Question 1

If 8 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes  ?

Accepted Answer

A) ?56 handshakes 
B)  ?28 handshakes 
C)  ?64 handshakes 
D)  ?168 handshakes 
E)  ?16 handshakes 
A) ?56 handshakes 
B)  ?28 handshakes 
C)  ?64 handshakes 
D)  ?168 handshakes 
E)  ?16 handshakes

Question 2

Let   $$\begin{array} { l } 
S = \{ \text { Apple, Dell, Gateway, Pomegranate, Compaq } \} \
B = \{ \text { Apple, Dell, Pomegranate, Compaq } \} \
G = \{ \text { Compaq } \} \
Q = \{ \text { Compaq } \}
\end{array}$$  
Use a Venn diagram to determine the relationships among the sets.

Accepted Answer

A)  $S \subset B$ , $G \subset B$ , $Q \subset B$ 
B)  $G \subset B$ , $Q \subset B$ , $B \subset S$ , $G = Q$ 
C)  $B \subset G$ , $B \subset Q$ 
D)  $B \subset G$ , $B \subset Q$ , $B \subset G$ , $G = Q$ 
E)  $\varnothing$ 
A)  $S \subset B$ , $G \subset B$ , $Q \subset B$ 
B)  $G \subset B$ , $Q \subset B$ , $B \subset S$ , $G = Q$ 
C)  $B \subset G$ , $B \subset Q$ 
D)  $B \subset G$ , $B \subset Q$ , $B \subset G$ , $G = Q$ 
E)  $\varnothing$

Question 3

List the elements in the set D, such that   $D = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}$

Accepted Answer

A)  $\{ 1,2,3,4,6 \}$ 
B)  $\{ 1,2,3,4,5,6 \}$ 
C)  $\{ 0,1,2,3,4,5,6 \}$ 
D)  $\{ 1,2,3,4,5,6,7 \}$ 
E)  $\varnothing$ 
A)  $\{ 1,2,3,4,6 \}$ 
B)  $\{ 1,2,3,4,5,6 \}$ 
C)  $\{ 0,1,2,3,4,5,6 \}$ 
D)  $\{ 1,2,3,4,5,6,7 \}$ 
E)  $\varnothing$

Question 4

Find how many outcomes are possible for the decision algorithms. $\begin{array}{ll}
{\text { Step } 1} & \text { Step } 2 \
\text { Alternative 1: } 1 \text { outcome } & \text { Alternative } 1: 1 \text { outcome } \
\text { Alternative } 2: 1 \text { outcome } & \text { Alternative } 2: 1 \text { outcome } \
\text { Alternative } 3: 2 \text { outcomes } &
\end{array}$

Accepted Answer

A) 6 
B)  8 
C)  3 
D)  4 
E)  2 
A) 6 
B)  8 
C)  3 
D)  4 
E)  2

Question 5

The following table shows the amount spent, in billions of dollars, on recreational boats and accessories in the United States during the period 1999-2001. (Let S be the set of all dollars represented in the table.) Compute the cardinality of the set described as $n ( A \cap ( N \cup U ) )$ . $$\begin{array} { | l | l | l | l | l | } 
\hline & \text { Used Boats, } \boldsymbol { U } & \text { New Boats, } \boldsymbol { N } & \text { Accessories, } \boldsymbol { R } & \text { Total } \
\hline \mathbf { 1 9 9 9 , \boldsymbol { A } } & 6 & 8 & 2 & 16 \
\hline \mathbf { 2 0 0 0 , } \boldsymbol { B } & 6 & 6.5 & 4 & 16.5 \
\hline \mathbf { 2 0 0 1 , } \boldsymbol { C } & 6 & 8 & 2 & 16 \
\hline \text { Total } & 18 & 22.5 & 8 & 48.5 \
\hline
\end{array}$$

Accepted Answer

A) 8 
B)  14 
C)  24.5 
D)  40.5 
E)  2 
A) 8 
B)  14 
C)  24.5 
D)  40.5 
E)  2

Question 6

Find how many outcomes are possible for the decision algorithms. $\begin{array}{cl}
{\text { Step 1 }} &{\text { Step 2 }} \
\text { Alternative 1:1 outcome } & \text { Alternative 1:2 outcomes } \
\text { Alternative 2: } 1 \text { outcome } & \text { Alternative } 2: 2 \text { outcomes } \
& \text { Alternative } 3: 2 \text { outcomes }
\end{array}$ ​
__________ outcomes

Accepted Answer

The answer of Find how many outcomes are possible for...

Question 7

If $n ( A ) = 37$ , $n ( B ) = 25$ , and $n ( A \cap B ) = 5$ , find $n ( A \cup B )$ .

Accepted Answer

A) 37 
B)  57 
C)  62 
D)  67 
E)  25 
A) 37 
B)  57 
C)  62 
D)  67 
E)  25

Question 8

You are searching for Hip-hop music that is neither American nor Dutch.
 
In set notation, for which subset of music files are you searching

Accepted Answer

The answer of You are searching for Hip-hop music that...

Question 9

Let  $$\begin{array} { l } 
A = \{ \text { June, Justine, Solly, Polly } \} \
B = \{ \text { Justine, Polly, Jelly } \} \
C = \{ \text { Ruth, Justine, Polly } \}
\end{array}$$ 
Find the set $A \cup ( B \cup C )$ .

Accepted Answer

A)  $\{ \text { June, Justine, Solly, Polly, Jelly, Ruth\} }$ 
B)   $\text { \{June, Justine, Solly, Polly, Ruth\} }$ 
C)    $\{ \text { Justine, Polly } \}$ 
D)    $\text { \{Justine, Solly, Polly, Jelly, Ruth\} }$ 
E)    $\varnothing$ 
A)  $\{ \text { June, Justine, Solly, Polly, Jelly, Ruth\} }$ 
B)   $\text { \{June, Justine, Solly, Polly, Ruth\} }$ 
C)    $\{ \text { Justine, Polly } \}$ 
D)    $\text { \{Justine, Solly, Polly, Jelly, Ruth\} }$ 
E)    $\varnothing$

Question 10

Let   $\begin{array} { l } 
C = \{ \text { red, green } \} \
N = \{ \text { circle, square } \}
\end{array}$ 
List the elements of $C \times N$ as ordered pairs in a set notation.

Accepted Answer

A)  $\text { (red, circle) }$ , $\text { (green, square) }$ 
B)  $\text { (red, circle) }$ , $\text { (red, square) }$ , $\text { (green, circle) }$ , $\text { (green, square) }$ 
C)  $\text { (red, green) }$ , $\text { (circle, square) }$ , $\text { (red, circle) }$ , $\text { (green, square) }$ 
D)  $\text { (red, square) }$ , $\text { (green, circle) }$ 
E)  $\text { (red, square) }$ , $\text { (green, circle) }$ , $\text { (red, green) }$ , $\text { (circle, square) }$ 
A)  $\text { (red, circle) }$ , $\text { (green, square) }$ 
B)  $\text { (red, circle) }$ , $\text { (red, square) }$ , $\text { (green, circle) }$ , $\text { (green, square) }$ 
C)  $\text { (red, green) }$ , $\text { (circle, square) }$ , $\text { (red, circle) }$ , $\text { (green, square) }$ 
D)  $\text { (red, square) }$ , $\text { (green, circle) }$ 
E)  $\text { (red, square) }$ , $\text { (green, circle) }$ , $\text { (red, green) }$ , $\text { (circle, square) }$

Question 11

Rather than study for math, you and your buddies decide to get together for a marathon movie-watching popcorn-gorging event on Saturday night. You decide to watch four movies selected at random from the list. How many sets of four movies are possible    $$\begin{array} { | c | c | } 
\hline \text { Name } & \text { Revenue (\$ million) } \
\hline \text { The Grudge } & \$ 9.24 \
\hline \text { Ray } & \$ 6.54 \
\hline \text { The Forgotten } & \$ 6.01 \
\hline \text { Friday Night Lights } & \$ 5.99 \
\hline \text { Cellular } & \$ 5.85 \
\hline \text { Shall We Dance } & \$ 5.82 \
\hline \text { The Village } & \$ 5.58 \
\hline \text { AVP: Alien Vs. Predator } & \$ 5.46 \
\hline \text { Catwoman } & \$ 5.10 \
\hline \text { Sky Captain and the World of } \
\text { Tomorrow } & \$ 5.09 \
\hline
\end{array}$$

Accepted Answer

A)  5,040 sets 
B)   210 sets 
C)   720 sets 
D)   182 sets 
E)   91 sets 
A)  5,040 sets 
B)   210 sets 
C)   720 sets 
D)   182 sets 
E)   91 sets

Question 12

The following table shows the amount spent, in billions of dollars, on recreational boats and accessories in the United States during the period 1999-2001. (Let S be the set of all dollars represented in the table.) Compute the cardinality of the set described as $$n ( N \cap C )$$ . $$\begin{array} { | l | l | l | l | l | } 
\hline & \text { Used Boats, } \boldsymbol { U } & \text { New Boats, } \boldsymbol { N } & \text { Accessories, } \boldsymbol { R } & \text { Total } \
\hline \mathbf { 1 9 9 9 , } , \boldsymbol { A } & 7 & 5 & 2 & 14 \
\hline \mathbf { 2 0 0 0 } , \boldsymbol { B } & 7 & 7.5 & 3 & 17.5 \
\hline \mathbf { 2 0 0 1 } , \boldsymbol { C } & 6 & 9 & 4 & 19 \
\hline \text { Total } & 20 & 21.5 & 9 & 50.5 \
\hline
\end{array}$$

Accepted Answer

A) 6 
B)  21.5 
C)  19 
D)  5 
E)  9 
A) 6 
B)  21.5 
C)  19 
D)  5 
E)  9

Question 13

Evaluate $\frac { 8 ! } { 7 ! }$ .

Accepted Answer

A) 56 
B)  16 
C)  8 
D)  1 
E)  15 
A) 56 
B)  16 
C)  8 
D)  1 
E)  15

Question 14

A surgical procedure requires choosing among three alternative methodologies. The first methodology can result in 7 possible outcomes, the second in 6 possible outcomes, and the third in 2 possible outcomes. What is the total number of outcomes possible  ?

Accepted Answer

A) 9 
B)  8 
C)  15 
D)  13 
E)  84 
A) 9 
B)  8 
C)  15 
D)  13 
E)  84

Question 15

A computer "byte" consists of 8 "bits", each bit being either a 0 or a 1. If characters are represented using a code that uses 4 bytes for each character, how many characters can be represented  ?
__________ characters

Accepted Answer

The answer of A computer "byte" consists of 8 "bits",...

Question 16

Evaluate $P ( 7,5 )$ .
​ $P ( 7,5 )$ __________

Accepted Answer

The answer of Evaluate $P ( 7,5 )$ .
​ \(P...

Question 17

Use a Venn diagram or some other method to obtain a formula for
 $n ( A \cup B \cup C )$ in terms of $n ( A )$ , $n ( B )$ , $n ( C )$ , $n ( A \cap B )$ , $n ( A \cap C )$ , $n ( B \cap C )$ , and $n ( A \cap B \cap C )$ .

Accepted Answer

A)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C ) + n ( A \cap B \cap C )$ 
B)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C ) - n ( A \cap B \cap C )$ 
C)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B \cap C )$ 
D)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) + n ( A \cap B ) + n ( A \cap C ) + n ( B \cap C ) - n ( A \cap B \cap C )$ 
E)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C )$ 
A)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C ) + n ( A \cap B \cap C )$ 
B)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C ) - n ( A \cap B \cap C )$ 
C)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B \cap C )$ 
D)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) + n ( A \cap B ) + n ( A \cap C ) + n ( B \cap C ) - n ( A \cap B \cap C )$ 
E)  $n ( A \cup B \cup C ) = n ( A ) + n ( B ) + n ( C ) - n ( A \cap B ) - n ( A \cap C ) - n ( B \cap C )$

Question 18

The following table shows the results of a survey of authors by a fictitious publishing company. $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 4 & 25 & 29 \
\hline \text { Unsuccessful } & 9 & 55 & 64 \
\hline \text { Total } & 13 & 80 & 93 \
\hline
\end{array}$$ ​
Consider the following subsets of the set S of all authors represented in the table: C, the set of successful authors; U, the set of unsuccessful authors; N, the set of new authors; and E, the set of established authors. Find the number of elements that set $C \cap N ^ { \prime }$ contains. $n \left( C \cap N ^ { \prime } \right) =$ __________

Accepted Answer

The answer of The following table shows the results of...

Question 19

The "Dogs of the Dow" refer to the stocks listed on the Dow with the highest dividend yield. The table shows the top ten stocks of the "Dogs of the Dow" list in February, 2005. You decide to make a small portfolio consisting of a collection of six of the top ten Dogs of the Dow. $$\begin{array} { | c | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Price } & \text { Yield } \
\hline \text { SBC } & \begin{array} { c } 
\text { SBC } \
\text { Communications }
\end{array} & 23.62 & 5.46 \% \
\hline \text { GM } & \text { General Motors } & 36.64 & 5.46 \% \
\hline \text { MRK } & \text { Merck } & 28.02 & 5.42 \% \
\hline \text { MO } & \text { Altria } & 63.20 & 4.62 \% \
\hline \text { VZ } & \text { Verizon } & 35.68 & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 37.00 & 3.68 \% \
\hline \text { C } & \text { Citigroup } & 48.38 & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 24.35 & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 47.23 & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 35.75 & 2.46 \% \
\hline
\end{array}$$  
How many portfolios are possible ?
__________ portfolios
How many of these portfolios contain SBC but not MO ?
__________ portfolios
How many of these portfolios contain at most one stock priced above $40 ?
__________ portfolios

Accepted Answer

The answer of  The "Dogs of the Dow" refer...

Question 20

Let $A = \{ \text { Dirk, Tina, Frans, Marie } \}$ , $B = \{ \text { Frans, Marie, Tina, Klaas, Henrika } \}$ , $C = \{ \text { Dirk, Frans } \}$ . Find $n ( A \cup ( B \cap C ) )$ .
​ $n ( A \cup ( B \cap C ) ) =$ __________

Accepted Answer

The answer of Let \(A = \{ \text { Dirk,...

If 8 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes ?

Let S=\{ Apple, Dell, Gateway, Pomegranate, Compaq \} B=\{ Apple, Dell, Pomegranate, Compaq \} G=\{ Compaq \} Q=\{ Compaq \} Use a Venn diagram to determine the relationships among the sets.

List the elements in the set D, such that $D = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}$

Find how many outcomes are possible for the decision algorithms. Step 1 Step 2 Alternative 1: 1 outcome Alternative 1:1 outcome Alternative 2:1 outcome Alternative 2:1 outcome Alternative 3:2 outcomes

Find how many outcomes are possible for the decision algorithms. Step 1 Step 2 Alternative 1:1 outcome Alternative 1:2 outcomes Alternative 2: 1 outcome Alternative 2:2 outcomes Alternative 3:2 outcomes __________ outcomes

If $n ( A ) = 37$ , $n ( B ) = 25$ , and $n ( A \cap B ) = 5$ , find $n ( A \cup B )$ .

You are searching for Hip-hop music that is neither American nor Dutch. In set notation, for which subset of music files are you searching

Let A=\{ June, Justine, Solly, Polly \} B=\{ Justine, Polly, Jelly \} C=\{ Ruth, Justine, Polly \} Find the set $A \cup ( B \cup C )$ .

Let C=\{ red, green \} N=\{ circle, square \} List the elements of $C \times N$ as ordered pairs in a set notation.

Evaluate $\frac { 8 ! } { 7 ! }$ .

A surgical procedure requires choosing among three alternative methodologies. The first methodology can result in 7 possible outcomes, the second in 6 possible outcomes, and the third in 2 possible outcomes. What is the total number of outcomes possible ?

A computer "byte" consists of 8 "bits", each bit being either a 0 or a 1. If characters are represented using a code that uses 4 bytes for each character, how many characters can be represented ? __________ characters

Evaluate $P ( 7,5 )$ . $P ( 7,5 )$ __________

Use a Venn diagram or some other method to obtain a formula for $n ( A \cup B \cup C )$ in terms of $n ( A )$ , $n ( B )$ , $n ( C )$ , $n ( A \cap B )$ , $n ( A \cap C )$ , $n ( B \cap C )$ , and $n ( A \cap B \cap C )$ .

Let $A = \{ \text { Dirk, Tina, Frans, Marie } \}$ , $B = \{ \text { Frans, Marie, Tina, Klaas, Henrika } \}$ , $C = \{ \text { Dirk, Frans } \}$ . Find $n ( A \cup ( B \cap C ) )$ . $n ( A \cup ( B \cap C ) ) =$ __________

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 7: Sets and Counting

If 8 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes ?

Let S=\{ Apple, Dell, Gateway, Pomegranate, Compaq \} B=\{ Apple, Dell, Pomegranate, Compaq \} G=\{ Compaq \} Q=\{ Compaq \} Use a Venn diagram to determine the relationships among the sets.

List the elements in the set D, such that D={n∣n is a positive integer and 0<n<7}D = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}D={n∣n is a positive integer and 0<n<7}

Find how many outcomes are possible for the decision algorithms. Step 1 Step 2 Alternative 1: 1 outcome Alternative 1:1 outcome Alternative 2:1 outcome Alternative 2:1 outcome Alternative 3:2 outcomes

Find how many outcomes are possible for the decision algorithms. Step 1 Step 2 Alternative 1:1 outcome Alternative 1:2 outcomes Alternative 2: 1 outcome Alternative 2:2 outcomes Alternative 3:2 outcomes ​ __________ outcomes

If n(A)=37n ( A ) = 37n(A)=37 , n(B)=25n ( B ) = 25n(B)=25 , and n(A∩B)=5n ( A \cap B ) = 5n(A∩B)=5 , find n(A∪B)n ( A \cup B )n(A∪B) .

You are searching for Hip-hop music that is neither American nor Dutch. In set notation, for which subset of music files are you searching

Let A=\{ June, Justine, Solly, Polly \} B=\{ Justine, Polly, Jelly \} C=\{ Ruth, Justine, Polly \} Find the set A∪(B∪C)A \cup ( B \cup C )A∪(B∪C) .

Let C=\{ red, green \} N=\{ circle, square \} List the elements of C×NC \times NC×N as ordered pairs in a set notation.

Evaluate 8!7!\frac { 8 ! } { 7 ! }7!8!​ .

A surgical procedure requires choosing among three alternative methodologies. The first methodology can result in 7 possible outcomes, the second in 6 possible outcomes, and the third in 2 possible outcomes. What is the total number of outcomes possible ?

A computer "byte" consists of 8 "bits", each bit being either a 0 or a 1. If characters are represented using a code that uses 4 bytes for each character, how many characters can be represented ? __________ characters

Evaluate P(7,5)P ( 7,5 )P(7,5) . ​ P(7,5)P ( 7,5 )P(7,5) __________

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

List the elements in the set D, such that $D = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}$

Find how many outcomes are possible for the decision algorithms. Step 1 Step 2 Alternative 1:1 outcome Alternative 1:2 outcomes Alternative 2: 1 outcome Alternative 2:2 outcomes Alternative 3:2 outcomes __________ outcomes

If $n ( A ) = 37$ , $n ( B ) = 25$ , and $n ( A \cap B ) = 5$ , find $n ( A \cup B )$ .

Let A=\{ June, Justine, Solly, Polly \} B=\{ Justine, Polly, Jelly \} C=\{ Ruth, Justine, Polly \} Find the set $A \cup ( B \cup C )$ .

Let C=\{ red, green \} N=\{ circle, square \} List the elements of $C \times N$ as ordered pairs in a set notation.

Evaluate $\frac { 8 ! } { 7 ! }$ .

Evaluate $P ( 7,5 )$ . $P ( 7,5 )$ __________