Question 1

Find the mean and median of $f ( x ) = \frac { 1 } { 17 } , [ 0,17 ]$ .

Accepted Answer

A)  $\begin{array} { l l } 
\text { mean: } & 34.00 \
\text { median: } & 34.00
\end{array}$ 
B)  $\begin{array} { l l } 
\text { mean: } & 34.00 \
\text { median: } & 0.12
\end{array}$ 
C)  $\begin{array} { l l } 
\text { mean: } & 5.67 \
\text { median: } & 0.50
\end{array}$ 
D)  $\begin{array} { l l } 
\text { mean: } & 8.50 \
\text { median: } & 8.50
\end{array}$ 
E)  $\begin{array} { l l } 
\text { mean: } & 0.50 \
\text { median: } & 0.50
\end{array}$ 
A)  $\begin{array} { l l } 
\text { mean: } & 34.00 \
\text { median: } & 34.00
\end{array}$ 
B)  $\begin{array} { l l } 
\text { mean: } & 34.00 \
\text { median: } & 0.12
\end{array}$ 
C)  $\begin{array} { l l } 
\text { mean: } & 5.67 \
\text { median: } & 0.50
\end{array}$ 
D)  $\begin{array} { l l } 
\text { mean: } & 8.50 \
\text { median: } & 8.50
\end{array}$ 
E)  $\begin{array} { l l } 
\text { mean: } & 0.50 \
\text { median: } & 0.50
\end{array}$ D

Question 2

A sales representative makes a sale at approximately one-third of the businesses he calls on. On a given day, he goes to four businesses. What is the probability that he will make a sale at all four businesses?

Accepted Answer

A)  $\frac { 8 } { 27 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 1 } { 81 }$ 
E)  $\frac { 16 } { 81 }$ 
A)  $\frac { 8 } { 27 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 1 } { 12 }$ 
D)  $\frac { 1 } { 81 }$ 
E)  $\frac { 16 } { 81 }$ D

Question 3

A coin is tossed three times. Describe the event A that at least two heads occur.

Accepted Answer

A)  $\{ \mathrm { HHH } , \mathrm { HTT } , \mathrm { HTH } , \mathrm { TTH } \}$ 
B)  $\{ \mathrm { TTT } , \mathrm { HHT } , \mathrm { HTH } , \mathrm { THH } \}$ 
C)  $\{ \mathrm { HHH } , \mathrm { HHT } , \mathrm { HTH } , \mathrm { THH } \}$ 
D)  $\{ \mathrm { HHHH } , \mathrm { HHHT } , \mathrm { HTHH } , \mathrm { TTHH } \}$ 
E)  $\{ \mathrm { HH } , \mathrm { HT } , \mathrm { TT } \}$ 
A)  $\{ \mathrm { HHH } , \mathrm { HTT } , \mathrm { HTH } , \mathrm { TTH } \}$ 
B)  $\{ \mathrm { TTT } , \mathrm { HHT } , \mathrm { HTH } , \mathrm { THH } \}$ 
C)  $\{ \mathrm { HHH } , \mathrm { HHT } , \mathrm { HTH } , \mathrm { THH } \}$ 
D)  $\{ \mathrm { HHHH } , \mathrm { HHHT } , \mathrm { HTHH } , \mathrm { TTHH } \}$ 
E)  $\{ \mathrm { HH } , \mathrm { HT } , \mathrm { TT } \}$ C

Question 4

There are 11 patients in Dr. Ziglar's waiting room. Dr. Ziglar can see 5 patients before lunch. In how many different orders can Dr. Ziglar see 5 of the patients before lunch?

Accepted Answer

A) 462 
B) 332,640 
C) 55 
D) 5 
E) 55,440 
A) 462 
B) 332,640 
C) 55 
D) 5 
E) 55,440

Question 5

Evaluate using Pascal's triangle. Show your work. $\left( \begin{array} { l } 
5 \
3
\end{array} \right)$

Accepted Answer

The answer of Evaluate using Pascal's triangle. Show your work....

Question 6

In a survey, Americans were asked how well informed they are about new scientific discoveries. The results are shown in the pie graph below.   If two people from the survey are chosen at random, what is the probability that neither person feels very informed about scientific discoveries? Round to the nearest ten-thousandth.

Accepted Answer

A) 0.3864 
B) 0.7921 
C) 0.8464 
D) 0.6853 
E) 0.7084 
A) 0.3864 
B) 0.7921 
C) 0.8464 
D) 0.6853 
E) 0.7084

Question 7

A meteorologist predicts that the amount of rainfall (in inches) expected for a certain coastal community during a hurricane has the probability density function $f ( x ) = \frac { \pi } { 30 } \sin \frac { \pi x } { 15 },$ $0 \leq x \leq 15$ . Find and interpret the probability $P ( 0 \leq x \leq 5 )$ .

Accepted Answer

A) 17% probability of receiving up to 5 inches of rain 
B) 25% probability of receiving up to 5 inches of rain 
C) 30% probability of receiving up to 5 inches of rain 
D) 75% probability of receiving up to 5 inches of rain 
E) 83% probability of receiving up to 5 inches of rain 
A) 17% probability of receiving up to 5 inches of rain 
B) 25% probability of receiving up to 5 inches of rain 
C) 30% probability of receiving up to 5 inches of rain 
D) 75% probability of receiving up to 5 inches of rain 
E) 83% probability of receiving up to 5 inches of rain

Question 8

Expand the binomial by using Pascal's triangle to determine the coefficients. Show your work. $( 3 x + 2 y ) ^ { 6 }$

Accepted Answer

The answer of Expand the binomial by using Pascal's triangle...

Question 9

Find Pk+1 for the given Pk. $P _ { k } = \frac { k ^ { 2 } } { 6 } ( 5 k + 5 )$

Accepted Answer

A)  $P _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 6 } ( 5 k + 10 )$ 
B)  $P _ { k + 1 } = \frac { k ^ { 2 } } { 6 } ( 5 k + 5 ) + 1$ 
C)  $P _ { k + 1 } = \frac { k ^ { 2 } } { 6 } ( 5 k + 10 )$ 
D)  $P _ { k + 1 } = \frac { k ^ { 2 } + 1 } { 6 } ( 5 k + 10 )$ 
E)  $P _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 6 } ( 5 k + 5 )$ 
A)  $P _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 6 } ( 5 k + 10 )$ 
B)  $P _ { k + 1 } = \frac { k ^ { 2 } } { 6 } ( 5 k + 5 ) + 1$ 
C)  $P _ { k + 1 } = \frac { k ^ { 2 } } { 6 } ( 5 k + 10 )$ 
D)  $P _ { k + 1 } = \frac { k ^ { 2 } + 1 } { 6 } ( 5 k + 10 )$ 
E)  $P _ { k + 1 } = \frac { ( k + 1 ) ^ { 2 } } { 6 } ( 5 k + 5 )$

Question 10

Two six-sided dice are tossed. Find the probability that the sum is odd.

Accepted Answer

A)  $\frac { 5 } { 6 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 5 } { 18 }$ 
E)  $\frac { 23 } { 36 }$ 
A)  $\frac { 5 } { 6 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 5 } { 18 }$ 
E)  $\frac { 23 } { 36 }$

Question 11

Sketch a graph of the probability distribution. $$\begin{array} { l c c c c c } 
x & 0 & 1 & 2 & 3 & 4 \
P ( x ) & \frac { 1 } { 25 } & \frac { 6 } { 25 } & \frac { 8 } { 25 } & \frac { 3 } { 25 } & \frac { 7 } { 25 }
\end{array}$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

Seven cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all seven cards are spades.

Accepted Answer

A)  $1716$ 
B)  $33,446,140$ 
C)  $4$ 
D)  $5040$ 
E)  $26,545$ 
A)  $1716$ 
B)  $33,446,140$ 
C)  $4$ 
D)  $5040$ 
E)  $26,545$

Question 13

Find the specified nth term in the expansion of the binomial. $( 4 x + 5 y ) ^ { 6 } , n = 4$

Accepted Answer

A)  $240 x ^ { 2 } y ^ { 4 }$ 
B)  $160,000 x ^ { 3 } y ^ { 3 }$ 
C)  $15 x ^ { 2 } y ^ { 4 }$ 
D)  $15,625 y ^ { 6 }$ 
E)  $360 x ^ { 2 } y ^ { 4 }$ 
A)  $240 x ^ { 2 } y ^ { 4 }$ 
B)  $160,000 x ^ { 3 } y ^ { 3 }$ 
C)  $15 x ^ { 2 } y ^ { 4 }$ 
D)  $15,625 y ^ { 6 }$ 
E)  $360 x ^ { 2 } y ^ { 4 }$

Question 14

A combination lock will open when the right choice of three numbers (from 1 to 32) is selected. How many different lock combinations are possible?

Accepted Answer

A) 98,304 
B) 1024 
C) 32 
D) 96 
E) 32,768 
A) 98,304 
B) 1024 
C) 32 
D) 96 
E) 32,768

Question 15

Buses arrive and depart from a college every 25 minutes. The probability density function for the waiting time t (in minutes) for a person arriving at the bus stop is $f ( t ) = \frac { 1 } { 25 }$ on the interval $[ 0,25 ]$ . Find the probability that the person will wait no longer than 10 minutes.

Accepted Answer

A)  $\frac { 1 } { 25 }$ 
B)  $\frac { 1 } { 10 }$ 
C)  $\frac { 2 } { 5 }$ 
D)  $\frac { 3 } { 5 }$ 
E)  $\frac { 1 } { 250 }$ 
A)  $\frac { 1 } { 25 }$ 
B)  $\frac { 1 } { 10 }$ 
C)  $\frac { 2 } { 5 }$ 
D)  $\frac { 3 } { 5 }$ 
E)  $\frac { 1 } { 250 }$

Question 16

A biology instructor gives her class a list of eight study problems, from which she will select five to be answered on an exam. A student knows how to solve six of the problems. Find the probability that the student will be able to answer all five questions on the exam.

Accepted Answer

A)  $\frac { 23 } { 28 }$ 
B)  $\frac { 3 } { 28 }$ 
C)  $\frac { 11 } { 14 }$ 
D)  $\frac { 1 } { 28 }$ 
E)  $\frac { 27 } { 28 }$ 
A)  $\frac { 23 } { 28 }$ 
B)  $\frac { 3 } { 28 }$ 
C)  $\frac { 11 } { 14 }$ 
D)  $\frac { 1 } { 28 }$ 
E)  $\frac { 27 } { 28 }$

Question 17

Find the mean, variance, and standard deviation of the normal density function $f ( x ) = \frac { 1 } { 2 \sqrt { 2 \pi } } e ^ { - ( x -- 1 ) ^ { 2 }/8}$ over $( - \infty , \infty )$ . Do not use integration.

Accepted Answer

A)  $\begin{array} { l l } 
\text { expected value(mean): } & - 1 \
\text { variance: } & 4 \
\text { standard deviation: } & 2
\end{array}$ 
B)  $\begin{array} { l l } 
\text { expected value (mean) } ) : & 4 \
\text { variance: } & - 1 \
\text { standard dev iation: } & 2
\end{array}$ 
C)  $\begin{array} { l l } 
\text { expected value(mean } ) : & 4 \
\text { variance: } & 2 \
\text { standard dev iation: } & - 1
\end{array}$ 
D)  $\begin{array} { l l } 
\text { expected value (mean): } & 2 \
\text { variance: } & - 1 \
\text { standard deviation: } & 4
\end{array}$ 
E)  $\begin{array} { l l } 
\text { expected value (mean): } & - 1 \
\text { variance: } & 2 \
\text { standard deviation: } & 4
\end{array}$ 
A)  $\begin{array} { l l } 
\text { expected value(mean): } & - 1 \
\text { variance: } & 4 \
\text { standard deviation: } & 2
\end{array}$ 
B)  $\begin{array} { l l } 
\text { expected value (mean) } ) : & 4 \
\text { variance: } & - 1 \
\text { standard dev iation: } & 2
\end{array}$ 
C)  $\begin{array} { l l } 
\text { expected value(mean } ) : & 4 \
\text { variance: } & 2 \
\text { standard dev iation: } & - 1
\end{array}$ 
D)  $\begin{array} { l l } 
\text { expected value (mean): } & 2 \
\text { variance: } & - 1 \
\text { standard deviation: } & 4
\end{array}$ 
E)  $\begin{array} { l l } 
\text { expected value (mean): } & - 1 \
\text { variance: } & 2 \
\text { standard deviation: } & 4
\end{array}$

Question 18

A state lottery game requires a person to select ten different numbers from thirty-three numbers. The order of the selection is not important. In how many ways can this be done?

Accepted Answer

A)  $286$ 
B)  $1,144,066$ 
C)  $92,561,040$ 
D)  $330$ 
E)  $2 , \mathrm { e } 10$ 
A)  $286$ 
B)  $1,144,066$ 
C)  $92,561,040$ 
D)  $330$ 
E)  $2 , \mathrm { e } 10$

Question 19

Use mathematical induction to prove the formula for every positive integer n. Show all your work. $7 + 10 + 13 + 16 + \mathrm { K } + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )$

Accepted Answer

1) When n = 1, @#IMG-DLM& . The formula

Question 20

Determine the number of ways a computer can randomly generate an integer divisible by 4 from 1 through 15.

Accepted Answer

A) 6 
B) 3 
C) 11 
D) 7 
E) 14 
A) 6 
B) 3 
C) 11 
D) 7 
E) 14

Find the mean and median of $f ( x ) = \frac { 1 } { 17 } , [ 0,17 ]$ .

A sales representative makes a sale at approximately one-third of the businesses he calls on. On a given day, he goes to four businesses. What is the probability that he will make a sale at all four businesses?

A coin is tossed three times. Describe the event A that at least two heads occur.

There are 11 patients in Dr. Ziglar's waiting room. Dr. Ziglar can see 5 patients before lunch. In how many different orders can Dr. Ziglar see 5 of the patients before lunch?

Evaluate using Pascal's triangle. Show your work. $\left( \begin{array} { l } 5 \\3\end{array} \right)$

Expand the binomial by using Pascal's triangle to determine the coefficients. Show your work. $( 3 x + 2 y ) ^ { 6 }$

Find Pk+1 for the given Pk. $P _ { k } = \frac { k ^ { 2 } } { 6 } ( 5 k + 5 )$

Two six-sided dice are tossed. Find the probability that the sum is odd.

Sketch a graph of the probability distribution. x 0 1 2 3 4 P(x)

Seven cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all seven cards are spades.

Find the specified nth term in the expansion of the binomial. $( 4 x + 5 y ) ^ { 6 } , n = 4$

A combination lock will open when the right choice of three numbers (from 1 to 32) is selected. How many different lock combinations are possible?

Buses arrive and depart from a college every 25 minutes. The probability density function for the waiting time t (in minutes) for a person arriving at the bus stop is $f ( t ) = \frac { 1 } { 25 }$ on the interval $[ 0,25 ]$ . Find the probability that the person will wait no longer than 10 minutes.

A biology instructor gives her class a list of eight study problems, from which she will select five to be answered on an exam. A student knows how to solve six of the problems. Find the probability that the student will be able to answer all five questions on the exam.

Find the mean, variance, and standard deviation of the normal density function $f ( x ) = \frac { 1 } { 2 \sqrt { 2 \pi } } e ^ { - ( x -- 1 ) ^ { 2 }/8}$ over $( - \infty , \infty )$ . Do not use integration.

A state lottery game requires a person to select ten different numbers from thirty-three numbers. The order of the selection is not important. In how many ways can this be done?

Use mathematical induction to prove the formula for every positive integer n. Show all your work. $7 + 10 + 13 + 16 + \mathrm { K } + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )$

Determine the number of ways a computer can randomly generate an integer divisible by 4 from 1 through 15.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

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Exam 17: Probability Web

Find the mean and median of f(x)=117,[0,17]f ( x ) = \frac { 1 } { 17 } , [ 0,17 ]f(x)=171​,[0,17] .

A sales representative makes a sale at approximately one-third of the businesses he calls on. On a given day, he goes to four businesses. What is the probability that he will make a sale at all four businesses?

A coin is tossed three times. Describe the event A that at least two heads occur.

There are 11 patients in Dr. Ziglar's waiting room. Dr. Ziglar can see 5 patients before lunch. In how many different orders can Dr. Ziglar see 5 of the patients before lunch?

Evaluate using Pascal's triangle. Show your work. (53)\left( \begin{array} { l } 5 \\3\end{array} \right)(53​)

Expand the binomial by using Pascal's triangle to determine the coefficients. Show your work. (3x+2y)6( 3 x + 2 y ) ^ { 6 }(3x+2y)6

Find Pk+1 for the given Pk. Pk=k26(5k+5)P _ { k } = \frac { k ^ { 2 } } { 6 } ( 5 k + 5 )Pk​=6k2​(5k+5)

Two six-sided dice are tossed. Find the probability that the sum is odd.

Sketch a graph of the probability distribution. x 0 1 2 3 4 P(x)

Seven cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all seven cards are spades.

Find the specified nth term in the expansion of the binomial. (4x+5y)6,n=4( 4 x + 5 y ) ^ { 6 } , n = 4(4x+5y)6,n=4

A combination lock will open when the right choice of three numbers (from 1 to 32) is selected. How many different lock combinations are possible?

A biology instructor gives her class a list of eight study problems, from which she will select five to be answered on an exam. A student knows how to solve six of the problems. Find the probability that the student will be able to answer all five questions on the exam.

Find the mean, variance, and standard deviation of the normal density function f(x)=122πe−(x−−1)2/8f ( x ) = \frac { 1 } { 2 \sqrt { 2 \pi } } e ^ { - ( x -- 1 ) ^ { 2 }/8}f(x)=22π​1​e−(x−−1)2/8 over (−∞,∞)( - \infty , \infty )(−∞,∞) . Do not use integration.

A state lottery game requires a person to select ten different numbers from thirty-three numbers. The order of the selection is not important. In how many ways can this be done?

Use mathematical induction to prove the formula for every positive integer n. Show all your work. 7+10+13+16+K+(3n+4)=n2(3n+11)7 + 10 + 13 + 16 + \mathrm { K } + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )7+10+13+16+K+(3n+4)=2n​(3n+11)

Determine the number of ways a computer can randomly generate an integer divisible by 4 from 1 through 15.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Filters

Find the mean and median of $f ( x ) = \frac { 1 } { 17 } , [ 0,17 ]$ .

Evaluate using Pascal's triangle. Show your work. $\left( \begin{array} { l } 5 \\3\end{array} \right)$

Expand the binomial by using Pascal's triangle to determine the coefficients. Show your work. $( 3 x + 2 y ) ^ { 6 }$

Find Pk+1 for the given Pk. $P _ { k } = \frac { k ^ { 2 } } { 6 } ( 5 k + 5 )$

Find the specified nth term in the expansion of the binomial. $( 4 x + 5 y ) ^ { 6 } , n = 4$

Find the mean, variance, and standard deviation of the normal density function $f ( x ) = \frac { 1 } { 2 \sqrt { 2 \pi } } e ^ { - ( x -- 1 ) ^ { 2 }/8}$ over $( - \infty , \infty )$ . Do not use integration.

Use mathematical induction to prove the formula for every positive integer n. Show all your work. $7 + 10 + 13 + 16 + \mathrm { K } + ( 3 n + 4 ) = \frac { n } { 2 } ( 3 n + 11 )$