guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{55}{100} \) = \( \frac{55 x 15}{100} \) = \( \frac{825}{100} \) = 8 shots

The center makes 50% 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 = \( \frac{8}{\frac{50}{100}} \) = 8 x \( \frac{100}{50} \) = \( \frac{8 x 100}{50} \) = \( \frac{800}{50} \) = 16 shots

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

Monica scored 80% on the test meaning she earned 80% of the possible points on the test. There were 140 possible points on the test so she earned 140 x 0.8 = 112 points. Each question is worth 2 points so she got \( \frac{112}{2} \) = 56 questions right.

The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{3 x 5}{6 x 5} \) + \( \frac{8 x 3}{10 x 3} \)

\( \frac{15}{30} \) + \( \frac{24}{30} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{15 + 24}{30} \) = \( \frac{39}{30} \) = 1\(\frac{3}{10}\)

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.