| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.27 |
| Score | 0% | 65% |
4! = ?
5 x 4 x 3 x 2 x 1 |
|
4 x 3 |
|
4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
What is the greatest common factor of 56 and 56?
| 46 | |
| 20 | |
| 16 | |
| 56 |
The factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 8 factors [1, 2, 4, 7, 8, 14, 28, 56] making 56 the greatest factor 56 and 56 have in common.
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 15 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?
| 15 | |
| 25 | |
| 23 | |
| 20 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 15 x \( \frac{60}{100} \) = \( \frac{60 x 15}{100} \) = \( \frac{900}{100} \) = 9 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 = \( \frac{9}{\frac{40}{100}} \) = 9 x \( \frac{100}{40} \) = \( \frac{9 x 100}{40} \) = \( \frac{900}{40} \) = 23 shots
to make the same number of shots as the guard and thus score the same number of points.
If all of a roofing company's 6 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 14 | |
| 1 | |
| 4 | |
| 6 |
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 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 12 - 6 = 6 new staff for the busy season.
What is -4y5 + 3y5?
| 7y-5 | |
| -y5 | |
| -y-10 | |
| 7y5 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-4y5 + 3y5
(-4 + 3)y5
-y5