| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.76 |
| Score | 0% | 55% |
Simplify \( \sqrt{80} \)
| 5\( \sqrt{10} \) | |
| 2\( \sqrt{5} \) | |
| 9\( \sqrt{5} \) | |
| 4\( \sqrt{5} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{80} \)
\( \sqrt{16 \times 5} \)
\( \sqrt{4^2 \times 5} \)
4\( \sqrt{5} \)
Find the average of the following numbers: 8, 4, 10, 2.
| 6 | |
| 4 | |
| 11 | |
| 7 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{8 + 4 + 10 + 2}{4} \) = \( \frac{24}{4} \) = 6
If all of a roofing company's 8 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 12 | |
| 15 | |
| 6 | |
| 8 |
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 8 workers at the company now and that's enough to staff 4 crews so there are \( \frac{8}{4} \) = 2 workers on a crew. 8 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 8 x 2 = 16 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 16 - 8 = 8 new staff for the busy season.
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 12 small cakes per hour. The kitchen is available for 2 hours and 38 large cakes and 500 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 13 | |
| 12 | |
| 31 | |
| 11 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 2 x 2 = 4 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{4} \) = 9\(\frac{1}{2}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 12 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 12 x 2 = 24 small cakes during that time. 500 small cakes are needed for the party so \( \frac{500}{24} \) = 20\(\frac{5}{6}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 10 + 21 = 31 cooks.
On average, the center for a basketball team hits 30% of his shots while a guard on the same team hits 35% 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?
| 27 | |
| 19 | |
| 40 | |
| 15 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{35}{100} \) = \( \frac{35 x 25}{100} \) = \( \frac{875}{100} \) = 8 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 = \( \frac{8}{\frac{30}{100}} \) = 8 x \( \frac{100}{30} \) = \( \frac{8 x 100}{30} \) = \( \frac{800}{30} \) = 27 shots
to make the same number of shots as the guard and thus score the same number of points.