guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{65}{100} \) = \( \frac{65 x 30}{100} \) = \( \frac{1950}{100} \) = 19 shots

The center makes 50% 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 = \( \frac{19}{\frac{50}{100}} \) = 19 x \( \frac{100}{50} \) = \( \frac{19 x 100}{50} \) = \( \frac{1900}{50} \) = 38 shots

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

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 $1,400
i = 0.03 x $1,400

No payments were made so the total amount due is the original amount + the accumulated interest:

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:

\( \frac{4!}{5!} \)
\( \frac{4 \times 3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5} \)
\( \frac{1}{5} \)

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{7}{100} \) x 6 = \( \frac{7 \times 6}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour

So, in an average hour, the machine will produce 6 - 0.42 = 5.58 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 5.58 = 83.7 error free parts were produced yesterday.

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

\( \frac{4}{6} \) x \( \frac{2}{6} \) = \( \frac{4 x 2}{6 x 6} \) = \( \frac{8}{36} \) = \(\frac{2}{9}\)