The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,200
i = 0.08 x $1,200
i = $96

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{15 + 9 + 15 + 9}{4} \) = \( \frac{48}{4} \) = 12

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{45}{100} \) = \( \frac{45 x 20}{100} \) = \( \frac{900}{100} \) = 9 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 = \( \frac{9}{\frac{40}{100}} \) = 9 x \( \frac{100}{40} \) = \( \frac{9 x 100}{40} \) = \( \frac{900}{40} \) = 23 shots

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

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{6} \) ÷ \( \frac{2}{7} \) = \( \frac{2}{6} \) x \( \frac{7}{2} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{6} \) x \( \frac{7}{2} \) = \( \frac{2 x 7}{6 x 2} \) = \( \frac{14}{12} \) = 1\(\frac{1}{6}\)