Quantitative Reasoning or Liberal Arts Math 1e By Pearson (Workbook Answers All Chapters, 100% Origi by StudyGuide

(Workbook Answers) Quantitative Reasoning or Liberal Arts Math 1e By Pearson All Chapters, 100% Original Verified, A+ Grade)

Quantitative Reasoning or Liberal Arts Math 1e By Pearson (Workbook Answers All Chapters, 100% Original Verified, A+ Grade) Answers Module 1 1.1.1 6 1 4 45 13 1. 2. 3. 4. 5. 7 5 9 77 17 1.1.2 1.

5. 1.1.3 2 1 12 12 1 2. 3.  4. 5.  1. 5 3 25 25 2 1.1.4 1. 105 2. 72 3. 350 4. 270 5. 180 1.1.5 9 60 10 78 406 1. 2. 3. 4. 5. 21 96 15 91 725 1.1.6 1. < 2. > 3. > 4. = 5. > 1.1.7 1 23 1 1 65 1. 2. 3. 4. 5. 6 20 5 36 18 1.1.8 3 27 7 4 5 2. 3. 4. 5. 1. 20 10 4 5 54 1.1.9 1024 1 1 9 196 2. 3. 4. 5. 1. 512 4 225 16,807 10,000,000 1.1.10 11 1 37 7 7 2. 3. 4. 5. 1. 14 21 12 30 400 1.1.11 1 7 7 3 1. 11 pounds 2. fluid ounces 3. 3 cups 4. miles 5. 6 pounds 8 20 8 256

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 1.2.1 1. tenths 2. ten-thousandths 3. hundredths 4. hundred-thousandths 5. millionths 1.2.2 1. < 2. > 3. > 4. < 5. > 1.2.3 1. 5.7 2. 6.45 3. 23.0003 4. 23.007 5. 28.597 1.2.4 1. 33.92 2. 8.76 3. 11.59 4. 46.2672 5. 28.624 1.2.5 1. 0.0625 2. 12.96 3. 2.56 4. 2.56 5. 0.00484 1.2.6 1. 15.32 2. 27.04 3. 90.6 4. 95.85 5. 200.475 1.2.7 1. 6.03 2. 24.0 3. 46.9183 4. 46.9182736 5. 7.00 1.2.8 1. 3 2. 315 3. 120 4. $108 5. $3.40 1.2.9 2 17 13 4 501 1. 2. 3. 4. 5. 5 25 40 125 2500 1.2.10 1. 0.7 2. 0.029 3. 0.68 4. 15.75 5. 7.15 1.2.11 1. $3.39 2. 2.8F 3. $302.44 4. $164.98 5. $1.45 1.3.1 1. 8 parts of 100 2. greater than 3. less than 4. yes 5. no 1.3.2 1 3 2 1. 25% 2. 37 % 3. 43 % 4. 41 % 5. 475% 2 4 3

1.3.3 7 1 26 3 1 2. 3. 4. 5. 1. 100 20 5 5 9 1.3.4 1. 87% 2. 3% 3. 15% 4. 240% 5. 15.5%

Core Skills 1.3.5 1. 0.16 2. 0.09 3. 0.034 4. 4 5. 0.005

1.3.6 1. 0.55, 55% 2.

6 1 1 22 , 0.24 3. , 0.25 4. 0.875, 87.5% or 87 % 5. , 88% 25 4 2 25

1.3.7 1. 168 2. 300 3. 1053 4. 7500 5. 0.36 1.3.8 1 1. 8% 2. 32% 3. 7 % or 7.5% 4. 7% 5. 20% 2

1.3.9 1. 5% 2. 1025 registered voters 3. $145 4. 300 milliliters 5. $5.12 1.4.1 5 5 12 7 9 1. , 5 : 24 2. , 5 :19 3. , 12 :19 4. , 7 :12 5. , 9 : 5 24 19 19 12 5 1.4.2 1 1 9 1 4 1. 2. 3. 4. 5. 4 3 1 4 1 1.4.3 1. $0.515/can 2. 63.6 miles/hour 3. 31.25 miles/gallon 4. 64.25 words/minute 5. 7.5 revolutions/second 1.4.4 1. 30 roses for $60 2. 6 tacos for $7.50 3. 24 bottles of water for $2.99 4. 6-month lease for $8850 5. 2-pound bag for $2.99 1.5.1 1. 135 2. 60 3. 35.2 4. 3 5. 5 1.5.2 1. 39 2. 64 3. 26 4. 11 5. 12

1 tablespoons 2

1.6.1 1. 16 ounces 2. 8 fluid ounces 3. 12 inches 4. 2000 pounds 5. 4 quarts 1.6.2 1 1. 8 quarts 2. 116 ounces 3. 1280 fluid ounces 4. 132 feet/second 5. 256 fluid ounces/second 2

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math

1.6.3 1. 1000 2. 1000 3. 1000 4. 1000 5. 0.001 1.6.4 1. 0.75 liters 2. 1200 grams 3. 0.0012 kilograms 4. 30 meters/second 5. 175 milliliters/second 1.6.5 1. 34.1 liters 2. 275 pounds 3. 322 kilometers 4. 280.5 fluid ounces 5. 4.0 kilograms 1.6.6 1. 15,840 feet on each side 2. Yes 3. 5 inches 4. 20 lawns 5. 80,784,000 gallons 1.7.1 1. a, b, c, d 2. d 3. e 4. d 5. b, c, d 1.7.2 1. 5 2. 13 3. 28 4.

9 7 5. 16 11

1.7.3 1. 1.41 2. 17.32 3. 0.71 4. 51.52 5. 12.65 1.7.4 1. 5 x  95 2.  6  9   x  54 x 3. 42 x  56 4. 16 x  22 5. No; examples will vary: 8  3  5 but 3  8  5 1.7.5 1. 820 2. 160 3. 89 4. 285 5. 23 1.7.6 1. $225 2. $7485 3. 10

1 pounds 4. 15 fluid ounces 5. $20.08 16

Core Skills Module 2 2.1.1 1. 91 2. 36 3. 12 4. 104 5. 24

2.1.2 1. 67x 2. 41m 3. 3x  68 4. 2 x  14 y 5. 3a  8b  4c  24 2.1.3 1. 7 x  11y 2. 78 x  63 3. 14 x  12 4. 31x  40 5. 4 x  17 2.1.4 1. x  15 2. 2x 3.

x 4. 4 x  13 5. 7  x  6  5

2.2.1 1. Equation 2. Equation 3. Expression 4. Expression 5. Equation 2.2.2 8  1. 19 2. 107 3.   4. 31 5. 46 3

2.2.3  50   20  1. 7 2.   3.   4. 539 5. 100 3 3

2.2.4 11  1.   2. 14 3. 9 4. 3 5. 12 2 2.2.5 1. x  9  37 ; the number is 46 2. 8 x  512 ; the number is 64 3. 4 x  30  78 ; the number is 27 3 4. x  9  27 ; the number is 24 5. 6 x  3.2  56.6 ; the number is 8.9 4 2.2.6 1. length: 20 inches, width 8 inches 2. 12 inches, 16 inches, 24 inches 3. 103, 104, 105, 106 4. 126, 128, 130 5. 57, 59, 61 2.3.1 1. x  9 2. x  5 3. x  7 4. x  6 5. x  0 2.3.2 1. 3. 5.

2. 4.

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 2.3.3 1.  x | x  8 2.  x | x  6 3.  x | x  5 4.  x | x  2 5.  x | x  5 2.3.4 1.  8,   2.  6,   3.  5,   4.  2,   5.  ,5 2.3.5 1. x  5 ;  ,5 2. x  2 ;  , 2  3. x  7 ;  7,  4. x  8 ;  , 8 5. x  3 ;  , 3 2.3.6 1. x  10 2. x  102 3. x  20 4. x  8 5. 25 x  200  500 2.3.7 1. At least $35 2. 12 or fewer 3. 500.5 miles or fewer 4. At least 186 5. 95 or higher 2.4.1 1. y 

A  2 r 2 4 x  19  x  10 3 x  5 z  12 P  2W 2. y  3. y  4. L  5. h  2 r 3 8 4 2

2.4.2 1. 84 centimeters 2. 13 feet 3. 24 millimeters 4. 26

2 inches 5. 106 inches 5

2.4.3 1. 94.2 centimeters 2. 37.7 feet 3. 125.7 millimeter 4. 17.0 inches 5. Twice as large 2.4.4 1. 528 square centimeters 2. 12 square feet 3. 201.1 square inches 4. 70.56 square inches 5. 54 square inches 2.4.5 1. 343 cubic inches 2. 2304 cubic inches 3. 754.0 cubic centimeters 4. 75.4 cubic inches 5. 434.9 cubic inches 2.4.6 1. 500 miles/hour 2. 500 miles 3. 195 kilometers 4. 6 hours 5. 1 hour

Core Skills Module 3 3.1.1 1.  5,3 2.  6,8  3.  3, 2  4.  0, 4  5.  20, 40 

3.1.2 1.

Created using the Desmos Graphing Calculator

3.1.3 1.

Created using the Desmos Graphing Calculator

x 2 0 2

y 12 6 0

x 3 3 9

y 7 3 1

x 2 6 8

y 0 10 25

x 3  2 0 7 4

y 21

15 8

x 0 8 4

y 6 0 9

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 3.1.4 1.

x 0 1 2

y 5 7 9

x 3 0 3

y 10 8 6

Created using the Desmos Graphing Calculator

x 0 4 8

y 10 5 0

x 0 2 2

Created using the Desmos Graphing Calculator

x 0 4 2

y 6 0 3

Created using the Desmos Graphing Calculator

y 9 2 3 6

Created using the Desmos Graphing Calculator

3.2.1  9  1.  6,0  ,  0,8  2.  2,0  ,  0, 5  3.  8,0  ,  0, 2  4.   ,0  ,  0, 6  5.  42,0  ,  0,35   2 

Core Skills 3.2.2 1.

Created using the Desmos Graphing Calculator

3.3.1 1. m  5 2. m 

11 5 3. m   4. m  0 5. Slope is undefined 4 2

3.3.2 1. m 

1 5 2 3 1 2. m   3. m  4. m   5. m  4 2 3 4 4

3.3.3 1.

Created using the Desmos Graphing Calculator

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 4.

Created using the Desmos Graphing Calculator

3.3.4 1.

Created using the Desmos Graphing Calculator

3.3.5 1.

Created using the Desmos Graphing Calculator

Core Skills 4.

Created using the Desmos Graphing Calculator

3.3.6 1.

Created using the Desmos Graphing Calculator

3.3.7 1. Parallel 2. Parallel 3. Neither 4. Perpendicular 5. Neither 3.3.8 1. y increases by 1 when x increases by 1. 2. y increases by 3 when x increases by 5. 3. y decreases by 4 when x increases by 7. 4. y increases by 1 when x increases by 5. 5. y does not change as x increases. 3.4.1 1. m  1 2. m  

6 4 3 3. m  0 4. m   5. m  5 3 2

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 3.4.2 4 2 5 1. y  5 x  8 2. y    6 3. y  x  4. y  x 5. y  16 3 9 3

3.4.3 2 3 1. y  8 x  1 2. y  5 x  26 3. y   x  12 4. y  x  36 5. y  18 x  6 3 4

3.4.4 4 1. y  4 x  13 2. y  3 x  12 3. y   x 4. x  2 5. y  8 3

Core Skills Module 4 4.1.1 1. 25 2. 81 3. 81 4.

8 5. x  5 27

4.1.2 10 1. x 60 2. x19 3.  x  8  4. x 50 5. 40x11 y 6 4.1.3 1. x18 2. x182 3. x 52 4. x 32 y 72 5. 729x 9 y 33 z18 4.1.4 1. x 4 2. x 3. x15 4. x 3 y 5 5. 2x8 4.1.5 1 1 1 625 1. 2. 3. 729 4. 5. 100,000 25 729 81 4.1.6 1. x 42 2.

x 6 z16 x 24 1 18 24 3. 4. 5. 64x y y16 z 40 49 y 4 x13

4.2.1 1. 1.35  103 2. 4.92  104 3. 0.000000729 4. 480,000 5. 1,004,000,000 4.2.2 1. 6.8  1013 2. 3.4  1024 3. 5.3  1021 4. 3.311 1020 5. 8.0  106 4.2.3 1. 112,500,000,000 calculations 2. Approximately 24,489 seconds 3. 334,800,000 miles 4. 109,500,000,000 posts 5. 0.0000000415 grams 4.3.1 1. Terms: 7 x 6 ,  4 x3 ,  x ; coefficients: 7,  4,  1 , degrees: 6, 3, 1 2. Term: 45x8 ; coefficient: 45, degree: 8 3. 9 x 3  4 x 2  16 x  7 ; leading coefficient: 9; degree: 3 4.  x 4  9 x  25 ; leading coefficient: 1 ; degree: 4 5. 5 x 6  3x 4  x 2  21 ; leading coefficient: 5; degree: 6 4.3.2 1. trinomial 2. monomial 3. trinomial 4. monomial 5. binomial 4.3.3 1. 5 2. 94 3. 7 4. 2500 5. 4160 4.3.4 1. 2 x 2  6 x  20 2. 2 x 2  4 x  39 3. 2 x 2  7 x  11 4. 2 x 2  25 5. 5 x 2  5 x  9 Copyright © 2020 Pearson Education, Inc. CS-345

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 4.3.5 1. 3 x 2  9 x  61 2. 5 x  38 3. x 3  5 x 2  7 x  30 4. 3 x 2  8 x  60 5. x 4  6 x 3  x 2  26 x  52 4.3.6 1. 2x15 2. 27x 7 3. 24x 60 4. 56x10 y18 5. 12x 9 y 2 z15 4.3.7 1. x 9  3x 7  11x 6 2. 24 x 3  16 x 2  160 x 3. 70 x 6  20 x5 4. 6 x8  9 x 7  12 x 6  24 x 5  63x 4  300 x 3 5. 9 x10 y 7  36 x 7 y 3  99 x 4 y16 4.3.8 1. x 2  17 x  30 2. x 2  5 x  176 3. 6 x 2  31x  170 4. 14 x 2  79 x  78 5. x 3  x 2  62 x  120 4.3.9 1. x 2  36 2. x 2  361 3. 64 x 2  121 4. x8  1 5. 25 x 4  49 4.3.10 1. x 2  8 x  16 2. x 2  18 x  81 3. 25 x 2  60 x  36 4. 49 x 2  182 x  169 5. 121x 2  176 x  64 4.4.1 1. 6 x 5  3x 4  11 2. 4  2 x 5  3 x 3  7  3. 9 x 5  3x 2  4 x  9  4. 10 x 3  2 x 4  5 x 3  1

5. 2 x 3 y 2  3x 4 y  7 x 2 y 3  10 

4.4.2 1.  x  6  x  9  2.  x  15  x  2  3.  x  3 x  10  4.  x  7  x  13 5.  x  28  x  10  4.4.3 1.  x  5  3x  2  2.  x  6  5 x  9  3.  2 x  3 3x  2  4.  2 x  3 3x  8  5. 8  x  5  x  2  4.4.4 1.  x  4   5 x 2  9  2.  x  15   x 2  13 3.  x  14   4 x 2  1 4.  x  5   4 x 2  11

5.  2 x  7  3x  5 

4.4.5 1.  x  15  x  15  2.  3x  10  3 x  10  3.  6 x 3  7 y 2  6 x 3  7 y 2  4. 10  x  12  x  12 

5.  x 2  9   x  3 x  3

4.4.6 1.  x  6   x 2  6 x  36  2.  3x  5   9 x 2  15 x  25  3. 4  x  5   x 2  5 x  25  4.  x  8 y   x 2  8 xy  64 y 2  5.  7 x  10 y   49 x 2  70 xy  100 y 2 

Core Skills 5.  x  9   x 2  9 x  81

4.5.1 3  1. 2,14 2. 7,7 3. 18,14 4. 3,15 5.  ,10  2 

4.5.2



1. 8  5i,8  5i 2. 3  2 15, 3  2 15



5. 3  3 2, 3  3 2











 3.  72 , 52  4.  7  43i 3 , 7  43i 3 

4.5.3



1. 8,12 2. 4  2i 2, 4  2i 2









 3. 1  3i,1  3i 4.  5  2 37 , 5  2 37 

 3  15 3  15  , 5.   2 2   4.5.4



1. 20, 16 2. 3  3 2, 3  3 2









 3. 10,8 4.  5  4185 , 5  4185 

 4  10 4  10  , 5.   3 3   4.5.5 1. quadratic 2. quadratic 3. quadratic 4. linear 5. quadratic 4.5.6 1. 8 and 10 2. length: 14 inches; width: 11 inches 3. length: 17 meters; width: 8 meters 4. 6 feet 5. 38.7 feet

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math Module 5 5.1.1 1. $41.93 2. $88 3. $44 4. $83.07 5. $860

5.1.2 1. $20,940 2. $12.50 3. $237.50 4. $258,500 5. $1012.50 5.1.3 1. $7.53 2. 12.5% 3. $76.11 4. $115.85 5. $44 5.1.4 1. $0.65 2. $382.50 3. $57.60 4. $1144.50 5. $62.64 5.2.1 1. $480 2. $16.80 3. $262.50 4. $25 5. $720 5.2.2 1. $2800 2. 6.25% 3. 8% 4. 3 years 5. 8 months 5.2.3 1. $1045 2. $460 3. $425 4. $17 5. $40 5.3.1 1. $1215.51 2. $1752.90 3. $30,761.26 4. $8080.84 5. $384.04 5.3.2 1. 5.6 years 2. $2965 3. $745 4. 7.1% 5. 10.3% 5.3.3 1. $6435.09 2. 7.8 years 3. Account B 4. $226.99 5. 5.6%

Core Skills Module 6 6.1.1 1. Not a function; more than one student will have earned each grade 2. Not a function; more than one person will have their birthday in the same month 3. Function; each student is only born in one month 4. Function; each input has only one output 5. Not a function; the inputs 1 and 4 each have two different outputs

6.1.2 1. 5 2. 28 3. 38 4. 384 5. 2 6.1.3 1. domain:  ,   ; range:  3,   2. domain:  ,   ; range:  ,   3. domain:  ,   ; range:  ,   4. domain:  ,   ; range:  ,7 5. domain: 1,  ; range:  6, 

6.1.4 1. No 2. No 3. Yes 4. No 5. No 6.2.1 1. No 2. No 3. Yes 4. Yes 5. Yes 6.2.2 1. 68.1F 2. 212F 3. 10C 4. 33,600 students 5. $900 6.2.3 2 1. m   , x-intercept:  9,0  , y-intercept:  0,6  2. m  0 , x-intercept: none, y-intercept:  0, 4  3 1 3. m  1 , x-intercept:  0,0  , y-intercept:  0,0  4. m   , x-intercept:  8,0  , y-intercept:  0, 2  4 5. m  0 , x-intercept: none, y-intercept:  0, 7 

6.2.4 1. 28C 2. 3.25 minutes 3. 2028 4. 2030 5. 7500 cases

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math Module 7 7.1.1 1.

7.1.2 1.

4. B 5. 3

7.1.3 1. Year Freshman Sophomore Junior Senior Grad Student

Rel. Freq. 0.34 0.26 0.175 0.15 0.075

2. Blood Type O A B AB

Frequency 9 8 2 1

3. Blood Type O A B AB

Rel. Freq. 0.45 0.4 0.1 0.05

Core Skills 4.

5. Age 40 to 49 50 to 59 60 to 69 70 to 79

Frequency 9 25 10 1

7.1.4 1.

Age 40 to 49 50 to 59 60 to 69 70 to 79

Rel. Freq. 0.2 0.556 0.222 0.022

4. 5 5. 28

7.1.5 1.

5. High school graduates

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 7.1.6 1.

7.2.1 1. 46.5 2. 99.4 3. 195.6 4. 116 5. $47,120 7.2.2 1. 89.2 2. 2.89 3. 2.36 4. 90.8 5. 77.25 7.2.3 1. 38.5 2. 109 3. 93 4. 95 5. 267 7.2.4 1. 32, 41 2. No mode 3. $199, $219, $259 4. 26 5. No mode 7.2.5 1. 54.5 2. 1359 3. 1067.5 4. 61 5. 132.5

Core Skills Module 8 8.1.1 1. 6 2. 120 3. 5040 4. 60, 480 5. 126

8.1.2 1. 288 2. 676,000 3. 336 4. 30, 240 5. 116, 280 8.2.1 1. A   HT , TH  2. S  1, 2,3, 4,5,6 3. A  1,3,5 4. 15 5. 33 8.2.2 5 1 1 7 5 1. 2. 3. 4. 5. 6 3 4 10 6 8.2.3 3 7 3 5 1. 2. 3. 16 possible outcomes 4. 5. 8 8 8 16

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math Module 9 9.1.1 1. Element 2. Empty set 3. If every element of A is also an element of B. 4. True 5. True

9.1.2 1.  , 2 2.  x | x  5 3. 4, 3, 2, 1,0,1, 2,3 4. 10,  5.  x | x  0 9.1.3 1. 1, 2,3, 4,5,6,7 2. 2,3,5,7 3. {September, October, November, December} 4. {January, June, July} 5. 3,5,7,11,13,17,19

9.1.4 1. Not equivalent 2. Not equivalent 3. Equivalent 4. Not equivalent 5. Not equivalent 9.1.5 1. 1, 4,8,9,16, 25, 27,64,125 2. People who are taller than 6 feet tall or are women 3. All real numbers 4. 0, 1, 2, 3, and 4 5. A and B have no elements in common. 9.1.6 1. 1,64 2. Women who are taller than 6 feet tall 3. Numbers that are between 0 and 5 4.  4, 4 5. A and B are exactly the same. 9.1.7 1. A = {All items on the menu that are not gluten free} 2. A = {Real numbers that are less than or equal to 3} 3. A = {February, March, April, May, August, September, October, November, December} 4. A  1,3,5,7,9 5. A  1, 4,6,8,9,10 9.2.1 1. Inductive 2. Inductive 3. Deductive 4. Deductive 5. Inductive 9.2.2 1. Valid 2. Valid 3. Invalid 4. Invalid 5. Valid 9.2.3 1. Compound statement 2. Quantified statement 3. Compound statement 4. Compound statement 5. Inverse

Answers 1.1: 1. A, E, B, D, C 2.

2 3. A, C, and D 4. A, D, C, E, B 4

5. a.

6. One whole unit is shaded, as well as half of a second:

1 1 . 2 The units are divided into halves, and 3 of them are shaded:

7. a.

3 . 2

8. Start at the first fraction on the number line, and use the second fraction to determine how far to move to the right. 9.

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 10. a.

1 2

1 3

1 1  2 3

Create a diagram where each unit is divided into the same number of pieces – this is the denominator of the sum. Determine how many pieces should be shaded for each fraction. Find the total number of shaded pieces – that is the numerator of the sum. 11.

3 4

1 6

3 1  4 6

1.2:

1 1 1 3 6 , one tenth b. , one hundredth c. , one thousandth d. , three tenths e. , six tenths 10 100 1000 10 10 8 7 9 20 f. , eight tenths g. , seven hundredths h. , nine thousandths i. , twenty thousandths j. 10 100 1000 1000 11 35 35 5 , eleven thousandths 2. ; 17.5 ; ; 17.5 3.  2.5 , so multiplying by 2.5 is equivalent to 1000 2 2 2 5 2 5 2 multiplying by ; dividing by is equivalent to multiplying by its reciprocal, ; 0.4  , so dividing by 0.4 2 5 2 5 1a.

is equivalent to multiplying by

2 9 729 3  3 2 4. 2.25; ; 11.390625; 5. 1.5    because 1.5  , and 5 4 64 2  2

9 3 9 2.25    because 2.25  6. 59.319; 18.369 7. To simplify 1.4  2.5 you must add before raising 4 4 3

the sum to the third power, you cannot simply raise each term to the third power. 1.3: 1a. 50% b. 100% c. 400% d. 20% 2a. 50% 5. 30.4%

b. 42.9% c. 16.7% d. 88% 3. 20.3% 4. 166.7%

1.4: 1. 20 − 16 = 4; Four more work in the private sector than in the public sector. 2. = 1 = 1.25; 125% 3. = = 0.25; 25% 4. 16 − 20 = −4; Four fewer work in the public sector than in the private sector. = = 0.8; 80% 5. 6.

= −0.2; 20%

Critical Thinking 7.

Public Sector Workers’ Modes of Transportation

8. a. 8; b. 3; c. 200%; d. 8; e. 33.3%; f. 66.7% 9. 15 − 5 = 10; Ten more drive their personal vehicle than take public transportation or carpool.; Yes. 10. = 3; No, the bar for personal vehicle is six times the height of the bar for public transit/carpool. 11. Private Sector Workers’ Mode of Transportation

1.5: 1. Percent

Students who were Surveyed

Entire Student Body

2900

1450

3625

4350

2175

2. Percent

Residents who were Surveyed

All Registered Voters

1764

156

5733

3528

192

7056

108

3969

100

600

22,050

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 3. Someone may say “Yes” to more than description. The total “Yesses” may exceed the total number of customers surveyed. 4. Answers will vary. Examples: a. Have every customer fill out a questionnaire. At the end of the shift, randomly select 25 of them to read. b. Ask the first 25 customers that come in that day. 5. a. 756 ; b. The customers surveyed did not accurately represent all the customers who came that day. Perhaps the survey was taken only by customers who were there during the morning shift. 1.6: 1a. 133,056 inches, 11,088 feet, 3696 yards b. 26,768 ounces, 119.5 stones, 0.84 tons c. 336 teaspoons, 112 tablespoons, 0.44 gallons 2a. 5 feet and 2 inches b. 8 pounds and 1 ounce c. 2 cups and 26 teaspoons d. 35 gallons 3a. 0.42 meters, 0.00042 kilometers, 420 millimeters b. 1,673,000 milligrams, 1.673 kilograms 4a. 4.488 gallons b. 842.6 pounds c. 6.44 kilometers d. 2.9718 meters 5. 55 meters; one meter is longer than 1 yard 6. 7 tablets 7. 217.92 milliliters 1.7: 1a. rational b. rational c. irrational d. rational e. irrational f. rational 2.

Estimate

a. b. c. d.

3.57 5.64 9.21 14.14

Approximation (Calculator) 3.61 5.66 9.22 14.14

Difference 0.04 0.02 0.01 0

3a. >, 50  49 b. >, 17  16 c. >, 9  5 4a. 3.20 b. 1077.68 c. 0.42 d. 6.67 e. 0.07 f. 2.24 2.1: 1a. 3 b. 1 c. 49 d. 77 2a. 134 b. 30 c. 134 d. 30 3

3a.  3x b. 5 x  2 y c. 4 x  3 y

d. 3x 2  3 x3 e.

x3 y 3 x3  r r

4. Answers will vary – examples are given. 4a. 3 x 2 , 4 x 2 b. 2 x ,  7 x ,  10 x c. x ,  10 x ,  2 y , 3 y

2.2: 1a. Multiply by 9, then add 2.

b. Subtract 2 from both sides, then divide both sides by 9.

9 x  2  34

9 x  2  2  34  2 9 x  36 9 x 36  9 9 x  4

Critical Thinking

2a. Multiply by 5, add 11, then multiply by 2.

b. Divide both sides by 2, subtract 11 from both sides, then divide both sides by 5.

2  5 x  11

2  5 x  11  102 102 2 2 5 x  11  51 

5 x  11  11  51  11 5 x  40 5 x 40  5 5 x 8

3a. Subtract 32, then multiply by

b. Divide both sides by (Dividing by reciprocal

5 . 9

5 , then add 32 to both sides. 9

5 is equivalent to multiplying by its 9

9 .) 5

5     F  32   10 9 9 5 9      F  32    10 5 9 5 F  32  18 F  32  32  18  32 F  50

For 4-6, answers will vary. Examples of correct answers are provided. 4. 2 x  5  17

x  7  20 3 6. 4  5 x  13  68

7. 5 x  3  42 8. 8 x  1  47 9. 2  3 x  11  46 2.3: 1a. x  5

b. x  7

c. x  6

2a. x  10 b. x  12 3a. x  6 b. x  12 4a. No; equality is not included in the sign. b. Yes; equality is included in the sign. c. Yes; equality is included in the sign. d. No; equality is not included in the sign. 5a. Yes; at least 12 means 12 or more. b. No; 12 is not more than 12. c. No; 12 is not less than 12. d. Yes; because 12 is 12 or lower. 6. Only use a closed circle if the inequality includes “equal to” at the endpoint. Otherwise, use an open circle. 7. If you used a closed circle on the number line (due to an inequality including “equal to” at the endpoint), then use a square bracket to indicate that the endpoint is included as a solution. Otherwise, use parentheses.

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 2.4: 1. 88 square inches 2. 80 square centimeters 3. 136 square inches 4. 139.25 square centimeters 5. 72 square inches 6. 62.8 square centimeters 7.

nxh 5 xh 8. 3xh 9. 4xh 10. 2 2

3.1: 1a. Minimum: 18 ; maximum: 14 b. Minimum: 12 ; maximum: 16 c. They are all multiples of 2; use a scale of 2.

Created using the Desmos Graphing Calculator

y  3x  8

x 2 0 2 4 6 8

14 8 2 4 10 16

Created using the Desmos Graphing Calculator

5. x 10 5 0 5

y  5 x  20 30 5 20 45

6. x 9 6 3 0 3

Created using the Desmos Graphing Calculator

y  4 x  12

24 12 0 12 24

Created using the Desmos Graphing Calculator

Critical Thinking 3.2: 1. Graphs will vary; all 3 should have the x-intercept labeled as an ordered pair. 2. They all have y-coordinates of 0.

9 2

 

3a.  12,0  b. 18,0  c.  ,0  4. Graphs will vary; all 3 should have the y-intercept labeled as an ordered pair. 5a.  0, 9  b.  0, 21 c.  0, 6  6. Graphs will vary, but the line will be vertical. 7. A vertical line 8.

Created using the Desmos Graphing Calculator

9. Answers will vary, but all points will have an x-coordinate of 6. 10. A horizontal line 11.

Created using the Desmos Graphing Calculator

12. Answers will vary, but all points will have a y-coordinate of 4. 13. Yes, examples will vary but the graph will pass through the origin. 14. Answers will vary, but all lines will pass through the origin. 15.  0,0  16.

Created using the Desmos Graphing Calculator

17. The y-coordinate is two times the x-coordinate.

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 3.3: 1. A. P1: (1,4) and P2: (4,6); 𝑚 = B. P1: (4,6) and P2: (1,4); 𝑚 = C. P1: (2,-1) and P2: (5,1); 𝑚 = D. P1: (-2,2) and P2: (7,8); 𝑚 = E. P1: (1,4) and P2: (-1,7); 𝑚 = − 2. Fact 1: A and B; Fact 2: A or B, AND C; Fact 3: A or B, AND D 3. Their slopes are negative-reciprocals, so yes, they are perpendicular; − × = −1; yes 4. P2: (2,5) and P3: (8,1); yes

Created using the Desmos Graphing Calculator

3.4: 1. y  2 x  4 2. y  2 x  4 3. m  2 4. y  2 x  4

5a.  0, 2  b. m  5 c. y  5 x  2

6a. Answers will vary; one point is 1,3 b. y  5 x  2

7a. Answers will vary; two points are 1,3 and  2,8  b. m  5 c. y  5 x  2

4.1: Answers will vary; an example is shown for each exercise. 1. 2.

x  x   x  x   x  x  x  x 2

 xxxxxx  x6  x 2 4

x   x  x  x  x 2 4

3. 2

 xy 4  xy  xy  xy  xy

 x8  x 24

 xxxx y y y y  x4 y 4

Critical Thinking

 x  0 1

x

 y  0 4

x4 x4

x6 x  x  x  x  x  x  xx x2 x xxxxx  x x

 x  0

x x x x x       y y y y y   xxxx  y y y y

By the quotient rule:

x4  x 44  x0 4 x Any nonzero number divided by itself equals 1:

 x 6 2



x4 1 x4

x4 y4

Thus,

x0  1 7.

 x  0 2

x xx  6 xxxxxx x 1

x x  x xxxxx 1

1  4 x By the quotient rule:

Thus,

x2  x 26 6 x  x 4

x 4 

1 x4

4.2: 1. 10, 100, 1000, 10,000, 100,000, 1,000,000 5

2. 2.15  10 , 2.0  10 , 1.23  10 , 3.0  10 3. 21,300 , 31, 400,000 , 670,000,000 4. 0.1 , 0.01 , 0.001 , 0.0001 , 0.00001 , 0.000001 5. Standard notation 0.00025 0.000297

0.0025

0.0000979

0.00000197

Scientific notation

2.5  103

9.79  105

1.97  106

2.5  104

2.97  104

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 6a. 1.484  10

7a. 3.566  10 8. $67,166

b. 2.145  10

2

b. 4.387  10

c. 1.976  10 6

c. 2.923  10

9. $4.2  10 4.3:

2 2 2 4 2 3 2 1. 8 x  42 x  27 2. 3x  10 x  48 3. x  22 x  117 4. 12 x  34 x  160 5. 2 x  13x  13x  10 3 2 6. 6 x  x  42 x  45 7. 10  70  10  5  6  70  6  5  700  50  420  30  1200 2 2 8. 80  90  80  6  4  90  4  6  7200  480  360  24  8064 9. 16 x  9 10. 25 x  64 2 2 2 11. 49 x  225 12. x 6  16 y 4 13. 2 x  9 and 2 x  9 14. 36 x  60 x  25 15. 81x  36 x  4 4 3 2 16. x  10 x  37 x  60 x  36

4.4: 1.  x  15  x  2  2.  x  3 x  10  3.  x  12  x  2  4.  x  4  x  6  5.  x  6  x  20  6.  x  30  x  4  7.  x  5  x  5  8.  x  7  x  7  9.  x  5  x  5  10.  x  7  x  7  11.  4 x  9  2 x  7  12.  2 x  15  3 x  8  13.  6 x  7  x  8  14.  3 x  10  4 x  5 

15.  2 x  5  3 x  4  16.  5 x  9  x  3 17. 6  x  7  x  4  18.  3 x  1 2 x  5  19.  7 x  2  x  4  20. 4  x  10  x  12 

4.5:



 5  2

1. 9,12 2.  2,  3. 2  4i 2, 2  4i 2

 7  3

 7 1  5 2

6. 8i,8i 7. 1,  8. 6 9. 15,14 10.   , 

5.1: 1. Sales tax Total price

$45.00 , 6% $2.70 $47.70

$45.00, 8% $3.60 $48.60

$50.00, 5.5% $2.75 $52.75

$62, 8.25% $5.12 $67.12

2. Tip Total bill

$41.99 15% $6.30 $48.29

$38.27 20% $7.65 $45.92

$8.99 20% $1.80 $10.79

Final price

$32 23% increase $39.36

$45.00 12% increase $50.40

$45.00 12% decrease $39.60

$50.00 13% increase $56.50









 4. 5  4 3,5  4 3 5.  7  2 41 , 7  2 41 

Critical Thinking 4. Commission Amount Remaining for the Seller

$155,000 4.5% $6975 $148,025

$155 4.5% $6.98 $148.02

$173,000 1.2% $2076 $170,924

5a. $990.00 b. $693.00 c. $750.17 6. $100.05 7. $9700 8. Option 1: $3150; Option 2: $2700 5.2: 1a. $3 b. $15 c. $6 d. $6 e. $12 2a. $12 , $412 b. $35 , $535 c. $6 , $306 d. $51 , $901 e. $9 , $234 3a. $60 , $460 b. $175 , $675 c. $345 , $2645 d. $108 , $508 e. $216 , $616 4a. $1000 , $2000 b. $2000 , $4000 c. $1000 , $2000 d. $2000 , $4000 e. $4000 , $8000 5. The principal has doubled. 6. The doubling time is the reciprocal of the simple interest rate r,

1 . r

5.3: 1a. $159.27 b. $338.23 c. $790.85 2. No, the interest is more than double when the rate is doubled. 3. No, the interest is more than doubled when the time period is doubled. 4a. $560.51 b. $565.68 c. $552.97 5. The interest will be greater. If the principal, rate, and time stay the same, the interest will be greater the more often it is compounded per year. 6a. $810.33 b. $6098.38 c. $1019.94 d. $4917.41 7. 72 6.1: 1. a. 25; b. 7; c. 144; d. 48; e. 49; f. 13 2. a. add, square; b. square, add; c. multiply, square; d. square, multiply; e. multiply, add, square; f. square, multiply, add 3. G, F, E, A, C, B, D 4. a. 4𝑓(𝑥); b. 𝑓(𝑥) + 5; c. −2𝑓(𝑥) + 4; d. 𝑓(𝑥 − 2); e. 7𝑓(𝑥 + 9); f. 𝑓(𝑥 − 3) + 1; g. 2𝑓(𝑥 − 5) − 6; h. −𝑓(2𝑥) + 3 5. 9 3 5 100 16 58 36 8 50 9 23 29 6. 25𝑥 4𝑥 𝑥

5𝑥 −2𝑥 𝑥

𝑥

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 7. Response 1: Correct Response 2: Line (2), following the minus sign, the 𝑥 + ℎ must be in parentheses. Response 3: To obtain 𝑓(𝑥 + ℎ), replace 𝑥 with 𝑥 + ℎ. The error was in adding ℎ to 𝑓(𝑥). Recall that 𝑓(𝑥 + ℎ) ≠ 𝑓(𝑥) + ℎ. 8. a. 𝑥 + 2𝑥ℎ + ℎ + 2𝑥 + 2ℎ b. 3𝑥 + 6𝑥ℎ + 3ℎ − 𝑥 − ℎ c. −𝑥 − 2𝑥ℎ − ℎ + 4𝑥 + 4ℎ − 2 9. a. 2𝑥ℎ + ℎ ; b. 2𝑥ℎ + ℎ − 2ℎ 6.2: 1a. Linear b. Not linear c. Linear d. Not linear 2a. m 

4 ,  0, 7  b. m  2 ,  0,9  3. m  5 ,  0, 2  4. m  3 ,  0,0  3

3a. C b. B c. D d. A 4. f  x   35 x  5000 , $6190

5a. f  x   4 x  160 b.  40,0  ; this suggests that crickets do not chirp for temperatures below 40°F. 7.1: 1. line graph: count the number of points on the graph that are connected by line segments. frequency distribution: sum of the frequency column histogram: sum of the heights of the bars scatterplot: count the number of points on the graph 2. bar graph and circle graph 3. bar graph and histogram 4. bar graph 5. line graph, histogram, scatterplot 6. bar graph 7. line graph, bar graph, frequency distribution, relative frequency distribution, histogram, circle graph 8. frequency distribution and histogram 9. circle graph 10. line graph 11. bar graph 12. histogram 13. scatterplot 14. relative frequency distribution 15. The circle represent the population of 100 online purchasers. Each sector represents a different retailer. 16. The horizontal axis represents the total cost in dollars. The vertical axis represent the frequency. The height of each bars gives number of students whose total cost falls in the interval forming the bottom of the bar. The sum of the bars is equal to 1200. 17. The horizontal axis represents amount of artificial sweetener, in milligrams. The vertical axis represents calories consumed. Each of the 36 points represents one of the individuals studied. Its position relative to the horizontal and vertical axes indicate both the amount of artificial sweetener consumed and number of calories consumed in one particular day.

Critical Thinking 7.2: 1. a. 3 + 20 + 5 + 3 + 1 = 32 b. This is a possible list for the histogram because it consists of 32 values, with the appropriate number of values falling into each class. c. Each number that is labeled on the horizontal axis falls into the bin on its right. For the first bin to have 3 values, only the ages 16 and 17 can fall into that bin; 18 must fall into the second bin, which is on its right. d. mean 24.2; median = 21; mode = 19; midrange = 31 e.

2. Answers will vary. 3. Score on Exam 1: mean 69.9; median = 73; Number of Days Until Next Birthday: mean 186.5; median = 185 4. Data Set Difference between Relative difference mean and median between mean and median Age 3.2 years 15.2% Number of Units

Answers will vary.

Score on Exam 1

−3.1 points

−4.2%

Days Until Birthday

1.5 days

0.8%

a. Age; b. Exam 1; c. Birthday (and probably Number of Units) d. skewed left: the median is greater than the mean; skewed right: the mean is greater than the median; normal or uniform. 8.1: 1. a. 120; b. 3,125 2. a. 5! ; b. 5 3. a. 8 = 16,777,216 b. 8! = 40,320 c. 8 = 262,144 4. 2 = 1,048,576 5. 40,320 720 6 6. 3,628,800 39,916,800 7. 360 30

360 12 120 4,989,600

604,800

1560

Workbook for Corequisite Support Modules for Quantitative Reasoning or Liberal Arts Math 8.2: 1. a. 68%; b. 95%; c. 60 inches; d. 75 inches; e. 163; g. 0.815; h. Area of shaded region: 815 square units; Total area: 1000 square units; Ratio: 0.815, same as probability. 2. a. 0.125; b. 0.594; c. 0.25; d. 0.719 3. a. = = 0.74; b. = = 0.75 4. Horizontal axis lables: 10, 15, 20, 25, 30, 35, 40; greater than; More than 50% of the total area of the histogram falls above the interval 15, 25). 9.1: 1a. 5 b. 8 c. 11 d. 3 e. 12 f. 9 g. 4 h. 2 i. 1 j. 6 k. 7 l. 10 2a. 4 b. 1 c. 2 d. 3 e. 6 f. 5 9.2: 1a.

2a. Invalid b. Valid c. Invalid d. Invalid e. Valid

Answers Activity 1: 1. Cancer: 613,200; Heart disease: 606,462; There were more deaths from cancer. 2. 0.2% 3a. 8760 hours b. 525,600 minutes c. 86, 400 seconds d. 604,800 seconds e. 31,536,000 seconds 4. 11.6 days 5. 31 years and 259 days 6. 31,710 years 7. 0.0003% 8. 0.2727% 9. Answers will vary; if a desk is 2 feet by 3 feet and has a height of 3 feet, the volume is 18 cubic feet and that would hold 900,000 pennies. 10. Answers will vary; divide the volume of the room by 20 cubic feet and then multiply by 1 million pennies. 11. Answers will vary; divide the size of your campus by 3921 square feet and then multiply by 1 million pennies Activity 2: 1. 23.89 in3 2. 13.14 fluid ounces 3. 72𝑥 0.30 13.73 4. $0.19 per ounce 5. $13.02 6. 2400 cans 7. 28,800 ounces 8. $5472 Activity 3: 1a. 26 inches, no b. 25 inches, yes c. 25 inches, yes d. 24 inches, yes 2a. m 

7 8 7 1 b. m  c. m  d. m  12 9 11 2

3a. 7 inches b. 7 inches c. 6 inches d. 6 inches 4. All measurements are given in the form step height: tread width. Eight possibilities: 7 in: 10 in, 7 in: 11 in, 6 in: 12 in, 6 in: 13 in, 5 in: 14 in, 5 in: 15 in, 4 in: 16 in, 4 in: 17 in 5. Steepest slope 7 in: 10 in; flattest slope: 4 in: 17 in 6. 24 steps; 34 feet 7. 15 steps; 12 feet and 6 inches Activity 4: 1. $32,000 2. $28,800 3. $25,920 4. $22,809.60 5.

Created using the Desmos Graphing Calculator

Workbook for Corequisite Support Modules for College Algebra or Precalculus 6a. 8000 b. 3200 c. 2880 d. 3110.4 7. The rates of decline are different for different years. 8. The quadratic model fits better because the points do not exactly follow a linear pattern. 9. $13,721.60 10. $23,820.72

Activity 5: 1a. $419.62 b. $696.89 c. 5-year loan: $1177.20; 3-year loan: $1088.04; the 3-year loan has less interest 2a. $1432.25 b. $215,610 3. $684.57 4. $4974.50 5. BALANCE BEGINNING AFTER ENDING MONTH BALANCE INTEREST PAYMENT BALANCE APRIL $3500.00 $3534.69 $500.00 $3034.69 (30 DAYS) MAY (31 DAYS) $ 3,034.69 $ 3,065.77 $ 500.00 $ 2,565.77 JUNE (30 DAYS) $ 2,565.77 $ 2,591.20 $ 500.00 $ 2,091.20 JULY (31 DAYS) $ 2,091.20 $ 2,112.62 $ 500.00 $ 1,612.62 AUGUST (31 DAYS) $ 1,612.62 $ 1,629.14 $ 500.00 $ 1,129.14 SEPTEMBER (30 DAYS) $ 1,129.14 $ 1,140.33 $ 500.00 $ 640.33 OCTOBER (31 DAYS) $ 640.33 $ 646.89 $ 500.00 $ 146.89 NOVEMBER (30 DAYS) $ 146.89 $ 148.35 $ 148.35 $ 6a. $3648.35 b. $148.35 c. 4.2% Activity 6: 1. y  0.10 x 2. $4453.50 3. 11.5% 4. 0.22 x  4060.50 5. $14,089.50 6. 17.1% 7.

0.10 x  0.12 x  190.50  0.22 x  4060.50  f ( x)  0.24 x  5710.50 0.32 x  18,310.50  0.35 x  24,310.50  0.37 x  34,310.50

0  x  9525 9526  x  38,700 38,701  x  82,500 82,501  x  157,500 157,501  x  200,000 200,001  x  500,000 500,001  x

8a. $32,089.50, 20.4% b. $45,689.50, 22.8% c. $150,689.50, 30.1% d. 335,689.50, 33.6%

Activities Activity 7: 1.

2. a. Distance in Frequency miles 0 4.9 3 5 9.9 13 10 14.9 5 15 19.9 5 20 24.9 3 25 29.9 0 30 34.9 2 35 39.9 0 40 44.9 1 b. The histogram is skewed right, which indicates that the mean is greater than the median. Mean = 13.4 mi Median = 9.9 mi c. Classes (min) Midpoints (min) Frequency Relative Frequency 2.5 2 0.063 0 4.9 7.5 5 0.156 5 9.9 12.5 9 0.281 10 14.9 17.5 2 0.063 15 19.9 22.5 6 0.188 20 24.9 27.5 2 0.063 25 29.9 32.5 3 0.094 30 34.9 37.5 0 0 35 39.9 42.5 1 0.031 40 44.9 47.5 0 0 45 49.9 52.5 1 0.031 50 54.9 57.5 0 0 55 59.9 62.5 1 0.031 60 64.9 d. Theoretically, the sum should be 1. The sum in this table is 1.001, due to rounding. e. mean 19.8 minutes

Workbook for Corequisite Support Modules for College Algebra or Precalculus 3. There should be a correlation between distance from campus and commute time. In general, the longer the distance, the more time it will take. This will be visible in the scatterplot by observing that the points should form around a line with positive slope. 4. a. The points do not form a straight line, because there is variation in the speed at which the students can travel due to traffic conditions. b. The line is shown on the scatterplot. Yes, it appears to fit the data well enough to use it for predictions as long as the values of the variables are within the respective ranges of the data. c. 49 minutes d. 10 miles

Activity 8: 1. a. 2 ; b. 1; c. 0.000; d. disbelieve him 2. a. 12!; b. 1; c. 0.000; d. disbelieve him 3. a. 0.083; b. not 4. a.

b. 0.10; c. not 5. a. 35; b. 1; c. 0.029; d. disbelieve him 6. a. 0.06; not 7. a. 0.002; b. disbelieve him Activity 9: 1a. 2 b. 1 c. 4 d. 3 2a. Invalid b. Valid c. Invalid d. Invalid 3a. 3 b. 4 c. 2 d. 1 4a. 4, 5, 6, 8 b. 5, 6 c. 3, 5 d. 4, 8, 9