| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.64 |
| Score | 0% | 73% |
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 30 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?
| 86 | |
| 31 | |
| 45 | |
| 55 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 30 x \( \frac{60}{100} \) = \( \frac{60 x 30}{100} \) = \( \frac{1800}{100} \) = 18 shots
The center makes 40% 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 = \( \frac{18}{\frac{40}{100}} \) = 18 x \( \frac{100}{40} \) = \( \frac{18 x 100}{40} \) = \( \frac{1800}{40} \) = 45 shots
to make the same number of shots as the guard and thus score the same number of points.
What is the greatest common factor of 44 and 36?
| 20 | |
| 36 | |
| 15 | |
| 4 |
The factors of 44 are [1, 2, 4, 11, 22, 44] and the factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36]. They share 3 factors [1, 2, 4] making 4 the greatest factor 44 and 36 have in common.
What is the distance in miles of a trip that takes 3 hours at an average speed of 75 miles per hour?
| 270 miles | |
| 150 miles | |
| 180 miles | |
| 225 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 75mph \times 3h \)
225 miles
What is the least common multiple of 4 and 8?
| 1 | |
| 5 | |
| 2 | |
| 8 |
The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 4 and 8 have in common.
How many hours does it take a car to travel 315 miles at an average speed of 35 miles per hour?
| 1 hour | |
| 9 hours | |
| 3 hours | |
| 7 hours |
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 = \( \frac{315mi}{35mph} \)
9 hours