| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
If all of a roofing company's 12 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?
| 14 | |
| 19 | |
| 9 | |
| 12 |
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 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 24 - 12 = 12 new staff for the busy season.
Simplify \( \sqrt{48} \)
| 4\( \sqrt{3} \) | |
| 7\( \sqrt{3} \) | |
| 2\( \sqrt{3} \) | |
| 2\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)
What is \( \frac{14\sqrt{18}}{7\sqrt{9}} \)?
| 2 \( \sqrt{\frac{1}{2}} \) | |
| \(\frac{1}{2}\) \( \sqrt{\frac{1}{2}} \) | |
| 2 \( \sqrt{2} \) | |
| \(\frac{1}{2}\) \( \sqrt{2} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{14\sqrt{18}}{7\sqrt{9}} \)
\( \frac{14}{7} \) \( \sqrt{\frac{18}{9}} \)
2 \( \sqrt{2} \)
The total water usage for a city is 20,000 gallons each day. Of that total, 12% is for personal use and 41% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,400 | |
| 8,100 | |
| 5,800 | |
| 3,300 |
41% of the water consumption is industrial use and 12% is personal use so (41% - 12%) = 29% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{29}{100} \) x 20,000 gallons = 5,800 gallons.
A factor is a positive __________ that divides evenly into a given number.
integer |
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mixed number |
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improper fraction |
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fraction |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.