| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.17 |
| Score | 0% | 63% |
What is the distance in miles of a trip that takes 2 hours at an average speed of 20 miles per hour?
| 520 miles | |
| 250 miles | |
| 270 miles | |
| 40 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 = \( 20mph \times 2h \)
40 miles
If all of a roofing company's 16 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 18 | |
| 9 | |
| 12 | |
| 17 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 7 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 7 x 4 = 28 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 28 - 16 = 12 new staff for the busy season.
Simplify \( \frac{40}{80} \).
| \( \frac{9}{13} \) | |
| \( \frac{1}{5} \) | |
| \( \frac{9}{11} \) | |
| \( \frac{1}{2} \) |
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 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 8 factors [1, 2, 4, 5, 8, 10, 20, 40] making 40 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{40}{80} \) = \( \frac{\frac{40}{40}}{\frac{80}{40}} \) = \( \frac{1}{2} \)
On average, the center for a basketball team hits 35% of his shots while a guard on the same team hits 40% 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?
| 19 | |
| 36 | |
| 16 | |
| 23 |
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 35% 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 = \( \frac{8}{\frac{35}{100}} \) = 8 x \( \frac{100}{35} \) = \( \frac{8 x 100}{35} \) = \( \frac{800}{35} \) = 23 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?
| 3:1 | |
| 1:8 | |
| 1:6 | |
| 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.