| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.93 |
| Score | 0% | 59% |
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 8 complete crews out on jobs?
| 13 | |
| 17 | |
| 8 | |
| 18 |
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. 8 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 8 x 2 = 16 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 16 - 8 = 8 new staff for the busy season.
What is \( 9 \)\( \sqrt{80} \) + \( 3 \)\( \sqrt{5} \)
| 12\( \sqrt{400} \) | |
| 27\( \sqrt{80} \) | |
| 12\( \sqrt{80} \) | |
| 39\( \sqrt{5} \) |
To add these radicals together their radicands must be the same:
9\( \sqrt{80} \) + 3\( \sqrt{5} \)
9\( \sqrt{16 \times 5} \) + 3\( \sqrt{5} \)
9\( \sqrt{4^2 \times 5} \) + 3\( \sqrt{5} \)
(9)(4)\( \sqrt{5} \) + 3\( \sqrt{5} \)
36\( \sqrt{5} \) + 3\( \sqrt{5} \)
Now that the radicands are identical, you can add them together:
36\( \sqrt{5} \) + 3\( \sqrt{5} \)A bread recipe calls for 3\(\frac{5}{8}\) cups of flour. If you only have 1\(\frac{1}{8}\) cups, how much more flour is needed?
| \(\frac{7}{8}\) cups | |
| 1\(\frac{1}{2}\) cups | |
| 2\(\frac{1}{2}\) cups | |
| 2\(\frac{1}{4}\) cups |
The amount of flour you need is (3\(\frac{5}{8}\) - 1\(\frac{1}{8}\)) cups. Rewrite the quantities so they share a common denominator and subtract:
(\( \frac{29}{8} \) - \( \frac{9}{8} \)) cups
\( \frac{20}{8} \) cups
2\(\frac{1}{2}\) cups
What is \( \frac{2}{8} \) ÷ \( \frac{4}{8} \)?
| 2 | |
| 4 | |
| \(\frac{1}{2}\) | |
| \(\frac{2}{5}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{8} \) ÷ \( \frac{4}{8} \) = \( \frac{2}{8} \) x \( \frac{8}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{8} \) x \( \frac{8}{4} \) = \( \frac{2 x 8}{8 x 4} \) = \( \frac{16}{32} \) = \(\frac{1}{2}\)
What is \( \frac{12\sqrt{63}}{6\sqrt{9}} \)?
| \(\frac{1}{7}\) \( \sqrt{2} \) | |
| \(\frac{1}{2}\) \( \sqrt{7} \) | |
| 2 \( \sqrt{7} \) | |
| 2 \( \sqrt{\frac{1}{7}} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{12\sqrt{63}}{6\sqrt{9}} \)
\( \frac{12}{6} \) \( \sqrt{\frac{63}{9}} \)
2 \( \sqrt{7} \)