Question 1

Write the first five terms of the sequence.(Assume that n begins with 1.)

Accepted Answer

A)  13, 18, 23, 28, 33 
B)  -8, -3, 2, 7, 12 
C)  -3, 10, 15, 20, 25 
D)  -3, 2, 7, 12, 17 
E)  -3, -11, -19, -27, -35

Question 2

Twenty-four students, of whom four are seniors, are selected as semifinalists for a literary award.Of the twenty-four students, twelve finalists will be selected.In how many ways can the twelve finalists contain two seniors?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Expand the binomial by using Pascal's triangle to determine the coefficients.Show your work.

Accepted Answer

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

Question 4

Find the sum of the infinite geometric series.

Accepted Answer

A)   
B)   
C)   
D)   
E)  undefined

Question 5

Write an expression for the most apparent nth term of the sequence.(Assume that  begins with 1.)

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

A deposit of $1000 is made in an account that earns 4% interest compounded monthly.The balance in the account after n months is given by  Find the balance in the account after 12 years by finding the 144th term of the sequence.Round to the nearest penny.

Accepted Answer

A)  $283,661.80 
B)  $1614.78 
C)  $1609.42 
D)  $144,480.00 
E)  $1620.17

Question 7

A shipment of nine calculators contains eight defective calculators.Three calculators are chosen from the shipment.Find the probability that exactly one is defective.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

A combination lock will open when the right choice of three numbers (from 1 to 36) is selected.How many different lock combinations are possible?

Accepted Answer

A)  139,968 
B)  1296 
C)  36 
D)  108 
E)  46,656

Question 10

Twenty-four students are selected as semifinalists for a literary award.Of the twenty-four students, fourteen finalists will be selected.In how many ways can fourteen finalists be selected from the twenty-four students?

Accepted Answer

A)  38,760 
B)  319,770 
C)  4,457,400 
D)  1,961,256 
E)  116,280

Question 11

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) -3, 2, 7, 12, 17

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

The annual sales  (in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model   where  represents the year, with  corresponding to 2001.Find the total sales from 2001 to 2005.Round to the nearest million.

Accepted Answer

A)  $4119 million 
B)  $5427 million 
C)  $2972 million 
D)  $3295 million 
E)  $2003 million

Question 13

Evaluate the expression.

Accepted Answer

A)  3 
B)  9 
C)  6 
D)  5 
E)  8

Question 14

Find a formula for an for the arithmetic sequence.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Use the Binomial Theorem to expand and simplify the expression.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

Consider a job offer with a starting salary of $37,700 and a given annual raise of $2325.Determine the total compensation from the company through three full years of employment.

Accepted Answer

A)  $366,700 
B)  $312,725 
C)  $77,725 
D)  $423,000 
E)  $120,075

Question 17

One card is randomly drawn from a standard deck of playing cards where aces are not considered numbered cards and are the highest card in the suit.The card is replaced and another card is drawn.What is the probability that both cards drawn are diamonds?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 18

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 somewhat informed about scientific discoveries? Round to the nearest ten-thousandth.

Accepted Answer

A)  0.3864 
B)  0.1764 
C)  0.5929 
D)  0.7921 
E)  0.3738

Question 19

A coin is tossed three times.Find the probability of getting two heads.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 7: Sequences, Series, and Probability

Write the first five terms of the sequence.(Assume that n begins with 1.)

Twenty-four students, of whom four are seniors, are selected as semifinalists for a literary award.Of the twenty-four students, twelve finalists will be selected.In how many ways can the twelve finalists contain two seniors?

Expand the binomial by using Pascal's triangle to determine the coefficients.Show your work.

Find the sum of the infinite geometric series.

Write an expression for the most apparent nth term of the sequence.(Assume that begins with 1.)

A deposit of $1000 is made in an account that earns 4% interest compounded monthly.The balance in the account after n months is given by Find the balance in the account after 12 years by finding the 144th term of the sequence.Round to the nearest penny.

A shipment of nine calculators contains eight defective calculators.Three calculators are chosen from the shipment.Find the probability that exactly one is defective.

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

A combination lock will open when the right choice of three numbers (from 1 to 36) is selected.How many different lock combinations are possible?

Twenty-four students are selected as semifinalists for a literary award.Of the twenty-four students, fourteen finalists will be selected.In how many ways can fourteen finalists be selected from the twenty-four students?

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.) -3, 2, 7, 12, 17

The annual sales (in millions of dollars) for a certain company from 2001 to 2006 can be approximated by the model where represents the year, with corresponding to 2001.Find the total sales from 2001 to 2005.Round to the nearest million.

Evaluate the expression.

Find a formula for a_n for the arithmetic sequence.

Use the Binomial Theorem to expand and simplify the expression.

Consider a job offer with a starting salary of $37,700 and a given annual raise of $2325.Determine the total compensation from the company through three full years of employment.

One card is randomly drawn from a standard deck of playing cards where aces are not considered numbered cards and are the highest card in the suit.The card is replaced and another card is drawn.What is the probability that both cards drawn are diamonds?

A coin is tossed three times.Find the probability of getting two heads.

Write an expression for the apparent nth term of the sequence.(Assume that n begins with 1.)