If 45% of the town's 27,000 voters cast ballots the number of votes cast is:

(\( \frac{45}{100} \)) x 27,000 = \( \frac{1,215,000}{100} \) = 12,150

The mayor got 80% of the votes cast which is:

(\( \frac{80}{100} \)) x 12,150 = \( \frac{972,000}{100} \) = 9,720 votes.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{45}{100} \) = \( \frac{45 x 10}{100} \) = \( \frac{450}{100} \) = 4 shots

The center makes 40% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{4}{\frac{40}{100}} \) = 4 x \( \frac{100}{40} \) = \( \frac{4 x 100}{40} \) = \( \frac{400}{40} \) = 10 shots

to make the same number of shots as the guard and thus score the same number of points.

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).

Latoya scored 80% on the test meaning she earned 80% of the possible points on the test. There were 60 possible points on the test so she earned 60 x 0.8 = 48 points. Each question is worth 2 points so she got \( \frac{48}{2} \) = 24 questions right.

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).