| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
Bob loaned Jennifer $1,300 at an annual interest rate of 1%. If no payments are made, what is the total amount owed at the end of the first year?
| $1,326 | |
| $1,352 | |
| $1,313 | |
| $1,391 |
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 $1,300
i = 0.01 x $1,300
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $1,300 + $13Convert c-5 to remove the negative exponent.
| \( \frac{1}{c^5} \) | |
| \( \frac{-1}{c^{-5}} \) | |
| \( \frac{-1}{-5c^{5}} \) | |
| \( \frac{-5}{c} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
If all of a roofing company's 15 workers are required to staff 5 roofing crews, how many workers need to be added during the busy season in order to send 9 complete crews out on jobs?
| 17 | |
| 11 | |
| 12 | |
| 6 |
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 15 workers at the company now and that's enough to staff 5 crews so there are \( \frac{15}{5} \) = 3 workers on a crew. 9 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 9 x 3 = 27 total workers to staff the crews during the busy season. The company already employs 15 workers so they need to add 27 - 15 = 12 new staff for the busy season.
What is \( \frac{9}{8} \) + \( \frac{2}{16} \)?
| 1\(\frac{1}{4}\) | |
| 2 \( \frac{1}{16} \) | |
| 2 \( \frac{8}{16} \) | |
| 1 \( \frac{4}{16} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 16 are [16, 32, 48, 64, 80, 96]. The first few multiples they share are [16, 32, 48, 64, 80] making 16 the smallest multiple 8 and 16 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 2}{8 x 2} \) + \( \frac{2 x 1}{16 x 1} \)
\( \frac{18}{16} \) + \( \frac{2}{16} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{18 + 2}{16} \) = \( \frac{20}{16} \) = 1\(\frac{1}{4}\)
What is \( \frac{3}{6} \) ÷ \( \frac{4}{8} \)?
| 1 | |
| \(\frac{4}{21}\) | |
| \(\frac{1}{18}\) | |
| 6 |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{6} \) ÷ \( \frac{4}{8} \) = \( \frac{3}{6} \) x \( \frac{8}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{6} \) x \( \frac{8}{4} \) = \( \frac{3 x 8}{6 x 4} \) = \( \frac{24}{24} \) = 1