Post on 01-Feb-2018
ANSWERS TO ALL
EXERCISES
266
Copyright © Houghton Mifflin Company. All rights reserved.
ANSWERS CHAPTER 1
EXERCISE 1.1
WARM-UPS A
1. 1 1021
2. 2 2340
3. 1 34
4. 378
5. -1 45
6. - 2 56
7. 1 14
8. 2 35
9. -4 25
10. -237
CLAST PRACTICE A
11. D
12. A
13. B
14. D
WARM-UPS B
15. 1 27
16. 13
17. 4 12
18. 6
19. 4 23
20. 19
21. 112
22. 213
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
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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. 63 × 63
6. 74 × 74
CLAST PRACTICE A
7. B
8. D
9. D
WARM-UPS B
10. 1
104
11. 1
103
12. (8 × 101) + (4 × 100)+
(6 × 110 ) + (7 ×
1102 ) +
(4 × 1
103 )
13. (2 × 102)+(9 × 101) +
(4 × 100) + (9 × 110 ) + (7 ×
1102 )
14. 0.11001
15. 0.20101
16. (3 × 104) + (4 × 102)
+(7 × 101) + (8 × 100)
17. (1 × 104)+(2 × 103)
(5 × 101)+(7 × 100)
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
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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. 114 and 37
58
12. 234 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
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EXERCISE 1.4
WARM-UPS A
1. 27
100
2. 2350
3. 115
4. 72
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. 2380
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. 16
CLAST PRACTICE C 81. D 82. A EXTRA PRACTICE 83. C 84. B 85. A 86. D
270 ANSWERS TO ALL EXERCISES
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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
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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
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ANSWERS CHAPTER 2 EXERCISE 2.1
WARM-UPS A
1. 14π - 5
2. 14π - 3
3. 7π - 7
4. - 5π − 2
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. 13
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. - 3613
40. - 2423
41. - 9910
42. - 10
43. 6t2 - 3t
44. 8t2 + 5t
45. 8t2 - 13t
46. 14t2 + 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
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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. (3a2a5)b4
10. (-5x3x7)y2
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
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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 = 83 or 2
23
8. y = 52 or 2
12
9. y = 132 or 6
12
10. y = 134 or 3
14
11. y = 3
12. y = 76 or 1
16
13. z = 28 14. z = -12 15. b = 6 16. b = 3
17. a = 5913 or 4
713
18. a = 269 or 2
89
19. a = 229 or 2
49
20. a = 118 or 1
38
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 ε -24 33. x ≤ 2 34. x ε 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
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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
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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 = - 12 , x = - 3
20. x = - 32 , x = -1
21. x = 0
22. x = 32 , x = -
43
23. x = - 13 , x = 2
24. x = 34 , x = -
23
25. y = 23 , y = 5
26. y = - 13 , y = 1
27. x = - 32 , x= - 2
28. x = -7 ± 97
4
29. x = 57 , 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
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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 = 34 x -
14 }
9. {(x, y) | y = - 32 x + 6}
10. The empty set CLAST PRACTICE A 11. D 12. B 13. A 14. D 15. C WARM-UPS B
5–5
5
–5
x + y = 3x + y = 316.
5–5
5
–5
x - y = - 3
17.
5–5
5
–5
2x + y = 42x + y = 418.
5–5
5
–5
x - 2y = 4x - 2y = 4
19.
5–5
5
–5
x = 3
20.
5–5
5
–5y = -3y = -3
21.
5–5
5
–5
x = -4x = -4
22.
5–5
5
–5
y = 4y = 423.
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
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EXERCISE 2.7 WARM-UPS A
1. 75 =
t30
2. L11 =
42
3. 68 =
39F or
34 =
39F
CLAST PRACTICE A 4. C 5. D 6. D WARM-UPS B
7. 112 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. x3 = 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 CLAST PRACTICE C 21. B 22. A 23. C 24. D 25. D
CHAPTER 3 Answers 279
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ANSWERS CHAPTER 3 EXERCISE 3.1
WARM-UPS A 1. 3 in.
2. 212 in.
CLAST PRACTICE A 3. D WARM-UPS B 4. 900 m 5. 0.900 km 6. 125 ft
7. 4123 yd
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.
19. 6000 cu. mm 20. 576π cu. in. 21. 300π cu. cm
22. 90π cu. ft
23. 43 π cu. ft
24. 323 π 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
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EXERCISE 3.2 WARM-UPS A 1. $972
2. 123
3. $270
4. 889
5. 0.8 liter 6. $360 7. $2160 8. 30π 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 + 12 πr2
21. P = 2πs
22. A = s2 + 12 πs2
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
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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 = 513 , y = 6
23
42. 12.5 43. 14
44. 313
45. 113
46. 4 CLAST PRACTICE C 47. B 48. A 49. A 50. B EXTRA PRACTICE 51. C 52. B
282
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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
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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
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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. 15
17. 45
18. 35
19. 25
20. 110
21. 81100
22. 145
23. 0.06 or 350
24. 0.20 or 15
25. 0.6 or 35
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 15
36. 0.90 or 910
37. 0.30 or 310
38. 60% or 35
39. 10% or 110
40. 37
41. 23
42. 55% or 1120
43. 35
44. 45% or 920
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
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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
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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
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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