Question 1

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

Accepted Answer

A) 720 
B) 8,145,060 
C) 45 
D) 977,407,200 
E) 6 
A) 720 
B) 8,145,060 
C) 45 
D) 977,407,200 
E) 6

Question 2

A single card is drawn from a deck. Find the probability that the card is either black or a face card.

Accepted Answer

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

Question 3

Use the binomial theorem to expand and simplify.

Accepted Answer

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

Question 4

A company is to distribute $34,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $5,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

Accepted Answer

A) $8,000, $7,600, $7,200, $6,800, $5,600 
B) $8,000, $7,700, $7,300, $6,900, $5,600 
C) $8,000, $7,500, $7,100, $6,700, $5,600 
D) $7,400, $6,800, $6,200, $5,600, $5,000 
E) $8,000, $7,400, $6,800, $6,200, $5,600 
A) $8,000, $7,600, $7,200, $6,800, $5,600 
B) $8,000, $7,700, $7,300, $6,900, $5,600 
C) $8,000, $7,500, $7,100, $6,700, $5,600 
D) $7,400, $6,800, $6,200, $5,600, $5,000 
E) $8,000, $7,400, $6,800, $6,200, $5,600

Question 5

During 1990, smoking caused 418,890 deaths in the United States. Of these deaths, cardiovascular disease accounted for 179,820, cancer for 151,322, and respiratory diseases such as emphysema for 84,475. Find the probability that a smoking-related death was the result of either emphysema or cancer.

Accepted Answer

A) 0.563 
B) 0.585 
C) 0.437 
D) 0.558 
E) 0.575 
A) 0.563 
B) 0.585 
C) 0.437 
D) 0.558 
E) 0.575

Question 6

If ten basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Accepted Answer

A) 720 
B) 90 
C) 6 
D) 7,920 
E) 5,040 
A) 720 
B) 90 
C) 6 
D) 7,920 
E) 5,040

Question 7

Find the sum.

Accepted Answer

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

Question 8

A pile of logs has 38 logs in the bottom layer, 37 in the second layer, 36 in the third, and so on. The top layer contains 28 logs. Find the total number of logs in the pile.

Accepted Answer

A) 363 logs 
B) 361 logs 
C) 726 logs 
D) 359 logs 
E) 365 logs 
A) 363 logs 
B) 361 logs 
C) 726 logs 
D) 359 logs 
E) 365 logs

Question 9

A man is 54 years old and a woman is 34 years old. The probability that the man will be alive in 10 years is 0.77, whereas the probability that the woman will be alive 10 years from now is 0.94. Assume that their life expectancies are unrelated. 
A. Find the probability that they will both be alive 10 years from now.
B. Find the probability that neither one will be alive 10 years from now.
C. Find the probability that at least one of the two will be alive 10 years from now.

Accepted Answer

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

Question 10

Evaluate the expression.

Accepted Answer

A) 24 
B) 360 
C) 120 
D) 60 
E) 121 
A) 24 
B) 360 
C) 120 
D) 60 
E) 121

Question 11

Find the total length of the red-line curve in the figure if the width of the maze formed by the curve is 48 inches and all halls in the maze have width 3 inches.     in. and   in.

Accepted Answer

A) 825 inches 
B) 816 inches 
C) 810 inches 
D) 822 inches 
E) 918 inches 
A) 825 inches 
B) 816 inches 
C) 810 inches 
D) 822 inches 
E) 918 inches

Question 12

A single card is drawn from a deck. Find the probability that the card is either red or a two.

Accepted Answer

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

Question 13

Find the fourth partial sum for the given sequence.

Accepted Answer

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

Question 14

Find the smallest positive integer j for which the statement is true.

Accepted Answer

A) 15 
B) 16 
C) 12 
D) 19 
E) 256 
A) 15 
B) 16 
C) 12 
D) 19 
E) 256

Question 15

If eleven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Accepted Answer

A) 110 
B) 6 
C) 7,920 
D) 990 
E) 11,880 
A) 110 
B) 6 
C) 7,920 
D) 990 
E) 11,880

Question 16

Find the total length of the red-line curve in the figure if the width of the maze formed by the curve is 48 inches and all halls in the maze have width 3 inches.     in. and   in.

Accepted Answer

A) 816 inches 
B) 810 inches 
C) 918 inches 
D) 804 inches 
E) 813 inches 
A) 816 inches 
B) 810 inches 
C) 918 inches 
D) 804 inches 
E) 813 inches

Question 17

Evaluate the expression.

Accepted Answer

A) 120 
B) 1 
C) 5 
D) 20 
E) 6 
A) 120 
B) 1 
C) 5 
D) 20 
E) 6

Question 18

If ten basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Accepted Answer

A) 720 
B) 90 
C) 6 
D) 7,920 
E) 5,040 
A) 720 
B) 90 
C) 6 
D) 7,920 
E) 5,040

Question 19

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 49. Find the total number of selections possible if a player selects only even numbers.

Accepted Answer

A) 96,909,120 
B) 60,410,085,120 
C) 134,596 
D) 6,991,908 
E) 144 
A) 96,909,120 
B) 60,410,085,120 
C) 134,596 
D) 6,991,908 
E) 144

Question 20

Find the fourth term of the recursively defined infinite sequence.

Accepted Answer

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

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

A single card is drawn from a deck. Find the probability that the card is either black or a face card.

Use the binomial theorem to expand and simplify.

A company is to distribute $34,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $5,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

During 1990, smoking caused 418,890 deaths in the United States. Of these deaths, cardiovascular disease accounted for 179,820, cancer for 151,322, and respiratory diseases such as emphysema for 84,475. Find the probability that a smoking-related death was the result of either emphysema or cancer.

If ten basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Find the sum.

A pile of logs has 38 logs in the bottom layer, 37 in the second layer, 36 in the third, and so on. The top layer contains 28 logs. Find the total number of logs in the pile.

Evaluate the expression.

Find the total length of the red-line curve in the figure if the width of the maze formed by the curve is 48 inches and all halls in the maze have width 3 inches. in. and in.

A single card is drawn from a deck. Find the probability that the card is either red or a two.

Find the fourth partial sum for the given sequence.

Find the smallest positive integer j for which the statement is true.

If eleven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Find the total length of the red-line curve in the figure if the width of the maze formed by the curve is 48 inches and all halls in the maze have width 3 inches. in. and in.

Evaluate the expression.

If ten basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 49. Find the total number of selections possible if a player selects only even numbers.

Find the fourth term of the recursively defined infinite sequence.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Topics From Analytic Geometry

Filters

Exam 10: Sequences, Series and Probability

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 45. Find the total number of selections possible.

A single card is drawn from a deck. Find the probability that the card is either black or a face card.

Use the binomial theorem to expand and simplify.

A company is to distribute $34,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $5,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.

During 1990, smoking caused 418,890 deaths in the United States. Of these deaths, cardiovascular disease accounted for 179,820, cancer for 151,322, and respiratory diseases such as emphysema for 84,475. Find the probability that a smoking-related death was the result of either emphysema or cancer.

If ten basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Find the sum.

A pile of logs has 38 logs in the bottom layer, 37 in the second layer, 36 in the third, and so on. The top layer contains 28 logs. Find the total number of logs in the pile.

Evaluate the expression.

Find the total length of the red-line curve in the figure if the width of the maze formed by the curve is 48 inches and all halls in the maze have width 3 inches. in. and in.

A single card is drawn from a deck. Find the probability that the card is either red or a two.

Find the fourth partial sum for the given sequence.

Find the smallest positive integer j for which the statement is true.

If eleven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

Find the total length of the red-line curve in the figure if the width of the maze formed by the curve is 48 inches and all halls in the maze have width 3 inches. in. and in.

Evaluate the expression.

If ten basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.

To win a state lottery game, a player must correctly select six numbers from the numbers 1 through 49. Find the total number of selections possible if a player selects only even numbers.

Find the fourth term of the recursively defined infinite sequence.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems of Equations and Inequalities

Topics From Analytic Geometry

Filters