| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.21 |
| Score | 0% | 64% |
What is \( \sqrt{\frac{64}{49}} \)?
| \(\frac{2}{5}\) | |
| 1\(\frac{1}{7}\) | |
| \(\frac{3}{5}\) | |
| \(\frac{1}{3}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{64}{49}} \)
\( \frac{\sqrt{64}}{\sqrt{49}} \)
\( \frac{\sqrt{8^2}}{\sqrt{7^2}} \)
\( \frac{8}{7} \)
1\(\frac{1}{7}\)
Convert b-3 to remove the negative exponent.
| \( \frac{-3}{b} \) | |
| \( \frac{1}{b^3} \) | |
| \( \frac{-1}{b^{-3}} \) | |
| \( \frac{3}{b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If all of a roofing company's 10 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 10 complete crews out on jobs?
| 19 | |
| 4 | |
| 6 | |
| 10 |
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 10 workers at the company now and that's enough to staff 5 crews so there are \( \frac{10}{5} \) = 2 workers on a crew. 10 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 10 x 2 = 20 total workers to staff the crews during the busy season. The company already employs 10 workers so they need to add 20 - 10 = 10 new staff for the busy season.
On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 70% of his shots. If the guard takes 25 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?
| 29 | |
| 37 | |
| 34 | |
| 40 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{70}{100} \) = \( \frac{70 x 25}{100} \) = \( \frac{1750}{100} \) = 17 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 = \( \frac{17}{\frac{50}{100}} \) = 17 x \( \frac{100}{50} \) = \( \frac{17 x 100}{50} \) = \( \frac{1700}{50} \) = 34 shots
to make the same number of shots as the guard and thus score the same number of points.
If a car travels 100 miles in 4 hours, what is the average speed?
| 25 mph | |
| 30 mph | |
| 20 mph | |
| 60 mph |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)