A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

First, solve for \( \left|b + 7\right| \):

\( \left|b + 7\right| \) - 8 = 7
\( \left|b + 7\right| \) = 7 + 8
\( \left|b + 7\right| \) = 15

The value inside the absolute value brackets can be either positive or negative so (b + 7) must equal + 15 or -15 for \( \left|b + 7\right| \) to equal 15:

So, b = -22 or b = 8.

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{40}{100} \) = \( \frac{40 x 20}{100} \) = \( \frac{800}{100} \) = 8 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 = \( \frac{8}{\frac{35}{100}} \) = 8 x \( \frac{100}{35} \) = \( \frac{8 x 100}{35} \) = \( \frac{800}{35} \) = 23 shots

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

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