| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.16 |
| Score | 0% | 63% |
Roger loaned Bob $1,400 at an annual interest rate of 8%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $15 | |
| $112 | |
| $22 | |
| $40 |
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 $1,400
i = 0.08 x $1,400
i = $112
What is \( 3 \)\( \sqrt{63} \) - \( 7 \)\( \sqrt{7} \)
| 2\( \sqrt{7} \) | |
| 21\( \sqrt{9} \) | |
| 21\( \sqrt{63} \) | |
| -4\( \sqrt{40} \) |
To subtract these radicals together their radicands must be the same:
3\( \sqrt{63} \) - 7\( \sqrt{7} \)
3\( \sqrt{9 \times 7} \) - 7\( \sqrt{7} \)
3\( \sqrt{3^2 \times 7} \) - 7\( \sqrt{7} \)
(3)(3)\( \sqrt{7} \) - 7\( \sqrt{7} \)
9\( \sqrt{7} \) - 7\( \sqrt{7} \)
Now that the radicands are identical, you can subtract them:
9\( \sqrt{7} \) - 7\( \sqrt{7} \)What is \( \frac{1}{5} \) ÷ \( \frac{3}{6} \)?
| \(\frac{3}{28}\) | |
| \(\frac{16}{45}\) | |
| \(\frac{2}{5}\) | |
| \(\frac{1}{8}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{1}{5} \) ÷ \( \frac{3}{6} \) = \( \frac{1}{5} \) x \( \frac{6}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{1}{5} \) x \( \frac{6}{3} \) = \( \frac{1 x 6}{5 x 3} \) = \( \frac{6}{15} \) = \(\frac{2}{5}\)
What is \( \frac{8}{6} \) - \( \frac{7}{14} \)?
| 2 \( \frac{7}{42} \) | |
| \(\frac{5}{6}\) | |
| 2 \( \frac{4}{11} \) | |
| 2 \( \frac{6}{42} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 14 are [14, 28, 42, 56, 70, 84, 98]. The first few multiples they share are [42, 84] making 42 the smallest multiple 6 and 14 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{8 x 7}{6 x 7} \) - \( \frac{7 x 3}{14 x 3} \)
\( \frac{56}{42} \) - \( \frac{21}{42} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{56 - 21}{42} \) = \( \frac{35}{42} \) = \(\frac{5}{6}\)
Find the average of the following numbers: 9, 3, 8, 4.
| 11 | |
| 6 | |
| 1 | |
| 4 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{9 + 3 + 8 + 4}{4} \) = \( \frac{24}{4} \) = 6