Question 1

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

Accepted Answer

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

Question 2

List the elements in the set A, such that
? $A = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}$ .
?
Please separate your answers with comma(s).
? $n =$ { ___________ }

Accepted Answer

The answer of List the elements in the set A,...

Question 3

Your favorite restaurant offers a total of 16 desserts, of which 9 have ice cream as a main ingredient, and 10 have fruit as a main ingredient. Assuming that all of them have either ice cream or fruit or both as a main ingredient, how many have both  ?
__________ desserts have both.

Accepted Answer

The answer of Your favorite restaurant offers a total of...

Question 4

Let   $\begin{aligned}
C & = \{ \text { small, medium, large } \} \
D & = \{ \text { oblong square } \}
\end{aligned}$  
Represent the elements of $C \times D$ as cells in a spreadsheet.

Accepted Answer

A)  $\left\{ \begin{array} { c c } 
\text { (small, oblong) } & \text { (small, square) } \
\text { (medium, oblong) } & \text { (medium, square) } \
\text { (large, oblong) } & \text { (large, square) }
\end{array} \right\}$ 
B)    $\left\{ \begin{array} { c c } 
\text { (large, square) } & \text { (small, square) } \
\text { (medium, oblong) } & \text { (medium, square) } \
\text { (large, oblong) } & \text { (small, oblong) }
\end{array} \right\}$ 
C)  $\left\{ \begin{array} { c c } 
\text { (small, oblong) } & \text { (small, square) } \
\text { (medium, oblong) } & \text { (medium, square) } \
\text { (large, square) } & \text { (large, oblong) }
\end{array} \right\}$ 
D)  $\left\{ \begin{array} { c c } 
\text { (small, square) } & \text { (small, oblong) } \
\text { (medium, oblong) } & \text { (medium, square) } \
\text { (large, oblong) } & \text { (large, square) }
\end{array} \right\}$ 
E)  $\left\{ \begin{array} { c c } 
\text { (small, oblong) } & \text { (small, square) } \
\text { (medium, square) } & \text { (medium, oblong) } \
\text { (large, oblong) } & \text { (large, square) }
\end{array} \right\}$

Question 5

Some written languages, such as Chinese and Japanese, use tens of thousands of different characters. If a language uses 16,384 characters, a computer code for this language would have to use how many bits (1 or 0) per character

Accepted Answer

The answer of Some written languages, such as Chinese and...

Question 6

Dripping wet after your shower, you have clean forgotten the combination of your lock. It is one of those "standard" combination locks, which uses a three number combination with each number in the range 0 through 39. All you remember is that the second number is either 25 or 35, while the third number ends with a 4. In desperation, you decide to go through all possible combinations using the information you remember. Assuming that it takes about 10 seconds to try each combination, what is the longest possible time you may have to stand dripping in front of your locker   
Assume that 4 does not end with a 4 .

Accepted Answer

A) 240 minutes 
B)  39 minutes 
C)  53 minutes 
D)  8 minutes 
E)  40 minutes

Question 7

The World Almanac features a "perpetual calendar", a collection of 14 possible calendars. Why does this suffice to be sure there is a calendar for every conceivable year

Accepted Answer

The answer of The World Almanac features a "perpetual calendar",...

Question 8

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations).
​
__________ hands

Accepted Answer

The answer of A poker hand consists of five cards...

Question 9

Dripping wet after your shower, you have clean forgotten the combination of your lock. It is one of those "standard" combination locks, which uses a three-number combination with each number in the range 0 through 39. All you remember is that the second number is either 27 or 37, while the third number ends in a 4. In desperation, you decide to go through all possible combinations using the information you remember. Assuming that it takes about 10 seconds to try each combination, what is the longest possible time you may have to stand dripping in front of your locker  ?
Assume that 4 does not end with a 4 .
 
__________ minutes

Accepted Answer

The answer of Dripping wet after your shower, you have...

Question 10

An experiment requires a sequence of three steps. The first step can result in 5 possible outcomes, the second in 2 possible outcomes, and the third in 3 possible outcomes. What is the total number of outcomes possible

Accepted Answer

The answer of An experiment requires a sequence of three...

Question 11

Professor Oger must choose between an extra writing assignment and an extra reading assignment for the upcoming spring break. For the writing assignment, there are 4 essay topics to choose from and three different mandatory lengths (30 pages, 35 pages, or 40 pages). The reading topic would consist of one scholarly biography combined with one volume of essays. There are 5 biographies and two volumes of essays to choose from. How many choices does she have  ?

Accepted Answer

A) 49 choices 
B)  84 choices 
C)  19 choices 
D)  22 choices 
E)  70 choices

Question 12

Use the given information to complete the solution of the partially solved Venn diagram.
​ $n ( A ) = 25$ , $n ( B ) = 14$ , $n ( C ) = 25$ , and $n ( S ) = 54$ ​
​  ​
​ $n ( d ) =$ __________
​ $n ( f ) =$ __________
​ $n ( g ) =$ __________
​ $n ( h ) =$ __________

Accepted Answer

The answer of Use the given information to complete the...

Question 13

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

Accepted Answer

A)  $\text { Hip-hop  (American UCanadian) }$ 
B)   $\text { Hip-hop  (AmericanU Canadian) }$ 
C)    $\text { Hip-hop  (American  Canadian) }$ 
D)    $\text { Hip-hopU(American  Canadian)' }$ 
E)    $\text { Hip-hopU(AmericanUCanadian) }$

Question 14

A surgical procedure requires four steps. The first step can result in 6 possible outcomes, the second in 4 possible outcomes, and the remaining two can each result in 3 possible outcomes. What is the total number of outcomes possible

Accepted Answer

The answer of A surgical procedure requires four steps. The...

Question 15

While selecting candy for students in his class, Professor Murphy must choose between gummy candy and licorice nibs. Gummy candy packets come in 3 sizes, and packets of licorice nibs come in 3 sizes. If he chooses gummy candy, he must select gummy kangaroos, gummy lions, gummy bears, gummy worms or gummy dinos. If he chooses licorice nibs, he must choose between red and black. How many choices does he have  ?

Accepted Answer

A) 14 
B)  17 
C)  19 
D)  21 
E)  24

Question 16

Let A be the set of outcomes when two distinguishable dice are rolled, let E be the subset of outcomes in which at least one die shows an even number.
​
List the elements of E'.
​ $E ^ { \prime } =$ __________

Accepted Answer

The answer of Let A be the set of outcomes...

Question 17

If $A = \{ \text { Dirk, Johan, Henrika, Sarie } \}$ and $C = \{ \text { Hans, Henrika } \}$ ,  
Then $n ( A \cup C ) = n ( A ) + n ( C ) - n ( A \cap C )$ .

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

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

Question 19

A surgical procedure requires choosing among three alternative methodologies. The first methodology can result in 5 possible outcomes, the second in 4 possible outcomes, and the third in 3 possible outcomes. What is the total number of outcomes possible

Accepted Answer

The answer of A surgical procedure requires choosing among three...

Question 20

While selecting candy for students in his class, Professor Murphy must choose between gummy candy and licorice nibs. Gummy candy packets come in 4 sizes, and packets of licorice nibs come in 2 sizes.
If he chooses gummy candy, he must select gummy lions, gummy bears, gummy worms or gummy dinos. If he chooses licorice nibs, he must choose between red and black. How many choices does he have

Accepted Answer

The answer of While selecting candy for students in his...

Exam 7: Sets and Counting

List the elements in the set A, such that ? $A = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}$ . ? Please separate your answers with comma(s). ? $n =$ { ___________ }

Your favorite restaurant offers a total of 16 desserts, of which 9 have ice cream as a main ingredient, and 10 have fruit as a main ingredient. Assuming that all of them have either ice cream or fruit or both as a main ingredient, how many have both ? __________ desserts have both.

Let $\begin{aligned}C & = \{ \text { small, medium, large } \} \\D & = \{ \text { oblong square } \}\end{aligned}$ Represent the elements of $C \times D$ as cells in a spreadsheet.

Some written languages, such as Chinese and Japanese, use tens of thousands of different characters. If a language uses 16,384 characters, a computer code for this language would have to use how many bits (1 or 0) per character

The World Almanac features a "perpetual calendar", a collection of 14 possible calendars. Why does this suffice to be sure there is a calendar for every conceivable year

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations). __________ hands

An experiment requires a sequence of three steps. The first step can result in 5 possible outcomes, the second in 2 possible outcomes, and the third in 3 possible outcomes. What is the total number of outcomes possible

Use the given information to complete the solution of the partially solved Venn diagram. $n ( A ) = 25$ , $n ( B ) = 14$ , $n ( C ) = 25$ , and $n ( S ) = 54$ $n ( d ) =$ $n ( f ) =$ $n ( g ) =$ $n ( h ) =$

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

A surgical procedure requires four steps. The first step can result in 6 possible outcomes, the second in 4 possible outcomes, and the remaining two can each result in 3 possible outcomes. What is the total number of outcomes possible

Let A be the set of outcomes when two distinguishable dice are rolled, let E be the subset of outcomes in which at least one die shows an even number. List the elements of E'. $E ^ { \prime } =$ __________

If $A = \{ \text { Dirk, Johan, Henrika, Sarie } \}$ and $C = \{ \text { Hans, Henrika } \}$ , Then $n ( A \cup C ) = n ( A ) + n ( C ) - n ( A \cap C )$ .

A surgical procedure requires choosing among three alternative methodologies. The first methodology can result in 5 possible outcomes, the second in 4 possible outcomes, and the third in 3 possible outcomes. What is the total number of outcomes possible

Exam 7: Sets and Counting

List the elements in the set A, such that ? A={n∣n is a positive integer and 0<n<7}A = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}A={n∣n is a positive integer and 0<n<7} . ? Please separate your answers with comma(s). ? n=n =n= { ___________ }

Your favorite restaurant offers a total of 16 desserts, of which 9 have ice cream as a main ingredient, and 10 have fruit as a main ingredient. Assuming that all of them have either ice cream or fruit or both as a main ingredient, how many have both ? __________ desserts have both.

Let C={ small, medium, large }D={ oblong square }\begin{aligned}C & = \{ \text { small, medium, large } \} \\D & = \{ \text { oblong square } \}\end{aligned}CD​={ small, medium, large }={ oblong square }​ Represent the elements of C×DC \times DC×D as cells in a spreadsheet.

Some written languages, such as Chinese and Japanese, use tens of thousands of different characters. If a language uses 16,384 characters, a computer code for this language would have to use how many bits (1 or 0) per character

The World Almanac features a "perpetual calendar", a collection of 14 possible calendars. Why does this suffice to be sure there is a calendar for every conceivable year

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations). ​ __________ hands

An experiment requires a sequence of three steps. The first step can result in 5 possible outcomes, the second in 2 possible outcomes, and the third in 3 possible outcomes. What is the total number of outcomes possible

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

A surgical procedure requires four steps. The first step can result in 6 possible outcomes, the second in 4 possible outcomes, and the remaining two can each result in 3 possible outcomes. What is the total number of outcomes possible

Let A be the set of outcomes when two distinguishable dice are rolled, let E be the subset of outcomes in which at least one die shows an even number. ​ List the elements of E'. ​ E′=E ^ { \prime } =E′= __________

A surgical procedure requires choosing among three alternative methodologies. The first methodology can result in 5 possible outcomes, the second in 4 possible outcomes, and the third in 3 possible outcomes. What is the total number of outcomes possible

List the elements in the set A, such that ? $A = \{ n \mid n \text { is a positive integer and } 0 < n < 7 \}$ . ? Please separate your answers with comma(s). ? $n =$ { ___________ }

Let $\begin{aligned}C & = \{ \text { small, medium, large } \} \\D & = \{ \text { oblong square } \}\end{aligned}$ Represent the elements of $C \times D$ as cells in a spreadsheet.

A poker hand consists of five cards from a standard deck of 52. Find the number of different poker hands of two of a kind (two of one denomination and three of different denominations). __________ hands

Let A be the set of outcomes when two distinguishable dice are rolled, let E be the subset of outcomes in which at least one die shows an even number. List the elements of E'. $E ^ { \prime } =$ __________