Question 1

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

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Group of answer choices

The Alabama paradox

The New States paradox

The Population paradox

None of the above

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

Group of answer choices

P ( A ) P ( B )

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

P ( B ) P ( A )

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

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

Group of answer choices

mutually exclusive events

dependent events

independent events

not mutually exclusive events

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

Group of answer choices

Nearest Neighbor Algorithm

Repeated Nearest Neighbor Algorithm

Brute Force Algorithm

Sorted Edges Algorithm

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

Group of answer choices

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?

Group of answer choices

1/4

1/2

3/4

1/3

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

Group of answer choices

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?

Group of answer choices

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.

Group of answer choices

3.25%

4.50%

3.45%

4.05%

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

Group of answer choices

7/10

3/7

7/3

3/10

Evaluate the permutation P(4,2).

Group of answer choices

32

24

6

12

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

Group of answer choices

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.

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

Group of answer choices

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.

Group of answer choices

The following graph is a ____.

Group of answer choices

line graph

frequency chart

histogram

pie chart

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

Group of answer choices

*I* and *IV*

*III*

*I*

*III* and *IV*

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

Group of answer choices

not equivalent

similar

not equal

equal

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

Group of answer choices

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.

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

Group of answer choices

a combination

neither a permutation nor a combination

a permutation

a two-part task

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.

Group of answer choices

85%

75%

80%

70%

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

Group of answer choices

permutation

one-part task

combination

multi-part task

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

Group of answer choices

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.

Group of answer choices

0.75

0.5

-0.75

-0.5

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

Group of answer choices

Vertices *A* and *E* are adjacent.

Vertex *E* has degree 2.

Edge *BE* is not a bridge.

This is a disconnected graph.

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.

Group of answer choices

68%

99.7%

47.5%

95%

**Question 26**

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

Group of answer choices

5.0

4.7

5.1

4.8

Evaluate the combination C(6, 3).

Group of answer choices

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?

Group of answer choices

25,847

100,000

27,216

90,000

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

Group of answer choices

*P*(*A*) – *P*(*B*)

*P*(*A*) + *P*(*B*)

*P*(*A*)/*P*(*B*)

*P*(*A*)**P*(*B*)

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

Group of answer choices

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.

The regression line that best fits the following data is *Y* = -0.65*X* + 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 |

Group of answer choices

4.00

2.43

4.55

5.73

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

Group of answer choices

8

10

7

9

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 | |

1^{st} Choice |
Natalia | Natalia | Brian | Nick | Rose |

2^{nd} Choice |
Nick | Rose | Rose | Brian | Nick |

3^{rd} Choice |
Brian | Brian | Nick | Natalia | Brian |

4^{th} Choice |
Rose | Nick | Natalia | Rose | Natalia |

Group of answer choices

Brian

Natalia

Nick

Rose

**Question 34**

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

Group of answer choices

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.

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

Group of answer choices

allowed; matters

not allowed; does not matter

allowed; does not matter

not allowed; matters

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

Group of answer choices

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

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.

Group of answer choices

$14,247

$14,382

$13,956

$13,913

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

Group of answer choices

The set of all vowels

{vowels}

{*x* | *x* is a vowel}

{a, e, i, o, u}

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.

Group of answer choices

$80,375

$79,669

$81,940

$82,745

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

Group of answer choices

17

9

14

15

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