A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{4!} \)
\( \frac{2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4 \times 3} \)
\( \frac{1}{12} \)

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 30% 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 = \( \frac{4}{\frac{30}{100}} \) = 4 x \( \frac{100}{30} \) = \( \frac{4 x 100}{30} \) = \( \frac{400}{30} \) = 13 shots

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

1

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 $900
i = 0.01 x $900
i = $9

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{36}{49}} \)
\( \frac{\sqrt{36}}{\sqrt{49}} \)
\( \frac{\sqrt{6^2}}{\sqrt{7^2}} \)
\(\frac{6}{7}\)