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
Copyright © Houghton Mifflin Company. All rights reserved.
268
ANSWERS TO ALL EXERCISES
EXERCISE 1.3 WARM-UPS A
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
Copyright © Houghton Mifflin Company. All rights reserved.
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
Copyright © Houghton Mifflin Company. All rights reserved.
270
ANSWERS TO ALL EXERCISES
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
Copyright © Houghton Mifflin Company. All rights reserved.
CHAPTER 1 Answers
271
EXERCISE 1.6 WARM-UPS A
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
Copyright © Houghton Mifflin Company. All rights reserved.
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
Copyright © Houghton Mifflin Company. All rights reserved.
CHAPTER 2 Answers
273
EXERCISE 2.2 WARM-UPS A
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
Copyright © Houghton Mifflin Company. All rights reserved.
274
ANSWERS TO ALL EXERCISES
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
Copyright © Houghton Mifflin Company. All rights reserved.
CHAPTER 2 Answers
275
EXERCISE 2.4 WARM-UPS A
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
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276
ANSWERS TO ALL EXERCISES
EXERCISE 2.5 WARM-UPS A
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
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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
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278
ANSWERS TO ALL EXERCISES
EXERCISE 2.7 WARM-UPS A
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
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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
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280
ANSWERS TO ALL EXERCISES
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
Copyright © Houghton Mifflin Company. All rights reserved.
35. C
CHAPTER 3 Answers
281
EXERCISE 3.3 WARM-UPS A
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
Copyright © Houghton Mifflin Company. All rights reserved.
282
ANSWERS CHAPTER 4 EXERCISE 4.1 WARM-UPS A
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
Copyright © Houghton Mifflin Company. All rights reserved.
CHAPTER 4 Answers
283
EXERCISE 4.2 WARM-UPS A
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
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284
ANSWERS TO ALL EXERCISES
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
Copyright © Houghton Mifflin Company. All rights reserved.
CHAPTER 5 Answers
285
ANSWERS CHAPTER 5 EXERCISE 5.1 WARM-UPS A
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
Copyright © Houghton Mifflin Company. All rights reserved.
286
ANSWERS TO ALL EXERCISES
EXERCISE 5.2 WARM-UPS A
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
Copyright © Houghton Mifflin Company. All rights reserved.
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
EXERCISE 5.3 WARM-UPS A
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
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