April scored 80% on the test meaning she earned 80% of the possible points on the test. There were 120 possible points on the test so she earned 120 x 0.8 = 96 points. Each question is worth 4 points so she got \( \frac{96}{4} \) = 24 questions right.

The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [24, 48, 72, 96] making 24 the smallest multiple 8 and 12 have in common.

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 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.

To multiply terms with radicals, multiply the coefficients and radicands separately:

5\( \sqrt{3} \) x 2\( \sqrt{5} \)
(5 x 2)\( \sqrt{3 \times 5} \)
10\( \sqrt{15} \)

To simplify this fraction, first find the greatest common factor between them. The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{40}{60} \) = \( \frac{\frac{40}{20}}{\frac{60}{20}} \) = \( \frac{2}{3} \)