| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
Convert b-2 to remove the negative exponent.
| \( \frac{-1}{-2b} \) | |
| \( \frac{-2}{b} \) | |
| \( \frac{1}{b^2} \) | |
| \( \frac{-1}{b^{-2}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A tiger in a zoo has consumed 84 pounds of food in 6 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 168 pounds?
| 10 | |
| 1 | |
| 7 | |
| 6 |
If the tiger has consumed 84 pounds of food in 6 days that's \( \frac{84}{6} \) = 14 pounds of food per day. The tiger needs to consume 168 - 84 = 84 more pounds of food to reach 168 pounds total. At 14 pounds of food per day that's \( \frac{84}{14} \) = 6 more days.
11 members of a bridal party need transported to a wedding reception but there are only 2 4-passenger taxis available to take them. How many will need to find other transportation?
| 8 | |
| 2 | |
| 3 | |
| 6 |
There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 11 people needing transportation leaving 11 - 8 = 3 who will have to find other transportation.
What is the least common multiple of 9 and 15?
| 45 | |
| 9 | |
| 134 | |
| 4 |
The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 have in common.
What is \( \frac{4}{8} \) - \( \frac{8}{10} \)?
| -\(\frac{3}{10}\) | |
| \( \frac{2}{40} \) | |
| 1 \( \frac{7}{40} \) | |
| 2 \( \frac{6}{40} \) |
To subtract 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 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 5}{8 x 5} \) - \( \frac{8 x 4}{10 x 4} \)
\( \frac{20}{40} \) - \( \frac{32}{40} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{20 - 32}{40} \) = \( \frac{-12}{40} \) = -\(\frac{3}{10}\)