guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{45}{100} \) = \( \frac{45 x 15}{100} \) = \( \frac{675}{100} \) = 6 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 = \( \frac{6}{\frac{40}{100}} \) = 6 x \( \frac{100}{40} \) = \( \frac{6 x 100}{40} \) = \( \frac{600}{40} \) = 15 shots

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

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:

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

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

8b⁵ x 7b³
(8 x 7)b^{(5 + 3)}
56b⁸

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

56% of the water consumption is industrial use and 33% is personal use so (56% - 33%) = 23% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{23}{100} \) x 30,000 gallons = 6,900 gallons.