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.

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 $1,000
i = 0.01 x $1,000
i = $10

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-6y⁵ + 4y⁵
(-6 + 4)y⁵
-2y⁵

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{35}{100} \) = \( \frac{35 x 25}{100} \) = \( \frac{875}{100} \) = 8 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 = \( \frac{8}{\frac{30}{100}} \) = 8 x \( \frac{100}{30} \) = \( \frac{8 x 100}{30} \) = \( \frac{800}{30} \) = 27 shots

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

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

39,000 fans x \( \frac{3}{4} \) = \( \frac{117000}{4} \) = 29,250 fans.