ANSWERS TO ALL EXERCISES - Cengage




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ANSWERS TO ALL EXERCISES - Cengage 37019_6ae.pdf

ANSWERS

TO ALL

EXERCISES

266

Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 1

EXERCISE 1.1

WARM-UPS A

1. 1 10

21

2. 2 23

40

3. 1 3

4

4. 37

8

5. -1 4

5 6 . - 2 5 6

7. 1 1

4

8. 2 3

5

9. -4 2

5

10. -23

7

CLAST PRACTICE A

11. D

12. A

13. B

14. D

WARM-UPS B

15. 1 2

7 16. 1 3

17. 4 1

2

18. 6

19. 4 2

3 20. 1 9 21.
1 12

22. 21

3

23. -68

24. -60

CLAST PRACTICE B

25. D

26. A

27. B

28. D EXTRA PRACTICE

29. D

30. C

31. C

CHAPTER 1 Answers 267 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.2

WARM-UPS A

1. (3 ×3 × 3 ×3 × 3)(2 ×2)

2. (4 ×4 ×4)(8 ×8 ×8 ×8)

3. (2)(2)(2) + (9)(9)(9)

4. (9)(9)(9) + (3)(3)(3)

5. 6

3

× 6

3

6. 7

4 × 7 4

CLAST PRACTICE A

7. B 8. D 9. D

WARM-UPS B

10. 1 10 4 11. 1 10 3

12. (8 ×10

1 ) + (4 ×10 0 )+ (6 ×1 10 ) + (7 ×1 10 2 ) + (4 × 1 10 3 )

13. (2 ×10

2 )+(9 ×10 1 ) + (4 ×10 0 ) + (9 ×1

10) + (7 ×1

10 2 )

14. 0.11001

15. 0.20101

16. (3 ×10 4 ) + (4 ×10 2 ) +(7 × 10 1 ) + (8 × 10 0 )

17. (1 ×10

4 )+(2 ×10 3 ) (5 × 10 1 )+(7 × 10 0 )

CLAST PRACTICE B

18. B

19. C

20 . A

21. C

22. C

EXTRA PRACTICE

23. B

24. B

25. C

26. D

27. A

268 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.3

WARM-UPS A

1. $12,600

2. $100

3. $19

4. $36

5. 900

6. 300

7. B

8. C

9. $20,000

10. $640

11. 11

4 and 375 8

12. 23

4 and 46

CLAST PRACTICE A

13. A

14. C

15. B

16. C

17. B

18. D

WARM-UPS B

19. 5.967

20. 5.875

21. 6.969 22. 15.803

23. -27.069

24. -14.851

25. 8.626

26. 9.231

27. 59.04

28. 97.03

29. -7.29

30. -46.25

31. 291.7

32. 347

33. -6.2

34. -5.8

CLAST PRACTICE B

35. B

36. A

37. C

38. A

39. D

40. B

41. C

42. A

EXTRA PRACTICE

43. B

44. C

45. D

46. A

CHAPTER 1 Answers 269 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.4

WARM-UPS A

1. 27 100
2. 23
50
3. 11 5 4. 7 2

5. 0.75

6. 0.12

7. 0.45

8. 1.75

9. 1.5

10. 4.5

11. 0.18

12. 0.49

13. 0.032

14. 0.089

15. 0.0825

16. 0.0975

17. 7%

18. 1%

19. 36%

20. 85%

21. 13.9%

22. 38.4%

23. 312%

24. 506%

25. 325%

26. 750%

27. 18.2%

28. 21.4%

29. 2.8%

30. 9.5%

31. 15% 32. 20%

33. 87.5%

34. 50%

35. 37.5%

36. 24%

37.
39
100
38.
3 25
39.
29
200
40.
23
80

CLAST PRACTICE A

41. A

42. D

43. C

44. A

45. D

46. A

47. <

48. >

49. >

50. <

51. <

52. >

53. >

54. <

55. =

56. =

57. >

58. <

59. >

60. < CLAST PRACTICE B

61. C

62. B

63. A

64. B

65. C

66. B

67. C

68. B

69. A

70. B

71. C

72. B

WARM-UPS C

73. -

2 243

74. - 4

243

75. 9

76. -20

77.
1 51
78.
1 60
79.
1 12 80.
1 6

CLAST PRACTICE C

81. D

82. A

EXTRA PRACTICE

83. C

84. B

85. A

86. D

270 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.5

WARM-UPS A

1. 60%

2. 60%

3. 25%

4. 20%

5. 40%

6. 60%

7. 104

8. 50

9. 48

10. 24

CLAST PRACTICE A

11. C

12. B

13. B

14. C

WARM-UPS B

15. 14

16. 25.2

17. 102

18. 133

19. 112.5

20. 128.8

21. 49.35

22. 8.1

23. 16.6

24. 150.75

25. 20%

26. 50%

27. 400%

28. 150%

29. 30

30. 60

31. 10

32. 50

33. 2

34. 100

CLAST PRACTICE B

35. C

36. B

37. D

38. D

39. C

40. B

WARM-UPS C

41. $2500

42. $24

43. $12

44. $5; $20

45. $9.80

46. $32

47. $48

48. $58

CLAST PRACTICE C

49. B

50. C

EXTRA PRACTICE

51. A

52. B

53. D

54. B

CHAPTER 1 Answers 271 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 1.6

WARM-UPS A

1. $730

2. $20.60

3. $1

4. $0.96

5. 43

6. 13

7. $72

8. $440

9. 13

10. 15

CLAST PRACTICE A

11. D

12. A

13. C

14. B

15. D

WARM-UPS B

16. 45

17. 9

18. 2 (6 and 12)

19. 3 (4, 8 and 16)

CLAST PRACTICE B

20. D

21. A

EXTRA PRACTICE

22. B

23. D

24. C

25. D

26. B

27. C

28. B

272

Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 2

EXERCISE 2.1

WARM-UPS A

1. 14 - 5 2. 14 - 3 3. 7 - 7

4. - 5

5. 5 2 6. 7 3 7. 7 8. 2 10 9. 7 5

10. 11

3 11. 5 6 12. 5 14 13. 4 5 5 14. 7 6 6 15. 3 2 4 16. 5 3 9 17. 6 6 18. 1 3

CLAST PRACTICE A

19. A

20. B

21. D

22. C

23. A

24. C

25. D

26. B

WARM-UPS B

27. 1,705,000

28. 21,600

29. 0.04185

30. 0.001584

31. 2 10

-8

32. 2 10

-5

33. 4.2 10

-6

34. 2 10

-9

CLAST PRACTICE B

35. A

36. D

37. B

38. A WARM-UPS C

39. - 361

3

40. - 242

3

41. - 99

10

42. - 10

43. 6t

2 - 3t

44. 8t

2 + 5t

45. 8t

2 - 13t

46. 14t

2 + 13t

CLAST PRACTICE C

47. A

48. D

49. A

50. C

EXTRA PRACTICE

51. B

52. C

53. A

54. B

CHAPTER 2 Answers 273 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.2

WARM-UPS A

1. 20(5 + 7)

2. a[(-4) + (-6)]

3. a[5 + (-3)]

4. -c(7 + 9)

5. (5 + 3) + 2

6. (9 + 3) + x

7. 3 × a + 3 × b

8. 7 × x + 7 × z

9. (3a

2 a 5 )b 4

10. (-5x

3 x 7 )y 2

CLAST PRACTICE A

11. B

12. D

13. B

14. A

15. D

16. C

17. A

WARM-UPS B

18. x - 7 = 2

19. x - 9 = 4

20. x - 17 = 20

21. 23x - 6 = 27

22. 12a - 90 = 7

23. 13a - 56 = 3

24. 3x > -3

25. 5x > 1

26. 7x < 5

27. 9x < 3

28. 3x >

6

29. 4x >

6

30. x >

-35

31. x >

- 24

CLAST PRACTICE B

32. D

33. A

34. A

35. D

EXTRA PRACTICE

36. B

37. A

38. A

39. C

40. D

41. B

42. A

43. C

274 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.3

WARM-UPS A

1. x = 14

2. x = - 5

3. x = -9

4. x = - 10

5. x = 3

6. x = - 3

7. y = 8

3 or 22

3

8. y = 5

2 or 21

2

9. y = 13

2 or 61 2

10. y = 13

4 or 31

4

11. y = 3

12. y = 7

6 or 11

6

13. z = 28

14. z = -12

15. b = 6

16. b = 3

17. a = 59

13 or 47 13

18. a = 26

9 or 28

9 19. a = 22

9 or 24 9

20. a = 11

8 or 13 8

CLAST PRACTICE A

21. B

22. C

23. C

24. A

25. A

26. C

WARM-UPS B

27. x 4

28. x 2

29. x -3

30. x -2

31. b -25

32. b -24

33. x 2

34. x 5

CLAST PRACTICE B

35. B

36. B

37. C

38. D

39. A

40. B

WARM-UPS C

41. No

42. Yes

43. Yes

44 Yes

45. No

46. Yes

47. Yes

48. Yes

49. Yes

50. No

CLAST PRACTICE C

51. A

52. D

53. D

54. C

CHAPTER 2 Answers 275 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.4

WARM-UPS A

1. a = 196

2. b = 169

3. c = 81

4. d = 6

5. W = 160 lbs

6. W = 100 lbs

7. H = 14 years

8. t = 4 hours

CLAST PRACTICE A

9. A

10. A

11. B

12. D

13. C

14. A

15. A

WARM-UPS B

16. 11

17. 15

18. -4

19. 14

CLAST PRACTICE B

20. D

21. A

22. B

23. A

24. C

25. A

276 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.5

WARM-UPS A

1. 2x + 3, x + 1

2. 2x + 1, x + 3

3. 4y - 3, y - 2

4. 3y - 2, y - 5

5. 3y + 1, y - 2

6. 4y - 3, 3y + 2

7. 5x + 1, x + 2

8. 5x + 3, x + 1

9. 3x + 1, x - 2

10. 5x + 4, x - 2

11. x + 1, x - 1

12. x + 6, x - 6

13. 3x + 2, 3x - 2

14. 4x + 5, 4x - 5

CLAST PRACTICE A

15. A

16. D

17. B

18. C

WARM-UPS B

19. x = - 1

2 , x = - 3

20. x = - 3

2 , x = -1

21. x = 0

22. x = 3

2 , x = - 4 3

23. x = - 1

3 , x = 2

24. x = 3

4 , x = - 2 3

25. y = 2

3 , y = 5

26. y = - 1

3 , y = 1

27. x = - 3

2 , x= - 2

28. x = -7

97
4

29. x = 5

7 , x = 1

30. x = -8 2

6 5 CLAST PRACTICE B

31. A

32. A

33. A

34. B

35. C

EXTRA PRACTICE

36. D

37. A

CHAPTER 2 Answers 277 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.6

WARM-UPS A

1. {(3, 1)}

2. {(-1, 2)}

3. {(-2, -3)}

4. {(3, -3)}

5. The empty set

6. The empty set

7. {(-3, -3)}

8. {(x, y) | y = 3

4 x - 1

4 }

9. {(x, y) | y = - 3

2 x + 6}

10. The empty set

CLAST PRACTICE A

11. D

12. B

13. A

14. D

15. C

WARM-UPS B

5-55 -5 x + y = 3x + y = 3 16. 5-55 -5 x - y = - 3 17. 5-55 -5

2x + y = 42x + y = 4

18. 5-55 -5 x - 2y = 4x - 2y = 4 19. 5-55 -5 x = 3 20. 5-55 -5 y = -3y = -3 21.
5-55 -5 x = -4x = -4 22.
5-55 -5 y = 4y = 4 23.

24. x -4

25.
y -4 26.

4x + y 4

27.
x - 2y -4 28.
x 1 and y 2 29.

2x + y 4

30.
4x - 3y > -12 x 0 and y 0 31.
-3x + y -3

CLAST PRACTICE B

32.
D 33.
B 34.
D 35.
D 36.
C 37.
D 38.
B 39.
C 40.
A 278 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 2.7

WARM-UPS A

1. 7

5 = t

30

2. L

11 = 4

2

3. 6

8 = 39

F or 3

4 = 39

F

CLAST PRACTICE A

4. C

5. D

6. D

WARM-UPS B

7. 11

2 lb per sq. in.

8. 900 lb per sq. in.

CLAST PRACTICE B

9. D

10. D

WARM-UPS C

11. x - (5x + 2) = 9

12. x - (4x + 6) = 5

13. x + 17 = 36

14. 5x = x - 2

15. x - 7 = 8 x

16. x

3 = x + 2

17. n + (n + 1) + (n + 2) =

(n + 1) 2

18. (n + 2)

2 n(n + 1)

19. 10x + (x - 4)=21(x - 4)

20. x

2 + 2x = x + 7

CLAST PRACTICE C

21. B

22. A

23. C

24. D

25. D

CHAPTER 3 Answers 279 Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 3

EXERCISE 3.1

WARM-UPS A

1.

3 in.

2. 21

2 in.

CLAST PRACTICE A

3. D

WARM-UPS B

4. 900 m

5. 0.900 km

6. 125 ft

7. 412

3 yd

8. 16Ǒ cm

9. 10Ǒ in.

10. 100Ǒ sq. m

11. 36Ǒ sq. ft

12. 80 sq. mm

13. 8 sq. yd

14. 6 sq. km

15. 7 sq. ft

16. 412 sq. cm

17. 352 sq. in.

18. 384 cu. in. 19.

6000 cu. mm
20. 576Ǒ cu. in.
21.
300Ǒ cu. cm

22. 90Ǒ cu. ft

23. 4

3 Ǒ cu. ft

24. 32

3 Ǒ cu. yd

25. 195 cl

26.
390 cl

CLAST PRACTICE B

27. C

28. C

29. B

30. C

31. D

32. B

33. A

34. A

35. C

36. D

37. C

38. B

WARM-UPS C

39. Linear

40. Linear

41. Square

42.
Square

43. Cubic (or gallons or

liters)

44. Cubic (or gallons or

liters)

CLAST PRACTICE C

45. B

46. C

47.
A

48. B

49. C

50. C

EXTRA PRACTICE

51.

B

52. A

280 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 3.2

WARM-UPS A

1. $972

2. 12

3

3. $270

4. 88

9

5. 0.8 liter

6. $360

7. $2160

8 . 30Ǒ

9. 60 ft

10. 50 mi

11. 97 9.8 ft

12. $900

CLAST PRACTICE A

13. C

14. D

15. B

16. C

17. C

WARM-UPS B

18. 25

3 2 sq. units

19. A = 3bh

20. A = rh + 1

2 Ǒr

2

21. P = 2Ǒs

22. A = s

2 + 1

2 Ǒs

2

CLAST PRACTICE B

23.
A 24
. C

25. C

26. C

27. A

28. A

29. D

30. B

31. D

EXTRA PRACTICE

32.

C

33. C

34. D

35. C

CHAPTER 3 Answers 281 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 3.3

WARM-UPS A

1.

1 and 6; 3 and 4

1 and 3; 4 and 6

2.

2 and 5

3.

2 and 5; 3 and 6;

1 and 4. 4.

2 and 5

5.

1, 3, 4, 6

6. No

7. 60o

8. 30o

9. 90o

10. y = 30o, z = 75o

11. Acute, equilateral

12. Obtuse, scalene

13. Right, scalene

14. Acute, isosceles

15. Square

16. Trapezoid

CLAST PRACTICE A

17. D

18. C

19. D

20. B

21. C

WARM-UPS B

22. 115o

23. 65o

24. 65o

25. 70o

26. 70o

27. 40o

28. 45o

29. 45o

30. 90o

31. 90o

32. 75o

33. 75o

34. 30o

35. B

CLAST PRACTICE B

36. B

37. D

38. B

39. C

40. D

WARM-UPS C

41. x = 51

3 , y = 62 3

42. 12.5

43. 14

44. 31

3

45. 11

3

46. 4

CLAST PRACTICE C

47. B

48. A

49. A

50. B

EXTRA PRACTICE

51. C

52. B

282

Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 4

EXERCISE 4.1

WARM-UPS A

1.

Not everybody in the

city has an equal chance. 2.

Not the target popula-

tion.

CLAST PRACTICE A

3. C 4. A

WARM-UPS B

5. 42%

6. 68%

7.

45-54

8. 55

+

9. 55

+

10. 40%; 45-54

11. Dept. Stores

12. Specialty Stores

13. Dept. Stores

14. Specialty Stores

15. 37%

16. 23%

17. 40%

18. 4%

CLAST PRACTICE B

19.

Never washed

20. D 21.
B 22.
C

23. C

WARM-UPS C

24. Increased

25.

Stabilized

26. Age Under 14

27. Age 65

+

28. 26 mpg

29. 23 mpg

30. As the speed in-creases, the mpg decreases.

CLAST PRACTICE C

31. C

32. B

33. D

EXTRA PRACTICE

34.

B

35. A

CHAPTER 4 Answers 283 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 4.2

WARM-UPS A

1. 8

2. 16

3. 6

CLAST PRACTICE A

4. C

5. D 6 . A

7. B

8 . C

WARM-UPS B

9. median < mean

10. mode < mean

11. mode < median

12. 5 years

CLAST PRACTICE B

13.

C

14. D

15. D

16. B

WARM-UPS C

17. 2

18. 2

19. 2.57

20. 2

21
. 0

22. 1.70

23. O.56

24. 14

25. 26

26. 29

27.
$34,999

28. $10,000

CLAST PRACTICE C

29. D

30. C

31. B

32. D

33. C

34.
A

35. D

EXTRA PRACTICE

36.
B 37
. D 38.
C

39. B

40. A

41. D

42. C

284 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 4.3

WARM-UPS A

1. 120

2. 720

3. 24

4. 15

5. 32

6. 10

7. 10

8. 60

CLAST PRACTICE A

9. D

10. C

11. B

12. C

13. D

14. A

15. C

WARM-UPS B

16. 1 5 17. 4 5 18. 3 5 19. 2 5 20. 1 10 21.
81
100
22.
1 45

23. 0.06 or 3

50

24. 0.20 or 1

5

25. 0.6 or 3

5

CLAST PRACTICE B

26.
A

27. B

28. C

29. C

30. B

31. C

32. D

33. C

34. B

WARM-UPS C

35. 0.20 or 1

5

36. 0.90 or 9

10

37. 0.30 or 3

10

38. 60% or 3

5

39. 10% or 1

10 40.
3 7 41.
2 3

42. 55% or 11

20 43.
3 5

44. 45% or 9

20

45. 80

CLAST PRACTICE C

46.
C

47. A

48. D

49. B

50. C

51. A

EXTRA PRACTICE

52.
B

53. B

54. A

CHAPTER 5 Answers 285 Copyright © Houghton Mifflin Company. All rights reserved.

ANSWERS CHAPTER 5

EXERCISE 5.1

WARM-UPS A

1. It is snowing or the

sun it not out.

2. It is not warm and the

air conditioner is not broken.

3. Bill will not study Math

and he will pass the test.

4. It does not rain and we

will not go to the beach.

5. The sun is out and the

temperature will not rise.

6. Some athletes are not in

good shape.

7. No athletes are in good

shape.

8. Some athletes are in

good shape.

9. All athletes are in good

shape.

CLAST PRACTICE A

10. D

11. C

12. D

13. B WARM-UPS B

14. Today is not Monday

or I will study. I will study or today is not Monday. If I will not study then today is not Monday.

15. Joe did not take Math

or Joe did not fail it.

16. Wendy is not

intelligent and Wendy is not aloof.

17. Pat is a not boy or

Jackie is a not boy.

CLAST PRACTICE B

18. B

19. C

20. C

21. A

WARM-UPS C

22. "Not all are p" is

equivalent to "Some are not p."

23. "Some are p" is

equivalent to "It is not true that none are p."

24. "Not all are p" is

equivalent to "Some are not p."

25. "All are not p" is

equivalent to "None are p."

CLAST PRACTICE C

26. A

27. C

28. A

29. D

30. D

31. A

EXTRA PRACTICE

32. B

33. A

34. C

35. D

286 ANSWERS TO ALL EXERCISES
Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 5.2

WARM-UPS A

1.

Every element of

set A is also an element of set B.

2. There is no element that is in both A and C.

3. There is no element that is in both C and B.

4. Every element of set A is also an

element of set U.

5. No.

6. Yes.

CLAST PRACTICE A

7. B 8. A 9. A

10. D

WARM-UPS B

11.

No supervisors are

lovable.

12. No politicians are reliable.

13. Some employees will not be promoted.

14. Some students are snobs.

15. Ms. A

16. Mr. S

CLAST PRACTICE B

17. A

18. C

19. D

20. B

21. A

WARM-UPS C

22.

You get a good job.

23. I will go to college.

24. If you are rich, then you visit France.

CLAST PRACTICE C

25.
C

26. C

27. D

28. B

CHAPTER 5 Answers 287 Copyright © Houghton Mifflin Company. All rights reserved.

EXERCISE 5.3

WARM-UPS A

1.

The car will start.

2. We do not want to save money.

3. The car will not start.

4. If you use the right bait, you will have a nice dinner.

5. All dogs have

legs.

6. Some Math students won't pass the course.

CLAST PRACTICE A

7. A 8. B 9. B

10. D

WARM-UPS B

11.

Valid

12. Invalid

13. Valid

14. Valid

15. Valid

16. Valid

CLAST PRACTICE B

17. B

18. C

19. A

20. B

EXTRA PRACTICE

21.
C

22. B

23. D

24. B

25. A


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