Go here to find the list of practice problems.

Answer Keys to Problems 1 to 10

Problem 1-A

$\displaystyle \frac{7}{16}$
Problem 1-B

$\displaystyle \frac{32}{3125}=0.01024$

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Problem 2-A

$\displaystyle 0.4437$
Problem 2-B

$\displaystyle 0.729$

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Problem 3-A

$\displaystyle 0.93456$
Problem 3-B

$\displaystyle 0.4$

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Problem 4-A

$\displaystyle 0.85$
Problem 4-B

$\displaystyle 0.894427191$

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Problem 5-A

$\displaystyle 0.1403718733$
Problem 5-B

$\displaystyle \frac{1}{12}$

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Problem 6-A-1

$\displaystyle 0.0931228413$
Problem 6-A-2

$\displaystyle 0.400978973$
Problem 6-B-1

$\displaystyle \frac{108}{400}=0.27$
Problem 6-B-2

$\displaystyle \frac{57}{108}=0.5278$

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Problem 7-A-1

$\displaystyle 0.08337$
Problem 7-A-2

$\displaystyle 4$
Problem 7-A-3

$\displaystyle 144$
Problem 7-B-1

$\displaystyle 0.0669916086$
Problem 7-B-2

$\displaystyle 3.2$
Problem 7-B-3

$\displaystyle 92.16$

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Problem 8-A

$\displaystyle 0.5053912139$
Problem 8-B

$\displaystyle 0.0203410294$

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Problem 9-A

$\displaystyle \frac{20}{9}$
Problem 9-B

$\displaystyle \frac{8}{27}=0.2963$

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Problem 10-A-1

$\displaystyle 0.07$
Problem 10-A-2

$\displaystyle 0.6$
Problem 10-A-3

$\displaystyle 4.44$
Problem 10-B-1

$\displaystyle 0.06046875$
Problem 10-B-2

$\displaystyle 0.48$
Problem 10-B-3

$\displaystyle 2.8416$

Answer Keys to Problems 11 to 20

Problem 11-A

$\displaystyle 0.111476736$
Problem 11-B

$\displaystyle \frac{63}{256}$

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Problem 12-A

$\displaystyle \17,340$
Problem 12-B

$\displaystyle 0.18394$

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Problem 13-A

$\displaystyle h(w)=0.1 \ e^{-0.05 \ w} - 0.1 \ e^{-0.1 \ w}$
Problem 13-B

$\displaystyle h(w)=e^{-0.2 \ w} - \ e^{-0.25 \ w}$

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Problem 14-A

$\displaystyle h(w)=\frac{1}{3} \ e^{-0.1 \ w}-e^{-0.2 \ w}+\frac{2}{3} \ e^{-0.25 \ w}$ where $w>0$
Problem 14-B

$\displaystyle h(w)=\frac{1}{6} \ e^{-0.05 \ w} - \frac{1}{3} \ e^{-0.1 \ w}+\frac{1}{3} \ e^{-0.2 \ w}-\frac{1}{6} \ e^{-0.25 \ w}$ where $w>0$

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Problem 15-A

$\displaystyle h(w)=\left\{\begin{matrix}0.1-0.1 \ e^{-0.1 \ w}& \ \ \ \ \ \ 0
Problem 15-B

$\displaystyle h(w)=\left\{\begin{matrix}-10 + 2w + 10 \ e^{-0.2 \ w}& \ \ \ \ \ \ 0

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Problem 16-A

$\displaystyle \frac{5}{6}$
Problem 16-B

$\displaystyle \frac{2}{7}$

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Problem 17-A

$\displaystyle Var(X+Y)=\frac{5}{36}$
Problem 17-B

$\displaystyle Var(X+Y)=\frac{37}{3}$

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Problem 18-A

$\displaystyle \frac{26}{225}$
Problem 18-B

$\displaystyle \frac{5}{\alpha^2}$

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Problem 19-A

$\displaystyle 0.69929$
Problem 19-B

$\displaystyle 0.43378$

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Problem 20-A

$\displaystyle 0.1449893$
Problem 20-B

$\displaystyle 0.1859634$

Answer Keys to Problems 21 to 30

Problem 21-A

$\displaystyle 0.31$
Problem 21-B

$\displaystyle 0.40929$

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Problem 22-A

$\displaystyle 0.18$
Problem 22-B

$\displaystyle 0.2376$

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Problem 23-A

$\displaystyle 0.11382415$
Problem 23-B

$\displaystyle \frac{694}{4096}=0.169434$

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Problem 24-A

$\displaystyle 0.13584584776$
Problem 24-B

$\displaystyle 0.59216578$

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Problem 25-1

$\displaystyle \frac{3}{4}$
Problem 25-2

$\displaystyle \frac{20}{3}$
Problem 25-3

$\displaystyle \frac{50}{9}$

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Problem 26-1

$\displaystyle \frac{5}{6}$
Problem 26-2

$\displaystyle \frac{295}{18}=16.39 \text{ min}$
Problem 26-3

$\displaystyle \frac{11075}{324}=34.182$

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Problem 27-A

$\displaystyle \frac{7}{16}$
Problem 27-B

$\displaystyle 0.0776$

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Problem 28-A

$\displaystyle 0.550671$
Problem 28-B

$\displaystyle 125 \%$

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Problem 29-A

$\displaystyle B$
Problem 29-B

$\displaystyle C$

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Problem 30-A

$\displaystyle \frac{5}{2}$
Problem 30-B

$\displaystyle \frac{29}{60}$

Answer Keys to Problems 31 to 40

Problem 31-A

$\displaystyle \frac{8}{9}$
Problem 31-B

$\displaystyle 25$

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Problem 32-A

$\displaystyle -\frac{4}{81}$
Problem 32-B

$\displaystyle -\frac{1}{36}$

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Problem 33-A

$\displaystyle 0.063048 \ e^{-1}=0.023194$
Problem 33-B

$\displaystyle 0.130248 \ e^{-1.2}=0.039$

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Problem 34-A

$\displaystyle \frac{3}{16}$
Problem 34-B

$\displaystyle \frac{51}{243}$

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Problem 35-A

$\displaystyle D$
Problem 35-B

$\displaystyle C$

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Problem 36-1

$\displaystyle \frac{1591}{3240} \ e^{-1}=0.180647$
Problem 36-2

$\displaystyle \frac{751}{1591}=0.47203017$

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Problem 37-A

1. $\displaystyle 0.3995764$
2. $\displaystyle 0.462117157$
Problem 37-B

1. $\displaystyle 0.329679954$
2. $\displaystyle 0.549833997$

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Problem 38-A

$\displaystyle 0.084015678$
Problem 38-B

$\displaystyle 0.030534554$

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Problem 39-A

$\displaystyle 0.33974$
Problem 39-B

$\displaystyle 0.83613$

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Problem 40-A

$\displaystyle \frac{517}{8000}=0.064625$
Problem 40-B

$\displaystyle \frac{55}{324}=0.169753$

Answer Keys to Problems 41 to 50

Problem 41-A

$\displaystyle 0.336$
Problem 41-B

$\displaystyle \frac{206}{47}$

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Problem 42-A

$\displaystyle \frac{781}{1024}$
Problem 42-B

$\displaystyle \frac{37}{64}$

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Problem 43-A

$\displaystyle \frac{5}{2}$
Problem 43-B

$\displaystyle 3$

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Problem 44-A

$\displaystyle \frac{80}{243}$
Problem 44-B

$\displaystyle \frac{1792}{6561}$

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Problem 45-A

$\displaystyle D$
Problem 45-B

$\displaystyle D$

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Problem 46-A

$\displaystyle \frac{53}{3}$
Problem 46-B

$\displaystyle \frac{15}{2}$

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Problem 47-A

$\displaystyle 0.2665$
Problem 47-B

$\displaystyle 0.2395$

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Problem 48-A

$\displaystyle D$
Problem 48-B

$\displaystyle B$

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Problem 49-A

$\displaystyle C$
Problem 49-B

$\displaystyle C$

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Problem 50-A

$\displaystyle C$
Problem 50-B

$\displaystyle D$

Answer Keys to Problems 51 to 60

Problem 51-A

$\displaystyle A$
Problem 51-B

$\displaystyle E$

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Problem 52-A

$\displaystyle D$
Problem 52-B

$\displaystyle B$

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Problem 53-A

$\displaystyle A$
Problem 53-B

$\displaystyle B$

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Problem 54-A

$\displaystyle D$
Problem 54-B

$\displaystyle B$

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Problem 55-A

$\displaystyle B$
Problem 55-B

$\displaystyle D$

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Problem 56-A

$\displaystyle B$
Problem 56-B

$\displaystyle D$

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Problem 57-A

$\displaystyle D$
Problem 57-B

$\displaystyle A$

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Problem 58-A

$\displaystyle C$
Problem 58-B

$\displaystyle A$

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Problem 59-A

$\displaystyle D$
Problem 59-B

$\displaystyle E$

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Problem 60-A

$\displaystyle B$
Problem 60-B

$\displaystyle C$

Answer Keys to Problems 61 to 70

Problem 61-A

$\displaystyle E$
Problem 61-B

$\displaystyle D$

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Problem 62-A

$\displaystyle A$
Problem 62-B

$\displaystyle B$

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Problem 63-A

$\displaystyle E$
Problem 63-B

$\displaystyle C$

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Problem 64-A

$\displaystyle C$
Problem 64-B

$\displaystyle E$

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Problem 65-A

$\displaystyle D$
Problem 65-B

$\displaystyle C$

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Problem 66-A

$\displaystyle C$
Problem 66-B

$\displaystyle B$

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Problem 67-A

$\displaystyle D$
Problem 67-B

$\displaystyle E$

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Problem 68-A

$\displaystyle B$
Problem 68-B

$\displaystyle D$

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Problem 69-A

$\displaystyle B$
Problem 69-B

$\displaystyle C$

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Problem 70-A

$\displaystyle D$
Problem 70-B

$\displaystyle B$

Answer Keys to Problems 71 to 80

Problem 71-A

$\displaystyle B$
Problem 71-B

$\displaystyle B$

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Problem 72-A

$\displaystyle D$
Problem 72-B

$\displaystyle E$

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Problem 73-A

$\displaystyle A$
Problem 73-B

$\displaystyle D$

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Problem 74-A

$\displaystyle B$
Problem 74-B

$\displaystyle D$

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Problem 75-A

$\displaystyle E$
Problem 75-B

$\displaystyle D$

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Problem 76-A

$\displaystyle D$
Problem 76-B

$\displaystyle D$

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Problem 77-A

$\displaystyle D$
Problem 77-B

$\displaystyle A$

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Problem 78-A

$\displaystyle B$
Problem 78-B

$\displaystyle C$

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Problem 79-A

$\displaystyle C$
Problem 79-B

$\displaystyle D$

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Problem 80-A

$\displaystyle D$
Problem 80-B

$\displaystyle E$

Answer Keys to Problems 81 to 90

Problem 81-A

$\displaystyle D$
Problem 81-B

$\displaystyle C$

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Problem 82-A

$\displaystyle D$
Problem 82-B

$\displaystyle C$

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Problem 83-A

$\displaystyle B$
Problem 83-B

$\displaystyle C$

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Problem 84-A

$\displaystyle E$
Problem 84-B

$\displaystyle D$

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Problem 85-A

$\displaystyle B$
Problem 85-B

$\displaystyle C$

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Problem 86-A

$\displaystyle C$
Problem 86-B

$\displaystyle B$

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Problem 87-A

$\displaystyle E$
Problem 87-B

$\displaystyle C$

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Problem 88-A

$\displaystyle C$
Problem 88-B

$\displaystyle D$

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Problem 89-A

$\displaystyle C$
Problem 89-B

$\displaystyle A$

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Problem 90-A

$\displaystyle A$
Problem 90-B

$\displaystyle B$

Answer Keys to Problems 91 to 100

Problem 91-A

$\displaystyle B$
Problem 91-B

$\displaystyle D$

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Problem 92-A

$\displaystyle B$
Problem 92-B

$\displaystyle E$

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Problem 93-A

$\displaystyle D$
Problem 93-B

$\displaystyle D$

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Problem 94-A

$\displaystyle D$
Problem 94-B

$\displaystyle A$

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Problem 95-A

$\displaystyle A$
Problem 95-B

$\displaystyle E$

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Problem 96-A

$\displaystyle B$
Problem 96-B

$\displaystyle C$

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Problem 97-A

$\displaystyle B$
Problem 97-B

$\displaystyle A$

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Problem 98-A

$\displaystyle C$
Problem 98-B

$\displaystyle E$

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Problem 99-A

$\displaystyle D$
Problem 99-B

$\displaystyle E$

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Problem 100-A

$\displaystyle D$
Problem 100-B

$\displaystyle C$

Answer Keys to Problems 101 to 110

Problem 101-A

$\displaystyle D$
Problem 101-B

$\displaystyle A$

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Problem 102-A

$\displaystyle E$
Problem 102-B

$\displaystyle C$

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Problem 103-A

$\displaystyle D$
Problem 103-B

$\displaystyle C$

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Problem 104-A

$\displaystyle E$
Problem 104-B

$\displaystyle B$

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Problem 105-A

$\displaystyle D$
Problem 105-B

$\displaystyle E$

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Problem 106-A

$\displaystyle C$
Problem 106-B

$\displaystyle A$

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Problem 107-A

$\displaystyle E$
Problem 107-B

$\displaystyle B$

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Problem 108-A

$\displaystyle B$
Problem 108-B

$\displaystyle C$

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Problem 109-A

$\displaystyle D$
Problem 109-B

$\displaystyle C$

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Problem 110-A

$\displaystyle C$
Problem 110-B

$\displaystyle A$

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$\copyright$ 2013 to 2019 – Dan Ma