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.

Jennifer scored 74% on the test meaning she earned 74% of the possible points on the test. There were 270 possible points on the test so she earned 270 x 0.74 = 201 points. Each question is worth 3 points so she got \( \frac{201}{3} \) = 67 questions right.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-3x⁴ + 8x⁴
(-3 + 8)x⁴
5x⁴

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 30mph \times 1h \)
30 miles

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.

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

\( \frac{2 x 3}{4 x 3} \) - \( \frac{6 x 2}{6 x 2} \)

\( \frac{6}{12} \) - \( \frac{12}{12} \)

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

\( \frac{6 - 12}{12} \) = \( \frac{-6}{12} \) = -\(\frac{1}{2}\)