| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
On average, the center for a basketball team hits 45% of his shots while a guard on the same team hits 55% of his shots. If the guard takes 20 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 21 | |
| 19 | |
| 42 | |
| 24 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{55}{100} \) = \( \frac{55 x 20}{100} \) = \( \frac{1100}{100} \) = 11 shots
The center makes 45% 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 = \( \frac{11}{\frac{45}{100}} \) = 11 x \( \frac{100}{45} \) = \( \frac{11 x 100}{45} \) = \( \frac{1100}{45} \) = 24 shots
to make the same number of shots as the guard and thus score the same number of points.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 5:4 | |
| 1:8 | |
| 3:6 | |
| 49:2 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
How many hours does it take a car to travel 385 miles at an average speed of 55 miles per hour?
| 7 hours | |
| 8 hours | |
| 6 hours | |
| 1 hour |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{385mi}{55mph} \)
7 hours
What is the least common multiple of 6 and 14?
| 3 | |
| 46 | |
| 72 | |
| 42 |
The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 have in common.
What is \( \frac{3}{2} \) - \( \frac{8}{10} \)?
| 2 \( \frac{1}{8} \) | |
| 1 \( \frac{5}{10} \) | |
| 2 \( \frac{7}{12} \) | |
| \(\frac{7}{10}\) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 5}{2 x 5} \) - \( \frac{8 x 1}{10 x 1} \)
\( \frac{15}{10} \) - \( \frac{8}{10} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{15 - 8}{10} \) = \( \frac{7}{10} \) = \(\frac{7}{10}\)