| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.41 |
| Score | 0% | 68% |
What is \( \frac{16\sqrt{21}}{8\sqrt{7}} \)?
| 2 \( \sqrt{\frac{1}{3}} \) | |
| \(\frac{1}{3}\) \( \sqrt{2} \) | |
| 3 \( \sqrt{2} \) | |
| 2 \( \sqrt{3} \) |
To divide terms with radicals, divide the coefficients and radicands separately:
\( \frac{16\sqrt{21}}{8\sqrt{7}} \)
\( \frac{16}{8} \) \( \sqrt{\frac{21}{7}} \)
2 \( \sqrt{3} \)
Simplify \( \frac{20}{80} \).
| \( \frac{7}{13} \) | |
| \( \frac{7}{17} \) | |
| \( \frac{3}{4} \) | |
| \( \frac{1}{4} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 80 are [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{20}{80} \) = \( \frac{\frac{20}{20}}{\frac{80}{20}} \) = \( \frac{1}{4} \)
What is 9z7 + 7z7?
| 16z-14 | |
| -2z-7 | |
| 16z7 | |
| 2z-7 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
9z7 + 7z7
(9 + 7)z7
16z7
If all of a roofing company's 12 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 8 complete crews out on jobs?
| 15 | |
| 19 | |
| 20 | |
| 7 |
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 3 crews so there are \( \frac{12}{3} \) = 4 workers on a crew. 8 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 8 x 4 = 32 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 32 - 12 = 20 new staff for the busy season.
Charlie loaned Betty $600 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $636 | |
| $648 | |
| $630 | |
| $612 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $600
i = 0.06 x $600
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $600 + $36