| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.25 |
| Score | 0% | 65% |
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 9 complete crews out on jobs?
| 19 | |
| 14 | |
| 12 | |
| 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 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. 9 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 9 x 2 = 18 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 18 - 8 = 10 new staff for the busy season.
Solve for \( \frac{2!}{5!} \)
| 336 | |
| 3024 | |
| \( \frac{1}{60} \) | |
| \( \frac{1}{15120} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{2!}{5!} \)
\( \frac{2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4 \times 3} \)
\( \frac{1}{60} \)
Find the average of the following numbers: 14, 6, 11, 9.
| 7 | |
| 10 | |
| 9 | |
| 12 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{14 + 6 + 11 + 9}{4} \) = \( \frac{40}{4} \) = 10
What is \( \frac{3}{9} \) + \( \frac{5}{15} \)?
| \( \frac{9}{12} \) | |
| \(\frac{2}{3}\) | |
| \( \frac{1}{6} \) | |
| 1 \( \frac{1}{45} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{3 x 5}{9 x 5} \) + \( \frac{5 x 3}{15 x 3} \)
\( \frac{15}{45} \) + \( \frac{15}{45} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{15 + 15}{45} \) = \( \frac{30}{45} \) = \(\frac{2}{3}\)
What is 7y3 - 4y3?
| 3y3 | |
| -3y-3 | |
| 11y6 | |
| -3y3 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
7y3 - 4y3
(7 - 4)y3
3y3