| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.92 |
| Score | 0% | 58% |
If all of a roofing company's 4 workers are required to staff 2 roofing crews, how many workers need to be added during the busy season in order to send 4 complete crews out on jobs?
| 4 | |
| 15 | |
| 16 | |
| 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 4 workers at the company now and that's enough to staff 2 crews so there are \( \frac{4}{2} \) = 2 workers on a crew. 4 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 4 x 2 = 8 total workers to staff the crews during the busy season. The company already employs 4 workers so they need to add 8 - 4 = 4 new staff for the busy season.
What is the least common multiple of 2 and 10?
| 8 | |
| 7 | |
| 16 | |
| 10 |
The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 have in common.
What is \( \frac{49\sqrt{25}}{7\sqrt{5}} \)?
| 7 \( \sqrt{5} \) | |
| 5 \( \sqrt{7} \) | |
| 5 \( \sqrt{\frac{1}{7}} \) | |
| \(\frac{1}{7}\) \( \sqrt{5} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{49\sqrt{25}}{7\sqrt{5}} \)
\( \frac{49}{7} \) \( \sqrt{\frac{25}{5}} \)
7 \( \sqrt{5} \)
What is \( 5 \)\( \sqrt{20} \) - \( 6 \)\( \sqrt{5} \)
| 4\( \sqrt{5} \) | |
| -1\( \sqrt{5} \) | |
| 30\( \sqrt{100} \) | |
| -1\( \sqrt{4} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{20} \) - 6\( \sqrt{5} \)
5\( \sqrt{4 \times 5} \) - 6\( \sqrt{5} \)
5\( \sqrt{2^2 \times 5} \) - 6\( \sqrt{5} \)
(5)(2)\( \sqrt{5} \) - 6\( \sqrt{5} \)
10\( \sqrt{5} \) - 6\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
10\( \sqrt{5} \) - 6\( \sqrt{5} \)The __________ is the smallest positive integer that is a multiple of two or more integers.
greatest common factor |
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least common factor |
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least common multiple |
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absolute value |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.