Unit 10
Answer Key
1
Unit 10 Answers
c) 16
d) 13
PM-2.
b) 12
PM-3.
d) 19 , 23 , 29
e) Give different points: B one point, C three points, A six points. You may want
to mention expected value here to show why this distribution of points makes
the game fair.
PM-4.
b) (1, 2)
PM-5.
a) (-4, -4)
PM-6.
b) (x - 5)2 -25
PM-7.
(x + 4)2 + (y - 6)2 = 64; circle, center (-4, 6), r = 8
PM-9.
a) 3p
2
b) (1, 2)
11p
d) 7p
6 , 6
PM-10. a) 52
b) 10
d) - 15
4
c) -3, 2
2 = 1
PM-11. b) 18
9
c) Probably not, since her probability of success is 19 and her pay off ratio is 10
1 ,
so Penny has a slightly better than "fair" expectation since 10
9 > 1.
1 , BR, 1
PM-12. YY, 16 , YR, 13 , RY, 19 , RR, 29 , BY, 18
9
PM-13. b) W6, R3
PM-14. a) 16
c) W4, R4
b) 11
36
d) W2, R4
c) 16
5
d) 36
PM-15. a) All the combinations of the faces that can occur when you roll two die.
b) yes
5
PM-16. a) 10
=
36 18
1
b) 36
c) 11
36
d) 25
36
PM-17. a) The diagram is the same as that of PM-14 but with two columns (rows)
labeled 6 and no 1.
b) 16
© 2000 CPM Educational Program
v. 5.0
Unit 10
1 , p(3) =
PM-18. p(2) = 36
6 , p(8) =
p(7) = 36
Answer Key
2 , p(4) =
36
5
36 , p(9) =
11
PM-20. a) ( 13
5 ,- 5 )
2
3 , p(5) = 4 , p(6) = 5 ,
36
36
36
4 , p(10) = 3 , p(11) = 2 , p(12) = 1
36
36
36
36
b) (-5, 12 )
PM-21. a) (2, 8), (4, 4) b) (3 + i, 6 - 2i), (3 - i, 6 + 2i)
c) (a) intersects and (b) does not.
PM-22. h = $0.75, m = $0.55
PM-24. TSA = 264 sq. cm, V = 216 cu. cm
PM-25. b) x = ab + ac c) x = a, b
d) x = 0, c
e) x = a +c b
f) x = b 1- a
PM-26. Each of the small rectangles represents one branch of the tree. Combinations
6 1
that look alike are placed together. P(YR) =
=
18 3
PM-27. Each section in this diagram has things that look alike, grouped together.
PM-29. The area of each small rectangle in the area model corresponds to multiplying
the probabilities to reach the end of each branch of the tree diagram.
PM-30. a) 18
38 = 0.474
b) 20
38 = 0.526
c) 0.225
PM-31. 18%
PM-32. a) (x + 2)2 + 2
PM-33. $1157
PM-34. a) ≈ 266.67
b) 37.5%
c) 27%
d) 135
PM-36. 4 (x - 5)2 + 1156 + 2 (x - 5) 2 + 256 + 2 (x - 5) 2 + 900
PM-37. 36.3˚
PM-38. x = 12
© 2000 CPM Educational Program
v. 5.0
Unit 10
PM-39.
Answer Key
3
x + 3 - 1; x ≥ -3, y ≥ -1
1
PM-40. a) (5, 5), (4, 6), (6, 4) c) 12
d) There are only three ways to get 10, and one of them is two 5's.
2
PM-41. b) 10
6
c) 10
PM-42. c) 13
d) 13
PM-43. a) 1 x 1 b)
3
8
c)
5
d) 10
2
3
SOLUTION:
B
B
R
R
G
1/4
1/16
G
For part (c), the possible
region is 3/8 of the area.
The desired region is 1/4
of the figure, so
1/4 divided by 3/8 = 2/3.
It is easier to see that
4/16 out of 6/16 = 4/6 or 2/3.
1/16
PM-44. b) 27
PM-45. a) 1 - x
c) x2 + (1 - x)2 or 2x2 - 2x + 1
x2
d)
2x 2 - 2x + 1
PM-46. a) 1 - 2x
d) 2x2 + (1 - 2x)2 or 6x2 - 4x +1
x2
e)
6x 2 - 4x + 1
PM-47. a) ≈ 80.86
b)
x
1-x
x
SOLUTION:
1-x
b)
x
x 1-2x
x
SOLUTION: x
1-2x
b) 24.05
PM-48. n = ± 72
PM-49. a) y = x3 + 6x2 + 12x + 12 b) It would not differ.
c) y = x3
PM-50. 10 minutes, 5m minutes
PM-51. a) (-15, 40)
© 2000 CPM Educational Program
v. 5.0
Unit 10
Answer Key
4
- 2i = 1.56 - 0.08i
PM-52. b) 3925
PM-53. a)
3 + 4i
b) 1 + 3i
5
c)-
4 7
- i
5 5
È1 -2 ˘
PM-54. b) not possible c) Í
†
Î6 -3 ˙˚
PM-56. a)
R B
Y
3/10 3/10 2/5
H 1/2 3/20 3/20 1/5
SOLUTIONS:
T 1/2
1/4
1/6
3/20
R
H
1/12
T
R 1/2 Y 1/3 B1/6
B
Y
R
3/20
1/5
1/4
Y
B
1/6
1/12
( )
1 + 1 = 7 or 0.233
b) probably the area diagram
c) 3 20
12 30
3
7
9
d) 20 ÷ 30 = 14 or 0.643
e) about 4 or 5
f) No, it was not worth it because, on average, you would expect to spend $4.00
or more playing the game to win a stuffed animal.
PM-57.
2 + 1 = 11
b) 10
6 30
1
c) 20 + 16 = 13
60
1
13
10
d) ÷ =
6 60 13
3
e) 13
a)
SOLUTION:
1/3
red (1/2) chicken
blue (1/2)
1/3
1/3
pig
cow
chicken
pig
1/2
2/5
c
o
w
1/10
†
© 2000 CPM Educational Program
v. 5.0
Unit 10
Answer Key
5
PM-58. a)
b)
study-not sick
0.5
A
0.8
not A
0.2
SOLUTION:
0.4
not A
0.2
0.4
0.1
study
0.5
0.1
A
0.05
0.1
not A
0.9 0.45
not study-sick
0.5
A 0.8
no study
0.5
0.05
SOLUTION:
A
0.1
d) 0.4 + 0.05 = 0.45
e)
PM-59. a) (0.99)3 0.970
c) 0.9979
0.45
notA 0.9
0. 4 8
=
0. 45 9
b) (0.99)50 0.605
d) x50 0.9
PM-60. 32.9 mm
PM-62. y = -2x + 34
PM-63. a) - 25 ± 4i5 6 or -0.4 ± 0.8i 6 or -0.4 ± 1.96i
PM-64. a) -12; 24 - 12n
e) curve or exponential
b) linear
f) 10
c) 54
b) x = 6
PM-66. a) 30°, 150°
d) ≈ 35°, 145°, 215˚, 325˚
2
PM-67. a) xx +2
c) x = 1 or
1
5
PM-65. a)x ≈ 781.36
d) 3; 24(0.5)x
d) x = 0 or 1 or 2
x -3
b) 2x
+1
1 = 0.015625
1 + 1 + 9 += 18 = 0.28125
PM-68. a) 64
b) 16
16 64
64
1 of $10 + 1 of $5 + 9 of $1 + of $100 + of $0 = $2.64
c) 16
16
64
d) no
PM-69. a) 2, but most people will probably say 1 c) 1.19
d) "Most likely" means the most probable outcome for one trial. On the other
hand, "expected value" means the number of points you would expect, on
average, in the long run.
PM-70. a) 0 points
c) 61.803%
d) -1 +2 5
PM-71. a ≤ 25
24
© 2000 CPM Educational Program
v. 5.0
Unit 10
Answer Key
PM-72. a) 1 -2 x
6
2
d) 3x -22x + 1
e)
2x 2
3x 2 - 2x + 1
PM-73. (-1, -3) and (3, 5)
PM-76. 30.96˚ and 149.04˚
PM-77. a) 10 + 11i
PM-78. b)
b) 13
d) a2 + b2
c) 29
x
2x - 2
1
8 of the time
PM-79. a) 12
b) 16
c) 12
1 + 1 + 2 of the time, so 1 - 4 = 8 .
d) You can move 12
12 12
12 12
PM-80. There are 8 possible non red arrangements with 3 spins: YYY, YBY, YYB, etc.
8 = 19 .
1- 27
27
PM-81. a) a tree diagram
c) i: 18 ii: 12 iii: 38 iv: 78
b) 8
v: 38 vi: 34 vii: neither
PM-82. Probability for both is 38 .
PM-83. a) 5
b) 6
log 17
PM-85. a) log 3
b) 3 17
c) 11
PM-87. a) (x + 52 )2 + 34 , vertex (- 52 , 34 )
5
d) 11
b) (0, 7)
c) (-5, 7)
PM-89. 10x10y = 10x + y so Joe is wrong, and Sam is correct.
PM-91. 31 units
© 2000 CPM Educational Program
v. 5.0
Unit 10
Answer Key
7
PM-92. a)
POSSIBLE DIAGRAM:
test
correct
99
0.99
test
wrong
0.01
98,901
1
999
sick
100
not sick
99,900
b) Out of 100 people who are HIV positive, 99 are identified correctly—there
are, however, 999 false-positives in a population of 100,000.
c) 91% are false positives.
PM-93. a) (0, 12) (1, 8.5) (3, 4.5)
b) f(x) = 0.5x2 - 4x + 12
c) 4 meters above the ground
PM-94. a) 18
b) -12 c) -1 + 7i
d) -14.5
e) 0, -7
PM-96. a) They are perpendicular.
b) They are opposite reciprocals, or their product is -1.
PM-98. a) x = -3, 4
d) never
b) x = -1.5, 3
f) x = 0
c) x =
-1 ± 57
4
PM-99. a) 200,000
b) 100,000
c) 220,000 homeowners and 80,000 renters
PM-100. H(1) = 0.4R(0) + 0.9H(0), R(1) = 0.6R(0) + 0.1H(0)
È 0. 9
PM-101. N = [ H(1) R(1)], C = [H(0) R(0)], T = Í
Î 0. 4
0.1 ˘
0. 6 ˙˚
PM-102. D5 = [ H(5) R(5) ] = [ 237,500 62,500 ] = number of homeowners and renters
after 5 years
PM-103. a) multiply by T
b) geometric
c) t(100) = 3(5100)
d) D5 = D0(T5)
e) D10 = [239,922 60,078] D20 = [240,000 60,000]. The numbers are leveling
off; they can expect 240,000 owners and 60,000 renters
© 2000 CPM Educational Program
v. 5.0
Unit 10
Answer Key
8
PM-104. a) 148,000 owners, 172,500 renters, 4,500 homeless
b)
c)
O
R
H
O
R H
O È 0. 90 0.10
0 ˘
R Í 0. 20 0. 79 0. 01˙
[120 200 5] ( in thousands)
Í
˙
H ÍÎ 0
0. 50 0. 50 ˙˚
d) ≈ 215,000 owners, 108,000 renters, and 2,000 homeless
c) a = 12 , b = 12 , c = 0
PM-105. a) Dot arrangements are triangular.
PM-106. c) Find D3 = D0(T3) and look at the first entry; find Dn = D0(Tn) for
several large values of n and look at the first entries; see what
number they are approaching; 39%, 65%.
d) Both probabilities approach 0.
e) The absorbing states are getting well and dying, because patients
who reach those states remain there.
f) The Markov Chain model predicts what will happen in the long run
to a given set of patients. However, new patients enter the
hospital all the time.
PM-107. a) f-1(x) = 2(x + 1 )2 - 4
c) x ≥ -1; y ≥ -4
d) 2
PM-108. 120 cubic units
PM-111. 1 and 3 is fair, so is 3 and 6, so is 6 and 10. These are successive triangular
numbers.
8 = 2
PM-112. c) 36
9
4 = 1
d) 36
9
3 = 1
PM-113. a) 36
12
4 = 2
e) 10
5
b) 39 = 13
2
f) 45
1
e) 12
36 = 3
c)
25 ,
g) 396
1
36
25 2 1
396 , 45 , 36
4 = 1
d) 36
9
PM-114. 7, or 11, or 4 and 4 before 7, or 5 and 5 before 7, etc.
8 + 1 + 2 + 25 + 25 + 2 + 1 = 244
a) 36
36 45 396 396 45 36
495
8 ÷ 244 = 55
251
b) 36
c) 495
495 122
PM-115. a) 7
b) 1.5
c) ≈1.75
d) ≈ 1.87
PM-116. c) [ 0.7 0.3 ] or [ 0.3 0.7 ] means there is a 70% chance of rain tomorrow.
© 2000 CPM Educational Program
v. 5.0
Unit 10
PM-117. a) 0.15
Answer Key
9
c) 0.40
x ; x ≈ 69.34'
PM-118. sin 34˚ = 124
b) 5.35
PM-119. b) ≈ 1.125.1015
c) quadrillion
© 2000 CPM Educational Program
v. 5.0