Question 1

Determine which of the following paradoxes might result when using Jefferson’s apportionment method.

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None of the above

Question 2

The probability that an event A occurs given that event B has occurred is given by ____.

P ( A ) P ( B )

P ( A a n d B ) P ( B )

P ( B ) P ( A )

P ( A a n d B ) P ( A )

Question 3

If the probability of A and B occurring simultaneously is zero, then A and B are ____.

mutually exclusive events

dependent events

independent events

not mutually exclusive events

Question 4

Which of the following algorithms can you use to find an optimal Hamiltonian circuit in a complete graph?

Nearest Neighbor Algorithm

Repeated Nearest Neighbor Algorithm

Brute Force Algorithm

Sorted Edges Algorithm

Question 5

Find the expected number of boys for a two-child family assuming boys and girls are equally likely.

1

0

2

3

Question 6

If the probability of an event is 3/4, what is the probability of the complement of this event?

1/4

1/2

3/4

1/3

Question 7

There are 15 students in a classroom, nine girls and six boys. What is the probability of randomly selecting two girls?

5/13

12/35

3/4

2/9

Question 8

Which fairness criterion is violated in an election in which the choice that is preferred in every one-to-one comparison with the other choices, is not the winner?

Condorcet criterion

Monotonicity criterion

Majority criterion

Independence of Irrelevant Alternatives criterion

Question 9

Find the simple interest rate if you borrowed \$5,500 and agreed to pay \$5,678.75 after one year? Round to two decimal places.

3.25%

4.50%

3.45%

4.05%

Question 10

The odds of raining tomorrow are 3 to 7. What is the probability that it will rain tomorrow?

7/10

3/7

7/3

3/10

Question 11

Evaluate the permutation P(4,2).

32

24

6

12

Question 12

Given the following scatter plot, determine which of the statements is true.

These variables have perfect positive correlation.

There is a strong negative correlation between these variables.

There is no correlation between these variables.

There is a weak negative correlation between these variables.

Question 13

Find the mode of the following data: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

0

5

9

There is no mode

Question 14

The IQ scores of 30 students enrolled in a math class are as follows: 102, 86, 111, 97, 93, 104, 114, 116, 97, 108, 100, 111, 96, 100, 114, 118, 99, 95, 110, 113, 111, 112, 107, 97, 116, 105, 108, 95, 100, 111. Create a pie chart to represent this data.

Question 15

The following graph is a ____.

line graph

frequency chart

histogram

pie chart

Question 16

Determine which region or regions in the Venn diagram below represent A’ ∩ B.

I and IV

III

I

III and IV

Question 17

The set of all consonants in the English alphabet and the set C = {x | x is a consonant in the English alphabet} are ____.

not equivalent

similar

not equal

equal

Question 18

Determine which of the following statements is true about standard deviation.

It cannot be zero.

It is negative if all the data values are equal.

Has the same unit as the original data.

It is not influenced by outliers.

Question 19

To determine the number of four-digit pins with no repeated digits you need to use ____.

a combination

neither a permutation nor a combination

a permutation

Question 20

Ann earned a score of 1,700 on her SAT with a corresponding Z-score of 0.85. She would like to know what percentile she falls in among all SAT test-takers.

85%

75%

80%

70%

Question 21

A ____ is an arrangement in which no repetitions are allowed and the order matters.

permutation

combination

Question 225 pts

Determine which of the following statements about the following graph are true. Check all that apply.

There is a Euler circuit.

There is a Euler path.

There is no Euler circuit.

There is no Euler path.

Question 23

A set of data values is normally distributed with a mean of 50 and standard deviation of 10. Determine the Z-score of 55.

0.75

0.5

-0.75

-0.5

Question 24

Determine which of the following statements about the graph below is true.

Vertices A and E are adjacent.

Vertex E has degree 2.

Edge BE is not a bridge.

This is a disconnected graph.

Question 25

ACT scores closely follow the normal model with mean 20 and standard deviation 5. Use the 68-95-99.7 Rule to determine the percentage of test takers who will score between 10 and 30.

68%

99.7%

47.5%

95%

Question 26

Calculate the mean of the following data: 2, 6, 3, 8, 5.

5.0

4.7

5.1

4.8

Question 27

Evaluate the combination C(6, 3).

20

120

35

720

Question 28

How many five-digit numbers exist if a number starting with zero is not considered a five-digit number?

25,847

100,000

27,216

90,000

Question 29

If two events A and B are independent, then P(A and B) = _____.

P(A) – P(B)

P(A) + P(B)

P(A)/P(B)

P(A)*P(B)

Question 30

Determine which of the following statements is true about the normal distribution.

68% of the data is within one standard deviation of the mean.

95% of the data is within three standard deviations of the mean.

99.7% of the data is within two standard deviations of the mean.

75% of the data is within one standard deviation of the mean.

Question 31

The regression line that best fits the following data is Y = -0.65X + 7.68. Use the regression line to predict the value of Y when X = 3.

 X Y 2 7 1 8 6 5 3 4 4 4

4.00

2.43

4.55

5.73

Question 32

Use a tree diagram to determine how many different outfits a person with five t-shirts and two pairs of jeans can wear.

8

10

7

9

Question 33

The downtown business association is electing a new chairperson. There are four candidates: Brian, Natalia, Nick, and Rose. The preference schedule for the election is found below. Find the winner under the plurality method.

 2 votes 2 votes 6 votes 3 votes 4 votes 1st Choice Natalia Natalia Brian Nick Rose 2nd Choice Nick Rose Rose Brian Nick 3rd Choice Brian Brian Nick Natalia Brian 4th Choice Rose Nick Natalia Rose Natalia

Brian

Natalia

Nick

Rose

Question 34

Determine which of the following statement is false about Pearson correlation.

A value of -1 indicates a weak negative correlation.

A value of 0 indicates no linear relationship between the variables.

A value of 1 indicates a perfect positive correlation.

It ranges between -1 and 1.

Question 35

A combination is an arrangement in which repetitions are ____ and the order ____.

allowed; matters

not allowed; does not matter

allowed; does not matter

not allowed; matters

Question 36

Determine which of the following form the Five-Number summary.

First quartile, second quartile, mean, third quartile, fourth quartile

Minimum, first quartile, median, third quartile, maximum

Minimum, first quartile, mode, third quartile, maximum

Minimum, first quartile, mean, third quartile, maximum

Question 37

You can afford \$250 per month as a car payment. If you can get an auto loan at 3% interest for 60 months, how expensive of a car can you afford? Round to the nearest dollar.

\$14,247

\$14,382

\$13,956

\$13,913

Question 38

Represent in set-builder notation the set containing all vowels.

The set of all vowels

{vowels}

{x | x is a vowel}

{a, e, i, o, u}

Question 39

You deposit \$500 each month into a savings account earning 6% compounded monthly. How much will you have in the account in ten years? Round to the nearest dollar.

\$80,375

\$79,669

\$81,940

\$82,745

Question 40

Calculate the range of the following data: 4, 12, 3, 6, 17, 2, 19, 16, 13.

17

9

14

15

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