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:

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

By buying two shirts, Frank will save $45 x \( \frac{50}{100} \) = \( \frac{$45 x 50}{100} \) = \( \frac{$2250}{100} \) = $22.50 on the second shirt.

So, his total cost will be
$45.00 + ($45.00 - $22.50)
$45.00 + $22.50
$67.50

To add these radicals together their radicands must be the same:

8\( \sqrt{48} \) + 9\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) + 9\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) + 9\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) + 9\( \sqrt{3} \)
32\( \sqrt{3} \) + 9\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{35}{100} \) = \( \frac{35 x 30}{100} \) = \( \frac{1050}{100} \) = 10 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 = \( \frac{10}{\frac{30}{100}} \) = 10 x \( \frac{100}{30} \) = \( \frac{10 x 100}{30} \) = \( \frac{1000}{30} \) = 33 shots

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

The amount of flour you need is (2 - 1\(\frac{3}{4}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{16}{8} \) - \( \frac{14}{8} \)) cups
\( \frac{2}{8} \) cups
\(\frac{1}{4}\) cups