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 $500
i = 0.02 x $500
i = $10

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{50}{100} \) = \( \frac{50 x 15}{100} \) = \( \frac{750}{100} \) = 7 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 = \( \frac{7}{\frac{40}{100}} \) = 7 x \( \frac{100}{40} \) = \( \frac{7 x 100}{40} \) = \( \frac{700}{40} \) = 18 shots

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

First, solve for \( \left|z - 1\right| \):

\( \left|z - 1\right| \) + 6 = -4
\( \left|z - 1\right| \) = -4 - 6
\( \left|z - 1\right| \) = -10

The value inside the absolute value brackets can be either positive or negative so (z - 1) must equal - 10 or --10 for \( \left|z - 1\right| \) to equal -10:

So, z = 11 or z = -9.

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

\( \frac{1}{9} \) ÷ \( \frac{4}{7} \) = \( \frac{1}{9} \) x \( \frac{7}{4} \)

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

\( \frac{1}{9} \) x \( \frac{7}{4} \) = \( \frac{1 x 7}{9 x 4} \) = \( \frac{7}{36} \) = \(\frac{7}{36}\)

The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 have in common.