answers to all exercises - Cengage

ANSWERS TO ALL EXERCISES

266

ANSWERS CHAPTER 1 EXERCISE 1.1 WARM-UPS A 10 1. 1 21 23 2. 2 40 3 3. 14 7 4. 38 4 5. -1 5 5 6. -26 1 7. 14 3 8. 25 2 9. -4 5 3 10. -27 CLAST PRACTICE A 11.

D

12.

A

13.

B

14.

D

WARM-UPS B 2 15. 17 1 16. 3 1 17. 42 18.

6

19.

2 43 1 9 1 12

20. 21. 1 22. 23

23. -68 24. -60 CLAST PRACTICE B 25.

D

26.

A

27.

B

28.

D

Copyright © Houghton Mifflin Company. All rights reserved.

EXTRA PRACTICE 29.

D

30.

C

31.

C

CHAPTER 1 Answers

267

EXERCISE 1.2 WARM-UPS A

16.

(3 × 104) + (4 × 102) +(7 × 101) + (8 × 100)

1. (3 × 3 × 3 × 3 × 3)(2 × 2) 2. (4 × 4 × 4)(8 × 8 × 8 × 8) 3. (2)(2)(2) + (9)(9)(9)

17.

(1 × 104)+(2 × 103) (5 × 101)+(7 × 100)

4. (9)(9)(9) + (3)(3)(3) 5. 63 × 63 6. 74 × 74

CLAST PRACTICE B

CLAST PRACTICE A

18.

B

7.

B

19.

C

8.

D

20.

A

9.

D

21.

C

WARM-UPS B 1 10. 104 1 11. 103

22.

C

12. (8 × 101) + (4 × 100)+ 1 1 (6 × 10 ) + (7 × 2 ) + 10 1 (4 × 3 ) 10

EXTRA PRACTICE 23.

B

24.

B

25.

C

26.

D

27.

A

13. (2 × 102)+(9 × 101) + 1 1 (4 × 100) + (9 × 10 ) + (7 × 2 ) 10

14. 0.11001 15. 0.20101


268



22.

15.803

EXTRA PRACTICE

1.

$12,600

23.

-27.069

43.

B

2.

$100

24.

-14.851

44.

C

3.

$19

25.

8.626

45.

D

4.

$36

26.

9.231

46.

A

5.

900

27.

59.04

6.

300

28.

97.03

7.

B

29.

-7.29

8.

C

30.

-46.25

9.

$20,000

31.

291.7

10.

$640 1 5 14 and 378 3 24 and 46

32.

347

33.

-6.2

34.

-5.8

11. 12.

CLAST PRACTICE A

CLAST PRACTICE B

13.

A

35.

B

14.

C

36.

A

15.

B

37.

C

16.

C

38.

A

17.

B

39.

D

18.

D

40.

B

WARM-UPS B

41.

C

19.

5.967

42.

A

20.

5.875

21.

6.969


CHAPTER 1 Answers

269

EXERCISE 1.4 WARM-UPS A 27 1. 100 23 2. 50 11 3. 5 7 4. 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% 39 100 3 25 29 200 23 80

37. 38. 39. 40.

CLAST PRACTICE A

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

41.

A

42.

D

43.

C

WARM-UPS C 2 73. - 243 4 74. - 243

44.

A

75.

9

45.

D

76.

46.

A

47.

<

48.

>

49.

>

50.

<

51.

<

52.

>

-20 1 51 1 60 1 12 1 6

53.

>

54.

<

55.

=

56.

=

57.

>

58.

<

59.

>

60.

<

77. 78. 79. 80.

CLAST PRACTICE C 81.

D

82.

A

EXTRA PRACTICE 83.

C

84.

B

85.

A

86.

D


270


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. 21. 22. 23. 24. 25. 26. 27.

128.8 49.35 8.1 16.6 150.75 20% 50% 400%

28. 29. 30. 31. 32. 33. 34.

150% 30 60 10 50 2 100

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


EXTRA PRACTICE

1.

$730

22.

B

2.

$20.60

23.

D

3.

$1

24.

C

4.

$0.96

25.

D

5.

43

26.

B

6.

13

27.

C

7.

$72

28.

B

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


272

ANSWERS CHAPTER 2 EXERCISE 2.1 WARM-UPS A 1.

14π - 5

19.

A

2.

14π - 3

20.

B

3.

7π - 7

21.

D

4.

- 5π − 2

22.

C

WARM-UPS C 1 39. - 363 2 40. - 243 9 41. - 910

5.

5 2

23.

A

42.

- 10

6.

7 3

24.

C

43.

6t2 - 3t

7.

7

25.

D

44.

8t2 + 5t

8.

2 10

26.

B

45.

8t2 - 13t

9.

7 5

WARM-UPS B

46.

14t2 + 13t

10.

11 3

27.

1,705,000

CLAST PRACTICE C

11.

5 6

28.

21,600

47.

A

12.

29.

0.04185

48.

D

13.

5 14 4 5 5

30.

0.001584

49.

A

31.

2 ∞ 10-8

50.

C

14.

7 6 6

2 ∞ 10-5

EXTRA PRACTICE

15.

3 2 4

32. 33.

4.2 ∞ 10-6

51.

B

16.

5 3 9

34.

2 ∞ 10-9

52.

C

6 6 1 3

CLAST PRACTICE B

53.

A

35.

A

54.

B

36.

D

37.

B

38.

A

17. 18.

CLAST PRACTICE A


CHAPTER 2 Answers

273


23.

13a - 56 = 3

1.

20(5 + 7)

24.

3x > -3

2.

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

25.

5x > 1

3.

a[5 + (-3)]

26.

7x < 5

4.

-c(7 + 9)

27.

9x < 3

5.

(5 + 3) + 2

28.

3x > 6

6.

(9 + 3) + x

29.

4x > 6

7.

3×a+3×b

30.

x > -35

8.

7×x+7×z

31.

x > - 24

9.

(3a2a5)b4

10.

(-5x3x7)y2

CLAST PRACTICE A

CLAST PRACTICE B

11.

B

32.

D

12.

D

33.

A

13.

B

34.

A

14.

A

35.

D

15.

D

EXTRA PRACTICE

16.

C

36.

B

17.

A

37.

A

WARM-UPS B

38.

A

18.

x-7=2

39.

C

19.

x-9=4

40.

D

20.

x - 17 = 20

41.

B

21.

23x - 6 = 27

42.

A

22.

12a - 90 = 7

43.

C


274


EXERCISE 2.3 WARM-UPS A 1. x = 14 2. x = - 5

22 4 19. a = 9 or 29

36. B 37. C

3. x = -9

11 3 20. a = 8 or 18

4. x = - 10

CLAST PRACTICE A

39. A

5. x = 3

21. B

40. B

6. x = - 3 8 2 7. y = 3 or 23

22. C

WARM-UPS C

23. C

41. No

5 1 8. y = 2 or 22

24. A

42. Yes

25. A

43. Yes

26. C

44 Yes

WARM-UPS B

45. No

27. x < 4

46. Yes

28. x > 2

47. Yes

29. x > -3 30. x < -2

48. Yes

13 1 9. y = 2 or 62 13 1 10. y = 4 or 34 11. y = 3 1 7 12. y = 6 or 16 13. z = 28 14. z = -12 15. b = 6 16. b = 3 59 7 17. a = 13 or 413 26 8 18. a = 9 or 29

31. b ≤ -25 32. b ε -24 33. x ≤ 2 34. x ε 5

38. D

49. Yes 50. No CLAST PRACTICE C 51. A 52. D

CLAST PRACTICE B

53. D

35. B

54. C


CHAPTER 2 Answers

275


WARM-UPS B

1. a = 196

16. 11

2. b = 169

17. 15

3. c = 81

18. -4

4. d = 6

19. 14

5. W = 160 lbs

CLAST PRACTICE B

6. W = 100 lbs

20. D

7. H = 14 years

21. A

8. t = 4 hours

22. B

CLAST PRACTICE A

23. A

9. A

24. C

10. A

25. A

11. B 12. D 13. C 14. A 15. A


276



WARM-UPS B

CLAST PRACTICE B

1. 2x + 3, x + 1

1 19. x = - 2 , x = - 3

31. A

2. 2x + 1, x + 3

32. A

3. 4y - 3, y - 2

3 20. x = - 2 , x = -1

33. A

4. 3y - 2, y - 5

21. x = 0

34. B

5. 3y + 1, y - 2

3 4 22. x = 2 , x = - 3

35. C

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

1 23. x = - 3 , x = 2 2 3 24. x = 4 , x = - 3 2 25. y = 3 , y = 5 1 26. y = - 3 , y = 1 3 27. x = - 2 , x= - 2 28. x =

-7 ± 97 4

5 29. x = 7 , x = 1 30. x =

-8 ± 2 6 5

17. B 18. C


EXTRA PRACTICE 36. D 37. A

CHAPTER 2 Answers

277

EXERCISE 2.6 WARM-UPS A 1. {(3, 1)}

17.

23.

5

5 y=4

x-y=-3

2. {(-1, 2)} –5

3. {(-2, -3)}

5

18.

5. The empty set

5

24. x ≥ -4 2x + y = 4

6. The empty set –5

7. {(-3, -3)} 3 1 8. {(x, y) | y = 4 x - 4 }

5

3 9. {(x, y) | y = - 2 x + 6}

5

28. x ≥ 1 and y ≥ 2

–5

5

x - 2y = 4

–5

20.

5

11. D –5

12. B

5 –5

13. A

21.

5

35. D 36. C

y = -3

37. D

x+y=3

5

38. B

x = -4

5 –5

5 –5

22. –5

32. D

34. D

–5

16.

CLAST PRACTICE B

33. B

5

15. C WARM-UPS B

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

x=3

14. D

26. 4x + y ≥ 4

29. 2x + y ≤ 4

10. The empty set CLAST PRACTICE A

25. y < -4

27. x - 2y > -4

–5

19.

5 –5

–5

4. {(3, -3)}

–5

–5

39. C 5

40. A

–5


278



WARM-UPS C

7 t 1. 5 = 30

11. x - (5x + 2) = 9 12. x - (4x + 6) = 5

L 4 2. 11 = 2 6 39 3 39 3. 8 = F or 4 = F

CLAST PRACTICE A 4. C 5. D 6. D WARM-UPS B 1 7. 12 lb per sq. in.

13. x + 17 = 36 14. 5x = x - 2 15. x - 7 = 8 x x 16. 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. x2 + 2x = x + 7

8. 900 lb per sq. in.

CLAST PRACTICE C

CLAST PRACTICE B

21. B

9. D

22. A

10. D

23. C 24. D 25. D


CHAPTER 3 Answers

279

ANSWERS CHAPTER 3 EXERCISE 3.1 WARM-UPS A

19. 6000 cu. mm

38. B

1. 3 in. 1 2. 22 in.

20. 576π cu. in.

WARM-UPS C

21. 300π cu. cm

39. Linear

CLAST PRACTICE A

22. 90π cu. ft 4 23. 3 π cu. ft 32 24. 3 π cu. yd

3. D WARM-UPS B

40. Linear 41. Square 42. Square 43. Cubic (or gallons or liters)

4. 900 m

25. 195 cl

5. 0.900 km

26. 390 cl

6. 125 ft 2 7. 413 yd

CLAST PRACTICE B

44. Cubic (or gallons or liters)

27. C

CLAST PRACTICE C

28. C

45. B

29. B

46. C

30. C

47. A

31. D

48. B

32. B

49. C

33. A

50. C

34. A

EXTRA PRACTICE

35. C

51. B

36. D

52. A

8. 16π cm 9. 10π in. 10. 100π sq. m 11. 36π 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.

37. C


280


EXERCISE 3.2 WARM-UPS A 1. $972 2 2. 13

3. $270 8 4. 89

WARM-UPS B 18.

25 3 sq. units 2

33. C

1 20. A = rh + 2 πr2

34. D

1 22. A = s2 + 2 πs2

6. $360 CLAST PRACTICE B 7. $2160 8. 30π 9. 60 ft 10. 50 mi 11.

97 ≈ 9.8 ft

12. $900 CLAST PRACTICE A 13. C 14. D

32. C

19. A = 3bh

21. P = 2πs

5. 0.8 liter

EXTRA PRACTICE

23. A 24. C 25. C 26. C 27. A 28. A 29. D 30. B 31. D

15. B 16. C 17. C


35. C

CHAPTER 3 Answers

281


CLAST PRACTICE A

CLAST PRACTICE B

1. ∠ 1 and ∠ 6; ∠ 3 and ∠ 4 ∠ 1 and ∠ 3; ∠ 4 and ∠ 6

17. D

36. B

18. C

37. D

19. D

38. B

20. B

39. C

4. ∠ 2 and ∠ 5

21. C

40. D

5. ∠ 1, ∠ 3, ∠ 4, ∠ 6

WARM-UPS B

WARM-UPS C

6. No

22. 115o

1 2 41. x = 53 , y = 63

7. 60o

23. 65o

8. 30o

24. 65o

9. 90o

25. 70o

2. ∠ 2 and ∠ 5 3. ∠ 2 and ∠ 5; ∠ 3 and ∠ 6; ∠ 1 and ∠ 4.

10. y = 30o, z = 75o

26. 70o

11. Acute, equilateral

27. 40o

12. Obtuse, scalene 13. Right, scalene 14. Acute, isosceles 15. Square 16. Trapezoid

28. 45o 29. 45o

42. 12.5 43. 14 44.

1 33

1 45. 13 46. 4 CLAST PRACTICE C 47. B

30. 90o

48. A

31. 90o

49. A

32. 75o

50. B

33. 75o

EXTRA PRACTICE

34. 30o

51. C

35. B

52. B


282


CLAST PRACTICE B

1. Not everybody in the city has an equal chance.

19. Never washed

2. Not the target population.

21. B

CLAST PRACTICE A 3. C 4. A WARM-UPS B 5.

42%

6. 68% 7. 45-54 8.

55+

9.

55+

20. D

22. C 23. C WARM-UPS C 24. Increased 25. Stabilized 26. Age Under 14 27. Age 65+ 28. 26 mpg 29. 23 mpg

11. Dept. Stores

30. As the speed increases, the mpg decreases.

12. Specialty Stores

CLAST PRACTICE C

13. Dept. Stores

31. C

14. Specialty Stores

32. B

15. 37%

33. D

16. 23%

EXTRA PRACTICE

17. 40%

34. B

18. 4%

35. A

10. 40%; 45-54


CHAPTER 4 Answers

283


WARM-UPS C

EXTRA PRACTICE

1.

8

17.

2

36. B

2.

16

18.

2

37. D

3.

6

19.

2.57

38.

C

CLAST PRACTICE A

20.

2

39.

B

4.

C

21.

0

40.

A

5.

D

22.

1.70

41.

D

6.

A

23. O.56

42.

C

7.

B

24. 14

8.

C

25. 26

WARM-UPS B 9.

median < mean

26. 29 27. $34,999

10. mode < mean 11. mode < median

28. $10,000

12. 5 years

CLAST PRACTICE C

CLAST PRACTICE B

29. D

13. C 14. D 15. D 16. B

30. C 31. B 32. D 33. C 34. A 35. D


284


EXERCISE 4.3 WARM-UPS A 1.

120

2.

720

3.

24

4.

15

5.

32

6.

10

7.

10

8.

60

1 20. 10 81 21. 100 1 22. 45 3 23. 0.06 or 50 1 24. 0.20 or 5 3 25. 0.6 or 5

3 38. 60% or 5 1 39. 10% or 10 3 40. 7 2 41. 3 11 42. 55% or 20 3 43. 5 9 44. 45% or 20

45. 80

CLAST PRACTICE A

CLAST PRACTICE B

CLAST PRACTICE C

9.

D

26. A

46. C

10. C

27. B

47. A

11. B

28. C

48. D

12. C

29. C

49. B

13. D

30. B

50. C

14. A

31. C

51. A

15. C

32. D

EXTRA PRACTICE

WARM-UPS B 1 16. 5 4 17. 5 3 18. 5 2 19. 5

33. C

52. B

34. B

53. B

WARM-UPS C 1 35. 0.20 or 5 9 36. 0.90 or 10 3 37. 0.30 or 10

54. A


CHAPTER 5 Answers

285


WARM-UPS B

WARM-UPS C

1.

It is snowing or the sun it not out.

22. "Not all are p" is equivalent to "Some are not p."

2.

It is not warm and the air conditioner is not broken.

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.

3.

4. 5.

Bill will not study Math and he will pass the test. It does not rain and we will not go to the beach. 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.

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

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

18. B 27. C 19. C 28. A 20. C 29. D 21. A 30. D 31. A

CLAST PRACTICE A 10. D

EXTRA PRACTICE 32. B

11. C

33. A

12. D

34. C

13. B

35. D


286



WARM-UPS B

WARM-UPS C

1.

11. No supervisors are lovable.

22. You get a good job.

2.

3.

4.

Every element of set A is also an element of set B. There is no element that is in both A and C. There is no element that is in both C and B.

12. No politicians are reliable. 13. Some employees will not be promoted. 14. Some students are snobs.

Every element of set A is also an element of set U.

15. Ms. A

5.

No.

CLAST PRACTICE B

6.

Yes.

17. A

16. Mr. S

CLAST PRACTICE A

18. C

7.

B

19. D

8.

A

20. B

9.

A

21. A

10. D


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


WARM-UPS B

1.

The car will start.

11. Valid

2.

We do not want to save money.

12. Invalid

3.

4.

The car will not start. If you use the right bait, you will have a nice dinner.

13. Valid 14. Valid 15. Valid 16. Valid CLAST PRACTICE B

5.

All dogs have legs.

6.

Some Math students won't pass the course.

17. B 18. C 19. A

CLAST PRACTICE A

20. B

7.

A

EXTRA PRACTICE

8.

B

21. C

9.

B

22. B

10. D

23. D 24. B 25. A


answers to all exercises - Cengage

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