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:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{45}{100} \) = \( \frac{45 x 20}{100} \) = \( \frac{900}{100} \) = 9 shots

The center makes 25% 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 = \( \frac{9}{\frac{25}{100}} \) = 9 x \( \frac{100}{25} \) = \( \frac{9 x 100}{25} \) = \( \frac{900}{25} \) = 36 shots

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

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

If the tiger has consumed 70 pounds of food in 10 days that's \( \frac{70}{10} \) = 7 pounds of food per day. The tiger needs to consume 105 - 70 = 35 more pounds of food to reach 105 pounds total. At 7 pounds of food per day that's \( \frac{35}{7} \) = 5 more days.