Question 1

If   ,   , and   , what is   ? ​

Accepted Answer

A)  17 
B)  8 
C)  15 
D)  13 
E)  6
F) 14 
A)  17 
B)  8 
C)  15 
D)  13 
E)  6
F) 14

Question 2

In a survey of 370 households regarding the ownership of VCRs and DVD players, the following data was obtained:
​
340 households own one or more VCRs.
​
170 households own one or more VCRs and one or more DVD players.
​
18 households do not own a VCR or a DVD player.
​
How many households only own one or more DVD players?
​
__________ households

Accepted Answer

The answer of In a survey of 370 households regarding...

Question 3

Refer to the accompanying figure and find the points that belong the set   .

Accepted Answer

t, s, x, y

Question 4

In a survey of   members of a local sports club,   members indicated that they plan to attend the next Summer Olympic Games,   indicated that they plan to attend the next Winter Olympic Games, and   indicated that they plan to attend both games. How many members of the club plan to attend at least one of the two game? ​

Accepted Answer

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

Question 5

Evaluate the expression.
​

Accepted Answer

The answer of Evaluate the expression.
​  ...

Question 6

A new state employee is offered a choice of ten basic health plans, three dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category? ​

Accepted Answer

A)  16 different plans 
B)  135 different plans 
C)  8 different plans 
D)  121 different plans 
E)  90 different plans
F) 46 different plans 
A)  16 different plans 
B)  135 different plans 
C)  8 different plans 
D)  121 different plans 
E)  90 different plans
F) 46 different plans

Question 7

List all subsets of the set   .

Accepted Answer

The answer of List all subsets of the set ...

Question 8

An opinion poll was conducted by the Morris Polling Group. Respondents were classified according to their sex (M or F), political affiliation (D, I, R), and the region of the country in which they reside (NW, W, C, S). ​
Use the generalized multiplication principle to determine the number of possible classifications.
​

Accepted Answer

A)  21 
B)  24 
C)  30 
D)  13 
E)  10 
A)  21 
B)  24 
C)  30 
D)  13 
E)  10

Question 9

Four items from four different departments of Metro Department Store will be featured in a one-page newspaper advertisement as shown in the following diagram.
​   ​
In how many different ways can the 16 featured items be arranged on the page?
​
__________
​
If items from the same department must be in the same row, how many arrangements are possible?
​
__________

Accepted Answer

20,922,789

Question 10

Refer to the accompanying figure and find the points that belong the set   . ​   ​

Accepted Answer

A)  x, z, w, r, v, u 
B)  s, x 
C)  x, z, w, r, v, u, s 
D)  u, s 
A)  x, z, w, r, v, u 
B)  s, x 
C)  x, z, w, r, v, u, s 
D)  u, s

Question 11

Let   and   . Find the set   .

Accepted Answer

The answer of Let   and   ....

Question 12

Let A and B be subsets of a universal set U and suppose   ,   ,   , and   . Compute   . ​

Accepted Answer

A)  40 
B)  90 
C)  30 
D)  20 
E)  170
F) 10 
A)  40 
B)  90 
C)  30 
D)  20 
E)  170
F) 10

Question 13

A coin is tossed 4 times and the sequence of heads and tails is recorded. Use the generalized multiplication principle to determine the number of outcomes of this activity. ​

Accepted Answer

A)  23 possible outcomes 
B)  7 possible outcomes 
C)  16 possible outcomes 
D)  3 possible outcomes 
E)  26 possible outcomes
F) 13 possible outcomes 
A)  23 possible outcomes 
B)  7 possible outcomes 
C)  16 possible outcomes 
D)  3 possible outcomes 
E)  26 possible outcomes
F) 13 possible outcomes

Question 14

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor?
​
__________ prisoners

Accepted Answer

The answer of On a certain day, the Wilton County...

Question 15

Let U denote the set of all employees in a hospital.
Let           Describe each set in words. 
a.   
b.

Accepted Answer

a. The set of all employees in

Question 16

Let A, B, and C be subsets of a universal set U and suppose   ,   ,   ,   ,   ,   ,   , and   . ​
Compute   .
​

Accepted Answer

A)  39 
B)  14 
C)  10 
D)  70 
E)  89
F) 64 
A)  39 
B)  14 
C)  10 
D)  70 
E)  89
F) 64

Question 17

A Social Security number has nine digits. How many Social Security numbers are possible? ​

Accepted Answer

A)  1,000,000,000 
B)  362,880 
C)  40,320 
D)  999,999,999 
E)  800,000,000 
A)  1,000,000,000 
B)  362,880 
C)  40,320 
D)  999,999,999 
E)  800,000,000

Question 18

Use Venn diagrams to illustrate the statement. ​   ​

Accepted Answer

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

Question 19

Let A and B be subsets of a universal set U and suppose   ,   ,   , and   . Compute:
​   __________
​   __________
​   __________

Accepted Answer

The answer of Let A and B be subsets of...

Question 20

Refer to the accompanying figure and find the points that belong to the set   .

Accepted Answer

A)  u 
B)  w 
C)  w, r 
D)    
A)  u 
B)  w 
C)  w, r 
D)

If , , and , what is ?

Refer to the accompanying figure and find the points that belong the set .

Evaluate the expression.

A new state employee is offered a choice of ten basic health plans, three dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category?

List all subsets of the set .

Refer to the accompanying figure and find the points that belong the set .

Let and . Find the set .

Let A and B be subsets of a universal set U and suppose , , , and . Compute .

A coin is tossed 4 times and the sequence of heads and tails is recorded. Use the generalized multiplication principle to determine the number of outcomes of this activity.

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? __________ prisoners

Let U denote the set of all employees in a hospital. Let Describe each set in words. a. b.

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . Compute .

A Social Security number has nine digits. How many Social Security numbers are possible?

Use Venn diagrams to illustrate the statement.

Let A and B be subsets of a universal set U and suppose , , , and . Compute: __

Refer to the accompanying figure and find the points that belong to the set .

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Exam 6: Sets and Counting

If , , and , what is ? ​

Refer to the accompanying figure and find the points that belong the set .

Evaluate the expression. ​

A new state employee is offered a choice of ten basic health plans, three dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category? ​

List all subsets of the set .

Refer to the accompanying figure and find the points that belong the set . ​ ​

Let and . Find the set .

Let A and B be subsets of a universal set U and suppose , , , and . Compute . ​

A coin is tossed 4 times and the sequence of heads and tails is recorded. Use the generalized multiplication principle to determine the number of outcomes of this activity. ​

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? ​ __________ prisoners

Let U denote the set of all employees in a hospital. Let Describe each set in words. a. b.

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . ​ Compute . ​

A Social Security number has nine digits. How many Social Security numbers are possible? ​

Use Venn diagrams to illustrate the statement. ​ ​

Let A and B be subsets of a universal set U and suppose , , , and . Compute: ​ __________ ​ __________ ​ __________

Refer to the accompanying figure and find the points that belong to the set .

Straight Lines and Linear Functions

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

If , , and , what is ?

Evaluate the expression.

A new state employee is offered a choice of ten basic health plans, three dental plans, and three vision care plans. How many different health-care plans are there to choose from if one plan is selected from each category?

Refer to the accompanying figure and find the points that belong the set .

Let A and B be subsets of a universal set U and suppose , , , and . Compute .

A coin is tossed 4 times and the sequence of heads and tails is recorded. Use the generalized multiplication principle to determine the number of outcomes of this activity.

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? __________ prisoners

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . Compute .

A Social Security number has nine digits. How many Social Security numbers are possible?

Use Venn diagrams to illustrate the statement.

Let A and B be subsets of a universal set U and suppose , , , and . Compute: __