guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{45}{100} \) = \( \frac{45 x 30}{100} \) = \( \frac{1350}{100} \) = 13 shots

The center makes 35% 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 = \( \frac{13}{\frac{35}{100}} \) = 13 x \( \frac{100}{35} \) = \( \frac{13 x 100}{35} \) = \( \frac{1300}{35} \) = 37 shots

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

The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 6 and 8 have in common.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

4y⁷ x 7y⁶
(4 x 7)y^{(7 + 6)}
28y¹³

If 46% of the town's 12,000 voters cast ballots the number of votes cast is:

(\( \frac{46}{100} \)) x 12,000 = \( \frac{552,000}{100} \) = 5,520

The mayor got 68% of the votes cast which is:

(\( \frac{68}{100} \)) x 5,520 = \( \frac{375,360}{100} \) = 3,754 votes.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).