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Graph

The above graph represents the results of a general election for two seats on the city council of Wilson City. Frankllin and Hall are Democrats; Johns and Lamont are Republicans; Carson is an independent.

4,987 people voted for Republicans. Which of the following is the best estimate of the number of people who voted in the election overall?

Explanation

The two wedges that represent the Republican candidates - purple (Johns) and blue (Lamont) - make up about 40% of the circle. The problem becomes, essentially, to figure out what 4,987 is 40% of. This can be done by dividing 4,987 by 0.40:

$4,987 \div 0.40 \approx 12,498$

12,500 is the best estimate.

What is the area of a right triangle if the hypotenuse is 10, and one of the side lengths is 6?

Explanation

To determine the other side length, we will need to use the Pythagorean Theorem.

Substitute the hypotenuse and the known side length as either or .

Subtract 36 from both sides and reduce.

Square root both sides and reduce.

The length and width of the triangle are now known.

Write the formula for the area of a triangle.

$A=\frac{1}{2}bh$

Substitute the dimensions.

$A=\frac{1}{2}(8)(6) = 24$

The answer is .

Determine the area of a circle with an diameter of .

$100\pi$

$400\pi$

$200\pi$

$1600\pi$

$800\pi$

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$A=\pi (10)^2 = 100\pi$

The answer is: $100\pi$

Pie_graph

Do NOT use a calculator for this question.

Refer to the above circle graph.

The top two finishers engage in a runoff election.

The third-place finisher tells his voters to choose the second-place finisher. The fourth- and fifth-place finishers tell their voters to choose the first-place finisher.

If each voter who selected one of the top two finishers stays with his choice, and every other voter does what is requested of him by his original chosen candidate, who will win the election?

Williams

Vickers

Zimmerman

Ullman

Explanation

In one group will be those who voted for first-place finisher Zimmerman, fourth-place finisher Ullman, and fifth-place finisher Young. These people will vote for Zimmerman.

In the second group will be those who voted for second-place finisher Williams and third-place finisher Vickers. These people will vote for Williams.

The pieces of the circle representing Vickers and Williams together make up more than half the circle. Therefore, Williams will win the runoff.

Find the area of a square with a side of .

Explanation

Write the formula for the area of a square.

Substitute the side.

The answer is:

A hexagon has a perimeter of 126in. Find the length of one side.

$21\text{in}$

$20\text{in}$

$18\text{in}$

$22\text{in}$

$9\text{in}$

Explanation

A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:

where a is the length of any side. Now, to find the length of one side, we will solve for a.

We know the perimeter of the hexagon is 126in. So, we will substitute and solve for a. We get

$126\text{in} = 6a$

$\frac{126\text{in}}{6} = \frac{6a}{6}$

$21\text{in} = a$

$a = 21\text{in}$

Therefore, the length of one side of the hexagon is 21in.

Find the area of a circle with a diameter of $5\pi$ .

$\frac{25}{4}\pi^3$

$\frac{25}{4}\pi^2$

$\frac{25}{2}\pi^3$

$\frac{25}{2}\pi^2$

$\textup{The answer is not given.}$

Explanation

Write the area of a circle.

$A=\pi r^2$

The radius is half the diameter.

$r= \frac{d}{2} = \frac{5\pi}{2}$

Substitute the radius into the equation.

$A=\pi (\frac{5\pi}{2})^2=\pi (\frac{5\pi}{2})(\frac{5\pi}{2})$

The answer is: $\frac{25}{4}\pi^3$

Give the expanded form of the following scientific notation.

Explanation

Give the expanded form of the following scientific notation.

To expand this, we need to move the decimal point. Because our exponent is positive, we will be moving it 7 spaces to the right.

In order to do so, we need to add a couple zeros

$7.9881*10^7\rightarrow 7.9881000*10^7\rightarrow79,881,000$

So, our answer is

Suppose two angles are complementary. If one angle measurement is 52 degrees, what is the other angle?

Explanation

Complementary angles sum up to 90 degrees.

Subtract the known angle from 90.

The answer is:

Given the data set $\left \{ 2, 3, 5, 6, 6, 6, 7, 7\right \}$ , which of the following quantities are equal to each other/one another?

I: The mean

II: The median

III: The mode

II and III only

I and II only

I and III only

I, II, and III

Explanation

Since this data set is arranged in ascending order and has an even number of elements, the median of the data set is the arithmetic mean of its middle two elements. Both elements are 6, so this is the median.

6 is the mode, since it occurs most frequently.

The mean is the sum of the elements divided by the number of elements, which is 8:

$\frac{2+3+ 5 + 6 + 6 + 6 + 7 +7}{8} =\frac{42}{8 } = 5.25$

The median and the mode are equal to each other, but not to the mean, so the correct answer is "II and III only".

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