| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.69 |
| Score | 0% | 54% |
If all of a roofing company's 8 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 1 | |
| 16 | |
| 53 | |
| 15 |
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 2 crews so there are \( \frac{8}{2} \) = 4 workers on a crew. 6 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 6 x 4 = 24 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 24 - 8 = 16 new staff for the busy season.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 5:1 | |
| 81:2 | |
| 3:2 | |
| 3:1 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. 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 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.
Simplify \( \sqrt{45} \)
| 4\( \sqrt{10} \) | |
| 6\( \sqrt{10} \) | |
| 3\( \sqrt{5} \) | |
| 4\( \sqrt{5} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{45} \)
\( \sqrt{9 \times 5} \)
\( \sqrt{3^2 \times 5} \)
3\( \sqrt{5} \)
What is \( 2 \)\( \sqrt{18} \) - \( 8 \)\( \sqrt{2} \)
| -2\( \sqrt{2} \) | |
| -6\( \sqrt{2} \) | |
| 16\( \sqrt{9} \) | |
| 16\( \sqrt{18} \) |
To subtract these radicals together their radicands must be the same:
2\( \sqrt{18} \) - 8\( \sqrt{2} \)
2\( \sqrt{9 \times 2} \) - 8\( \sqrt{2} \)
2\( \sqrt{3^2 \times 2} \) - 8\( \sqrt{2} \)
(2)(3)\( \sqrt{2} \) - 8\( \sqrt{2} \)
6\( \sqrt{2} \) - 8\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
6\( \sqrt{2} \) - 8\( \sqrt{2} \)What is \( \frac{7}{6} \) + \( \frac{7}{10} \)?
| 2 \( \frac{1}{30} \) | |
| 2 \( \frac{2}{30} \) | |
| 1\(\frac{13}{15}\) | |
| \( \frac{8}{30} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 5}{6 x 5} \) + \( \frac{7 x 3}{10 x 3} \)
\( \frac{35}{30} \) + \( \frac{21}{30} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 21}{30} \) = \( \frac{56}{30} \) = 1\(\frac{13}{15}\)