to solve the problem. Round dollar amounts to the nearest cent and percents to the nearest tenth. Table 8.1 2021 Marginal Tax Rates and Standard deductions

Tax Rate 10% 12% 22% 24% 32% 35% 37% Standard Deduction

Unmarried and paying more than half the cost of supporting a child or parent

Unmarried divorced, or Legally seperated

Married and each Partner files a separate tax return

Married and both partners file a single tax return

Single up to $9950 $9951 to $40,525 $40,526 to $86,375 $86,376 to $164,925 $164,926 to $209,425 $209,426 to $523,600 more than $523,600

Married Filing separately up to $9950 $9951 to $40,525 $40,526 to $86,375 $86,376 to $164,925 $164,926 to $209,425 $209,426 to $314,150 more than $314,150

Married Filing Jointly up to $19,900 $19,901 to $81,050 $81,050 to $172,750 $172,751 to $329,850 $329,850 to $418,850 $418,851 to $628,300 more than $628,300

Head of Household up to $14,200 $14,201 to $54,200 $54,201 to $86,350 $86,351 to $164,900 $164,901 to $209,400 $209,401 to $523,600 more than $523,600

$12,550

$25,100

$18,800

Table 8.2 2021 FICA Tax Rates Employee's Rates D 7.65% on first $142,800 of income

Matching Rates Paid by the Employer D 7.65% on first $142,800 paid in wages

Self-Employed Rates D 15.3% on first $142,800 of net profits

D 1.45% of income in excess of $142,800

D 1.45% of wages paid in excess of $142,800

D 2.9% of net profits in excess of $142,800

49) To help pay for college, you worked part-time at a local restaurant, earning $25,000 in wages and tips. (a) Calculate your FICA taxes. (b) Use the tax table to calculate your income tax. Assume you are single with no dependents, have no adjustments or tax credit, and you take the standard deduction. (c) Including both FICA and income tax, what percentage of your gross income are your federal taxes? A) (a) $1,912.50 B) (a) $362.50 C) (a) $362.50 D) (a) $1,912.50 (b) $2,801.00 (b) $2,801.00 (b) $1,295.00 (b) $1,295.00 (c) 18.9% (c) 12.7% (c) 6.6% (c) 12.8% Objective: (8.2) Solve Problems Involving Working Teens and Taxes

50) You decide to work part-time at a local supermarket. The job pays $8.80 per hour and you work 24 hours per week. Your employer withholds 10% of your gross pay for federal taxes, 7.65% for FICA taxes, and 2% for state taxes. (a) What is your weekly gross pay? (b) How much is withheld per week for federal taxes? (c) How much is withheld per week for FICA taxes? (d) How much is withheld per week for state taxes? (e) What is your weekly net pay? (f) What percentage of your gross pay is withheld for taxes? A) (a) $211.20 B) (a) $211.20 C) (a) $252.70 D) (a) $252.70 (b) $21.12 (b) $2,112.00 (b) $4.22 (b) $21.12 (c) $16.16 (c) $16.16 (c) $16.16 (c) $16.16 (d) $4.22 (d) $422.40 (d) $21.12 (d) $4.22 (e) $169.70 (e) $173.92 (e) $211.20 (e) $21.12 (f) 19.6% (f) 1,207.7% (f) 0.2% (f) 19.6% Objective: (8.2) Solve Problems Involving Working Teens and Taxes

The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year and round answer to the nearest cent. 51) P = $2,000 r = 6% t = 1 year A) $1,200 B) $120 C) $60 D) $6 Objective: (8.3) Calculate Simple Interest

52) P = $110 r = 4% t = 3 years A) $4.40

B) $13.20

C) $12.00

D) $123.20

C) $45.00

D) $540.00

C) $8,619.75

D) $519.75

C) $140.00

D) $11.67

Objective: (8.3) Calculate Simple Interest

53) P = $900.00 r = 6% t = 10 months A) $945.00

B) $1,440.00

Objective: (8.3) Calculate Simple Interest

54) P = $8,100 r = 5.5% t = 14 months A) $567.00

B) $6,237.00

Objective: (8.3) Calculate Simple Interest

55) P = $200 r = 8.75% t = 8 months A) $211.67

B) $12.73

Objective: (8.3) Calculate Simple Interest

56) P = $16,000.00 r = 11% t = 120 days A) $1,760.00

B) $578.63

C) $586.67

D) $3,520.00

Objective: (8.3) Calculate Simple Interest

The principal P is borrowed at simple interest rate r for a period of time t. Find the loan's future value, A, or the total amount due at time t. Round answer to the nearest cent. 57) P = $4,000, r = 3%, t = 1 year A) $4,003 B) $4,120 C) $5,200 D) $1,030 Objective: (8.3) Use the Future Value Formula

58) P = $140, r = 8%, t = 4 years A) $172.00

B) $184.80

C) $151.20

D) $1,044.80

C) $375.00

D) $306.25

C) $6,050.25

D) $6,055.25

C) $690.00

D) $515.83

C) $12,592.47

D) $12,606.75

Objective: (8.3) Use the Future Value Formula

59) P = $300.00, r = 5%, t = 5 months A) $311.25 B) $1,006.25 Objective: (8.3) Use the Future Value Formula

60) P = $5,400, r = 8.5%, t = 17 months A) $6,109.36 B) $13,203.00 Objective: (8.3) Use the Future Value Formula

61) P = $500, r = 4.75%, t = 8 months A) $517.27 B) $520.83 Objective: (8.3) Use the Future Value Formula

62) P = $12,500.00, r = 9%, t = 30 days A) $46,255.00 B) $12,593.75 Objective: (8.3) Use the Future Value Formula

The principal P is borrowed and the loan's future value, A, at time t is given. Determine the loan's simple interest rate, r, to the nearest tenth of a percent. 63) P = $2,000, A = $2,120, t = 1 year A) 6.9% B) 6% C) 12% D) 6.2% Objective: (8.3) Use the Future Value Formula

64) P = $170, A = $238.00, t = 4 years A) 10.4% B) 20%

C) 5.5%

D) 10%

C) 25.2%

D) 50%

C) 31.5%

D) 6%

Objective: (8.3) Use the Future Value Formula

65) P = $300.00, A = $337.50, t = 6 months A) 5.5% B) 25% Objective: (8.3) Use the Future Value Formula

66) P = $7,800, A = $9,210.50, t = 14 months A) 31% B) 15.5% Objective: (8.3) Use the Future Value Formula

Determine the present value, P, you must invest to have the future value, A, at simple interest rate r after time t. Round answer to the nearest dollar. 67) A = $5,000, r = 7.1%, t = 8 years A) $7,840 B) $3,196 C) $3,189 D) $3,246 Objective: (8.3) Use the Future Value Formula

68) A = $3,240, r = 8%, t = 1 year A) $3040

B) $3,000

C) $3,008

D) $3080

C) $110

D) $112

C) $800.00

D) $8014.00

C) $7305

D) $7314

Objective: (8.3) Use the Future Value Formula

69) A = $132.00, r = 10%, t = 2 years A) $112.100 B) $117 Objective: (8.3) Use the Future Value Formula

70) A = $874.67, r = 14%, t = 8 months A) $200.00 B) $801.00 Objective: (8.3) Use the Future Value Formula

71) A = $8,449.75, r = 13.5%, t = 14 months A) $7,300 B) $7373 Objective: (8.3) Use the Future Value Formula

Solve the problem. 72) Lonnie needs extra money to buy a truck to start up a delivery service. He takes out a simple interest loan for $8,000.00 for 9 months at a rate of 8.25% . How much interest must he pay, and what is the future value of the loan? A) interest: $495.00 ; future value: $8,495.00 B) interest: $540.00 ; future value: $8,540.00 C) interest: $5,940.00 ; future value: $13,940.00 D) interest: $495.00 ; future value: $8,508.00 Objective: (8.3) Use the Future Value Formula

73) A bank offers a CD that pays a simple interest rate of 7%. How much must you put in this CD now in order to have $9,360 to replace all the windows in your house in 8 years? A) $3,360 B) $336 C) $6,000 D) $6,720 Objective: (8.3) Use the Future Value Formula

The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Find how much money will be in the account after the given number of years (Assume 360 days in a year.), and how much interest was earned. A=P 1+

r nt n

A 1+

r nt n

A = Pe rt

Y= 1+

r n -1 n

74) Principal: $10,000 Rate: 7% Compounded: annually Time: 3 years A) amount in account: $12,250.43; interest earned: $2,250.43 B) amount in account: $12,273.43; interest earned: $2,273.43 C) amount in account: $32,100.00; interest earned: $22,100.00 D) amount in account: $5,120,000.00; interest earned: $5,110,000.00 Objective: (8.4) Use Compound Interest Formulas

75) Principal: $7,000 Rate: 5% Compounded: semiannually Time: 3 years A) amount in account: $7,538.23; interest earned: $538.23 B) amount in account: $9,380.67; interest earned: $2,380.67 C) amount in account: $8,103.38; interest earned: $1,103.38 D) amount in account: $8,117.85; interest earned: $1,117.85 Objective: (8.4) Use Compound Interest Formulas

76) Principal: $6,000 Rate: 6% Compounded: quarterly Time: 5 years A) amount in account: $10,745.09; interest earned: $4,745.09 B) amount in account: $8,081.13; interest earned: $2,081.13 C) amount in account: $19,242.81; interest earned: $13,242.81 D) amount in account: $6,463.70; interest earned: $463.70 Objective: (8.4) Use Compound Interest Formulas

77) Principal: $8,000 Rate: 7.5% Compounded: monthly Time: 3 years A) amount in account: $10,011.57; interest earned: $2,011.57 B) amount in account: $12,069.21; interest earned: $1,938.38 C) amount in account: $8,150.94; interest earned: $150.94 D) amount in account: $8,621.06; interest earned: $621.06 Objective: (8.4) Use Compound Interest Formulas

78) Principal: $9,000 Rate: 7.5% Compounded: daily Time: 3.5 years A) amount in account: $9,700.88; interest earned: $700.88 B) amount in account: $11,592.37; interest earned: $2,592.37 C) amount in account: $123,902.38; interest earned: $114,902.38 D) amount in account: $11,701.27; interest earned: $2,701.27 Objective: (8.4) Use Compound Interest Formulas

79) Principal: $40,000 Rate: 6.5% Compounded: daily Time: 10 years A) amount in account: $76,617.37; interest earned: $36,617.37 B) amount in account: $75,085.50; interest earned: $35,085.50 C) amount in account: $76,617.14; interest earned: $36,617.14 D) amount in account: $42,686.11; interest earned: $2,686.11 Objective: (8.4) Use Compound Interest Formulas

Solve the problem. 80) If you placed $1 into an account that paid interest at a rate of 6% and compounded the interest monthly, how much would that account be worth in 300 years? A) $62,780,146.30 B) $31,390,073.15 C) $4.46 D) $8,012.59 Objective: (8.4) Use Compound Interest Formulas

81) A mother invests $11,000 in a bank account at the time of her daughter's birth. The interest is compounded quarterly at a rate of 7%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period? A) $3,084.92 B) $12,339.68 C) $61,600.00 D) $44,070.31 Objective: (8.4) Use Compound Interest Formulas

82) Which is the better choice: $1000 deposited for a year at a rate of 4.7% compounded quarterly or at a rate of 4.6% compounded monthly? A) The rate of 4.6% compounded monthly is better. B) They are the same. C) The rate of 4.7% compounded quarterly is better. Objective: (8.4) Use Compound Interest Formulas

83) Suppose Carla has $9,000 to invest. Which investment yields the greater return over 2 years: 7% compounded monthly or 6.85% compounded daily? A) The rate of 7% compounded monthly is better. B) They are the same. C) The rate of 6.85% compounded daily is better. Objective: (8.4) Use Compound Interest Formulas

Solve the problem. Round to the nearest cent. A=P 1+

r nt n

A 1+

r nt n

A = Pe rt

Y= 1+

r n -1 n

84) How much money should be deposited today in an account that earns 5% compounded semiannually so that it will accumulate to $9,000 in 7 years? A) $6,396.13 B) $6,369.54 C) $2,630.46 D) $12,716.76 Objective: (8.4) Calculate Present Value

85) How much money should be deposited today in an account that earns 4% compounded quarterly so that it will accumulate to $5,300 in 3 years? A) $4,711.68 B) $596.52 C) $4,703.48 D) $5,972.17 Objective: (8.4) Calculate Present Value

86) James and Susan wish to have $10,000 available for their wedding in 3 years. How much money should they set aside now at 6% compounded monthly in order to reach their financial goal? A) $8,356.45 B) $9,419.05 C) $3,333.33 D) $10,616.78 Objective: (8.4) Calculate Present Value

87) Brad wants to have $17,000 available to buy a car in 5 years. How much must he deposit now at 5.5% compounded monthly to reach that goal? A) $22,366.96 B) $22,905.95 C) $12,920.84 D) $12,395.17 Objective: (8.4) Calculate Present Value

Solve the problem. Round to the nearest tenth of a percent. A=P 1+

r nt n

A 1+

r nt n

A = Pe rt

Y= 1+

r n -1 n

88) A passbook savings account has a rate of 5.3%. Find the effective annual yield if the interest is compounded quarterly. A) 5.5% B) 5.4% C) 5.3% D) 5.6% Objective: (8.4) Understand and Compute Effective Annual Yield

89) A passbook savings account has a rate of 6%. Find the effective annual yield if the interest is compounded monthly. A) 6.2% B) 6% C) 6.1% D) 6.3% Objective: (8.4) Understand and Compute Effective Annual Yield

90) A passbook savings account has a rate of 6.7%. Find the effective annual yield if the interest is compounded semiannually. A) 6.9% B) 6.8% C) 6.7% D) 6.6% Objective: (8.4) Understand and Compute Effective Annual Yield

91) A passbook savings account has a rate of 7%. Find the effective annual yield if the interest is compounded daily. Assume 360 days in a year. A) 7.5% B) 7.3% C) 7.2% D) 7.8% Objective: (8.4) Understand and Compute Effective Annual Yield

92) A passbook savings account has a rate of 7%. Find the effective annual yield if the interest is compounded 100,000 times per year. A) 6.5% B) 7.3% C) 7.2% D) 7.6% Objective: (8.4) Understand and Compute Effective Annual Yield

Determine the effective annual yield for each investment. Then select the better investment. Assume 360 days in a year. Round to the nearest hundredth of a percent when necessary. A=P 1+

r nt n

A 1+

A = Pe rt

r nt n

Y= 1+

93) 7% compounded monthly; 7.25% compounded annually A) 7%; 7.3%; 7.25% compounded annually C) 7.3%; 7.25%; 7% compounded monthly

r n -1 n

B) 7.4%; 7.3%; 7% compounded monthly D) 7.23%; 7.25%; 7.25% compounded annually

Objective: (8.4) Understand and Compute Effective Annual Yield

94) 7.4% compounded semiannually; 7.3% compounded daily A) 7.7%; 7.6%; 7.4% compounded semiannually C) 7.54%; 7.57%; 7.3% compounded daily

B) 7.4%; 7.6%; 7.3% compounded daily D) 7.5%; 7.4%; 7.4% compounded semiannually

Objective: (8.4) Understand and Compute Effective Annual Yield

Find the value of the annuity and the interest. Round to the nearest dollar.

P[(1 + r)t - 1] r

P 1+ A=

r nt -1 n

A P=

r n

95) Periodic Deposit: $100 at the end of each year Rate: 4% compounded annually Time: 7 years A) $663; $37 B) $790; $90

r n

r nt -1 n

C) $3,290; $2,590

D) $316; $384

C) $2,546; $6,454

D) $11,732; $2,732

Objective: (8.5) Determine the Value of an Annuity

96) Periodic Deposit: $1000 at the end of each year Rate: 6.5% compounded annually Time: 9 years A) $27,116; $18,116 B) $10,077; $1,077 Objective: (8.5) Determine the Value of an Annuity

97) Periodic Deposit: $7500 at the end of every six months Rate: 5% compounded semianually Time: 3 years A) $347,908; $302,908 B) $165,375; $120,375

C) $47,908; $2,908

D) $39,422; $5,578

C) $59,665; $38,065

D) $27,681; $6,081

C) $333,514; $213,514

D) $76,890; $43,110

Objective: (8.5) Determine the Value of an Annuity

98) Periodic Deposit: $900 at the end of every six months Rate: 6.5% compounded semiannually Time: 12 years A) $31,973; $10,373 B) $30,095; $8,495 Objective: (8.5) Determine the Value of an Annuity

99) Periodic Deposit: $2500 at the end of every three months Rate: 6.5% compounded quarterly Time: 12 years A) $174,334; $54,334 B) $179,667; $59,667 Objective: (8.5) Determine the Value of an Annuity

100) Periodic Deposit: $10,000 at the end of every three months Rate: 5.25% compounded quarterly Time: 9 years A) $456,439; $96,439 C) $440,655; $80,655

B) $111,407; $248,593 D) $1,218,344; $858,344

Objective: (8.5) Determine the Value of an Annuity

101) Periodic Deposit: $50 at the end of every month Rate: 4.25% compounded monthly Time: 7 years A) $18,999; $15,499 B) $4,862; $1,362

C) $4,882; $682

D) $451,631; $447,431

Objective: (8.5) Determine the Value of an Annuity

Solve the problem. Round to the nearest dollar. 102) Suppose that you earned a bachelor's degree and now you're teaching middle school. The school district offers teachers the opportunity to take a year off to earn a master's degree. To achieve this goal, you deposit $1500 at the end of every three months in an annuity that pays 4.5% compounded quarterly. How much will you have saved at the end of 11 years? Find the interest. A) $84,796; $18,796 B) $218,129; $152,129 C) $82,369; $16,369 D) $51,766; $14,234 Objective: (8.5) Determine the Value of an Annuity

103) Suppose that at age 25, you decide to save for retirement by depositing $95 at the end of every month in an IRA that pays 5.25% compounded monthly. How much will you have from the IRA when you retire at age 65? Find the interest. A) $154,798; $109,198 B) $1,007,756,740,396,159; $1,007,756,740,350,559 C) $176,512; $130,912 D) $153,202; $107,602 Objective: (8.5) Determine the Value of an Annuity

Determine the periodic deposit. Round up to the nearest dollar. How much of the financial goal comes from deposits and how much comes from interest?

P[(1 + r)t - 1] A= r

P 1+ A=

r nt -1 n

A P=

r n

r nt -1 n

104) Periodic Deposit: $? at the end of each year Rate: 8% compounded annually Time: 12 years Financial Goal: $28,000 A) $1,682; $20,184 from deposits and $7,816 from interest B) $2,632; $15,792 from deposits and $12,208 from interest C) $2,276; $27,312 from deposits and $688 from interest D) $1,475; $17,700 from deposits and $10,300 from interest Objective: (8.5) Determine Regular Annuity Payments Needed to Achieve a Financial Goal

105) Periodic Deposit: $? at the end of every six months Rate: 6% compounded semiannually Time: 8 years Financial Goal: $350,000 A) $7,269; $116,304 from deposits and $233,696 from interest B) $36,653; $293,224 from deposits and $56,776 from interest C) $30,605; $244,840 from deposits and $105,160 from interest D) $17,364; $277,824 from deposits and $72,176 from interest Objective: (8.5) Determine Regular Annuity Payments Needed to Achieve a Financial Goal

106) Periodic Deposit: $? at the end of each month Rate: 7.5% compounded monthly Time: 3 years Financial Goal: $17,000 A) $423; $15,228 from deposits and $1,772 from interest B) $1,276; $15,312 from deposits and $1,688 from interest C) $453; $16,308 from deposits and $692 from interest D) $377; $13,572 from deposits and $3,428 from interest Objective: (8.5) Determine Regular Annuity Payments Needed to Achieve a Financial Goal

107) Periodic Deposit: $? at the end of every three months Rate: 4.25% compounded quarterly Time: 5 years Financial Goal: $24,000 A) $806; $16,120 from deposits and $7,880 from interest B) $1,290; $12,900 from deposits and $11,100 from interest C) $1,199; $23,980 from deposits and $20 from interest D) $1,083; $21,660 from deposits and $2,340 from interest Objective: (8.5) Determine Regular Annuity Payments Needed to Achieve a Financial Goal

Solve the problem. Round up to the nearest dollar. 108) You would like to have $29,000 in 5 years for the down payment on a new house following college graduation by making deposits at the end of every three months in an annuity that pays 4.25% compounded quarterly. How much should you deposit at the end of every three months? How much of the $29,000 comes from deposits and how much comes from interest? A) $1,559; $15,590 from deposits and $13,410 from interest B) $1,309; $26,180 from deposits and $2,820 from interest C) $1,448; $28,960 from deposits and $40 from interest D) $974; $19,480 from deposits and $9,520 from interest Objective: (8.5) Determine Regular Annuity Payments Needed to Achieve a Financial Goal

109) How much should you deposit at the end of each month into an IRA that pays 8.5% compounded monthly to have $5 million when you retire in 45 years? How much of the $5 million comes from interest? A) $801; $4,567,460 B) $3,806; $608,960 C) $801; $432,540 D) $3,806; $4,391,040 Objective: (8.5) Determine Regular Annuity Payments Needed to Achieve a Financial Goal

Provide an appropriate response. 110) True or False? Investing in stocks and bonds is risky because it is possible to lose all or part of your principal. A) True B) False Objective: (8.5) Understand Stocks and Bonds as Investments

111) True or False? People who buy bonds own a share of a company, same as when they buy stock in the company. A) True B) False Objective: (8.5) Understand Stocks and Bonds as Investments

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Refer to the stock table to answer the questions. Where necessary, round dollar amounts to the nearest cent. 112) 52-week Yld Vol Net High Low Stock Sym Div % PE 100s Hi Lo Close Chg 29 17.5 Icarus ICR 0.39 1.2 22 1,062 25.5 24.38 25.5 ...... Use the stock table for Icarus to answer the following questions. a. What were the high and low prices for the last 52 weeks? b. If you owned 3,000 shares of Icarus stock last year, what is the dollar amount of the dividend you received? c. What is the annual return for dividends alone? d. How many shares of Icarus were traded yesterday? e. What were the high and low prices for Icarus shares yesterday? f. What was the price at which Icarus traded when the stock exchange closed yesterday? g. What does ... in the net change column mean? h. Compute Icarus's annual earnings per share using Annual earnings per share =

Yesterday's closing price per share . PE ratio

Objective: (8.5) Read Stock Tables

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. Round to the nearest dollar. 113) Suppose that between the ages of 25 and 45, you contribute $5,000 per year to a 401(k) and your employer contributes $2,500 per year on your behalf. The interest rate is 8.3% compounded annually. (a) What is the value of the 401(k), rounded to the nearest dollar, after 20 years? (b) Suppose that after 20 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the 401(k). How much money, to the nearest dollar, will you have in the plan when you reach age 65? (c) What is the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan? A) (a) The value of the 401(k) after the 20 years is approximately $354,836. (b) You will have approximately $1,165,480 in the 401(k) when you reach age 65. (c) $1,065,480 B) (a) The value of the 401(k) after the 20 years is approximately $236,557. (b) You will have approximately $1,748,223 in the 401(k) when you reach age 65. (c) $1,648,223 C) (a) The value of the 401(k) after the 20 years is approximately $354,836. (b) You will have approximately $1,748,223 in the 401(k) when you reach age 65. (c) $1,648,223 D) (a) The value of the 401(k) after the 20 years is approximately $236,557. (b) You will have approximately $1,165,480 in the 401(k) when you reach age 65. (c) $1,065,480 Objective: (8.5) Understand Accounts Designed for Retirement Savings

114) Suppose that between the ages of 20 and 39, you contribute $3,000 per year to a 401(k) and your employer matches this contribution dollar for dollar on your behalf. The interest rate is 8.25% compounded annually. (a) What is the value of the 401(k), rounded to the nearest dollar, after 19 years? (b) Suppose that after 19 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the 401(k). How much money, to the nearest dollar, will you have in the plan when you reach age 65? (c) What is the difference between the amount of money you will have accumulated in the 401(k) and the amount you contributed to the plan? A) (a) The value of the 401(k) after the 19 years is approximately $255,238. (b) You will have approximately $2,004,799 in the 401(k) when you reach age 65. (c) $1,947,799 B) (a) The value of the 401(k) after the 19 years is approximately $127,619. (b) You will have approximately $2,004,799 in the 401(k) when you reach age 65. (c) $1,947,799 C) (a) The value of the 401(k) after the 19 years is approximately $127,619. (b) You will have approximately $1,002,400 in the 401(k) when you reach age 65. (c) $945,400 D) (a) The value of the 401(k) after the 19 years is approximately $255,238. (b) You will have approximately $1,002,400 in the 401(k) when you reach age 65. (c) $945,400 Objective: (8.5) Understand Accounts Designed for Retirement Savings

P Use PMT =

r n

r -nt 1- 1+ n

. Round to the nearest dollar.

115) Suppose that you borrow $30,000 for four years at 8% toward the purchase of a car. Find the monthly payments and the total interest for the loan. A) $2,095; $70,560 B) $857; $41,136 C) $732; $5,136 D) $732; $35,136 Objective: (8.6) Compute the Monthly Payment and Interest Cost for a Car Loan

116) Suppose that you borrow $15,000 for a new car. You can select one of the following loans, each requiring regular monthly payments: Installment Loan A: three-year loan at 5.1% Installment Loan B: five-year loan at 6.1%. Find the monthly payments and the total interest for both Loan A and Loan B. Compare the monthly payments and the total interest for the two loans. A) Loan A: $804, $33,240; Loan B: $821, $14,556; The monthly payment is lower with the shorter-term loan but the total interest is less with the longer-term loan. B) Loan A: $450, $1,200; Loan B: $291, $2,460; The monthly payment is lower with the longer-term loan but the total interest is less with the shorter-term loan. C) Loan A: $291, $2,460; Loan B: $450, $1,200; The monthly payment is lower with the shorter-term loan but the total interest is less with the longer-term loan. D) Loan A: $821, $14,556; Loan B: $804, $33,240; The monthly payment is lower with the longer-term loan but the total interest is less with the shorter-term loan. Objective: (8.6) Compute the Monthly Payment and Interest Cost for a Car Loan

117) Suppose that you decide to buy a car for $25,921, including taxes and license fees. You saved $5,000 for a down payment and can get a five-year loan at 6.53%. Find the monthly payment and the total interest for the loan. A) $410; $3,679 B) $605; $15,379 C) $410; $15,379 D) $508; $4,559 Objective: (8.6) Compute the Monthly Payment and Interest Cost for a Car Loan

118) Suppose that you are buying a car for $50,000, including taxes and license fees. You saved $10,000 for a down payment. The dealer is offering you two incentives: Incentive A is a $5000 off the price of the car, followed by a five-year loan at 7.38%. Incentive B does not have a cash rebate, but provides free financing (no interest) over five years. What is the difference in monthly payments between the two offers? Which incentive is the better deal? A) approximately $32; Incentive B is the better deal. B) approximately $16; Incentive A is the better deal. C) approximately $68; Incentive A is the better deal. D) approximately $84; Incentive B is the better deal. Objective: (8.6) Compute the Monthly Payment and Interest Cost for a Car Loan

Determine whether the statement is true or false. 119) Leasing is essentially a long-term rent-to-own agreement. A) True

B) False

Objective: (8.6) Understand the Types of Leasing Contracts

120) If you have to make a fixed payment based on the car's residual value, then you have made an open-end lease agreement. A) True B) False Objective: (8.6) Understand the Types of Leasing Contracts

121) One advantage of leasing is that you can usually afford to lease a more expensive car than you would be able to buy. A) True B) False Objective: (8.6) Understand the Pros and Cons of Leasing Versus Buying a Car

122) One disadvantage of leasing is that when the lease ends, you are responsible for selling the car. A) True B) False Objective: (8.6) Understand the Pros and Cons of Leasing Versus Buying a Car

123) Liability insurance pays for damage or loss of your car if you are in an accident. A) True B) False Objective: (8.6) Understand the Different Kinds of Car Insurance

124) Comprehensive coverage protects you from the cost of lawsuits, damage to other cars, acts of nature and basically any kind of loss associated with unexpected events. A) True B) False Objective: (8.6) Understand the Different Kinds of Car Insurance

P Use PMT =

r n

r -nt 1- 1+ n

. Round to the nearest dollar.

125) Suppose you are thinking about buying a car and have narrowed down your choices to two options: The new-car option: The new car costs $28,000 and can be financed with a four-year loan at 6.19%. The used-car option: A two-year old model of the same car costs $12,000 and can be financed with a four-year loan at 6.84%. What is the difference in monthly payments between financing the new car and financing the used car? A) $0 B) $374 C) $307 D) $382 Objective: (8.6) Compare Monthly Payments on New and Used Cars

P 1+ Use A =

r nt -1 n r n

. Round all computations to the nearest dollar.

126) Suppose that you drive 30,000 miles per year and gas averages $3 per gallon. (i) What will you save in annual fuel expenses by owning a hybrid car averaging 30 miles per gallon rather than an SUV averaging 12 miles per gallon? (ii) If you deposit your monthly fuel savings at the end of each month into an annuity that pays 5.1% compounded monthly, how much will you have saved at the end of seven years? A) (i) $4,600; B) (i) $5,500; C) (i) $4,400; D) (i) $4,500; (ii) $38,600 (ii) $46,152 (ii) $36,922 (ii) $37,761 Objective: (8.6) Solve Problems Related to Owning and Operating a Car

The table shows the expense of operating and owning four selected cars, by average costs per mile. Use the appropriate information in the table to solve the problem. 127) Average Annual Costs of Owning and Operating a Car for Selected Cars Average Costs Per Mile Operating Ownership Total $0.21 $0.78 $0.99 $0.14 $0.56 $0.70 $0.26 $0.32 $0.58 $0.19 $0.64 $0.83

Model Car A Car B Car C Car D

(a) If you drive 20,000 miles per year, what is the total annual expense for Car B? (b) If the total annual expense for Car B is deposited at the end of each year into an IRA paying 8.1% compounded yearly, how much will be saved at the end of five years? Round your answer to the nearest dollar, if necessary. A) (a) $28,571; (b) $318,481 B) (a) $14,000; (b) $10,237,324 C) (a) $28,571; (b) $1,031,362 D) (a) $14,000; (b) $82,296 Objective: (8.6) Solve Problems Related to Owning and Operating a Car

128) Average Annual Costs of Owning and Operating a Car for Selected Cars Average Costs Per Mile Operating Ownership Total $0.23 $0.72 $0.95 $0.12 $0.57 $0.69 $0.26 $0.31 $0.57 $0.17 $0.62 $0.79

Model Car A Car B Car C Car D

If you drive 40,000 miles per year, by how much does the total annual expense for Car A exceed that of Car C over five years? A) $304,000 B) $60,800 C) $76,000 D) $15,200 Objective: (8.6) Solve Problems Related to Owning and Operating a Car

P Use PMT =

r n

r -nt 1- 1+ n

to determine the regular payment amount, rounded to the nearest dollar.

129) The price of a home is $230,000. The bank requires a 20% down payment and one point at the time of closing. The cost of the home is financed with a 15-year fixed-rate mortgage at 7%. a. Find the required down payment. b. Find the amount of the mortgage. c. How much must be paid for the one point at closing? d. Find the total cost of interest over 15 years, to the nearest dollar. A) a. down payment: $46,000 B) a. down payment: $43,700 b. amount of mortgage: $184,000 b. amount of mortgage: $186,300 c. points paid at closing: $1,840 c. points paid at closing: $2,300 d. total cost of interest over 15 years: $113,720 d. total cost of interest over 15 years: $113,720 C) a. down payment: $46,000 D) a. down payment: $46,000 b. amount of mortgage: $184,000 b. amount of mortgage: $184,000 c. points paid at closing: $2,300 c. points paid at closing: $1,840 d. total cost of interest over 15 years: $67,720 d. total cost of interest over 15 years: $297,720 Objective: (8.7) Compute the Monthly Payment and Interest Costs for a Mortgage

130) In terms of paying less in interest over the full term of the mortgage, which is more economical for a $250,000 mortgage : 25-year fixed at 8.00% or 15-year fixed at 7.50%? A) They are the same. B) The 15-year fixed rate at at 7.50% is more economical. C) The 25-year fixed rate at at 8.00% is more economical. Objective: (8.7) Compute the Monthly Payment and Interest Costs for a Mortgage

131) The price of a home is $400,000. The bank requires a 20% down payment. After the down payment, the balance is financed with a 20-year fixed-rate mortgage at 8%. Determine the monthly mortgage payment (excluding escrowed taxes and insurance) to the nearest dollar. A) $2,777 B) $2,692 C) $2,665 D) $2,677 Objective: (8.7) Compute the Monthly Payment and Interest Costs for a Mortgage

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 132) The cost of a home on a particular island is $1,000,000. The bank requires a 15% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed rate at 8%. a. Find the required down payment b. Find the amount of the mortgage c. Find the amount that must be paid for the three points at closing d. Find the monthly payment e. Find the total cost of interest over 30 years. Objective: (8.7) Compute the Monthly Payment and Interest Costs for a Mortgage

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 133) The cost of a home is financed with a $220,000, 30-year fixed-rate mortgage at 7%. The buyer will make 360 payments of $1,463.00. Prepare a loan amortization schedule for the first three months of the mortgage. Round to the nearest cent. Payment Number 1 2 3

Interest Payment

Principal Payment

Balance of Loan

A) Payment Number 1 2 3

Interest Payment $1,283.33 $1,282.29 $1,372.75

Principal Payment $179.67 $180.71 $90.25

Balance of Loan $219,820.33 $219,639.62 $219,549.37

Payment Number 1 2 3

Interest Payment $1,283.33 $1,282.29 $1,281.23

Principal Payment $179.67 $180.71 $181.77

Balance of Loan $219,820.33 $219,819.29 $219,457.85

Payment Number 1 2 3

Interest Payment $1,283.33 $1,282.29 $1,281.23

Principal Payment $179.67 $180.71 $181.77

Balance of Loan $219,820.33 $219,639.62 $219,457.85

Payment Number 1 2 3

Interest Payment $1,283.33 $1,282.61 $1,281.23

Principal Payment $179.67 $180.39 $181.77

Balance of Loan $219,876.33 $219,516.62 $219,457.85

Objective: (8.7) Prepare a Partial Loan Amortization Schedule

Use the following advice from most financial advisors to solve the problem. · Spend no more than 28% of your gross monthly income for your mortgage payment. · Spend no more than 36% of your gross monthly income for your total monthly debt. Round all calculations to the nearest dollar, if necessary. 134) Suppose that your gross annual income is $96,000. (a) What is the maximum amount you should spend each month on a mortgage payment? (b) What is the maximum amount you should spend each month for total credit obligations? (c) If your monthly mortgage payment is 80% of the maximum amount you can afford, what is the maximum amount you should spend each month for all other debt? A) (a) $2,240; (b) $2,880; (c) $1,792 B) (a) $2,240; (b) $2,880; (c) $1,088 C) (a) $26,880; (b) $34,560; (c) $13,056 D) (a) $2,240; (b) $2,880; (c) $64 Objective: (8.7) Solve Problems Involving What You Can Afford to Spend for a Mortgage

Determine whether the statement is true or false. 135) Renting a home is generally less costly than buying when staying in it for more than three years. A) True B) False Objective: (8.7) Understand the Pros and Cons of Renting Versus Buying

136) Owning a home provides significant tax advantages, including deduction of mortgage interest and property taxes. A) True B) False Objective: (8.7) Understand the Pros and Cons of Renting Versus Buying

P Use PMT =

r n

r -nt 1- 1+ n

to determine the regular payment amount, rounded to the nearest dollar.

137) Suppose your credit card has a balance of $3,600 and an annual interest rate of 19%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, (a) How much must you pay each month? (b) How much total interest will you pay? Now suppose you instead get a bank loan at 10.5% with a term of four years. (c) How much will you pay each month? How does this compare with your credit-card payment? (d) How much total interest will you pay? How does this compare with your credit-card interest? A) (a) $132 B) (a) $132 (b) $1,152 (b) $2,736 (c) $93, which is a lower monthly payment (c) $93, which is a lower monthly payment (d) $864, which is less interest. (d) $864, which is less interest. C) (a) $93 D) (a) $93 (b) $864 (b) $252 (c) $132, which is a higher monthly payment (c) $132, which is a higher monthly payment (d) $1,152, which is more interest. (d) $1,152, which is more interest. Objective: (8.8) Find the Interest, the Balance Due, and the Minimum Monthly Payment for Credit Card Loans

138) Suppose your credit card has a balance of $5,900 and an annual interest rate of 16%. You decide to pay off the balance over three years. If there are no further purchases charged to the card, (a) How much must you pay each month? (b) How much total interest will you pay? Now suppose decide to pay off the balance over one year rather than three. (c) How much more must you pay each month? (d) How much less will you pay in total interest? A) (a) $207 B) (a) $217 (b) $520 (b) $628 (c) $328 more per month (c) $327 more per month; (d) $1,032 less in total interest (d) $1,284 less in total interest C) (a) $217 D) (a) $207 (b) $1,912 (b) $1,552 (c) $327 more per month; (c) $328 more per month (d) $1,284 less in total interest (d) $1,032 less in total interest Objective: (8.8) Find the Interest, the Balance Due, and the Minimum Monthly Payment for Credit Card Loans

Solve the problem. 139) A credit card has a monthly rate of 1.7% and uses the average daily balance method for calculating interest. Here are some of the details in the June 1-June 30 itemized billing: June 1 Unpaid Balance: $450.83 Payment Received June 5: $135 Purchases Charged to the Account: $256.22 Average Daily Balance: $333.83 Last Day of the Billing Period: June 30 Payment Due Date: July 9 a. Find the interest due on the payment due date. b. Find the total balance owed on the last day of the billing period. c. Minimum payment terms are shown below. What is the minimum payment due by July 9? New Balance $0.01 to $10.00 $10.01 to $200.00 $200.01 to $250.00 $250.01 to $300.00 $300.01 to $350.00 $350.01 to $400.00 $400.01 to $450.00 $450.01 to $500.00 Over $500.00

A) a. $5.75 b. $315.83 c. $20.00

Minimum Payment No payment due $10.00 $15.00 $20.00 $25.00 $30.00 $35.00 $40.00 1/10 of New Balance

B) a. $5.49 b. $321.32 c. $20.00

C) a. $5.68 b. $577.73 c. $57.77

D) a. $5.75 b. $649.66 3. $57.77

Objective: (8.8) Find the Interest, the Balance Due, and the Minimum Monthly Payment for Credit Card Loans

Determine whether the statement is true or false. 140) An advantage of using a credit card is that it allows you to shop over the phone or on the Internet. A) True B) False Objective: (8.8) Understand the Pros and Cons of Using Credit Cards

141) Paying the required minimum on your credit card bill ensures that you will not be charged any interest and is a good way to avoid credit-card debt. A) True B) False Objective: (8.8) Understand the Pros and Cons of Using Credit Cards

142) Unlike a debit card, a credit card will still work if the money needed is not in your checking or savings account. A) True B) False Objective: (8.8) Understand the Difference Between Credit Cards and Debit Cards

143) Unlike writing a check, using a debit card frees you from paying overdraft charges. A) True B) False Objective: (8.8) Understand the Difference Between Credit Cards and Debit Cards

144) Credit reports include details about all of your open and closed credit accounts. A) True B) False Objective: (8.8) Know What is Contained in a Credit Report

145) Credit reports include personal information about you including your race, gender, and religious affiliation. A) True B) False Objective: (8.8) Know What is Contained in a Credit Report

146) The lower your credit score, the more likely you are to get credit. A) True B) False Objective: (8.8) Understand Credit Scores as Measures of Creditworthiness

147) The higher your credit score, the more likely you are to get the best interest rates on loans. A) True B) False Objective: (8.8) Understand Credit Scores as Measures of Creditworthiness

Answer Key Testname: 08-BLITZER_TM8E_TEST_ITEM_FILE

1) A 2) D 3) C 4) A 5) B 6) A 7) B 8) C 9) D 10) C 11) D 12) C 13) C 14) B 15) B 16) B 17) A 18) C 19) A 20) C 21) C 22) D 23) A 24) D 25) B 26) A 27) D 28) C 29) A 30) C 31) C 32) D 33) D 34) The tax is $20.93. The total cost is $319.93 35) C 36) A 37) C 38) D 39) C 40) D 41) D 42) D 43) D 44) B 45) C 46) B 47) D 48) D 49) D

50) A 51) B 52) B 53) C 54) D 55) D 56) C 57) B 58) B 59) D 60) C 61) D 62) B 63) B 64) D 65) B 66) B 67) C 68) B 69) C 70) C 71) A 72) A 73) C 74) A 75) D 76) B 77) A 78) D 79) C 80) A 81) D 82) C 83) A 84) B 85) C 86) A 87) C 88) B 89) A 90) B 91) B 92) B 93) D 94) C 95) B 96) D 97) C 98) A 99) B

100) A 101) C 102) A 103) A 104) D 105) D 106) A 107) D 108) B 109) A 110) A 111) B 112) a. 52-week high: $ 29.00; 52-week low $ 17.50 b. $1,170 c. 1.2% d. 106,200 shares e. yesterday's high: $ 25.50; yesterday's low: $24.38 f. $25.50 g. This means there was no change in price for a share of stock from the market close two days ago to yesterday's market close. h. $1.16 113) C 114) A 115) C 116) B 117) A 118) A 119) B 120) A 121) A 122) B 123) B 124) B 125) B 126) D 127) D 128) C 129) A 130) B 131) D 28

132) a. $150,000; b. $850,000 133) C 134) B 135) B 136) A 137) A 138) D 139) C 140) A 141) B 142) A 143) B 144) A 145) B 146) B 147) A

Blitzer, Thinking Mathematically, 8e Chapter 9 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use dimensional analysis to convert the quantity to the indicated units. If necessary, round the answer to two decimal places. 1) 90 in. to ft A) 15 ft B) 30 ft C) 1,080 ft D) 7.5 ft Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

2) 4.9 mi to ft A) 25,872 ft

B) 718.67 ft

C) 2,156 ft

D) 8,624 ft

Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

3) 30 ft to yd A) 90 yd

B) 10 yd

C) 3.33 yd

D) 1,080 yd

Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

4) 10,560 ft to mi A) 2.50 mi

B) 3 mi

C) 52.8 mi

D) 2 mi

Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

5) 12 ft to in. A) 144 in.

B) 432 in.

C) 48 in.

D) 36 in.

Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

6) 16 yd to ft A) 576 ft

B) 144 ft

C) 192 ft

D) 48 ft

Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

7) 54 in. to yd A) 0.25 yd

B) 108 yd

C) 1.50 yd

D) 324 yd

Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

8) 9 yd to in. A) 324 in.

B) 108 in.

C) 0.75 in.

D) 0.25 in.

Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement

Selecting from millimeter, meter, dekameter, and kilometer, determine the best unit of measure to express the given length. 9) a door's height A) meter B) dekameter C) millimeter D) kilometer Objective: (9.1) Understand and Use Metric Prefixes

10) the length of a shoe A) kilometer

B) meter

C) dekameter

Objective: (9.1) Understand and Use Metric Prefixes

D) millimeter

11) the distance from Nashville to San Francisco A) meter B) millimeter

C) dekameter

D) kilometer

C) dekameter

D) kilometer

C) kilometer

D) meter

C) dekameter

D) meter

C) 7 km

D) 7 mm

C) 4.8 mm

D) 4.8 m

C) 60.6 m

D) 60.6 km

C) 97 km

D) 97 cm

C) 0.576 cm

D) 0.0576 cm

C) 0.198 m

D) 19,840 m

C) 6.728 dm

D) 6,728 dm

Objective: (9.1) Understand and Use Metric Prefixes

12) the length of a horse A) millimeter

B) meter

Objective: (9.1) Understand and Use Metric Prefixes

13) the width of a brick A) millimeter

B) dekameter

Objective: (9.1) Understand and Use Metric Prefixes

14) the altitude of a mountain peak A) millimeter B) kilometer Objective: (9.1) Understand and Use Metric Prefixes

Select the best estimate for the measure of the given quantity. 15) the distance Sam jogged yesterday A) 7 m B) 7 cm Objective: (9.1) Understand and Use Metric Prefixes

16) the length of a bedroom wall A) 4.8 km

B) 4.8 cm

Objective: (9.1) Understand and Use Metric Prefixes

17) the length of a bookshelf A) 60.6 mm

B) 60.6 cm

Objective: (9.1) Understand and Use Metric Prefixes

18) the width of a calculator A) 97 mm

B) 97 m

Objective: (9.1) Understand and Use Metric Prefixes

Convert the given measurement to the unit indicated. 19) 5.76 m to cm A) 576 cm B) 57.6 cm Objective: (9.1) Convert Units Within the Metric System

20) 19.84 mm to m A) 1,984 m

B) 0.01984 m

Objective: (9.1) Convert Units Within the Metric System

21) 67.28 m to dm A) 672.8 dm

B) 0.673 dm

Objective: (9.1) Convert Units Within the Metric System

22) 94.87 dam to m A) 948.7 m

B) 9,487 m

C) 0.949 m

D) 9.487 m

C) 0.812 m

D) 812 m

C) 981 hm

D) 0.0981 hm

C) 4.85 dm

D) 48,500 dm

C) 918 mm

D) 0.918 mm

C) 8,340 cm

D) 834 cm

Objective: (9.1) Convert Units Within the Metric System

23) 81.2 dm to m A) 8,120 m

B) 8.12 m

Objective: (9.1) Convert Units Within the Metric System

24) 9.81 m to hm A) 0.981 hm

B) 98.1 hm

Objective: (9.1) Convert Units Within the Metric System

25) 48.5 hm to dm A) 4,850 dm

B) 485 dm

Objective: (9.1) Convert Units Within the Metric System

26) 9.18 dm to mm A) 91.8 mm

B) 9,180 mm

Objective: (9.1) Convert Units Within the Metric System

27) 0.834 dam to cm A) 8.34 cm

B) 83.4 cm

Objective: (9.1) Convert Units Within the Metric System

Solve the problem. 28) A race track is 507 meters long. If a driver goes around the race track twice, how many kilometers did the driver travel? A) 507,000 km B) 1,014,000 km C) 0.507 km D) 1.014 km Objective: (9.1) Convert Units Within the Metric System

Use dimensional analysis to convert the unit indicated. 29) 4 in. to cm A) 0.64 cm B) 1.57 cm

C) 0.10 cm

D) 10.16 cm

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

30) 27 cm to in. A) 0.09 cm

B) 0.01 cm

C) 68.58 cm

D) 10.63 cm

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

31) 599 mi to km A) 2.7 km

B) 0.001 km

C) 374.4 km

D) 958.4 km

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

32) 105 km to mi A) 168.0 mi

B) 65.6 mi

C) 0.015 mi

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

D) 0.006 mi

33) 4 m to yd A) 0.2 yd

B) 3.6 yd

C) 4.4 yd

D) 0.3 yd

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

34) 7 dm to in. A) 0.28 in.

B) 1.778 in.

C) 27.56 in.

D) 177.8 in.

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

35) 4.9 dam to in. A) 0.08 in.

B) 1.93 in.

C) 1,929.13 in.

D) 12.45 in.

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

36) 160 in. to dam A) 4,064 dam

B) 0.4064 dam

C) 406.4 dam

D) 406,400 dam

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

37) 390 in. to hm A) 0.09906 hm

B) 1.54 hm

C) 9,906,000 hm

D) 153.54 hm

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

38) 9 ft to m A) 10.0 m

B) 24.3 m

C) 0.1 m

D) 2.7 m

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

39) 7 m to ft A) 2.1 ft

B) 23.0 ft

C) 6.3 ft

D) 7.8 ft

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

Use 1 mi = 1.6 km to solve the problem. 40) Express 43 kilometers per hour in miles per hour. A) 26.9 mi/hr B) 41,280 mi/hr

C) 68.8 mi/hr

D) 1,612.5 mi/hr

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

41) Express 53 miles per hour in kilometers per hour. A) 47.7 km/hr B) 33.1 km/hr

C) 84.8 km/hr

D) 58.9 km/hr

Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 42) The speed limit in many neighborhoods is 35 miles per hour. How many kilometers per hour is this? Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given figure to find its area in square units. 43)

A) 25 square units

B) 16 square units

C) 9 square units

D) 20 square units

C) 9 square units

D) 3 square units

Objective: (9.2) Use Square Units to Measure Area

44)

A) 4.5 square units

B) 6 square units

Objective: (9.2) Use Square Units to Measure Area

Select the best estimate for the measure of the area of the object described. 45) the area of the floor of hall A) 50 km2 B) 50 m 2 C) 500 cm2

D) 50 cm2

Objective: (9.2) Use Square Units to Measure Area

46) the area of a microwave door A) 250 cm2

B) 250 m 2

C) 250 dm2

D) 250 mm2

C) 65 dm2

D) 65 cm2

C) 10,000 cm2

D) 10,000 km2

Objective: (9.2) Use Square Units to Measure Area

47) the area of the end of an eraser A) 65 mm2 B) 6.5 m 2 Objective: (9.2) Use Square Units to Measure Area

48) the area of a rooftop of a large building A) 10,000 ha

B) 10,000 m 2

Objective: (9.2) Use Square Units to Measure Area

Use dimensional analysis to convert the given square unit to the square unit indicated. Where necessary, round the answer to two decimal places. 49) 38 cm2 to in.2

A) 247 in.2

B) 34.2 in.2

C) 5.85 in.2

D) 96.52 in.2

Objective: (9.2) Use Dimensional Analysis to Change Units for Area

50) 20 m2 to ft2 A) 180 ft2

B) 18 ft2

C) 22.22 ft2

D) 222.22 ft2

Objective: (9.2) Use Dimensional Analysis to Change Units for Area

51) 20 m2 to yd2 A) 25 yd2

B) 222.22 yd2

C) 16 yd2

D) 2.5 yd2

Objective: (9.2) Use Dimensional Analysis to Change Units for Area

52) 12 mi2 to km2 A) 4.62 km2

B) 7.50 km2

C) 31.2 km2

D) 19.2 km2

Objective: (9.2) Use Dimensional Analysis to Change Units for Area

53) 16.5 ha to acres A) 6.6 acres

B) 1.03 acres

C) 264 acres

D) 41.25 acres

Objective: (9.2) Use Dimensional Analysis to Change Units for Area

54) 23 in.2 to cm2 A) 3.54 cm2

B) 58.42 cm2

C) 0.28 cm2

D) 149.5 cm2

Objective: (9.2) Use Dimensional Analysis to Change Units for Area

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 55) A television set has an area of 169 square inches (in2 ). How many square feet (ft2) is this? Round to the nearest hundredth. Objective: (9.2) Use Dimensional Analysis to Change Units for Area

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 56) The population of a certain county is 907,106 and its area is 239,252 square miles. Find the population density of the county to the nearest tenth. A) 7.6 people per square mile B) 667,854 people per square mile C) 3.8 people per square mile D) 1,146,358 people per square mile Objective: (9.2) Use Dimensional Analysis to Change Units for Area

57) A property that measures 4 hectares is for sale. If the property is selling for $300,000, what is the price per acre? A) $30,000.00 per acre B) $13,333.33 per acre C) $1,875,000.00 per acre D) $75,000.00 per acre Objective: (9.2) Use Dimensional Analysis to Change Units for Area

Use the figure below to find its volume in cubic units. 58)

A) 7 units3

B) 6 units3

C) 10 units3

D) 12 units3

Objective: (9.2) Use Cubic Units to Measure Volume

Use dimensional analysis to convert the given unit to the unit indicated. Where necessary, round answer to two decimal places. 59) 50,000 ft3 to gal

A) 1,155 gal

B) 1,000 gal

C) 3,740,000 gal

D) 374,000 gal

C) 67.32 gal

D) 1,800 gal

C) 1,400 gal

D) 52.36 gal

C) 6.95 yd3

D) 26 yd3

C) 90 ft3

D) 67.32 ft3

Objective: (9.2) Use English and Metric Units to Measure Capacity

60) 9 yd3 to gal A) 0.05 gal

B) 1,152 gal

Objective: (9.2) Use English and Metric Units to Measure Capacity

61) 1,617 in.3 to gal A) 7 gal

B) 373,527 gal

Objective: (9.2) Use English and Metric Units to Measure Capacity

62) 5,200 gal to yd3 A) 104 yd3

B) 388.96 yd3

Objective: (9.2) Use English and Metric Units to Measure Capacity

63) 6,732 gal to ft3 A) 673.2 ft3

B) 900 ft3

Objective: (9.2) Use English and Metric Units to Measure Capacity

Use the fact that a solid with a volume of 1000 cubic centimeters has a capacity of 1 liter, along with dimensional analysis, to convert the given unit to the unit indicated. 64) 402.2 mL to cm3

A) 402.2 cm3

B) 40,220 cm3

C) 402,200 cm3

D) 0.4022 cm3

C) 56 cm3

D) 5.6 cm3

Objective: (9.2) Use English and Metric Units to Measure Capacity

65) 56 L to cm3 A) 56,000 cm3

B) 5,600 cm3

Objective: (9.2) Use English and Metric Units to Measure Capacity

66) 80,000 cm3 to L A) 80 L

B) 8 L

C) 800 L

D) 80,000 L

C) 16 mL

D) 0.016 mL

Objective: (9.2) Use English and Metric Units to Measure Capacity

67) 16 cm3 to mL A) 160 mL

B) 16,000 mL

Objective: (9.2) Use English and Metric Units to Measure Capacity

Solve the problem. 68) A tank has a capacity of 20,000 cubic feet. How many gallons of water does the tank hold? A) 2,674 gal B) 87 gal C) 149,600 gal D) 20,000 gal Objective: (9.2) Use English and Metric Units to Measure Capacity

69) A container of motor oil has a volume of 8,000 cubic centimeters. How many liters of oil does the container hold? A) 80 L B) 8,000 L C) 800 L D) 8 L Objective: (9.2) Use English and Metric Units to Measure Capacity

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 70) A volume of 2 liters is a common capacity to bottle beverages such as soft drinks. What is this capacity in cubic centimeters (cm3 )? Objective: (9.2) Use English and Metric Units to Measure Capacity

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Selecting from milligram, gram, kilogram, and tonne, determine the best unit of measure to express the given weight. 71) a grain of sand A) tonne B) gram C) kilogram D) milligram Objective: (9.3) Apply Metric Prefixes to Units of Weight

72) a bridge A) milligram

B) tonne

C) gram

D) kilogram

C) milligram

D) kilogram

C) kilogram

D) milligram

C) 10 t

D) 10 mg

Objective: (9.3) Apply Metric Prefixes to Units of Weight

73) a pad of paper A) tonne

B) gram

Objective: (9.3) Apply Metric Prefixes to Units of Weight

74) a cat A) tonne

B) gram

Objective: (9.3) Apply Metric Prefixes to Units of Weight

Select the best estimate for the weight of the given item. 75) the weight of a pebble A) 10 g B) 10 kg Objective: (9.3) Apply Metric Prefixes to Units of Weight

76) the amount of sodium in a frozen dinner A) 400 mg B) 400 g

C) 400 kg

D) 400 t

C) 17 kg

D) 17 t

C) 4,000 g

D) 4,000 kg

C) 0.46 g

D) 0.046 g

C) 14,900 g

D) 149,000 g

C) 24 mg

D) 240 mg

C) 700 cg

D) 0.07 cg

C) 59 g

D) 0.0059 g

Objective: (9.3) Apply Metric Prefixes to Units of Weight

77) the weight of a child A) 17 g

B) 17 mg

Objective: (9.3) Apply Metric Prefixes to Units of Weight

78) the weight of a newly constructed cruise ship A) 4,000 mg B) 4,000 t Objective: (9.3) Apply Metric Prefixes to Units of Weight

Convert the given unit of weight to the unit indicated. 79) 46 kg to g A) 46,000 g B) 4,600 g Objective: (9.3) Convert Units of Weight Within the Metric System

80) 149 mg to g A) 0.149 g

B) 1.49 g

Objective: (9.3) Convert Units of Weight Within the Metric System

81) 2.4 dg to mg A) 0.24 mg

B) 2,400 mg

Objective: (9.3) Convert Units of Weight Within the Metric System

82) 7 g to cg A) 70 cg

B) 7,000 cg

Objective: (9.3) Convert Units of Weight Within the Metric System

83) 0.059 mg to g A) 0.000059 g

B) 0.00059 g

Objective: (9.3) Convert Units of Weight Within the Metric System

Solve the problem. 84) Eight items purchased in a hardware store weigh 15 kilograms. One of the items is a tool that weighs 290 g. What is the total weight, in kilograms, of the other seven items? A) 275 kg B) 0.29 kg C) 14.71 kg D) 15.29 kg Objective: (9.3) Convert Units of Weight Within the Metric System

85) Which is more economical: purchasing the economy size sack of beans at 9 kilograms for $11, or purchasing the regular size bag at 57 grams for $1.40? A) The economy size is more economical. B) Neither is more economical. C) The regular size is more economical. Objective: (9.3) Convert Units of Weight Within the Metric System

Convert as indicated. 86) 68 m 3 to kg A) 68,000 kg

B) 0.68 kg

C) 0.068 kg

D) 6,800 kg

Objective: (9.3) Use Relationships Between Volume and Weight Within the Metric System

87) 930 kg to cm3 A) 930,000 cm3

B) 0.93 cm3

C) 9.3 cm3

D) 93,000 cm3

Objective: (9.3) Use Relationships Between Volume and Weight Within the Metric System

88) 120 m 3 to t A) 1.2 t

B) 120,000 t

C) 12,000 t

D) 120 t

Objective: (9.3) Use Relationships Between Volume and Weight Within the Metric System

89) 0.62 kL to g A) 620,000 g

B) 62,000 g

C) 620 g

D) 6.2 g

Objective: (9.3) Use Relationships Between Volume and Weight Within the Metric System

90) 74 t to m 3 A) 74,000 m 3

B) 74 m 3

C) 0.74 m 3

D) 0.074 m 3

Objective: (9.3) Use Relationships Between Volume and Weight Within the Metric System

Use dimensional analysis to convert the given quantity to the units indicated. When necessary, round answers to two decimal places. 91) 83 oz to g A) 1,328 g B) 2.96 g C) 2,324 g D) 37.35 g Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

92) 250 kg to lb A) 112.5 lb

B) 225 lb

C) 555.56 lb

D) 277.78 lb

Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

93) 30 lb to g A) 52.50 g

B) 17.14 g

C) 13,500 g

D) 480 g

Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

94) 940 lb to kg A) 423 kg

B) 20,888.89 kg

C) 2,088.89 kg

D) 4,230 kg

Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

95) 900t to T A) 1,000.00 T

B) 81 T

C) 100.00 T

D) 810 T

Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

Solve the problem. 96) If a freight carrier charges 59 cents for a package up to one ounce and 35 cents for each additional ounce or fraction of an ounce, find the cost of shipping a package that weighs 224 grams. A) $5.07 B) $3.04 C) $3.15 D) $3.39 Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

97) For each kilogram of a person's weight, 70 milligrams of a drug is to be given. What dosage should be given to an adult who weighs 220 pounds? A) 1.54 mg B) 34,222.22 mg C) 15,400 mg D) 6,930 mg Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 98) The Holly cousins, Crash and Bob, have a combined weight of 800 pounds. What is their weight in kilograms (kg)? Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the given Celsius temperature to its equivalent temperature on the Fahrenheit scale. Where appropriate, round to the nearest tenth of a degree. 99) 23°C A) 9.4°F B) -4°F C) 31.6°F D) 73.4°F Objective: (9.3) Understand Temperature Scales

100) -8°C A) 27.6°F

C) -22.2°F

B) 17.6°F

D) -46.4°F

Objective: (9.3) Understand Temperature Scales

Convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. Where appropriate, round to the nearest tenth of a degree. 101) 37°F A) 98.6°C B) 9.0°C C) 52.6°C D) 2.8°C Objective: (9.3) Understand Temperature Scales

102) 122°F A) 251.6°C

B) 50°C

C) 85.6°C

D) 162°C

C) -20.2°C

D) -33.9°C

Objective: (9.3) Understand Temperature Scales

103) -29°F A) 1.7°C

B) -48.1°C

Objective: (9.3) Understand Temperature Scales

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Convert the temperature to Celsius. 104) On a fall night in Tampa, Florida, the low temperature was 45°F. Objective: (9.3) Understand Temperature Scales

Answer Key Testname: 09-BLITZER_TM8E_TEST_ITEM_FILE

1) D 2) A 3) B 4) D 5) A 6) D 7) C 8) A 9) A 10) D 11) D 12) B 13) A 14) B 15) C 16) D 17) B 18) A 19) A 20) B 21) A 22) A 23) B 24) D 25) D 26) C 27) D 28) D 29) D 30) D 31) D 32) B 33) C 34) C 35) C 36) B 37) A 38) D 39) B 40) A 41) C 42) 56 43) D 44) A 45) B 46) A 47) A 48) B 49) C 50) D

51) A 52) C 53) D 54) D

100) B 101) D 102) B 103) D 104) 7.2°C

55) 1.17 in2 56) C 57) A 58) D 59) D 60) D 61) A 62) D 63) B 64) A 65) A 66) A 67) C 68) C 69) D 70) 2000 cm3 71) D 72) B 73) B 74) C 75) A 76) A 77) C 78) B 79) A 80) A 81) D 82) C 83) A 84) C 85) A 86) A 87) A 88) D 89) A 90) B 91) C 92) C 93) C 94) A 95) A 96) B 97) D 98) 360 kg 99) D 12

Blitzer, Thinking Mathematically, 8e Chapter 10 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide the following information. a. Name the vertex of the angle. b. Name the sides of the angle. c. Name the angle in three different ways. 1)

A) a. point C

B) a. point C

b. BA and CA c. 6 A, 6 BAC, 6 ABC C) a. point BAC

b. AB and AC c. 6 A, 6 ABC, 6 CAB D) a. point A

b. BA and CA c. 6 A, 6 BAC, 6 CAB

b. AB and AC c. 6 A, 6 BAC, 6 CAB

Objective: (10.1) Understand Points, Lines, and Planes as the Basis of Geometry

Solve the problem. 2) The hour hand of a clock moves from 12 to 11 o'clock. Through how many degrees does it move? A) 11° B) 330° C) 396° D) 132° Objective: (10.1) Solve Problems Involving Angle Measures

Use the protractor to find the measure of the angle. Then indicate if the angle is acute, right, obtuse, or straight. 3)

A) 45°, acute

B) 145°, obtuse

C) 35°, acute

Objective: (10.1) Solve Problems Involving Angle Measures

D) 155°, obtuse

Classify the angle as acute, right, straight or obtuse. 4)

A) right

B) obtuse

C) acute

D) straight

C) obtuse

D) right

C) straight

D) acute

C) obtuse

D) acute

C) 147°

D) 52°

Objective: (10.1) Solve Problems Involving Angle Measures

A) straight

B) acute

Objective: (10.1) Solve Problems Involving Angle Measures

A) right

B) obtuse

Objective: (10.1) Solve Problems Involving Angle Measures

7) A) right

B) straight

Objective: (10.1) Solve Problems Involving Angle Measures

Find the measure of the angle in which ?° appears. 8)

33°

A) 112°

B) 57°

Objective: (10.1) Solve Problems Involving Angle Measures

72°

A) 18°

B) 28°

C) 162°

D) 108°

C) 229°

D) 139°

C) 51.2°

D) 140.8°

1 C) 126 ° 2

D) 90°

C) 239°

D) 329°

C) 169°

D) 79°

1 C) 44 ° 4

3 D) 45 ° 4

C) 30°

D) 29.2°

Objective: (10.1) Solve Problems Involving Angle Measures

Find the measure of the complement of the angle. 10) Find the complement of 41°. A) 319° B) 49° Objective: (10.1) Solve Problems Involving Angle Measures

11) 39.2° A) 50.8°

B) 90°

Objective: (10.1) Solve Problems Involving Angle Measures

1 12) 53 ° 2

A) 37°

1 B) 36 ° 2

Objective: (10.1) Solve Problems Involving Angle Measures

Find the measure of the supplement of the angle. 13) Find the supplement of 31°. A) 59° B) 149° Objective: (10.1) Solve Problems Involving Angle Measures

14) Find the supplement of 101°. A) 259°

B) 191°

Objective: (10.1) Solve Problems Involving Angle Measures

1 15) 134 ° 4

A) 180°

B) 46°

Objective: (10.1) Solve Problems Involving Angle Measures

16) 150.8° A) 60.8°x

B) 30.8°

Objective: (10.1) Solve Problems Involving Angle Measures

Find the measures of angles 1, 2, and 3. 17)

99°

A) m61 = 99°, m62 = 81°, m63 = 99° C) m61 = 81°, m62 = 99°, m63 = 81°

B) m61 = 99°, m62 = 9°, m63 = 99° D) m61 = 9°, m62 = 99°, m63 = 9°

Objective: (10.1) Solve Problems Involving Angle Measures

18)

51°

A) 6 1 = 39°; 6 2 = 90°; 6 3 = 39° C) 6 1 = 39°; 6 2 = 90°; 6 3 = 51°

B) 6 1 = 129°; 6 2 = 51°; 6 3 = 129° D) 6 1 = 39°; 6 2 = 102°; 6 3 = 39°

Objective: (10.1) Solve Problems Involving Angle Measures

The figure shows two parallel lines intersected by a transversal. One of the angle measures is given. Find the measure of the indicated angle. 19)

35°

Find the measure of 66. A) 55°

B) 125°

C) 35°

Objective: (10.1) Solve Problems Involving Angles Formed by Parallel Lines and Transversals

D) 25°

Find the measure of angle A for the triangle shown. 20)

36° 106°

A) 54°

B) 16°

C) 38°

D) 218°

Objective: (10.2) Solve Problems Involving Angle Relationships in Triangles

21)

44°

A) 46°

B) 56°

C) 90°

D) 136°

Objective: (10.2) Solve Problems Involving Angle Relationships in Triangles

Find the measure of the angle. 22) Find the measure of angle 4 in the figure shown.

A) 120°

B) 140°

C) 130°

D) 110°

Objective: (10.2) Solve Problems Involving Angle Relationships in Triangles

Solve the problem. 23) A surveyor measured a triangular plot of ground, measuring the three angles as 31.1°, 69.1°, and 81.3°. Are these measurements correct? If not, how much of an error is there? A) The total is 1.7° too low. B) The total is 2.5° too high. C) The total is 1.5° too high. D) The measurements are correct. Objective: (10.2) Solve Problems Involving Angle Relationships in Triangles

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Name the corresponding angles and the corresponding sides in the pair of similar triangles. 24)

Objective: (10.2) Solve Problems Involving Similar Triangles

25)

Objective: (10.2) Solve Problems Involving Similar Triangles

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x. 26) 50 m 48 m A) 21 m

25 m 24 m

B) 10 m

C) 14 m

Objective: (10.2) Solve Problems Involving Similar Triangles

D) 7 m

27) 10 m

15 m

9m 12 m

A) 12 m

B) 19 m

C) 25 m

D) 20 m

C) 30 in.

D) 7.5 in.

Objective: (10.2) Solve Problems Involving Similar Triangles

28)

15 in.

4 in. A) 2.1 in.

8 in.

B) 480 in.

Objective: (10.2) Solve Problems Involving Similar Triangles

Use similar triangles and the fact that corresponding sides are proportional to find the length of the segment marked with an x. 29)

7 in. 5 in.

7 in.

A) 2 in.

B) 2.8 in.

C) 9.8 in.

Objective: (10.2) Solve Problems Involving Similar Triangles

D) 2.84 in.

Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x. 30)

18 in. 30 in. 24 in.

A) 24.5 in.

B) 14.4 in.

C) 22.5 in.

D) 40 in.

Objective: (10.2) Solve Problems Involving Similar Triangles

Use similar triangles to solve the problem. 31) A flagpole casts a shadow of 25 ft, Nearby, a 9-ft tree casts a shadow of 3 ft. What is the height of the flag pole? A) 1.1 ft B) 675 ft C) 75 ft D) 8.3 ft Objective: (10.2) Solve Problems Involving Similar Triangles

Use the Pythagorean Theorem to find the missing length in the right triangle. Use a calculator to find square roots, rounding, if necessary, to the nearest tenth. 32)

12 km

16 km A) 20 km

B) 19 km

C) 10.6 km

D) 14 km

C) 12 m

D) 15 m

C) 320 cm

D) 160 cm

Objective: (10.2) Solve Problems Using the Pythagorean Theorem

33) 9m

15 m

A) 10.5 m

B) 14 m

Objective: (10.2) Solve Problems Using the Pythagorean Theorem

34)

8 cm 16 cm A) 17.9 cm

B) 12 cm

Objective: (10.2) Solve Problems Using the Pythagorean Theorem

35) c 10 in. 19 in. A) 230.5 in.

B) 461 in.

C) 21.5 in.

D) 14.5 in.

C) 14 in.

D) 84 in.

Objective: (10.2) Solve Problems Using the Pythagorean Theorem

36) a 11 in. 17 in. A) 13 in.

B) 168 in.

Objective: (10.2) Solve Problems Using the Pythagorean Theorem

Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. 37) A 21-inch-square TV is on sale at the local electronics store. If 21 inches is the measure of the diagonal of the screen, use the Pythagorean theorem to find the length of the side of the screen. A) 220.5 in. B) 4.6 in. C) 14.8 in. D) 2.3 in. Objective: (10.2) Solve Problems Using the Pythagorean Theorem

38) A square sheet of paper measures 49 centimeters on each side. What is the length of the diagonal of this paper? A) 98 cm B) 49 cm C) 69.3 cm D) 4,802 cm Objective: (10.2) Solve Problems Using the Pythagorean Theorem

39) A 12-foot pole is supported by two wires that extend from the top of the pole to points that are each 16 feet from the base of the pole. Find the total length of the two wires. A) 800 ft B) 20 ft C) 56 ft D) 40 ft Objective: (10.2) Solve Problems Using the Pythagorean Theorem

40) If you drive 9 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? A) 1.7 mi B) 15 mi C) 7.9 mi D) 4.6 mi Objective: (10.2) Solve Problems Using the Pythagorean Theorem

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 41) Dwayne Johnson is on his way to an autograph signing. His limousine drove 24 miles east and then drove 50 miles south. How far is the limo from where it started? Round to the nearest tenth. Objective: (10.2) Solve Problems Using the Pythagorean Theorem

42) Brothers Matt and Jeff are leaning a 20-foot ladder against their house. If the ladder reaches 15 feet up the house, how far is the bottom of the ladder from the base of the house? Round to the nearest tenth. Objective: (10.2) Solve Problems Using the Pythagorean Theorem

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the number of sides to name the polygon. 43)

A) quadrilateral

B) pentagon

C) hexagon

D) heptagon

Objective: (10.3) Name Certain Polygons According to the Number of Sides

44)

A) octagon

B) hexagon

C) quadrilateral

D) heptagon

Objective: (10.3) Name Certain Polygons According to the Number of Sides

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the quadrilaterals below to solve the problem.

45) Which of the quadrilaterals shown have any opposite sides that are parallel? Name these quadrilaterals.

Objective: (10.3) Recognize the Characteristics of Certain Quadrilaterals

46) Which of the quadrilaterals shown have sides of equal length? Name these quadrilaterals.

Objective: (10.3) Recognize the Characteristics of Certain Quadrilaterals

47) Which of the quadrilaterals shown have right angles? Name these quadrilaterals.

Objective: (10.3) Recognize the Characteristics of Certain Quadrilaterals

48) Which of the quadrilaterals shown is not a parallelogram? Name this quadrilateral.

Objective: (10.3) Recognize the Characteristics of Certain Quadrilaterals

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the perimeter of the figure named and shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 49) Rectangle 4 cm 6 cm

6 cm

4 cm A) 16 cm

B) 20 cm

C) 4 cm

D) 10 cm

C) 38 ft

D) 19 ft

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

50) Rectangle 11 ft 8 ft 11 ft A) 32 ft

8 ft

B) 6 ft

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

51) Square 2.8 ft 2.8 ft

2.8 ft

2.8 ft A) 11.2 ft

B) 5.6 ft

C) 21.2 ft

D) 15.68 ft

C) 59 m

D) 91 m

C) 59 mi

D) 58 mi

C) 112.5 yd

D) 44 yd

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

52) Parallelogram 32 m 27 m

27 m

32 m A) 86 m

B) 118 m

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

53) Triangle 23 mi

12 mi

24 mi

A) 47 mi

B) 144 mi

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

54) Equilateral triangle 15 yd

A) 30 yd

B) 45 yd

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

55) regular octagon

7 yd

A) 42 yd

B) 56 yd

C) 49 yd

D) 8 yd

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

Find the perimeter of the figure shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 56) 6m 7m 6m 24 m

19 m

A) 92 m

B) 111 m

C) 98 m

D) 74 m

C) 40 ft

D) 43 ft

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

57) 15 ft 3.5 ft 5 ft

8 ft 1.5 ft 7 ft

A) 38.5 ft

B) 36.5 ft

Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

Solve the problem. 58) A garden is in the shape of a rectangle 49 feet long and 24 feet wide. If fencing costs $5 a foot, what will it cost to place fencing around the garden? A) $365 B) $730 C) $5,880 D) $1,460 Objective: (10.3) Solve Problems Involving a Polygon's Perimeter

59) Find the sum of the measures of the angles of a 7-sided polygon. A) 900° B) 720° C) 1,260° Objective: (10.3) Find the Sum of the Measures of a Polygon's Angles

D) 180°

60) Find the sum of the measures of the angles of a pentagon. A) 360° B) 180°

C) 540°

D) 900°

Objective: (10.3) Find the Sum of the Measures of a Polygon's Angles

The figure shows a regular polygon. Find the measure of angle 1. 61)

A) 135°

B) 180°

C) 108°

D) 120°

Objective: (10.3) Find the Sum of the Measures of a Polygon's Angles

a. Find the sum of the measures of the angles for the figure shown; b. Find the measure of angle 1. 62) 130° 60°

A) a. 540° ; b. 170°

B) a. 540° ; b. 165°

C) a. 450° ; b. 80°

Objective: (10.3) Find the Sum of the Measures of a Polygon's Angles

D) a. 540° ; b. 175°

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. A tessellation formed by two or more regular polygons is shown. a. Name the types of regular polygons that surround each vertex. b. Determine the number of angles that come together at each vertex, as well as the measures of these c. Use the angle measures from part (b) to explain why the tessellation is possible.

63)

Objective: (10.3) Understand Tessellations and Their Angle Requirements

64)

Objective: (10.3) Understand Tessellations and Their Angle Requirements

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use formulas to find the area of the figure. 65) 2 in 11 in A) 26 in2

B) 8 in2

C) 22 in2

D) 13 in2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

angles

66) 12 units 2 units 16 units A) 12 units2

B) 32 units2

C) 16 units2

D) 96 units2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

67)

6 yd

A) 10 yd2

B) 36 yd2

C) 12 yd2

D) 24 yd2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

68)

7 ft

14 ft 8 ft 13 ft

A) 28 ft2

B) 49 ft2

C) 91 ft2

D) 45.5 ft2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

69) 30 m

23 m

19 m

23 m

30 m

A) 5,700 m 2

B) 53 m 2

C) 570 m 2

D) 690 m 2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

70) 11 km

12.2 km

19 km 2 A) 231.8 km

B) 134.2 km2

C) 366 km2

D) 183 km2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

71) 21 in. 4 in. 14 in. 5 in. A) 129 in.2

B) 154 in.2

C) 96 in.2

D) 112 in.2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

72)

5 ft

10 ft

10 ft 9 ft

A) 180 ft2

B) 9,000 ft2

C) 50 ft2

D) 230 ft2

Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

Solve the problem. 73) What will it cost to tile a rectangular floor measuring 251 feet by by 27 feet if the tile costs $20 per square foot? A) $135,540 B) $6,777 C) $298 D) $11,120 Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

74) The rectangular front of a house measures 15 feet by 27 feet. A rectangular door on the front of the house measures 6 feet by 3 feet. There are also 5 rectangular windows on the front of the house, each measuring 3 feet by 4 feet. How many square feet of siding will be needed to cover the front of the house not counting the area covered by the door and windows? A) 78 ft2 B) 375 ft2 C) 405 ft2 D) 327 ft2 Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

75) A parking area that is to be resurfaced is shaped like a trapezoid. The bases are 70 feet and 80 feet, and the height is 50 feet. What is the cost if the price of the resurfacing is $1.35 per square foot? A) $10,125.00 B) $3,750.00 C) $5,062.50 D) $7,560.00 Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems

Find the circumference and area of the circle. Round the answer to the nearest whole number. 76)

23 in

A) 72 in, 289 in2

B) 145 in, 145 in2

C) 72 in, 6,648 in2

D) 145 in, 1,662 in2

Objective: (10.4) Use Formulas for a Circle's Circumference and Area

77) 16 cm

A) 50 cm, 201 cm2

B) 25 cm, 100 cm2

C) 50 cm, 50 cm2

D) 25 cm, 804 cm2

Objective: (10.4) Use Formulas for a Circle's Circumference and Area

Solve the problem. Round all circumference and area calculations to the nearest whole number. 78) How much fencing is required to enclose a circular garden whose radius is 21 m? A) 1,385 m B) 33 m C) 132 m

D) 66 m

Objective: (10.4) Use Formulas for a Circle's Circumference and Area

79) How many flowers spaced every 4 inches are needed to surround a circular garden with a 15-foot radius? Round all circumference and area calculations to the nearest whole number. A) 282 flowers B) 376 flowers C) 266 flowers D) 141 flowers Objective: (10.4) Use Formulas for a Circle's Circumference and Area

80) If asphalt pavement costs $0.90 per square foot, find the cost to pave the circular road (indicated by dots) in the figure shown.

80 ft 70 ft

A) $18,032.58

B) $56.55

C) $4,241.15

Objective: (10.4) Use Formulas for a Circle's Circumference and Area

D) $13,854.43

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 81) A 7-inch apple pie sells for $4. What is its cost per square inch (in2 )? Round to the nearest cent. Objective: (10.4) Use Formulas for a Circle's Circumference and Area

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the volume of the figure. If necessary, round the answer to the nearest whole number. 82)

6 cm

4 cm 2 cm

A) 24 cm3

B) 144 cm3

C) 32 cm3

D) 48 cm3

Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

83) 15 yd

20 yd

A) 14,137 yd3

B) 3,534 yd3

C) 942 yd3

D) 471 yd3

Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

84) Cone

7 in.

8 in.

A) 117 in.3

B) 938 in.3

C) 469 in.3

D) 704 in.3

Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

85)

4 yd

A) 268 yd3

B) 67 yd3

C) 34 yd3

D) 151 yd3

Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

86) 19 m

9m 13 m

A) 741 m 3

B) 2,223 m 3

C) 2,327 m 3

D) 86,697 m 3

Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

Use two formulas for volume to find the volume of the figure. Round the answer to the nearest whole number. 87) 12 cm

16 cm

A) 1,056 cm3

B) 1,508 cm3

C) 32,572 cm3

D) 2,262 cm3

Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

Solve the problem. 88) A special stainless-steel cone sits on top of a cable television antenna. The cost of the stainless steel is $4.00 per cm3 . The cone has a radius of 9 cm and a height of 11 cm. What is the cost of the stainless steel needed to make this solid steel cone? Round to the nearest cent. A) $1,188.00 B) $829.38

C) $3,732.21

D) $414.69

Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

89) A new pyramid has been found in South America. The pyramid has a rectangular base that measures 92 yd by 130 yd, and has a height of 70 yd. The pyramid is not hollow like the Egyptian pyramids and is composed of layer after layer of cut stone. The stone weighs 408 lb per cubic yard. How many pounds does the pyramid weigh? A) 279,066.7 lb B) 684 lb C) 113,859,200 lb D) 341,577,600 lb Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

90) A building contractor is to dig a foundation 45 feet long, 16 feet wide, and 6 feet deep. The contractor pays $14 per load for trucks to remove the dirt. Each truckload holds 4 cubic yards. What is the cost to the contractor to have all the dirt hauled away? A) $560 B) $15,120 C) $2,240 D) $40 Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

91) Two cylindrical cans of beef stew sell for the same price. One can has a diameter of 6 inches and a height of 4 inches. The other has a diameter of 4 inches and a height of 5 inches. Which can contains more stew and is, therefore, a better buy? A) The can with the diameter of 6 inches is the better buy. B) They are both equally good buys. C) The can with the diameter of 4 inches is the better buy. Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 92) What is the volume of a rectangular storage facility that is 75 feet tall, 80 feet wide and 15 feet tall? Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the surface area of the figure. 93) 2m

7m 5m

A) 140 m 2

B) 59 m 2

C) 70 m 2

Objective: (10.5) Compute the Surface Area of a Three-Dimensional Figure

D) 118 m 2

94)

7 ft 7 ft 7 ft

A) 294 ft2

B) 392 ft2

C) 147 ft2

D) 343 ft2

Objective: (10.5) Compute the Surface Area of a Three-Dimensional Figure

Use the given right triangle to find the trigonometric function. 95) sin B

4 5

4 3

3 5

5 3

40 9

Objective: (10.6) Use the Lengths of the Sides of a Right Triangle to Find Trigonometric Ratios

96) cos A

40 41

41 9

9 41

Objective: (10.6) Use the Lengths of the Sides of a Right Triangle to Find Trigonometric Ratios

97) cos A

13 5

12 5

12 13

5 13

Objective: (10.6) Use the Lengths of the Sides of a Right Triangle to Find Trigonometric Ratios

Find the measure of the side of the right triangle whose length is designated by the lowercase letter. Round your answer to the nearest whole number. 98)

a 39° b = 120 cm A) 97 cm

B) 111 cm

C) 106 cm

D) 93 cm

Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles

99)

129 in.

34°

A) 107 in.

B) 100 in.

C) 102 in.

D) 96 in.

Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles

100)

16 yd 37°

A) 21 yd

B) 8 yd

C) 23 yd

Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles

D) 18 yd

Find the measures of the parts of the right triangle that are not given. Round your answers to the nearest whole number. 101)

c a 32° b = 65 yd A) a = 41 yd; c = 77 yd; 6 B = 58° C) a = 45 yd; c = 77 yd; 6 B = 58°

B) a = 45 yd; c = 75 yd; 6 B = 58° D) a = 41 yd; c = 75 yd; 6 B = 58°

Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles

Use the inverse trigonometric keys on a calculator to find the measure of angle A, rounded to the nearest whole degree. 102)

69 m 52 m

A) 50°

B) 49°

C) 52°

D) 51°

Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles

103)

10 m

28 m

A) 19°

B) 21°

C) 20°

D) 18°

Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles

104)

34 cm

28 cm

A) 32°

B) 34°

C) 35°

Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles

D) 33°

Solve the problem. 105) To find the distance across a large pond, a surveyor took the measurements in the figure shown. Use these measurements to determine how far it is across the lake. Round to the nearest foot.

60° 80 feet A) 69 feet

B) 139 feet

C) 40 feet

D) 46 feet

Objective: (10.6) Use Trigonometric Ratios to Solve Applied Problems

106) A building 230 feet tall casts a 50 foot long shadow. Find the angle of elevation of the sun to the nearest degree.

230 feet

50 feet

A) 77°

B) 12°

C) 78°

D) 13°

Objective: (10.6) Use Trigonometric Ratios to Solve Applied Problems

107) At a certain time of day, the angle of elevation of the sun is 64°. To the nearest foot, find the height of a pole whose shadow at that time is 14 feet long.

64° 14 ft A) 30 feet

B) 32 feet

C) 6 feet

Objective: (10.6) Use Trigonometric Ratios to Solve Applied Problems

D) 29 feet

108) For one instant, a hot air balloon is 530 feet above the ocean. The figure shows that the angle of depression from the balloon to point P is 39°. How far, to the nearest foot, is point P to the point directly below the balloon on the surface of the water?

39° 530 ft

A) 456 feet

B) 16,594 feet

C) 654 feet

D) 376 feet

Objective: (10.6) Use Trigonometric Ratios to Solve Applied Problems

109) A kite flies to a height of 35 feet when 74 feet of string is out. If the string is in a straight line, find the angle that it makes with the ground. Round to the nearest tenth of a degree. A) 30.8° B) 28.2° C) 29.4° D) 26.5° Objective: (10.6) Use Trigonometric Ratios to Solve Applied Problems

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 110) Is the network shown below traversable? If it is, describe a path that will traverse it.

Objective: (10.7) Gain an Understanding of Some of the General Ideas of Other Kinds of Geometries

111) Is the network shown below traversable? If it is, describe a path that will traverse it.

Objective: (10.7) Gain an Understanding of Some of the General Ideas of Other Kinds of Geometries

112) The figure on the left shows the floor plan of a four-room house. By representing rooms as vertices, the outside as a vertex, and doors as arcs, the figure on the right is a graph that corresponds to the floor plan. According to the floor plan, how many doors connect the outside, E, with room A? How is this shown in the graph?

Objective: (10.7) Gain an Understanding of Some of the General Ideas of Other Kinds of Geometries

113) The figure on the left shows the floor plan of a four-room house. By representing rooms as vertices, the outside as a vertex, and doors as arcs, the figure on the right is a graph that corresponds to the floor plan. Is the graph traversable? Explain your answer.

Objective: (10.7) Gain an Understanding of Some of the General Ideas of Other Kinds of Geometries

114) What is the genus of a compact disc (CD)? Objective: (10.7) Gain an Understanding of Some of the General Ideas of Other Kinds of Geometries

115) What is the genus of the object shown?

Objective: (10.7) Gain an Understanding of Some of the General Ideas of Other Kinds of Geometries

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 116) Choose the correct statement about the figures shown below.

A) Figure A exhibits self-similarity; figure B does not. B) Both figure A and figure B exhibit self-similarity. C) Neither figure A nor figure B exhibits self-similarity. D) Figure B exhibits self-similarity; figure A does not. Objective: (10.7) Gain an Understanding of Some of the General Ideas of Other Kinds of Geometries

Answer Key Testname: 10-BLITZER_TM8E_TEST_ITEM_FILE

1) D 2) B 3) C 4) A 5) B 6) B 7) B 8) B 9) D 10) B 11) A 12) B 13) B 14) D 15) D 16) D 17) C 18) A 19) C 20) C 21) A 22) A 23) C 24) corresponding angles: 6 J and 6 L, 6 H and 6 M, 6 K and 6 N corresponding sides: JH and LM, KH and NM, KJ and NL 25) corresponding angles: 6 B and 6 D, 6 C and 6 E, 6 A and 6F corresponding sides:

CB and ED, CA and EF, AB and FD 26) C 27) D 28) A 29) B 30) C 31) C 32) A 33) C 34) A 35) C 36) A 37) C 38) C

39) D 40) B 41) 55.5 mi 42) 13.2 ft 43) B 44) B 45) a. rhombus, b. rectangle, c. trapezoid, d. square, e. parallelogram 46) a. rhombus, d. square 47) b. rectangle, d. square 48) c. trapezoid 49) B 50) C 51) A 52) B 53) C 54) B 55) B 56) C 57) C 58) B 59) A 60) C 61) A 62) A 63) a. Square and octagon b. 3 angles; one 90° angle and two 135° angles c. 90° + (2)(135°) = 360° 64) a. Triangle and hexagon b. 5 angles; four 60° angle and one 120° angles c. (4)(60°) + 120° = 360° 65) C 66) C 67) B 68) D 69) C 70) D 71) B

72) D 73) A 74) D 75) C 76) D 77) A 78) C 79) A 80) C $0.10 81) in2 82) D 83) B 84) C 85) A 86) A 87) A 88) C 89) C 90) A 91) A 92) 90,000 ft3 93) D 94) A 95) C 96) C 97) D 98) A 99) A 100) A 101) A 102) B 103) C 104) C 105) B 106) C 107) D 108) C 109) B 110) Yes, the network is traversable. The path E-B-A-C-B-D-C-E -D traverses the network. 111) The network is not traversable.

112) According to the floor plan, one door connects the outside, E, with room A. This is shown in the graph by the one arc that connects vertex E with vertex A. (Answers will vary somewhat.) 113) Yes, the graph is traversable. All the vertices are even, therefore the graph is traversable starting at any vertex. (Answers will vary somewhat.) 114) 1 115) The bowling ball has genus 0. 116) A

Blitzer, Thinking Mathematically, 8e Chapter 11 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem by applying the Fundamental Counting Principle with two groups of items. 1) A restaurant offers 11 entrees and 7 desserts. In how many ways can a person order a two-course meal? A) 20 B) 77 C) 18 D) 154 Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

2) In how many ways can a girl choose a two-piece outfit from 6 blouses and 7 skirts? A) 84 B) 13 C) 42

D) 15

Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

3) A restaurant offers a choice of 4 salads, 7 main courses, and 4 desserts. How many possible 3-course meals are there? A) 28 B) 224 C) 112 D) 15 Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

4) There are 4 roads leading from Bluffton to Hardeeville, 8 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon? A) 160 B) 32 C) 17 D) 320 Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

5) An apartment complex offers apartments with four different options, designated by A through D. A = number of bedrooms (one through four) B = number of bathrooms (one through three) C = floor (first through fifth) D = outdoor additions (balcony or no balcony) How many apartment options are available? A) 16 B) 240

C) 14

D) 120

Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

6) A person can order a new car with a choice of 12 possible colors, with or without air conditioning, with or without heated seats, with or without anti-lock brakes, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered in terms of these options? A) 384 B) 192 C) 24 D) 768 Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

7) You are taking a multiple-choice test that has 6 questions. Each of the questions has 3 choices, with one correct choice per question. If you select one of these options per question and leave nothing blank, in how many ways can you answer the questions? A) 216 B) 729 C) 9 D) 18 Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

8) License plates in a particular state display 2 letters followed by 3 numbers. How many different license plates can be manufactured? (Repetitions are allowed.) A) 260 B) 6 C) 36 D) 676,000 Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

9) How many different four-letter secret codes can be formed if the first letter must be an S or a T? A) 421,824 B) 35,152 C) 456,976 D) 72 Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 10) Jamie is joining a music club. As part of her 4-CD introductory package, she can choose from 12 rock selections, 10 alternative selections, 7 country selections and 5 classical selections. If Jamie chooses one selection from each category, how many ways can she choose her introductory package? Objective: (11.1) Use the Fundamental Counting Principle to Determine the Number of Possible Outcomes in a Given Situation

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the Fundamental Counting Principle to solve the problem. 11) There are 9 performers who are to present their acts at a variety show. How many different ways are there to schedule their appearances? A) 72 B) 81 C) 9 D) 362,880 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

12) There are 8 performers who are to present their acts at a variety show. One of them insists on being the first act of the evening. If this request is granted, how many different ways are there to schedule the appearances? A) 40,320 B) 64 C) 56 D) 5,040 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

13) You want to arrange 10 of your favorite CD's along a shelf. How many different ways can you arrange the CD's assuming that the order of the CD's makes a difference to you? A) 3,628,800 B) 90 C) 362,880 D) 100 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

14) A teacher and 10 students are to be seated along a bench in the bleachers at a basketball game. In how many ways can this be done if the teacher must be seated in the middle and a difficult student must sit to the teacher's immediate left? A) 20 B) 40,320 C) 362,880 D) 3,628,800 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

Use the formula for nPr to solve.

15) A church has 10 bells in its bell tower. Before each church service 4 bells are rung in sequence. No bell is rung more than once. How many sequences are there? A) 151,200 B) 5,040 C) 302,400 D) 210 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

16) A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 10 members and any member can be elected to each position? No person can hold more than one office. A) 240 B) 360 C) 5,040 D) 720 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

17) In a contest in which 7 contestants are entered, in how many ways can the 4 distinct prizes be awarded? A) 70 B) 210 C) 840 D) 420 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

18) How many arrangements can be made using 4 letters of the word HYPERBOLAS if no letter is to be used more than once? A) 302,400 B) 5,040 C) 151,200 D) 210 Objective: (11.2) Use the Fundamental Counting Principle to Count Permutations

Evaluate the factorial expression. 4! 19) 2! A) 2!

B) 12

4 2

D) 4

C) 900

D) 899

C) 4

D) 24

C) 6

D) 5,036

C) 144

D) 6

Objective: (11.2) Evaluate Factorial Expressions

20)

900! 899!

A) 809,100

B) 1

Objective: (11.2) Evaluate Factorial Expressions

21) 9! - 5! A) 362,875

B) 362,760

Objective: (11.2) Evaluate Factorial Expressions

22) (7 - 4)! A) 3

B) 5,016

Objective: (11.2) Evaluate Factorial Expressions

23)

12 ! 3

A) 79,833,600

B) 24

Objective: (11.2) Evaluate Factorial Expressions

24)

5! (5 - 3)!

A) 4

B) 60

C) 30

D) 20

C) 604,800

D) 151,200

C) 1

D) 0

C) 2

D) 1

C) 24

D) 30

C) 5

D) 2

C) 45

D) 8

C) 720

D) 21

Objective: (11.2) Evaluate Factorial Expressions

Use the formula for nPr to evaluate the expression.

25) 10P6 A) 5,040

B) 3,628,800

Objective: (11.2) Use the Permutations Formula

26) 5 P0 A) 120

B) 50

Objective: (11.2) Use the Permutations Formula

27) 10P10 A) 3,628,800

B) 1,814,400

Objective: (11.2) Use the Permutations Formula

28) 6 P4 A) 2

B) 360

Objective: (11.2) Use the Permutations Formula

29) 10P5 A) 30,240

B) 252

Objective: (11.2) Use the Permutations Formula

30) 10P2 A) 90

B) 19

Objective: (11.2) Use the Permutations Formula

31) 6 P5 A) 0

B) 1

Objective: (11.2) Use the Permutations Formula

Solve the problem. 32) In how many distinct ways can the letters in MANAGEMENT be arranged? A) 453,600 B) 226,800 C) 3,628,800

D) 22,680

Objective: (11.2) Solve Application

33) A signal can be formed by running different colored flags up a pole, one above the other. Find the number of different signals consisting of 7 flags that can be made if 3 of the flags are white, 3 are red, and 1 is blue. A) 35 B) 15 C) 140 D) 9 Objective: (11.2) Solve Application

34) In how many distinct ways can a 9-digit number be made using seven 2's and two 7's? A) 8 B) 9 C) 16

D) 36

Objective: (11.2) Solve Application

35) How many ways can 6 people be chosen and arranged in a straight line if there are 8 people to choose from? A) 40,320 B) 48 C) 720 D) 20,160 Objective: (11.2) Solve Application

36) A pollster wants to minimize the effect the order of the questions has on a person's response to a survey. How many different surveys are required to cover all possible arrangements if there are 11 questions on the survey? A) 3,628,800 B) 121 C) 11 D) 39,916,800 Objective: (11.2) Solve Application

37) There are 7 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible? A) 210 B) 35 C) 5,040 D) 343 Objective: (11.2) Solve Application

In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not necessary to solve the problem. 38) A record club offers a choice of 7 records from a list of 45. In how many ways can a member make a selection? A) Combinations, because the order of the records selected does not matter. B) Permutations, because the order of the records selected does matter. Objective: (11.3) Distinguish Between Permutation and Combination Problems

39) One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded? A) Permutations, because the order of the prizes awarded matters. B) Combinations, because the order of the prizes awarded does not matter. Objective: (11.3) Distinguish Between Permutation and Combination Problems

40) How many different user ID's can be formed from the letters W, X, Y, Z if no repetition of letters is allowed? A) Combinations, because the order of the letters does not matter. B) Permutations, because the order of the letters matters. Objective: (11.3) Distinguish Between Permutation and Combination Problems

41) Five of a sample of 100 computers will be selected and tested. How many ways are there to make this selection? A) Combinations, because the order of the computers selected does not matter. B) Permutations, because the order of the computers selected does matter. Objective: (11.3) Distinguish Between Permutation and Combination Problems

Use the formula for nCr to evaluate the expression.

42) 4 C3 A) 3

B) 12

C) 24

Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula

D) 4

43) 7 C4 A) 210

B) 12

C) 35

D) 420

Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula

44) 6 C0 A) 180

B) 360

C) 6

D) 1

Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula

45) 4 C1 A) 2

B) 4

C) 12

D) 24

Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula

46) 9 C9 A) 362,880

B) 1

C) 0.5

D) 90,720

Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula

47)

11C3 6 C4

A) 443520

11 2

11 4

D) 11

Objective: (11.3) Solve Problems Involving Combinations Using the Combinations Formula

Evaluate the expression. 48)

6 P2 - 6 C2 2!

1 2

B) 0

C) 1

D) 2

Objective: (11.3) Evaluate Expressions

49) 1 -

7 P5 8 P4

3 4

1 4

3 2

1 2

Objective: (11.3) Evaluate Expressions

50)

9 C4 3 C2

65! 62!

A) -3782

B) -262,038

C) -4118

Objective: (11.3) Evaluate Expressions

D) -261,702

51)

6 C1 · 8 C3 11C4

112 55

7 24

14 55

85 24

Objective: (11.3) Evaluate Expressions

Solve the problem. 52) From 10 names on a ballot, a committee of 3 will be elected to attend a political national convention. How many different committees are possible? A) 604,800 B) 360 C) 120 D) 720 Objective: (11.3) Solve Application I

53) To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 51 numbers (one through 51). The order in which the selections is made does not matter. How many different selections are possible? A) 15,890,700 B) 306 C) 18,009,460 D) 720 Objective: (11.3) Solve Application I

54) In how many ways can a committee of three men and four women be formed from a group of 12 men and 12 women? A) 165 B) 108,900 C) 15,681,600 D) 6,652,800 Objective: (11.3) Solve Application I

55) A physics exam consists of 9 multiple-choice questions and 6 open-ended problems in which all work must be shown. If an examinee must answer 6 of the multiple-choice questions and 4 of the open-ended problems, in how many ways can the questions and problems be chosen? A) 1,260 B) 21,772,800 C) 1,296 D) 261,273,600 Objective: (11.3) Solve Application I

56) There are 9 members on a board of directors. If they must form a subcommittee of 6 members, how many different subcommittees are possible? A) 60,480 B) 84 C) 531,441 D) 720 Objective: (11.3) Solve Application I

57) If the police have 8 suspects, how many different ways can they select 5 for a lineup? A) 6,720 ways B) 40 ways C) 56 ways

D) 336 ways

Objective: (11.3) Solve Application I

58) A committee is to be formed consisting of 4 men and 5 women. If the committee members are to be chosen from 9 men and 8 women, how many different committees are possible? A) 7,056 B) 24,310 C) 182 D) 20,321,280 Objective: (11.3) Solve Application I

59) How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 7 forwards, 8 midfield players, and 6 defensive players? A) 125 B) 352,716 C) 42,336,000 D) 49,000 Objective: (11.3) Solve Application I

60) From a group of 17 women and 10 men, a researcher wants to randomly select 7 women and 7 men for a study. In how many ways can the study group be selected? A) 2,333,760 B) 98,622,720 C) 20,058,300 D) 19,568 Objective: (11.3) Solve Application I

Numerous quotes have been made about living life. The problem below is based on the following observations: · "Always remember that you are absolutely unique. Just like everyone else." --Margaret Mead · "Life is hard. After all, it kills you." -- Katherine Hepburn · "The secret of life is honesty and fair dealing. If you can fake that, you've got it made." --Groucho Marx · "Life is what happens while you are busy making other plans." -- John Lennon · "Choose a job you love, and you will never have to work a day in your life." -- Confucius [Source: www.brainyquote.com]

61) In how many ways can these five quotes be ranked from best to worst? A) 150 B) 60 C) 120

D) 720

Objective: (11.3) Solve Application II

62) If Confucious's thoughts about life are excluded, in how many ways can the remaining four quotes be ranked from worst to best? A) 4 B) 48 C) 24 D) 120 Objective: (11.3) Solve Application II

63) In how many ways can people select their two favorite quotes from these thoughts about life? A) 60 B) 10 C) 30 D) 20 Objective: (11.3) Solve Application II

64) If the order in which these quotes are read makes a difference in terms of how they are received, how many ways can they be delivered if a quote by a woman (Mead or Hepburn) is read first? A) 48 B) 24 C) 64 D) 120 Objective: (11.3) Solve Application II

65) In how many ways can people select their favorite quote by a woman (Mead or Hepburn) and their two favorite quotes by a man? A) 6 B) 12 C) 4 D) 8 Objective: (11.3) Solve Application II

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. 66) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 7. 7 A) 0 B) 7 C) D) 1 6 Objective: (11.4) Compute Theoretical Probability

67) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 2. 1 1 A) B) 2 C) 0 D) 3 6 Objective: (11.4) Compute Theoretical Probability

68) You are dealt one card from a standard 52-card deck. Find the probability of being dealt a picture card. 3 3 3 1 A) B) C) D) 26 52 13 13 Objective: (11.4) Compute Theoretical Probability

69) You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 9. 13 2 5 A) B) C) 10 D) 2 13 13 Objective: (11.4) Compute Theoretical Probability

70) A fair coin is tossed two times in succession. The set of equally likely outcomes is {HH, HT, TH, TT}. Find the probability of getting the same outcome on each toss. 3 1 1 A) 1 B) C) D) 4 4 2 Objective: (11.4) Compute Theoretical Probability

71) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is less than 13. 1 1 A) 1 B) C) D) 0 4 2 Objective: (11.4) Compute Theoretical Probability

72) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 9. 1 1 1 A) 6 B) C) D) 6 12 4 Objective: (11.4) Compute Theoretical Probability

73) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on 3 or 2.

2 3

B) 3

C) 1

Objective: (11.4) Compute Theoretical Probability

2 5

74) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again. Find the probability that the arrow will land on an odd number.

A) 1

2 5

C) 0

3 5

Objective: (11.4) Compute Theoretical Probability

75) This problem deals with eye color, an inherited trait. For purposes of this problem, assume that only two eye colors are possible, brown and blue. We use b to represent a blue eye gene and B a brown eye gene. If any B genes are present, the person will have brown eyes. The table shows the four possibilities for the children of two Bb (brown-eyed) parents, where each parent has one of each eye color gene.

First Parent

B b

Second Parent B b BB Bb Bb bb

Find the probability that these parents give birth to a child who has blue eyes. 1 A) B) 0 C) 1 4

1 2

Objective: (11.4) Compute Theoretical Probability

Find the probability of the event. 76) If a single die is tossed once, find the probability of the following event. An odd number. 1 1 1 A) B) C) 6 2 3

D) 3

Objective: (11.4) Compute Theoretical Probability

77) If a single die is rolled, find the probability of the following event. A number less than 2? 5 1 1 A) B) C) 6 9 3 Objective: (11.4) Compute Theoretical Probability

1 6

Use the empirical probability formula to solve the exercise. Express the answer as a fraction. Then express the probability as a decimal, rounded to the nearest thousandth, if necessary. 78) The table below represents a random sample of the number of deaths per 100 cases for a certain illness over time. If a person infected with this illness is randomly selected from all infected people, find the probability that the person lives 3-4 years after diagnosis. Years after Diagnosis Number deaths 1-2 15 3-4 35 5-6 16 7-8 9 9-10 6 11-12 4 13-14 2 15+ 13

35 ; 0.35 100

1 ; 0.029 35

7 ; 0.058 120

35 ; 0.538 65

Objective: (11.4) Compute Empirical Probability

79) In 1999 the stock market took big swings up and down. A survey of 1,015 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily? How frequently? Response Daily 233 Weekly 286 Monthly 296 Couple times a year 145 Don't track 55 296 233 145 286 ; 0.292 ; 0.23 ; 0.143 ; 0.282 A) B) C) D) 1,015 1,015 1,015 1,015 Objective: (11.4) Compute Empirical Probability

The chart below shows the percentage of people in a questionnaire who bought or leased the listed car models and were very satisfied with the experience. Model A Model B Model C Model D Model E Model F

81% 79% 73% 61% 59% 57%

80) With which model was the greatest percentage satisfied? Estimate the empirical probability that a person with this model is very satisfied with the experience. Express the answer as a fraction with a denominator of 100. 0.57 57 0.81 81 A) Model F; B) Model F; C) Model A: D) Model A; 100 100 100 100 Objective: (11.4) Compute Empirical Probability

81) The empirical probability that a person with a model shown is very satisfied with the experience is the model? A) D

B) B

C) C

73 . What is 100

D) A

Objective: (11.4) Compute Empirical Probability

The table shows the number of people in Country X who moved in a recent year, categorized by where they moved and whether they were an owner or a renter. Use the data in the table, expressed in millions, to solve the problem. Moved to a Different Moved within Country in the Moved to a Different the Same Same Continent Country Continent Owner 12.4 3.6 0.2 Renter 19.1 5.8 0.9 Use the table above to find the probability, expressed as a decimal rounded to the nearest hundredth, that a randomly selected person from Country X who moved was as described. 82) a renter A) 0.52 B) 0.75 C) 0.61 D) 0.39 Objective: (11.4) Solve Applications

83) a person who moved within the same country A) 0.75 B) 0.84

C) 0.61

D) 0.22

C) 0.02

D) 0.17

85) an owner who moved to a different country in the same continent A) 0.09 B) 0.11 C) 0.07

D) 0.14

Objective: (11.4) Solve Applications

84) a renter who moved to a different continent A) 0.12 B) 0.03 Objective: (11.4) Solve Applications

Objective: (11.4) Solve Applications

Solve the problem. 86) Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last. 1 1 1 1 A) 120; 10; B) 720; 15; C) 720; 24; D) 120; 6; 12 48 30 20 Objective: (11.5) Compute Probabilities with Permutations

87) Six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is determined by random selection. Find the probability that (a) E will speak first (b) that C will speak fifth and B will speak last (c) that the students will speak in the following order: DECABF (d) that A or B will speak first. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ; ; ; ; ; ; ; ; A) ; B) ; C) ; D) ; 6 36 720 12 6 30 720 3 6 12 720 3 6 36 360 3 Objective: (11.5) Compute Probabilities with Permutations

88) A group consists of 6 men and 5 women. Five people are selected to attend a conference. In how many ways can 5 people be selected from this group of 11? In how many ways can 5 men be selected from the 6 men? Find the probability that the selected group will consist of all men. 1 1 1 1 A) 55440; 720; B) 462; 6; C) 462; 6; D) 462; 6; 77 518400 55440 77 Objective: (11.5) Compute Probabilities with Combinations

89) To play the lottery in a certain state, a person has to correctly select 5 out of 45 numbers, paying $1 for each five-number selection. If the five numbers picked are the same as the ones drawn by the lottery, an enormous sum of money is bestowed. What is the probability that a person with one combination of five numbers will win? What is the probability of winning if 100 different lottery tickets are purchased? 1 1 1 100 ; ; A) B) 5,864,443,200 58,644,432 1,221,759 1,221,759 C)

1 1 ; 8,145,060 814,506

1 10 ; 146,611,080 14,661,108

Objective: (11.5) Compute Probabilities with Combinations

90) A box contains 27 widgets, 4 of which are defective. If 4 are sold at random, find the probability that (a) all are defective (b) none are defective. 1 4 1 1 4 23 1 1771 ; ; ; ; A) B) C) D) 27 27 421200 105300 27 27 17550 3510 Objective: (11.5) Compute Probabilities with Combinations

91) A committee consisting of 6 people is to be selected from eight parents and four teachers. Find the probability of selecting three parents and three teachers. 10 2 8 100 A) B) C) D) 11 33 33 231 Objective: (11.5) Compute Probabilities with Combinations

92) If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that all 5 cards are picture cards. 3 1 1 33 A) B) C) D) 13 2598960 216580 108290 Objective: (11.5) Compute Probabilities with Combinations

93) If you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting 3 jacks and 3 aces. 3 2 2 1 A) B) C) D) 26 13 2544815 1017926 Objective: (11.5) Compute Probabilities with Combinations

You are dealt one card from a 52-card deck. Find the probability that you are not dealt: 94) a 2. 1 1 12 A) B) C) 13 10 13 Objective: (11.6) Find the Probability that an Event Will Not Occur

9 10

95) a diamond. 2 A) 5

1 4

3 4

4 13

Objective: (11.6) Find the Probability that an Event Will Not Occur

In 5-card poker, played with a standard 52-card deck, 52C5 , or 2,598,960 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 2,598,960. Find the probability of not being dealt this type of hand. 96) Four of a kind: 4 cards with the same number, plus 1 additional card, if the number of ways this hand can occur is 624 624, and the probability of this hand is 2,598,960

1248 2,598,960

624 2,598,960

625 2,598,960

2,598,336 2,598,960

Objective: (11.6) Find the Probability that an Event Will Not Occur

The chart shows the probability of a certain disease for men by age. Use the information to solve the problem. Express all probabilities as decimals, estimated to two decimal places. Age 20-24 25-34 35-44 45-54 55-64 65-74 75+

Probability of Disease X less than 0.008 0.009 0.14 0.39 0.42 0.67 0.79

97) What is the probability that a randomly selected man between the ages of 55 and 64 does not have this disease? A) 0.39 B) 0.42 C) 0.58 D) 0.61 Objective: (11.6) Find the Probability that an Event Will Not Occur

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 98) A card is dealt from a 52-card deck. What is the probability of not being dealt a queen of hearts? Objective: (11.6) Find the Probability that an Event Will Not Occur

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph shows the probability of Disease Z, by age and gender. Use the information in the graph to solve the problem. Express all probabilities as decimals, rounded to two decimal places.

99) a) What is the probability that a randomly selected woman between the ages of 55 and 64 has Disease Z? b) What is the probability that a randomly selected woman between the ages of 55 and 64 does not have Disease Z? A) a) 0.62, B) a) 0.48, C) a) 0.38, D) a) 0.52, b) 0.38 b) 0.52 b) 0.62 b) 0.48 Objective: (11.6) Find the Probability that an Event Will Not Occur

The table shows the distribution, by age, of a random sample of 4000 moviegoers in a certain country aged 12 through 74. Use this distribution to solve the problem. Age Distribution of Moviegoers Ages Number 12 - 24 1050 25-44 1540 45-64 760 65-74 650 If one moviegoer is randomly selected from this population, find the probability, expressed as a simplified fraction, of the given situation. 100) the moviegoer is not in the 12-24 age range 11 29 59 21 A) B) C) D) 40 40 80 80 Objective: (11.6) Find the Probability that an Event Will Not Occur

101) the moviegoer's age is less than 65 7 67 A) B) 30 90

Objective: (11.6) Find the Probability that an Event Will Not Occur

21 100

67 80

102) the moviegoer's age is at least 45 259 141 A) B) 400 400

65 100

35 100

Objective: (11.6) Find the Probability that an Event Will Not Occur

Solve the problem. 103) The table below shows the results of a consumer survey of annual incomes in 100 households. Income Number of households $0 - 14,999 7 $15,000 - 24,999 21 $25,000 - 34,999 27 $35,000 - 44,999 28 $45,000 or more 17 What is the probability that a household has an annual income of $25,000 or more? A) 0.55 B) 0.27 C) 0.45

D) 0.72

Objective: (11.6) Find the Probability: Tables

104) The table below shows the results of a consumer survey of annual incomes in 100 households. Income Number of households $0 - 14,999 8 $15,000 - 24,999 23 $25,000 - 34,999 28 $35,000 - 44,999 29 $45,000 or more 12 What is the probability that a household has an annual income less than $25,000? A) 0.31 B) 0.23 C) 0.59

D) 0.69

Objective: (11.6) Find the Probability: Tables

105) The table below shows the results of a consumer survey of annual incomes in 100 households. Income Number of households $0 - 14,999 9 $15,000 - 24,999 24 $25,000 - 34,999 30 $35,000 - 44,999 25 $45,000 or more 12 What is the probability that a household has an annual income between $15,000 and $44,999 inclusive? A) 0.79 B) 0.54 C) 0.49 D) 0.3 Objective: (11.6) Find the Probability: Tables

You randomly select one card from a 52-card deck. Find the probability of selecting the card in the problem. 106) a red ace 1 1 1 1 A) B) C) D) 52 2 26 13 Objective: (11.6) Find the Probability: Mixed

107) a red card 1 A) 52

1 2

13 52

1 26

7 26

2 13

C) 16

4 13

Objective: (11.6) Find the Probability: Mixed

108) an ace or a 6 A) 7

13 2

Objective: (11.6) Find the Probability: Mixed

109) a face card or a 5 2 A) 13

12 13

Objective: (11.6) Find the Probability: Mixed

Solve the problem that involves probabilities with events that are not mutually exclusive. 110) In a class of 50 students, 33 are Democrats, 16 are business majors, and 5 of the business majors are Democrats. If one student is randomly selected from the class, find the probability of choosing a Democrat or a business major. 27 22 49 11 A) B) C) D) 25 25 50 50 Objective: (11.6) Find the Probability: Mixed

111) The physics department of a college has 5 male professors, 9 female professors, 12 male teaching assistants, and 13 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female. 34 22 25 7 A) B) C) D) 39 39 39 13 Objective: (11.6) Find the Probability: Mixed

Solve the problem. 112) The biology faculty at a college consists of 5 professors, 10 associate professors, 11 assistant professors, and 6 instructors. If one faculty member is randomly selected, find the probability of choosing a professor or an instructor. 3 11 11 5 A) B) C) D) 16 32 21 32 Objective: (11.6) Find the Probability: Mixed

113) A spinner has regions numbered 1 through 21. What is the probability that the spinner will stop on an even number or a multiple of 3? 1 2 10 A) 17 B) C) D) 9 3 3 Objective: (11.6) Find the Probability: Mixed

The table shows the educational attainment of the population of Country X, ages 25 and over. Use the data in the table, expressed in millions, to solve the problem.

Find the probability, expressed as a simplified fraction, that a randomly selected person from Country X, age 25 or over, has done what is stated in the problem. 114) has not completed four years of high school 73 57 27 43 A) B) C) D) 176 176 176 176 Objective: (11.6) Find the Probability: Mixed

115) has completed less than four years of high school or four years of high school only 23 27 21 A) B) C) 44 44 44

19 44

Objective: (11.6) Find the Probability: Mixed

The table shows the educational attainment of the population of Country X, ages 25 and over. Use the data in the table, expressed in millions, to solve the problem.

Find the odds in favor and the odds against a randomly selected person from Country X, age 25 and over, with the stated amount of education. 116) four years (or more) of college A) 25:63, 63:25 B) 21:67, 67:21 C) 25:88, 88:25 D) 63:88, 88:63 Objective: (11.6) Find the Probability: Mixed

The game of Scrabble has 100 tiles. The diagram shows the number of tiles for each letter and the letter's point value.

In the problem, one tile is drawn from Scrabble's 100 tiles. Find the probability, expressed as a simplified fraction. 117) Find the probability of selecting a T or an E. 3 9 3 1 A) B) C) D) 50 50 25 50 Objective: (11.6) Find the Probability: Scrabble

118) Find the probability of selecting one of the letters needed to spell out the word HOME. 27 6 3 A) B) C) 100 25 25

9 100

Objective: (11.6) Find the Probability: Scrabble

The game of Scrabble has 100 tiles. The diagram shows the number of tiles for each letter and the letter's point value.

Refer to the diagram showing the Scrabble tiles. If one tile is drawn from the 100 tiles, a) find the odds in favor and b) the odds against in the described situation. 119) selecting an L A) a) 1:24, B) a) 1:99, C) a) 1:100, D) a) 1:25, b) 24:1 b) 99:1 b) 100:1 b) 25:1 Objective: (11.6) Find the Odds: Scrabble

120) selecting a letter worth three points A) a) 2:23, B) a) 2:98, b) 23:2 b) 98:2

C) a) 1:49, b) 49:1

Objective: (11.6) Find the Odds: Scrabble

D) a) 2:25, b) 25:2

A single die is rolled. Find the odds: 121) in favor of getting a number less than 3. A) 1:2 B) 1:1

C) 2:1

D) 1:3

C) 1:1

D) 3:2

Objective: (11.6) Find the Odds: Die

122) against getting a number less than 4. A) 1:2 B) 2:1 Objective: (11.6) Find the Odds: Die

The circle graphs show the percentage of men and women from Country X who consider owning a home an important part of adult life. Use the information to solve the problem.

123) a) What are the odds in favor of a man from Country X agreeing that owning a home is an important part of adult life? b) What are the odds against of a man from Country X agreeing that owning a home is an important part of adult life? A) a) 19:6, B) a) 19:31, C) a) 31:19 D) a) 6:19, b) 6:19 b) 31:19 b) 19:31 b) 19:6 Objective: (11.6) Find the Odds: Circles

124) a) What are the odds in favor of a woman from Country X agreeing that owning a home is an important part of adult life? b) What are the odds against of a woman from Country X agreeing that owning a home is an important part of adult life? A) a) 6:19, B) a) 31:19, C) a) 21:82, D) a) 12:7, b) 19:31 b) 19:6 b) 82:21 b) 7:12 Objective: (11.6) Find the Odds: Circles

The following table shows the percentage of children in the U.S. whose parents ae college graduates in one-parent households and two-parent households. Use the information shown to solve the problem. Percentage of U.S. Children Whose Parents are College Graduates In One-Parent Households 9% In Two-Parent Households 29%

125) What are the odds in favor of a child in a one-parent household having a parent who is a college graduate? What are the odds against a child in a one-parent household having a parent who is a college graduate? A) 91 to 9: 9 to 91 B) 9 to 91; 91 to 9 C) 91 to 100; 100 to 91 D) 9 to 100; 100 to 9 Objective: (11.6) Solve Apps: Odds

One card is randomly selected from a deck of cards. Find the odds: 126) in favor of getting a spade. A) 4 to 1 B) 3 to 1

C) 1 to 4

D) 1 to 3

C) 26 to 25

D) 1 to 25

Objective: (11.6) Solve Apps: Odds

127) against getting a red queen. A) 25 to 26

B) 25 to 1

Objective: (11.6) Solve Apps: Odds

Solve the problem. 128) The winner of a raffle will receive a new car. If 10,000 raffle tickets were sold and you purchased 13 tickets, what are the odds against your winning the car? A) 10000 to 13 B) 13 to 9,987 C) 13 to 10000 D) 9,987 to 13 Objective: (11.6) Solve Apps: Odds

129) The probability of a resident of a certain city being the victim of a serious crime at some point in his or her life is 33 approximately . What are the odds in favor of a resident of this city never being the victim of a serious crime 100 during his or her lifetime? A) 33 to 67

B) 100 to 33

C) 33 to 100

D) 67 to 33

Objective: (11.6) Solve Apps: Odds

130) If you are given odds 3 to 7 in favor of winning a bet, what is the probability of winning the bet? 3 3 1 7 A) B) C) D) 7 10 10 10 Objective: (11.6) Solve Apps: Odds

131) Based on his skills in basketball, it was computed that when Joe Sureshot threw a free throw, the odds in favor of his making it were 5 to 23. Find the probability that when Joe shot a free throw, he made it. Out of every 100 free throws he attempted on the average how many did he miss? 5 5 23 23 ; 82 ; 17 ; 82 ; 17 A) B) C) D) 28 28 28 28 Objective: (11.6) Solve Apps: Odds

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 132) Rolling a die, what are the odds in favor of getting an even number? Objective: (11.6) Solve Apps: Odds

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 133) Of the 18 movies directed by a famous movie director, 12 were dramas, 4 were thrillers, and 2 were action movies. One movie is randomly selected from these 18 movies. Find the odds in favor of selecting a thriller or an action movie. A) 2:1 B) 3:1 C) 1:2 D) 1:3 Objective: (11.6) Solve Apps: Odds

134) Of the 47 novels written by a certain author, 25 were mysteries, 13 were romances, 8 were satires, and 1 was a fantasy novel. One novel is randomly selected from these 47 novels. Find the odds against selecting a romance or a fantasy novel. A) 14:33 B) 22:25 C) 25:22 D) 33:14 Objective: (11.6) Solve Apps: Odds

Solve the problem involving probabilities with independent events. 135) A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If the pointer is spun once, find the probability it will land on green and then yellow. 1 1 1 1 A) B) C) D) 6 3 18 9 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

136) A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If the pointer is spun three times, find the probability it will land on green every time. 1 1 2 1 A) B) C) D) 18 27 27 9 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

137) A single die is rolled twice. Find the probability of getting a 2 the first time and a 6 the second time. 1 1 1 1 A) B) C) D) 6 36 3 12 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

138) You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of getting a picture card the first time and a diamond the second time. 3 3 1 1 A) B) C) D) 13 52 13 4 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

139) If you toss a fair coin 8 times, what is the probability of getting all heads? 1 1 1 A) B) C) 512 128 2 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

1 256

140) The probability that a region prone to hurricanes will be hit by a hurricane in any single year is probability of a hurricane at least once in the next 5 years? 1 A) 0.99999 B) 2

C) 0.00001

1 . What is the 10

D) 0.40951

Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

141) A card is drawn from a 52-card deck and a fair coin is flipped. What is the probability of getting jack and heads? 1 1 3 1 A) B) C) D) 13 26 52 4 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

142) The chart shows a certain city's population by age. Assume that the selections are independent events. If 9 residents of this city are selected at random, find the probability that the first 2 are 65 or older, the next 4 are 25-44 years old, the next 2 are 24 or younger, and the last is 45-64 years old. City X's Population by Age 0-24 years old 33% 25-44 years old 22% 45-64 years old 21% 65 or older 24%

A) 0.000015

B) 0.000028

C) 0.000054

D) 0.000003

Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

Solve the problem that involves probabilities with events that are not mutually exclusive. 143) There are 26 chocolates in a box, all identically shaped. There are 7 filled with nuts, 8 with caramel, and 11 are solid chocolate. You randomly select one piece, eat it, and then select a second piece. Find the probability of selecting 2 solid chocolates in a row. 121 55 11 11 A) B) C) D) 676 338 65 650 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

144) Consider a political discussion group consisting of 5 Democrats, 8 Republicans, and 7 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting an Independent and then a Democrat. 7 1 7 7 A) B) C) D) 380 76 80 76 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

145) An ice chest contains 9 cans of apple juice, 6 cans of grape juice, 3 cans of orange juice, and 2 cans of pineapple juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting no grape juice. 343 91 273 1 A) B) C) D) 855 285 1000 57 Objective: (11.7) Find the Probability of One Event and a Second Event Occurring

Solve the problem. 146) Numbered disks are placed in a box and one disk is selected at random. If there are 8 red disks numbered 1 through 8, and 5 yellow disks numbered 9 through 13, find the probability of selecting a disk numbered 3, given that a red disk is selected. 1 1 8 5 A) B) C) D) 13 8 13 13 Objective: (11.7) Compute Conditional Probabilities

147) Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 4 yellow disks numbered 7 through 10, find the probability of selecting a red disk, given that an odd-numbered disk is selected. 3 1 3 2 A) B) C) D) 5 5 10 5 Objective: (11.7) Compute Conditional Probabilities

148) Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 4 yellow disks numbered 7 through 10, find the probability of selecting a yellow disk, given that the number selected is less than or equal to 3 or greater than or equal to 8. 3 3 1 3 A) B) C) D) 4 10 2 5 Objective: (11.7) Compute Conditional Probabilities

149) The table shows the number of employed and unemployed workers in the U.S., in thousands.

Male Female

Employed 67,761 58,655

Unemployed 2433 2285

Assume that one person will be randomly selected from the group described in the table. Find the probability of selecting a person who is employed, given that the person is male. 2285 2433 67,761 2433 A) B) C) D) 70,194 70,194 70,194 67,761 Objective: (11.7) Compute Conditional Probabilities

150) The table shows the number of minority officers in the U.S. military. Army African Americans 9162 Hispanic Americans 2105 Other Minorities 4075

Navy 3524 2732 2653

Marines 1341 914 599

Air Force 4282 1518 3823

Assume that one person will be randomly selected from the group described in the table. Find the probability of selecting an officer who is in the Navy, given that the officer is African American. 3542 8909 3524 3524 A) B) C) D) 14785 18,309 18,309 8909 Objective: (11.7) Compute Conditional Probabilities

A spinner has a pointer which can land on one of three regions labelled 1, 2, and 3 respectively. 151) Compute the expected value for the number on which the pointer lands if the probabilities for the three regions are 1 1 1 , , and respectively. 6 2 3 A)

11 6

17 6

7 6

5 3

Objective: (11.8) Compute Expected Value

The table shows claims and their probabilities for an insurance company. Amount of Claim $0 $50,000 $100,000 $150,000 $200,000 $250,000

Probability 0.60 0.25 0.09 0.04 0.01 0.01

152) (a) Calculate the expected value. (b) How much should the company charge as an average premium so that it breaks even on its claim costs? (c) How much should the company charge to make a profit of $80 per policy? A) (a) $16,000 (b) $32,000 (c) 32,080 B) (a) $32,000 (b) $16,,000 (c) 32,080 C) (a) $32,000 (b) $16,000 (c) 16,080 D) (a) $32,000 (b) $32,000 (c) 32,080 Objective: (11.8) Use Expected Value to Solve Applied Problems

Solve the problem. 153) An architect is considering bidding for the design of a new shopping mall. The cost of drawing plans and submitting a model is $10,000. The probability of being awarded the bid is 0.15, and anticipated profits are $100,000, resulting in a possible gain of this amount minus the $10,000 cost for plans and a model. What is the expected value in this situation? A) B) $13,500 C) $14,000 D) $15,000 Objective: (11.8) Use Expected Value to Solve Applied Problems

154) A 25 year old can purchase a one-year life insurance policy for $10,000 at a cost of $100. Past history indicates that the probability of a person dying at age 25 is 0.0021. Determine the company's expected gain per policy. A) 979 B) 21 C) 121 D) 79 Objective: (11.8) Use Expected Value to Solve Applied Problems

155) A store specializing in electronics is to open in one of two malls. If the first mall is selected, the store anticipates a 1 yearly profit of $290,000 if successful and a yearly loss of 110,000 otherwise. The probability of success is . If the 2 second mall is selected, it is estimated that the yearly profit will be $130,000 if successful; otherwise, the annual 3 loss will be $40,000. The probability of success at the second mall is . What is the expected profit at each of the 4 two malls? A) first mall: $90,000; second mall: $55,000 C) first mall: $117,500; second mall: $87,500

B) first mall: $117,500; second mall: $55,000 D) first mall: $90,000; second mall: $87,500

Objective: (11.8) Use Expected Value to Solve Applied Problems

156) A mining company is considering two sites on which to dig, described as follows: Site A: Profit if diamonds are found: $60 million. Loss if no diamonds are found: $15 million. Probability of finding diamonds: 0.2 Site B: Profit if diamonds are found $140 million. Loss if no diamonds are found $17 million. Probability of finding diamonds: 0.1 What is the expected profit for each site? A) site A: $0 million; site B: -$1.3 million C) site A: $12 million: site B: $14 million

B) site A: $12 million; site B: -$1.3 million D) site A: $0 million; site B: $14 million

Objective: (11.8) Use Expected Value to Solve Applied Problems

157) A service that repairs televisions sells maintenance agreements for $12 a year. The average cost for repairing a television is $35 and 3 in every 100 people who purchase maintenance agreements have televisions that require repair. Find the service's expected profit per maintenance agreement. A) $11.65 B) $11.97 C) $11.30 D) $10.95 Objective: (11.8) Use Expected Value to Solve Applied Problems

Solve the problem that involves computing expected values in a game of chance. 158) A game is played using one die. If the die is rolled and shows a 4, the player wins $7. If the die shows any number other than 4, the player wins nothing. If there is a charge of $1 to play the game, what is the game's expected value? A) -$1 B) -$0.17 C) $6.00 D) $0.17 Objective: (11.8) Use Expected Value to Determine the Average Payoff or Loss in a Game of Chance

159) One option in a roulette game is to bet on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $3 that you paid to play the game and you are awarded $3. If the ball lands elsewhere, you are awarded nothing and the $3 that you bet is collected. Find the expected value for playing roulette if you bet $3 on red. A) -$0.08 B) $0.08 C) $0.16 D) -$0.16 Objective: (11.8) Use Expected Value to Determine the Average Payoff or Loss in a Game of Chance

160) A numbers game run by many state governments allows a player to select a three-digit number from 000 to 999. There are 1000 such numbers. A bet of $15 is placed on a number. If the number is selected, the player wins $1,500. If any other number is selected, the player wins nothing. Find the expected value for the game. A) -$13.50 B) -$1.50 C) $13.50 D) $1.50 Objective: (11.8) Use Expected Value to Determine the Average Payoff or Loss in a Game of Chance

Answer Key Testname: 11-BLITZER_TM8E_TEST_ITEM_FILE

1) B 2) C 3) C 4) A 5) D 6) A 7) B 8) D 9) B 10) 4200 11) D 12) D 13) A 14) C 15) B 16) D 17) C 18) B 19) B 20) C 21) B 22) C 23) B 24) B 25) D 26) C 27) A 28) B 29) A 30) A 31) C 32) B 33) C 34) D 35) D 36) D 37) A 38) A 39) A 40) B 41) A 42) D 43) C 44) D 45) B 46) B 47) D 48) B 49) C 50) B

51) A 52) C 53) C 54) B 55) A 56) B 57) C 58) A 59) D 60) A 61) C 62) C 63) B 64) A 65) A 66) A 67) D 68) C 69) B 70) D 71) A 72) B 73) D 74) D 75) A 76) B 77) D 78) A 79) B 80) D 81) C 82) C 83) A 84) C 85) A 86) C 87) B 88) D 89) B 90) D 91) C 92) D 93) C 94) C 95) C 96) D 97) C 51 98) 52

100) C 101) D 102) B 103) D 104) A 105) A 106) C 107) B 108) D 109) D 110) B 111) A 112) B 113) C 114) C 115) C 116) A 117) B 118) B 119) A 120) A 121) A 122) C 123) A 124) B 125) B 126) D 127) B 128) D 129) D 130) B 131) A 132) 1:1 133) C 134) D 135) C 136) B 137) B 138) B 139) D 140) D 141) B 142) D 143) C 144) D 145) B 146) B 147) A 148) C 149) C

99) B 27

150) C 151) D 152) D 153) A 154) D 155) D 156) A 157) D 158) D 159) D 160) A

Blitzer, Thinking Mathematically, 8e Chapter 12 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The exercise presents numerical information. Describe the population whose properties are analyzed by the data. 1) There were 537 crimes in a certain city per 100,000 residents. A) criminals in the country B) criminals in the city C) residents of the country D) residents of the city Objective: (12.1) Describe the Population Whose Properties are to be Analyzed

2) 54% of households in City A were online. A) online households in City A C) households in City A

B) households in the country D) online households in the country

Objective: (12.1) Describe the Population Whose Properties are to be Analyzed

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 3) A recent survey revealed that 92% of computer owners in a certain city have access to the Internet. Describe the population this statement is referring to. Objective: (12.1) Describe the Population Whose Properties are to be Analyzed

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) The government of a town needs to determine if the city's residents will support the construction of a new town hall. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents? A) Survey a random sample of employees at the old city hall. B) Survey a random sample of persons within each geographic region of the city. C) Survey the first 500 people listed in the town's telephone directory. D) Survey every 14th person who walks into city hall on a given day. Objective: (12.1) Select an Appropriate Sampling Technique

5) The city council of a small town needs to determine if the town's residents will support the building of a new library. The council decides to conduct a survey of a sample of the town's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents? A) Survey a random sample of persons within each neighborhood of the town. B) Survey 300 individuals who are randomly selected from a list of all people living in the state in which the town is located. C) Survey a random sample of librarians who live in the town. D) Survey every 14th person who enters the old library on a given day. Objective: (12.1) Select an Appropriate Sampling Technique

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 6) A random sample of 30 high school students is selected. Each student is asked how much time he or she spent watching television during the previous week. The following times (in hours) are obtained: 13, 21, 15, 18, 15, 13, 15, 14, 12, 18, 16, 14, 14, 13, 16, 15, 12, 12, 17, 14, 12, 14, 21, 16, 13, 17, 13, 16, 15, 14 Construct a frequency distribution for the data. Objective: (12.1) Organize and Present Data

7) The ages of 30 swimmers who participated in a swim meet are as follows: 18, 36, 30, 33, 40, 18, 50, 59, 19, 43, 51, 19, 26, 28, 41, 20, 29, 20, 58, 49, 24, 37, 46, 53, 33, 22, 22, 41, 30, 49 Construct a grouped frequency distribution for the data. Use the classes 18 - 27, 28 - 37, 38 - 47, 48 - 57, 58 - 67. Objective: (12.1) Organize and Present Data

8) Construct a histogram and a frequency polygon for the given data. Years of Education Number of People (thousands) Beyond High School 1 23 2 13 3 12 4 14 5 4 6 2 Objective: (12.1) Organize and Present Data

9) A random sample of 30 attorneys is selected. The following list gives their ages: 40, 68, 52, 55, 65, 73, 62, 51, 39, 45, 53, 41, 71, 54, 70, 42, 39, 49, 54, 61, 48, 41, 58, 63, 77, 64, 40, 63, 82, 81 Construct a stem-and-leaf plot for the data. What does the shape of the display reveal about the ages of the attorneys? Objective: (12.1) Organize and Present Data

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 10) The stem-and-leaf plot below displays the ages of 30 attorneys at a small law firm. Stems Attorneys 2 99 3 00112589 4 1234458 5 1233458 6 0137 7 12 What is the age of the oldest attorney? What is the age of the youngest attorney? A) The oldest attorney is 72 years old. The youngest attorney is 29 years old. B) The oldest attorney is 62 years old. The youngest attorney is 39 years old. C) The oldest attorney is 71 years old. The youngest attorney is 28 years old. D) The oldest attorney is 82 years old. The youngest attorney is 11 years old. Objective: (12.1) Organize and Present Data

11) Which one of the following is true according to the graph?

A) The graph is based on a sample of approximately 62 thousand people. B) More people had 4 years of education beyond high school than 3 years. C) If the sample is truly representative, then for a group of 50 people, we can expect about 32 of them to have one year of education beyond high school. D) The percent of people with years of higher education greater than those shown by any rectangular bar is equal to the percent of people with years of education less than those shown by that bar. Objective: (12.1) Organize and Present Data

12) The frequency polygon below shows a distribution of test scores.

Which one of the following is true based on the graph? A) The percent of scores above any given score is equal to the percent of scores below that score. B) More people had a score of 77 than a score of 73. C) More people had a score of 75 than any other, and as the deviation from 75 increases or decreases, the scores fall off in a symmetrical manner. D) The graph is based on a sample of approximately 15 thousand people. Objective: (12.1) Organize and Present Data

Describe the error in the visual display shown. 13)

The volume of our sales has doubled!!! A) The length of a side has doubled, but the area has been multiplied by 4. B) The length of a side has doubled, but the area has been unchanged. C) There is no error. D) The length of a side has doubled, but the area has been multiplied by 8. Objective: (12.1) Identify Deceptions in Visual Displays of Data

Find the mean for the group of data items. Round to the nearest hundredth, if necessary. 14) 10, 11, 6, 9, 7, 12, 3, 6 A) 8 B) 8.29 C) 7.25

D) 9.14

Objective: (12.2) Determine the Mean for a Data Set

15) 23, 23, 50, 45, 80, 23 A) 48.8

B) 44.2

C) 40.67

D) 36.83

C) 4.63

D) 4.17

Objective: (12.2) Determine the Mean for a Data Set

16) 2.3, 8.9, 7.3, 4.8, 2.3, 6.3, 2.3, 5.1, 5.1, 1.9 A) 5.14 B) 4.12 Objective: (12.2) Determine the Mean for a Data Set

Find the mean for the data items in the given frequency distribution. Round to the nearest hundredth, if necessary. 17) Score Frequency x f 1 1 2 4 3 5 4 7 5 9 6 6 7 10 8 11 9 8 10 8 A) 5.38

B) 7.39

C) 6.42

D) 5.95

Objective: (12.2) Determine the Mean for a Data Set

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 18) Six people from different occupations were interviewed for a survey, and their annual salaries were as follows: $12,000, $20,000, $25,000, $37,000, $67,500 and $125,000. What is the mean annual salary for the six people? Objective: (12.2) Determine the Mean for a Data Set

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the median for the group of data items. 19) 10, 9, 4, 0, 1, 1, 1, 0, 0 A) 1 B) 5

C) 0

D) 4

C) 94

D) 100

C) 1.3

D) 2.05

Objective: (12.2) Determine the Median for a Data Set

20) 100, 100, 94, 37, 77, 100 A) 97

B) 37

Objective: (12.2) Determine the Median for a Data Set

21) 1.3, 2.1, 1.6, 2.9, 1.3, 2.1, 1.3, 9.3, 9.3, 2 A) 2 B) 2.1 Objective: (12.2) Determine the Median for a Data Set

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 22) Six people from different occupations were interviewed for a survey, and their annual salaries were as follows: $12,000, $20,000, $25,000, $37,000, $67,500 and $125,000. What is the median annual salary for the six people? Objective: (12.2) Determine the Median for a Data Set

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mode for the group of data items.If there is no mode, so state. 23) 12, 9, 4, 0, 1, 1, 1 A) 12 B) no mode C) 1

D) 9

Objective: (12.2) Determine the Mode for a Data Set

24) 99, 99, 92, 60, 71, 99 A) 92

B) 60

C) no mode

D) 99

C) 1.2

D) no mode

C) 6

D) 9

C) 73

D) 94

C) 1.95

D) 5.05

Objective: (12.2) Determine the Mode for a Data Set

25) 1.2, 2.2, 1.6, 2.7, 1.2, 2.2, 1.2, 8.9, 8.9, 2 A) 8.9 B) 1.6 Objective: (12.2) Determine the Mode for a Data Set

Find the midrange for the group of data items. 26) 11, 7, 5, 7, 1, 5, 1 A) 8 B) 4 Objective: (12.2) Determine the Midrange for a Data Set

27) 96, 96, 92, 50, 73, 96 A) 71

B) 84.5

Objective: (12.2) Determine the Midrange for a Data Set

28) 1.3, 2.2, 1.7, 2.6, 1.3, 2.2, 1.3, 8.8, 8.8, 2 A) 1.75 B) 5.25 Objective: (12.2) Determine the Midrange for a Data Set

For the given data set, find the a. mean b. median c. mode (or state that there is no mode) d. midrange. 29) Ages of teachers in the mathematics department of a certain high school: 26, 52, 33, 58, 26, 52, 26, 50, 50, 43 A) a. 41.6 B) a. 31.2 C) a. 26.2 D) a. 41.6 b. 46.5 b. 46.5 b. 46.5 b. 46.5 c. 50 c. 26 c. 26 c. 26 d. 42 d. 42 d. 42 d. 42 Objective: (12.2) Determine the Midrange for a Data Set

30) A company advertised that, on the average, 97% of their customers reported "very high satisfaction" with their services. The actual percentages reported in 15 samples were the following: 97, 97, 90, 46, 75, 97, 90, 75, 97, 97, 46, 90, 90, 97, 46 a. Find the mean, median, mode and midrange. b. Which measure of central tendency was given in the advertisement? c. Which measure of central tendency is the best indicator of the "average" in this situation? A) a. mean = 82, median = 90, mode = 97, midrange = 71.5 b. mode c. mode B) a. mean = 82, median = 90, mode = 97, midrange = 71.5 b. median c. mean C) a. mean = 82, median = 90, mode = 97, midrange = 71.5 b. mode c. mean D) a. mean = 82, median = 90, mode = 97, midrange = 71.5 b. mode c. median Objective: (12.2) Determine the Midrange for a Data Set

Find the range for the group of data items. 31) 12, 13, 14, 15, 16 A) 4 B) 12

C) 14

D) 16

C) 23

D) 31

C) 4

D) 28

Objective: (12.3) Determine the Range for a Data Set

32) 4, 4, 4, 19, 27, 27, 27 A) 15

B) 19

Objective: (12.3) Determine the Range for a Data Set

33) 12, 16, 12, 16, 12, 16, 12, 16 A) 16

B) 14

Objective: (12.3) Determine the Range for a Data Set

A group of data items and their mean are given. Find a. the deviation from the mean for each of the data items and b. the sum of the deviations in part a. 34) 48, 48, 50, 53, 53, 53, 54, 55, 58, 58; Mean = 53 A) 5, 5, 3, 0, 0, 0, 1, 2, 5, 5; 0 B) -5, -5, -3, 0, 0, 0, 1, 2, 5, 5; 0 C) -5, -5, -3, 0, 0, 0, 1, 2, 5, 5; 26 D) 5, 5, 3, 0, 0, 0, 1, 2, 5, 5; 26 Objective: (12.3) Determine the Standard Deviation for a Data Set

Find a. the mean b. the deviation from the mean for each data item: and c. the sum of the deviations in part b. 35) 142, 149, 151, 156, 157 A) a. 149 b. -9, -2, 0, 5, 6 c. 0 B) a. 151 b. -9, -2, 0, 5, 6 c. 22 C) a. 151 b. -9, -2, 0, 5, 6 c. 11 D) a. 151 b. -9, -2, 0, 5, 6 c. 0 Objective: (12.3) Determine the Standard Deviation for a Data Set

Find the standard deviation for the group of data items (to the nearest hundredth). 36) 12, 13, 14, 15, 16 A) 0 B) 2.5 C) 1.25 Objective: (12.3) Determine the Standard Deviation for a Data Set

D) 1.58

37) 14, 14, 14, 17, 20, 20, 20 A) 2.85

B) 3

C) 9

D) 8.14

C) 81

Objective: (12.3) Determine the Standard Deviation for a Data Set

Find the standard deviation for the group of data items. 38) 7, 16, 7, 16, 7, 16, 7, 16 9 2 81 A) B) 4 7

9 2 7

Objective: (12.3) Determine the Standard Deviation for a Data Set

Compute the mean, range, and standard deviation for the data items in each of the three samples. Then name one way in which the samples are alike and one way in which they are different. 39) Sample A: 14, 16, 18, 20, 22, 24, 26 Sample B: 14, 17, 17, 20, 23, 23, 26 Sample C: 14, 14, 14, 20, 26, 26, 26 A) Mean (for A, B and C): 20 Range (for A, B, and C): 12 Standard deviation: (A) 7 (B) 4.24 (C) 6. Samples have the same mean but different standard deviations. B) Mean (A) 16 (B) 17 (C) 18. Range (for A, B, and C): 12 Standard deviation: (A) 6 (B) 6 (C) 6. Samples have the same standard deviation but different means. C) Mean (for A, B and C): 20 Range (for A, B, and C): 12 Standard deviation: (A) 4.32 (B) 4.24 (C) 6. Samples have the same mean but different standard deviations. D) Mean (A) 19 (B) 20 (C) 21. Range (for A, B, and C): 12 Standard deviation: (A) 6 (B) 6 (C) 6. Samples have the same standard deviation but different means. Objective: (12.3) Determine the Standard Deviation for a Data Set

Find the a. mean and b. standard deviation for the data set. Round to two decimal places. 40) Country Number of Television Sets per 100 people A 94 B 64 C 99 D 79 E 84 A) a. 84 b. 169 B) a. 84 b. 13.69 C) a. 83 b. 13.69

D) a. 85 b. 13.69

Objective: (12.3) Determine the Standard Deviation for a Data Set

41) International Travel Destinations of U.S. Citizens Country U.S. Citizens, in thousands A 1,000 B 600 C 220 D 200 E 160 F 105 G 103 H 102 I 90 J 80 A) a. 266 b. 9000 B) a. 260 b. 300.55

C) a. 260 b. 9000

Objective: (12.3) Determine the Standard Deviation for a Data Set

D) a. 266 b. 300.55

Provide an appropriate response. 42) True or False? In a normal distribution, as the sample size increases, so does the graph's symmetry. A) True B) False Objective: (12.4) Recognize Characteristics of Normal Distributions

43) True or False? In a bell curve distribution, the median is less than the mean and is located to the left of the mean on the graph of the distribution. A) True B) False Objective: (12.4) Recognize Characteristics of Normal Distributions

44) In a normal distribution, approximately what percent of data items fall within 1 standard deviation of the mean (in both directions)? A) 65% B) 99.7% C) 95% D) 68% Objective: (12.4) Understand the 68-95-99.7 Rule

45) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume? A) He is taller than about 99.7% of the other men whose heights were measured. B) His height measurement is in the same range as about 95% of the other adult males whose heights were measured. C) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured. D) He is taller than about 95% of the other men whose heights were measured. Objective: (12.4) Understand the 68-95-99.7 Rule

46) If an adult male is told that his height is 3 standard deviations above the mean of the normal distribution of heights of adult males, what can he assume? A) His height measurement is in the same range as about 95% of the other adult males whose heights were measured. B) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured. C) He is taller than about 99.7% of the other men whose heights were measured. D) He is taller than about 95% of the other men whose heights were measured. Objective: (12.4) Understand the 68-95-99.7 Rule

The scores on a driver's test are normally distributed with a mean of 100. Find the score that is: 47) Find the score that is 3 standard deviations above the mean, if the standard deviation is 14. A) 114 B) 103 C) 142 D) 128 Objective: (12.4) Find Scores at a Specified Standard Deviation from the Mean

48) Find the score that is 2 A) 130

1 standard deviations above the mean, if the standard deviation is 30. 2

B) 175

C) 145

D) 115

Objective: (12.4) Find Scores at a Specified Standard Deviation from the Mean

49) Find the score that is 2 standard deviations below the mean, if the standard deviation is 10. A) 120 B) 110 C) 80 D) 90 Objective: (12.4) Find Scores at a Specified Standard Deviation from the Mean

50) Find the score that is 2 A) 70

1 standard deviations below the mean, if the standard deviation is 30. 2

B) 175

C) 25

D) 40

Objective: (12.4) Find Scores at a Specified Standard Deviation from the Mean

Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid: 51) between $148,100 and $151,900 if the standard deviation is $1,900. A) 68% B) 34% C) 99.7% D) 95% Objective: (12.4) Use the 68-95-99.7 Rule

52) between $150,000 and $152,200 if the standard deviation is $1,100. A) 34% B) 47.5% C) 99.7%

D) 68%

Objective: (12.4) Use the 68-95-99.7 Rule

53) between $150,000 and $157,500 if the standard deviation is $2,500. A) 49.85% B) 47.5% C) 34%

D) 99.7%

Objective: (12.4) Use the 68-95-99.7 Rule

54) more than $155,000 if the standard deviation is $2,500. A) 95% B) 97.5%

C) 47.5%

D) 2.5%

C) 97.5%

D) 47.5%

Objective: (12.4) Use the 68-95-99.7 Rule

55) less than $147,000 if the standard deviation is $1,500. A) 2.5% B) 95% Objective: (12.4) Use the 68-95-99.7 Rule

A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 56) data item: 63; standard deviation: 3 A) 20 B) 63 C) 3 D) 1 Objective: (12.4) Convert a Data Item to a z-score

57) data item: 84; standard deviation: 6 A) 6

B) 24

5 2

C) 4

C) 12

D) 18

C) 12

D) 0

Objective: (12.4) Convert a Data Item to a z-score

58) data item: 78; standard deviation: 12 A) 5 B) 1.5 Objective: (12.4) Convert a Data Item to a z-score

59) data item: 60; standard deviation: 12 A) 1 B) 5 Objective: (12.4) Convert a Data Item to a z-score

60) data item: 53; standard deviation: 7 A) 1 B) -1

C) -7

D) 7

C) -3.75

D) 3.75

Objective: (12.4) Convert a Data Item to a z-score

61) data item: 15; standard deviation: 12 A) 12 B) -12 Objective: (12.4) Convert a Data Item to a z-score

A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score. 62) z = 2, if the standard deviation is 20. A) 502 B) 520 C) 540 D) 460 Objective: (12.4) Convert a Data Item to a z-score

63) z = 1.5, if the standard deviation is 70. A) 850 B) 605

C) 570

D) 535

C) 440

D) 497

Objective: (12.4) Convert a Data Item to a z-score

64) z = -3, if the standard deviation is 20. A) 560 B) 480 Objective: (12.4) Convert a Data Item to a z-score

Solve the problem. 65) A student scores 74 on a geography test and 261 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 5. The mathematics test has a mean of 300 and a standard deviation of 26. If the data for both tests are normally distributed, on which test did the student score better? A) The student scored the same on both tests. B) The student scored better on the geography test. C) The student scored better on the mathematics test. Objective: (12.4) Convert a Data Item to a z-score

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 66) The combined SAT scores of the freshman class at a particular university are normally distributed with a mean of 1000 and a standard deviation of 100. What percentage of the freshmen class had combined SAT scores above 1110? Objective: (12.4) Convert a Data Item to a z-score

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 67) The histogram shows the ages (in months) that babies learned to walk. Use this histogram to solve the problem.

(i) Find the median age that a baby learned to walk. (ii) Find the first quartile by determining the median of the lower half of the data. A) (i) median = 12; B) (i) median = 13; (ii) first quartile = 10.5 (ii) first quartile = 12.5 C) (i) median = 11; D) (i) median = 11.5; (ii) first quartile = 10 (ii) first quartile = 9.5 Objective: (12.4) Understand Percentiles and Quartiles

68) The histogram shows the ages (in months) that babies learned to walk. Use this histogram to solve the problem.

(i) Find the median age that a baby learned to walk. (ii) Find the third quartile by determining the median of the upper half of the data. A) (i) median = 11.5; B) (i) median = 12; (ii) first quartile = 12.5 (ii) third quartile = 13 C) (i) median = 11; D) (i) median = 12.5; (ii) first quartile = 12 (ii) first quartile = 13 Objective: (12.4) Understand Percentiles and Quartiles

69) The histogram shows suicide rates per 100,000 residents of Country X and the number of states that had these rates. Use this histogram to solve the problem.

(i) Find the median suicide rate per 100,000 residents for Country X by state. (ii) Find the first quartile by determining the median of the lower half of the data. A) (i) median = 18.5; B) (i) median = 19; (ii) first quartile = 16 (ii) first quartile = 15.5 C) (i) median = 19.5; D) (i) median = 18; (ii) first quartile = 17 (ii) first quartile = 14.5 Objective: (12.4) Understand Percentiles and Quartiles

70) The histogram shows suicide rates per 100,000 residents of Country X and the number of states that had these rates. Use this histogram to solve the problem.

(i) Find the median suicide rate per 100,000 residents for Country X by state. (iii) Find the third quartile by determining the median of the upper half of the data. A) (i) median = 19.5; B) (i) median = 19; (ii) third quartile = 20.5 (ii) third quartile = 22 C) (i) median = 18; D) (i) median = 18; (ii) third quartile = 21 (ii) third quartile = 22.5 Objective: (12.4) Understand Percentiles and Quartiles

71) A survey was conducted of 439 teenagers. Thirty-five percent of the teenagers said they occasionally smoked cigarettes. a. Find the margin of error for this survey. b. Write a statement about the percentage of teenagers who occasionally smoke cigarettes. A) a. ± 4.8% b. There is a 95% probability that the true population percentage lies between 30.2% and 39.8%. B) a. ± 20.952% b. There is a 95% probability that the true population percentage lies between 30.2% and 39.8%. C) a. ± 4.8% b. There is a 99% probability that the true population percentage lies between 30.2% and 39.8%. D) a. ± 4.8% b. There is a 95% probability that the true population percentage lies between 25.2% and 34.8%. Objective: (12.4) Use and Interpret Margins of Error

72) Using a random sample of 3,700 households, a media research company finds that 55.1% watched a particular episode of a popular situation comedy. a. Find the margin of error in this percent. b. Write a statement about the percentage of TV households in the population who watched the episode of the situation comedy. A) a. ± 60.828% b. There is a 95% probability that the true population percentage lies between 53.5% and 56.7% . B) a. ± 1.6% b. There is a 99% probability that the true population percentage lies between 53.5% and 56.7% . C) a. ± 1.6% b. There is a 95% probability that the true population percentage lies between 53.5% and 56.7% . D) a. ± 1.6% b. There is a 95% probability that the true population percentage lies between 48.4% and 51.6% . Objective: (12.4) Use and Interpret Margins of Error

73) A media research company increased the size of their random samples from 3,600 to 4,900. By how much, to the nearest tenth of a percent, did this improve their margin of error? A) 0.2% B) 1.7% C) 1.4% D) 3.1% Objective: (12.4) Use and Interpret Margins of Error

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 74) In a recent poll 4000 people were asked this question, "If you could pick anyone you want for Hero of the Year, who would it be?" 56% of the respondents picked Michael Phelps. What is the margin of error for this poll? Write a statement about the percentage of people who picked Michael Phelps? Objective: (12.4) Use and Interpret Margins of Error

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the histograms shown to answer the question. 75)

Is either histogram symmetric? A) The second is symmetric, but the first is not symmetric. B) The first is symmetric, but the second is not symmetric. C) Neither is symmetric. D) Both are symmetric. Objective: (12.4) Recognize Distributions that are not Normal

76)

Can the number of A defects or the number of B defects be described using the normal distribution? A) Both are normal. B) The first is normal, but the second is not normal. C) The second is normal, but the first is not normal. D) Neither is normal. Objective: (12.4) Recognize Distributions that are not Normal

Use the table of z-scores and percentiles to find the percentage of data items in a normal distribution that lie a. above and b. below the given score. 77) z = 0.4 A) 65.54%, 34.46% B) 34.46%, 65.54% C) 0%, 100% D) 65.54%, 65.54% Objective: (12.5) Solve Applied Problems Involving Normal Distributions

78) z = -0.4 A) 34.46%, 34.46%

B) 65.54%, 34.46%

C) 0%, 100%

D) 34.46%, 65.54%

Objective: (12.5) Solve Applied Problems Involving Normal Distributions

Use a table of z-scores and percentiles to find the percentage (to the nearest whole percentage) of data items in a normal distribution that lie between: 79) z = 1 and z = 2 A) 6% B) 14% C) 12% D) 8% Objective: (12.5) Solve Applied Problems Involving Normal Distributions

Use a table of z-scores and percentiles to find the percentage of data items in a normal distribution that lie between: 80) z = 0.4 and z = 1.4 A) 65.54% B) 26.38% C) 91.92% D) 34.46% Objective: (12.5) Solve Applied Problems Involving Normal Distributions

81) z = -0.7 and z = 0.7 A) 24.2%

B) 51.6%

C) 50%

D) 75.8%

Objective: (12.5) Solve Applied Problems Involving Normal Distributions

82) z = -2 and z = -0.4 A) 32.18%

B) 65.54%

C) 34.46%

D) 2.28%

Objective: (12.5) Solve Applied Problems Involving Normal Distributions

Test scores are normally distributed with a mean of 500. Convert the given score to a z-score, using the given standard deviation. Then find the percentage of students who score: 83) below 635 if the standard deviation is 90. A) 6.68% B) 90% C) 56.68% D) 93.32% Objective: (12.5) Solve Applied Problems Involving Normal Distributions

Make a scatter plot for the given data. Use the scatter plot to describe whether or not the variables appear to be related. 84) x 6 11 9 8 12 7 y 9 12 10 10 11 8 A) B)

The variables appear to be related.

The variables do not appear to be related.

Objective: (12.6) Make a Scatter Plot for a Table of Data Items

85) x y

10 8 3 7 6 12 5 12 14 10 13 16 12 19

The variables do not appear to be related.

The variables appear to be related.

The variables do not appear to be related.

Objective: (12.6) Make a Scatter Plot for a Table of Data Items

86) Subject Time watching TV Time on Internet A)

A B C D E F G 10 6 4 9 9 7 8 13 11 7 16 17 8 17

The variables appear to be related.

The variables do not appear to be related.

The variables appear to be related. Objective: (12.6) Make a Scatter Plot for a Table of Data Items

87) The data show the number of felony convictions, in hundreds, and the crime rate, in crimes per 100,000, for seven randomly selected states. Felony convictions Crime rate /100,000 A)

14.4 11.1 9.7 6.4 5.4 5.3 3.4 14.6 12.1 13 11.6 6.8 8.1 5.9

The variables do not appear to be related.

The variables appear to be related.

The variables do not appear to be related.

The variables appear to be related.

Objective: (12.6) Make a Scatter Plot for a Table of Data Items

The scatter plot shows the relationship between average number of years of education and births per woman of child bearing age in selected countries. Use the scatter plot to determine whether the statement is true or false. 88)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age There is a strong positive correlation between years of education and births per woman. A) True B) False Objective: (12.6) Interpret Information Given in a Scatter Plot

89)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age There is no correlation between years of education and births per woman. A) False B) True Objective: (12.6) Interpret Information Given in a Scatter Plot

90)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age There is a strong negative correlation between years of education and births per woman. A) True B) False Objective: (12.6) Interpret Information Given in a Scatter Plot

91)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age There is a causal relationship between years of education and births per woman. A) False B) True Objective: (12.6) Interpret Information Given in a Scatter Plot

92)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age With approximately 8 years of education in country J, there are 5 births per woman. A) False B) True Objective: (12.6) Interpret Information Given in a Scatter Plot

93)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age With approximately 3 years of education in country C, there are 9 births per woman. A) False B) True Objective: (12.6) Interpret Information Given in a Scatter Plot

94)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age No two countries have a different number of births per woman with the same number of years of education. A) True B) False Objective: (12.6) Interpret Information Given in a Scatter Plot

95)

Births per Woman

Average number of years of education of Married Women of Child-Bearing Age The country with the greatest number of births per woman also has the smallest number of years of education. A) False B) True Objective: (12.6) Interpret Information Given in a Scatter Plot

Use the scatter plots shown, labelled a through f to solve the problem.

96) a

Which scatter plot indicates a perfect negative correlation? A) f B) c Objective: (12.6) Interpret Information Given in a Scatter Plot

97) a

C) a

D) b

In which scatter plot is r = 0.01? A) f B) d

C) e

D) c

Objective: (12.6) Interpret Information Given in a Scatter Plot

Compute r, the correlation coefficient, rounded to the nearest thousandth, for the following data: 98) x 11 16 14 13 17 12 y 6 9 7 7 8 5 A) 0.9 B) 0.855 C) -0.9

D) -0.855

Objective: (12.6) Compute the Correlation Coefficient

99) x y

6 4 -1 3 2 8 1 11 13 19 12 15 11 18 A) -0.75 B) -0.905

C) 0.905

Objective: (12.6) Compute the Correlation Coefficient

D) 0.75

Solve the problem. 100) Use the following data to a. determine the coefficient of correlation, rounded to the nearest thousandth, b. find the equation of the regression line for time watching TV and time on the Internet, c. approximate how much time on the Internet can we predict for a person who spends 10 hours weekly watching TV. Subject A B C D E F G Time watching TV 11 7 5 10 10 8 9 Time on Internet 13 11 7 16 17 8 17 A) a. r = -0.752 b. y = -1.52x - 0.31 c. 15.5 hours C) a. r = -0.752 b. y = -0.31x + 1.52 c. 1.6 hours

B) a. r = 0.752 b. y = 1.52x + 0.31 c. 15.5 hours D) a. r = 0.752 b. y = 1.52x - 0.31 c. 14.9 hours

Objective: (12.6) Write the Equation of the Regression Line

101) The data show the number of felony convictions, in hundreds, and the crime rate, in crimes per 100,000, for seven randomly selected states. For the given data, a. determine the correlation coefficient between the number of felony convictions and the crime rate, (b) find the equation of the regression line, (c) approximate what crime rate can we anticipate in a state that has 12 hundred felony convictions. Felony convictions 13.1 9.8 8.4 5.1 4.1 4 2.1 Crime rate /100,000 10.6 8.1 9 7.6 2.8 4.1 1.9 A) a. r = 0.906 b. y = 1.13x + 0.777 c. 14.3 C) a. r = 0.906 b. y = 0.777x + 1.13 c. 10.5

B) a. r = -0.906 b. y = 0.777x - 1.13 c. 8.2 D) a. r = -0.906 b. y = -0.777x + 1.13 c. 8.2

Objective: (12.6) Write the Equation of the Regression Line

The correlation coefficient, r is given for a sample of n data points. Use the α = 0.05 column in a correlation significance table to determine whether or not we may conclude that a correlation does exist in the population. 102) n = 67 r = 0.5 A) No, we may not conclude that there is a correlation. B) Yes, we may conclude that there is a correlation. Objective: (12.6) Use a Sample's Correlation Coefficient to Determine Whether There Is a Correlation in the Population

103) n = 67 r = 0.04 A) Yes, we may conclude that there is a correlation. B) No, we may not conclude that there is a correlation. Objective: (12.6) Use a Sample's Correlation Coefficient to Determine Whether There Is a Correlation in the Population

104) n = 42 r = -0.395 A) No, we may not conclude that there is a correlation. B) Yes, we may conclude that there is a correlation. Objective: (12.6) Use a Sample's Correlation Coefficient to Determine Whether There Is a Correlation in the Population

105) n = 27 r = -0.301 A) Yes, we can conclude that there is a correlation. B) No, we can not conclude that there is a correlation. Objective: (12.6) Use a Sample's Correlation Coefficient to Determine Whether There Is a Correlation in the Population

Answer Key Testname: 12-BLITZER_TM8E_TEST_ITEM_FILE

1) D 2) C 3) The population is the set containing all computer owners in the city. 4) B 5) A 6) Hours Number of of TV HS Students 12 4 13 5 14 6 15 5 16 4 17 2 18 2 21 2 Age Number of Sw 18 - 27 10 8 7) 28 - 37 38 - 47 5 48 - 57 5 58 - 67 2

10) A 11) B 12) C 13) A 14) A 15) C 16) C 17) C 18) $47,750 19) A 20) A 21) D 22) $31,000 23) C 24) D 25) C 26) C 27) C 28) D 29) D 30) C 31) A 32) C 33) C 34) B 35) D 36) D 37) B 38) B 39) C 40) B 41) D 42) A 43) B 44) D 45) B 46) C 47) C 48) B 49) C 50) C 51) A 52) B 53) A 54) D 55) A 56) D 57) C 58) B 59) D

9) Stems Attorneys 3 99 4 00112589 5 1234458 6 1233458 7 0137 8 12 The ages tend to be concentrated in the middle of the range.

60) B 61) C 62) C 63) B 64) C 65) B 66) 13.57% 67) A 68) B 69) B 70) B 71) A 72) C 73) A 74) ±1.6%; We can be 95% confident that between 54.4% and 57.6% of all respondents picked Michael Phelps for Hero of the Year. 75) C 76) D 77) A 78) B 79) B 80) B 81) B 82) A 83) D 84) A 85) A 86) D 87) D 88) B 89) A 90) A 91) A 92) B 93) A 94) B 95) A 96) C 97) C 98) B 99) B 100) D 101) C 102) B 103) B

Answer Key Testname: 12-BLITZER_TM8E_TEST_ITEM_FILE

104) B 105) B

Blitzer, Thinking Mathematically, 8e Chapter 13 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the given information to answer the question. 1) The preference ballots for presidency of the Jazz Appreciation Club (A, B, and C) are shown. Fill in the number of votes in the first row of the preference table. ACB ACB BAC CBA BAC ACB ACB BAC

ACB ACB BAC BAC

CBA BAC ACB ACB

Number of Votes __ First choice A Second choice C Third choice B

__ B A C

__ C B A

Number of Votes First choice A) Second choice Third choice

9 5 2 A B C C A B B C A

Number of Votes First choice B) Second choice Third choice

8 6 2 A B C C A B B C A

Number of Votes First choice C) Second choice Third choice

8 7 1 A B C C A B B C A

Number of Votes First choice D) Second choice Third choice

8 6 2 A C B C B A B A C

Objective: (13.1) Understand and Use Preference Tables

2) Four students are running for president of the Mathemetics Club: Arthur (A), Brandy (B), Chandra (C), and Darrell (D). The preference ballots for the candidates are shown. Construct a preference table to illustrate the results of the voting. DBAC CABD

DABC DBAC DBAC DABC DBAC DABC

DABC ACBD ACBD DABC

Number of votes 4 2 5 First choice D D A A) Second choice B A C Third choice A B B Fourth choice C C D

1 C A B D

Number of votes First choice B) Second choice Third choice Fourth choice

5 4 2 D D A A B C B A B C C D

Number of votes First choice C) Second choice Third choice Fourth choice

1 A C B D

Number of votes First choice D) Second choice Third choice Fourth choice

4 5 2 1 D D A C B A C A A B B B C C D D

5 4 2 D D C A B A B A B C C D

Objective: (13.1) Understand and Use Preference Tables

1 C A B D

Use the preference table to answer the question. 3) Diners at the Taste of Paris restaurant answer a questionnaire about their favorite course in a French meal. The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following table. Number of Votes First choice Second choice Third choice

18 A E D

14 D A E

8 6 A D D E E A

Which course is selected as the most favorite using the plurality method? A) Entree B) Dessert

C) Appetizer

Objective: (13.1) Use the Plurality Method to Determine an Election's Winner

4) Four students are running for president of their graduating class: Debra (D), Farah (F), Jorge (J), and Hillary (H). The votes of their fellow students are summarized in the following preference table. Number of Votes 48 47 17 7 5 First choice J F J F H Second choice D J F J J Third choice F H H D D Fourth choice H D D H F Who is declared the new president using the plurality method? A) Jorge B) Hillary C) Farah

D) Debra

Objective: (13.1) Use the Plurality Method to Determine an Election's Winner

5) Diners at the Taste of Paris restaurant answer a questionnaire about their favorite course in a French meal. The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following table.

Number of Votes 18 First choice A Second choice E Third choice D

14 8 6 D A D A D E E E A

Which course is selected as the most favorite using the Borda count method? A) Dessert B) Tie between Appetizer and Dessert C) Appetizer D) Entree Objective: (13.1) Use the Borda Count Method to Determine an Election's Winner

6) Four students are running for president of their residence hall: Debra (D), Farah (F), Jorge (J), and Hillary (H). The votes of their fellow students are summarized in the following preference table. Number of Votes 52 45 13 9 4 First choice D F J F H Second choice F J F J J Third choice H H H D D Fourth choice J D D H F Who is declared the new president using the Borda count method? A) Farah B) Hillary C) Debra

D) Jorge

Objective: (13.1) Use the Borda Count Method to Determine an Election's Winner

7) Diners at the Monsieur Herni restaurant answer a questionnaire about their favorite course in a French meal. The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following table.

Number of Votes 19 First choice E Second choice D Third choice A

13 7 7 D A D A D E E E A

Which course is selected as the most favorite using the plurality-with-elimination method? A) Entree B) Tie between Appetizer and Entree C) Appetizer D) Dessert Objective: (13.1) Use the Plurality-with-Elimination Method to Determine an Election's Winner

8) Four students are running for president of their dormitory: Debra (D), Farah (F), Jorge (J), and Hillary (H). The votes of their fellow students are summarized in the following preference table. Number of Votes 52 35 22 10 4 First choice D F J F H Second choice F J F J J Third choice H H H D D Fourth choice J D D H F Who is declared the new president using the plurality-with-elimination method? A) Farah B) Debra C) Jorge Objective: (13.1) Use the Plurality-with-Elimination Method to Determine an Election's Winner

D) Hillary

9) Diners at the Monsieur Herni restaurant answer a questionnaire about their favorite course in a French meal. The choices are: Appetizer (A), Entree (E), and Dessert (D). Their votes are summarized in the following table.

Number of Votes 19 First choice E Second choice D Third choice A

13 7 7 D A D A D E E E A

Which course is selected as the most favorite using the pairwise comparison method? A) Appetizer B) Dessert C) Tie between Appetizer and Dessert D) Entree Objective: (13.1) Use the Pairwise Comparison Method to Determine an Election's Winner

10) Four students are running for president of their graduating class: Debra (D), Farah (F), Jorge (J), and Hillary (H). The votes of their fellow students are summarized in the following preference table. Number of Votes 48 47 17 7 5 First choice J F J F H Second choice D J F J J Third choice F H H D D Fourth choice H D D H F Who is declared the new president using the pairwise comparison method? A) Farah B) Debra C) Hillary

D) Jorge

Objective: (13.1) Use the Pairwise Comparison Method to Determine an Election's Winner

11) The preference table shows the results of an election among three candidates, A, B, and C. Number of votes First choice Second choice Third choice

10 A B C

4 B C A

2 C B A

(a) Using the plurality method, who is the winner? (b) Is the majority criterion satisfied? A) A; yes B) B; yes

C) A; no

D) C; yes

Objective: (13.2) Use the Majority Criterion to Determine a Voting System's Fairness

12) The preference table shows the results of an election among three candidates, A, B, and C. Number of votes 7 6 3 First choice A B C Second choice B C B Third choice C A A (a) Using the plurality method, who is the winner? (b) Is the head-to head criterion satisfied? A) C; no B) B; yes

C) A; yes

Objective: (13.2) Use the Head-to-Head Criterion to Determine a Voting System's Fairness

D) A; no

13) The preference table shows the results of a straw vote among three candidates, A, B, and C. Number of votes 7 6 3 First choice A B B Second choice B C A Third choice C A C (a) Using the plurality-with-elimination method, which candidate wins the straw vote? (b) In the actual election, the 3 voters in the last column who voted B, A, and C, in that order, change their votes to A, B, C. Using plurality-with-elimination method, which candidate wins the actual election. (c) Is the monotonicity criterion satisfied? A) B; A; no B) B; B; yes C) B; A; yes D) A; A; yes Objective: (13.2) Use the Monotonicity Criterion to Determine a Voting System's Fairness

14) The preference table shows the results of an election among three candidates, A, B, and C. Number of votes First choice Second choice Third choice

10 A B C

4 2 B C C B A A

(a) Using the plurality method, who is the winner? (b) The voters in the two columns on the right move their last-place candidates from last place to first place. Construct a new preference table for the election. Using the table and the plurality method, who is the winner? (c) Suppose that candidate C drops out of the new table, but the winner is still chosen by the plurality method. Is the irrelevant alternatives criterion satisfied? A) A; B; yes B) A; A; no C) A; A; yes D) B; A; no Objective: (13.2) Use the Irrelevant Alternatives Criterion to Determine a Voting System's Fairness

Answer the question. 15) Choose the sentence or sentences that accurately restate Arrow's Impossibility Theorem. I. It is mathematically impossible for any democratic voting system to satisfy any of the four fairness criteria. II. It is mathematically impossible for any democratic voting system to satisfy all of the four fairness criteria. III. It is mathematically impossible for any democratic voting system to satisfy some of the four fairness criteria. IV. It is mathematically impossible for any democratic voting system to satisfy any more than one of the four fairness criteria. A) IV only B) I, III, and IV C) II only D) I, II, and III Objective: (13.2) Understand Arrow's Impossibility Theorem

Solve. 16) A country is made up of four regions A, B, C, and D. The population of each region, in thousands, is given in the following table. Region Population (in thousands)

A 512

B 630

C 483

D Total 615 2,240

According to the country's constitution, the congress will have 40 seats, divided among the four regions according to their respective populations. (a) Find the standard divisor , in thousands. (b) How many people are there for each seat in the congress? A) 58; 58,000 B) 56; 56,000 C) 40; 40,000

D) 55; 55,000

Objective: (13.3) Find Standard Divisors and Standard Quotas

17) A country is made up of four regions A, B, C, and D. The population of each region, in thousands, is given in the following table. Region A Population 364 (in thousands)

B 261

C 298

D Total 237 1,160

According to the country's constitution, the congress will have 20 seats, divided among the four regions according to their respective populations. Find the standard quota for each region. Round to the nearest hundredth. A) A, 6.28; B, 4.50; C, 6.23; D, 4.09 B) A, 6.28; B, 4.50; C, 5.14; D, 4.09 C) A, 6.28; B, 5.07; C, 5.14; D, 4.09 D) A, 6.28; B, 4.50; C, 5.14; D, 5.31 Objective: (13.3) Find Standard Divisors and Standard Quotas

Provide an appropriate response. 18) The apportionment problem is to determine a method for rounding standard the sum is the total number of allocated items. A) populations; divisors C) divisors; quotas

into

B) quotas; whole numbers D) quotas; populations

Objective: (13.3) Understand the Apportionment Problem

19) True or False? The lower quota is the standard quota rounded down to the nearest whole number. A) True B) False Objective: (13.3) Understand the Apportionment Problem

20) True or False? The upper quota is the standard quota rounded up to the nearest whole number. A) True B) False Objective: (13.3) Understand the Apportionment Problem

so that

Use the table to answer the question. 21) For the apportionment of 50 seats in congress among four states, the standard quotas are as shown in the following table. Region Standard quota

A B C D 9.14 11.25 18.63 10.98

Create an extended table by entering the final quotas using Hamilton's method. Region A B C D Standard quota 9.14 11.25 18.63 10.98 Quota using Hamilton's method ___ ___ ___ ___

A) Region A B C D Standard quota 9.14 11.25 18.63 10.98 Quota using Hamilton's method 9 12 18 11

B) Region A B C D Standard quota 9.14 11.25 18.63 10.98 Quota using Hamilton's method 9 11 19 11

C) Region A B C D Standard quota 9.14 11.25 18.63 10.98 Quota using Hamilton's method 9 11 20 10

D) Region A B C D Standard quota 9.14 11.25 18.63 10.98 Quota using Hamilton's method 8 12 19 11 Objective: (13.3) Use Hamilton's Method

Solve the problem. 22) For the apportionment of 30 seats among four states, the standard quotas are as shown in the following table. State A B C D Standard quota 8.28 8.50 7.14 6.09 Create an extended table by showing each state's upper quota and lower quota. State Standard quota Upper quota Lower quota

A B C D 8.28 8.50 7.14 6.09 ___ ___ ___ ___ ___ ___ ___ ___

B) State A B C D Standard quota 8.28 8.50 7.14 6.09 Upper quota 8.28 8.50 7.14 6.09 Lower quota 8 8 7 6

State A B C D Standard quota 8.28 8.50 7.14 6.09 Upper quota 9 9 8 7 Lower quota 8.28 8.50 7.14 6.09

D) State A B C D Standard quota 8.28 8.50 7.14 6.09 Upper quota 9 9 8 7 Lower quota 8 8 7 6

State A B C D Standard quota 8.28 8.50 7.14 6.09 Upper quota 9 10 8 6 Lower quota 8 9 7 5

Objective: (13.3) Understand the Quota Rule

23) An organization helping to provide meals to city shelters for the homeless has a membership of 100 volunteers. They are assigned among the four city areas A, B, C, and D in proportion to the number of people fed in the respective areas. The numbers of people fed at the city shelters in each city area are shown in the following table. City area A B C D Number fed 1760 2340 2420 1580 Use Jefferson's method to extend the table and apportion the 100 volunteers among the city areas. City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers ___ ___ ___ ___

A) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 22 29 30 19

B) City area A Number fed 1760 Number of volunteers 23

B 2340 28

C 2420 31

D 1580 18

C) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 23 29 29 19

D) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 22 28 30 20 Objective: (13.3) Use Jefferson's Method

24) An organization helping to provide meals to city shelters for the homeless has a membership of 60 volunteers. They are assigned among the four city areas A, B, C, and D in proportion to the number of people fed in the respective areas. The numbers of people fed at the city shelters in each city area are shown in the following table. City area A B C D Number fed 1760 2340 2420 1580 Use Adams's method to extend the table and apportion the 60 volunteers among the city areas. City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers ___ ___ ___ ___

A) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 15 16 17 12

B) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 15 15 20 10

C) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 13 17 18 12

D) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 13 15 18 14 Objective: (13.3) Use Adams's Method

25) An organization helping to provide meals to city shelters for the homeless has a membership of 100 volunteers. They are assigned among the four city areas A, B, C, and D in proportion to the number of people fed in the respective areas. The numbers of people fed at the city shelters in each city area are shown in the following table. City area A B C D Number fed 1760 2340 2420 1580 Use Webster's method to extend the table and apportion the 100 volunteers among the city areas. City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers ___ ___ ___ ___

A) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 24 27 32 17

B) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 22 27 30 21

C) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 22 29 30 19

D) City area A B C D Number fed 1760 2340 2420 1580 Number of volunteers 25 28 29 18 Objective: (13.3) Use Webster's Method

26) In the year 2001, the economics department of a university had 25 teaching assistants (TAs) to be divided among three courses, according to their respective enrollments. Table 1 shows the courses and the standard quotas as calculated for 25 TAs and 26 TAs Table 2 shows the same data for year 2002, when the enrollment levels were different. TABLE 1 (2001) Course Standard quota with 25 TAs Standard quota with 26TAs

General Economics Business Economics Theory Economics 13.35 7.28 4.37 13.88 7.57 4.54

TABLE 2 (2002) Course Standard quota with 25 TAs Standard quota with 26TAs

General Economics Business Economics Theory Economics 13.26 7.34 4.41 13.79 7.63 4.58

The Alabama paradox is said to exist when an increase in the total number of items to be apportioned results in the loss of an item for a group. Using the Hamilton method to determine final quotas, decide which of the statements below is true.

A) The Alabama paradox would have occurred only in 2001. B) The Alabama paradox would have occurred in neither 2001 nor 2002. C) The Alabama paradox would have occurred in both 2001 and 2002. D) The Alabama paradox would have occurred only in 2002. Objective: (13.4) Understand and Illustrate the Alabama Paradox

27) Four regions (A, B, C, and D) in a country control seats in a national congress apportioned according to the respective populations in each region. The table shows the percentage of population growth in each region from 1,996 to 1,997. Population Growth 1,996 to 1,997 Region A 3.8% Region B 1.4% Region C 2.7% Region D 1.9% The following two statements were made about the information contained in the table: I. The population paradox occurred if Region B lost a seat to region A in 1,997. II. The population paradox occurred if Region C lost a seat to region D in 1,997. Which, if either, of these statements is accurate?

A) I and II are both true. B) I is false and II is true. C) I is true and II is false. D) Not enough information is given to answer the question. Objective: (13.4) Understand and Illustrate the Population Paradox

28) A national business has a small West Coast regional office responsible for 1059 customers and a larger East Coast regional office responsible for 9041 customers. The table shows the number of customers handled by each regional office. Regional office Customers

West Coast East Coast Total 1059 9041 10,100

The national sales manager makes 100 visits total each year to the regional offices, apportioned between the two offices with respect to the number of customers fo which each is responsible. Suppose that a new St. Louis regional office is opened with 510 brand-new customers, resulting in a distribution shown in the following table. Regional office West Coast East Coast St. Louis Total Customers 1059 9041 510 10,610 The sales manager adds 5 additional annual visits to his schedule for the St. Louis regional office. Use Hamilton's method to apportion the sales manager's visits for when there were two regional offices and for when there were three regional offices. Then decide which, if either, of the following statements is true. I. The new-states paradox occurs, with respect to the sales manager's visits, when the third regional office is added. II. When the third regional office is added, the West Coast office will get one fewer visit from the sales manager than before. A) I and II are both true. B) I and II are both false. C) I is true and II is false. D) I is false and II is true. Objective: (13.4) Understand and Illustrate the New-States Paradox

29) New-states Paradox: The addition of a new group changes the apportionments of other groups. Suppose there are 40 states in a country where congressional seats are alloted to the states in proportion to the population of each respective state. Total population is 12 million people. Suppose also that a 41st state is admitted, adding its own population to that of the nation. If the new-states paradox occurs, which of the following statements are true: I. In the original 40 states, only one state will end up with a different number of congressional seats. II. In the original 40 states, at least two states will end up with a different number of congressional seats. III. The original 40 states will all retain the same number of seats if the 41st state has a population of under 500,000. IV. If the 41st state has a population greater than one million, at least two of the original states will end up with a different number of congressional seats. A) I and III B) II and IV C) II D) II and III Objective: (13.4) Understand and Illustrate the New-States Paradox

Provide an appropriate response. 30) Which of the following statements about Balinski and Young's Impossibility Theorem is true? A) It is impossible to apply an apportionment method that does not violate the quota rule. B) It is impossible to apply an apportionment method that does not produce paradoxes. C) All apportionment methods basically produce equivalent results. D) Any apportionment method either violates the quota rule or produces paradoxes. Objective: (13.4) Understand Balinski and Young's Impossibility Theorem

Answer Key Testname: 13-BLITZER_TM8E_TEST_ITEM_FILE

1) B 2) B 3) C 4) A 5) C 6) A 7) D 8) A 9) B 10) D 11) A 12) D 13) A 14) C 15) C 16) B 17) B 18) B 19) B 20) A 21) B 22) C 23) A 24) C 25) C 26) C 27) B 28) C 29) B 30) D

Blitzer, Thinking Mathematically, 8e Chapter 14 Test Item File MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph models the football schedule for 5 area high schools. The vertices represent the teams and each game played is represented as an edge between two teams. Use the information in the graph to answer the question.

1) How many games are scheduled for East? A) 4 B) 6

C) 7

D) 5

Objective: (14.1) Understand Relationships in a Graph

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 2) List all the teams that West is playing. Objective: (14.1) Understand Relationships in a Graph

3) How may times will West play each of the other teams? Objective: (14.1) Understand Relationships in a Graph

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which of the following is another way to represent the graph shown. 4)

Objective: (14.1) Understand Relationships in a Graph

Answer true or false. 5) A graph consists of edges and vertices. A) True

B) False

Objective: (14.1) Understand Relationships in a Graph

Which of the following is a possible representation for the graph with the given edges. 6) QR, RS, RT, and SS A) B) Q Q R

S T

D) None of these Q

S Objective: (14.1) Model Relationships Using Graphs

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 7) In a group of 8 friends, many have dated other members of the group. Phoebe has dated Eric, Scott, and Russell. Ruth has dated Scott; Claire has dated Eric and Russell; and Anne has dated Eric, Scott, Russell, and Matt. Draw a graph that models the dating relationships of the friends. Objective: (14.1) Model Relationships Using Graphs

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

8) Create a graph that models the bordering relationship among the states shown in the map. Use vertices to represent the states and edges to represent common borders.

Objective: (14.1) Model Relationships Using Graphs

9) Draw a graph that models the floor plan. Use vertices to represent the rooms and the outside, and edges to represent the doors.

outside

B) OF

OF LV

LV outside

outside

BR KT

D) OF

OF LV

LV outside

outside

BR KT

Objective: (14.1) Model Relationships Using Graphs

Use the graph below to answer the question.

10) What is the degree of vertex F? A) 1 B) 0

C) 2

D) 3

Objective: (14.1) Understand and Use the Vocabulary of Graph Theory

11) Identify the vertex as odd or even. Vertex E. A) odd

B) even

Objective: (14.1) Understand and Use the Vocabulary of Graph Theory

12) Is vertex A adjacent to vertex B? A) no

B) yes

Objective: (14.1) Understand and Use the Vocabulary of Graph Theory

13) True or false? DE is a bridge. A) true

B) false

Objective: (14.1) Understand and Use the Vocabulary of Graph Theory

14) Which of the following is NOT a path starting at vertex A and ending at vertex E? A) A, D, G, E B) A, D, E C) A, C, D, E Objective: (14.1) Understand and Use the Vocabulary of Graph Theory

15) Which edges are not included in the following path: A, B, C, D, E, G, F, D? A) AD, DH, AE, DG B) AD, BD, DH, AE, HH, DG C) AD, BD, DH, AE, DG D) AD, BD, DH, DG Objective: (14.1) Understand and Use the Vocabulary of Graph Theory

D) A, B, C, D, E

Determine whether the given path is an Euler Path, an Euler Circuit, or neither. 16)

F,G,E,D,G,B,C,D,B,A A) Euler circuit

B) neither

C) Euler path

Objective: (14.2) Understand the Definition of an Euler Path

Answer the question. 17) An Euler path can start and end at the same vertex. A) True

B) False

Objective: (14.2) Understand the Definition of an Euler Path

Solve. 18)

The graph above has a possible path E-B-A-C-B-D-C-E. Trace this path with your pencil and determine whether it is an Euler circuit. A) no B) yes Objective: (14.2) Understand the Definition of an Euler Circuit

Answer true or false. 19) An Euler circuit always starts and ends at the same vertex. A) True Objective: (14.2) Understand the Definition of an Euler Circuit

B) False

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve. 20)

The graph shown above has no Euler paths or Euler circuits. Why? Objective: (14.2) Use Euler's Theorem

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use Euler's theorem to determine whether the graph has an Euler path (but not an Euler circuit), Euler circuit, or neither. 21)

A) neither

B) Euler circuit

C) Euler path

Objective: (14.2) Use Euler's Theorem

Answer true or false. 22) A graph with no odd vertices has at least one Euler circuit? A) true

B) false

Objective: (14.2) Use Euler's Theorem

Use Euler's theorem to determine whether the graph has an Euler path (but not an Euler circuit), Euler circuit, or neither. 23) A connected graph has 78 even vertices and no odd vertices. A) Euler path B) Euler circuit C) neither Objective: (14.2) Use Euler's Theorem

24) A connected graph has 81 even vertices and two odd vertices. A) Euler circuit B) neither

C) Euler path

Objective: (14.2) Use Euler's Theorem

25) A connected graph has 50 even vertices and three odd vertices. A) neither B) Euler path Objective: (14.2) Use Euler's Theorem

C) Euler circuit

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. The figure shows the floor plan of a four-room house. Draw a graph to model the floor plan and then determine if it is possible to walk through every room and the outside, using each door only once. 26)

Objective: (14.2) Solve Problems Using Euler's Theorem

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. 27) The layout of a city with land masses and bridges is shown. Can the city residents, starting out at either the East Bank or West Bank, walk across all of the bridges without crossing the same bridge twice?

A) Yes

B) No

Objective: (14.2) Solve Problems Using Euler's Theorem

28) The map below shows states in the upper midwest of the United States. Use Euler's theorem to determine whether a family could visit each state shown while crossing each common border only once. If such a path or circuit exists, use trial and error or Fleury's algorithm to find one.

A) Euler path; MI, IN, IL, MO, IA, MN, WI, IA, IL, WI B) not possible C) Euler circuit; IN, IL, MO, IA, MN, WI, IA, IL, WI, MI, IN Objective: (14.2) Solve Problems Using Euler's Theorem

Use Fleury's Algorithm to find an Euler path or Euler circuit if one exists. 29)

A) Euler circuit- E-B-A-C-B-D-C-E B) Euler path-E-B-A-C-B-D-C-E-D C) No path or circuit exists. Objective: (14.2) Use Fleury's Algorithm to Find Possible Euler Paths and Euler Circuits

Determine whether the graph has an Euler path, Euler circuit, or neither. If the graph has an Euler path or circuit, use Fleury's algorithm to find one. 30)

A) Euler path; A, B, C, F, A, C, D, E, C, G, E, C, A B) Euler circuit; A, B, C, D, E, G, C, F, A C) neither Objective: (14.2) Use Fleury's Algorithm to Find Possible Euler Paths and Euler Circuits

31)

A) Euler path; A, B, D, F, D, E, C, D, A B) Euler circuit; A, B, D, F, D, E, C, D, A C) neither Objective: (14.2) Use Fleury's Algorithm to Find Possible Euler Paths and Euler Circuits

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use Fleury's algorithm to find an Euler path. 32)

Objective: (14.2) Use Fleury's Algorithm to Find Possible Euler Paths and Euler Circuits

Use Fleury's algorithm to find an Euler circuit. 33)

Objective: (14.2) Use Fleury's Algorithm to Find Possible Euler Paths and Euler Circuits

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer true or false. 34) When using Fleury's algorithm to find an Euler circuit, always begin with an even vertex. A) True B) False Objective: (14.2) Use Fleury's Algorithm to Find Possible Euler Paths and Euler Circuits

Use the graph shown to answer the question.

35) A, B, F, I, K, E, G, L, J, H, D, C is a Hamilton path. A) False

B) True

Objective: (14.3) Understand the Definitions of Hamilton Paths and Hamilton Circuits

36) C, D, H, J, I, F, E, K, J, L, G, A, B, C is a Hamilton circuit. A) True

B) False

Objective: (14.3) Understand the Definitions of Hamilton Paths and Hamilton Circuits

Answer true or false. 37) A Hamilton path must contain every edge in the graph exactly once. A) false B) true Objective: (14.3) Understand the Definitions of Hamilton Paths and Hamilton Circuits

38) A Hamilton circuit must begin and end at the same edge. A) true

B) false

Objective: (14.3) Understand the Definitions of Hamilton Paths and Hamilton Circuits

Determine if the graph must have Hamilton circuits. If so, determine the number of such circuits. 39)

A) Yes, 7

B) No

C) Yes, 5040

Objective: (14.3) Find the Number of Hamilton Circuits in a Complete Graph

D) Yes, 40320

40)

A) Yes, 7

B) Yes, 720

C) No

D) Yes, 5040

Objective: (14.3) Find the Number of Hamilton Circuits in a Complete Graph

41)

A) Yes, 24

B) Yes, 120

C) No

D) Yes, 5

Objective: (14.3) Find the Number of Hamilton Circuits in a Complete Graph

42)

A) Yes, 5040

B) No

C) Yes, 720

Objective: (14.3) Find the Number of Hamilton Circuits in a Complete Graph

Determine the number of Hamilton circuits in a complete graph with the given number of vertices. 43) 3 A) 24 B) 6 C) cannot be determined D) 2 Objective: (14.3) Find the Number of Hamilton Circuits in a Complete Graph

44) 21 A) cannot be determined C) 22!

B) 21! D) 20!

Objective: (14.3) Find the Number of Hamilton Circuits in a Complete Graph

D) Yes, 6

Use the weighted graph shown to answer the question.

45) Find the weight of edge BD. A) 225

B) 16

C) 15

D) 30

46) Find the total weight of the Hamilton circuit C, G, F, A, B, D, E, C. A) 85 B) 174 C) 78

D) 82

Objective: (14.3) Understand and Use Weighted Graphs

Use the complete weighted graph shown to answer the question.

47) Using the Brute Force Method, which of the following is not an optimal solution? I. A, B, C, D, A II. A, C, B, D, A III. A, B, D, C, A IV. A, D, C, B, A A) II B) I C) III Objective: (14.3) Use the Brute Force Method to Solve Traveling Salesperson Problems

D) IV

48)

Jon is a traveling salesman for a pharmaceutical company. His territory includes 5 cities and he needs to find the least expensive route to the cities and home. Starting at city A, which of the following is the optimal route using the Brute Force Method? I. A, D, B, E, C, A II. A, E, B, C, D,A III. A, D, B, C, E, A IV. A, B, C, E, D, A A) IV B) II C) I D) III Objective: (14.3) Use the Brute Force Method to Solve Traveling Salesperson Problems

49) Using the Nearest Neighbor Method starting with vertex A, which of the following is an approximate optimal solution? I. A, B, C, D, A II. A, C, B, D, A III. A, D, B, C, A IV. A, D, C, B, A A) I B) II C) IV D) III Objective: (14.3) Use the Nearest Neighbor Method to Approximate Solutions to Traveling Salesperson Problems

50)

Jon is a traveling salesman for a pharmaceutical company. His territory includes 5 cities and he needs to find the least expensive route to the cities and home. Starting at city A, which of the following is the optimal route using the Nearest Neighbor Method? I. A, E, C, B, D, A II. A, E, B, D, C, A III. A, E, D, B, C, A IV. A, E, D, C, B, A A) IV B) III C) I D) II Objective: (14.3) Use the Nearest Neighbor Method to Approximate Solutions to Traveling Salesperson Problems

Determine whether the graph is a tree. 51)

A) No

B) Yes

Objective: (14.4) Understand the Definition and Properties of a Tree

52)

A) No

B) Yes

Objective: (14.4) Understand the Definition and Properties of a Tree

Answer the question. 53) True or false? In the graph of a tree, the number of vertices is one more than the number of edges. A) True B) False Objective: (14.4) Understand the Definition and Properties of a Tree

54) Which of the following is not a property of a tree? I. There is one and only one path joining any two vertices. II. A tree with n vertices must have (n - 1) edges. III. A tree must contain exactly one circuit. IV. Every edge is a bridge. A) IV B) III

C) II

D) I

Objective: (14.4) Understand the Definition and Properties of a Tree

Find a spanning tree for the connected graph. 55)

Objective: (14.4) Find a Spanning Tree for a Connected Graph

56)

Objective: (14.4) Find a Spanning Tree for a Connected Graph

Answer true or false. 57) A spanning tree contains one and only one circuit. A) True

B) False

Objective: (14.4) Find a Spanning Tree for a Connected Graph

58) A spanning tree is a subgraph that contains all of a connected graph's vertices, is connected, and contains no circuits. A) True B) False Objective: (14.4) Find a Spanning Tree for a Connected Graph

Use Kruskal's algorithm to find the minimum spanning tree for the weighted graph. Give the total weight of the minimum spanning tree. 59)

A) 119

B) 202

C) 75

Objective: (14.4) Find the Minimum Spanning Tree for a Weighted Graph

D) 164

60)

A) 232

B) 290

C) 445

D) 155

Objective: (14.4) Find the Minimum Spanning Tree for a Weighted Graph

61)

A) 156

B) 98

C) 278

Objective: (14.4) Find the Minimum Spanning Tree for a Weighted Graph

D) 46

Solve the problem. 62) A corporate campus plans to run computer network cable between buildings. Use Krustal's algorithm to find the minimum spanning tree that allows the network to connect all the buildings. How much cable is needed?

A) 870 feet

B) 526 feet

C) 912 feet

D) 547 feet

Objective: (14.4) Find the Minimum Spanning Tree for a Weighted Graph

Answer true or false. 63) A minimum spanning tree for a weighted graph is a spanning tree with the smallest possible total weight. A) true B) false Objective: (14.4) Find the Minimum Spanning Tree for a Weighted Graph

Answer Key Testname: 14-BLITZER_TM8E_TEST_ITEM_FILE

1) D 2) North, South, East, Ce 3) South-twice, East-onc 4) C 5) A 6) B 7) Phoebe Ruth Claire

Eric Scott Russe 8) D 9) C 10) C 11) A 12) B 13) B 14) C 15) B 16) B 17) A 18) A 19) A 20) The graph has more than 2 odd vertices. 21) C 22) A 23) B 24) C 25) A 26)

possible route: E-B-C-D-E-C-A-E 27) A 28) C 29) B 30) B

31) B 32) E, G, H, F, G, D, E, F, D, A, B, A, C, B, D, C (other answers are possible, but they must start with E and end with C or start with C and end with E) 33) A, B, F, I, K, E, F, D, I, J, K, G, E, B, C, D, H, J, L, G, A (other answers are possible, but they must start and end with the same point) 34) A 35) B 36) B 37) A 38) B 39) B 40) C 41) C 42) C 43) D 44) D 45) C 46) D 47) C 48) D 49) C 50) B 51) A 52) B 53) A 54) B 55) B 56) B 57) B 58) A 59) A 60) B 61) B 62) B 63) A