| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.06 |
| Score | 0% | 61% |
What is (y2)2?
| y0 | |
| 2y2 | |
| 56 | |
| y4 |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(y2)2Damon loaned Frank $1,000 at an annual interest rate of 9%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $60 | |
| $22 | |
| $10 | |
| $90 |
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 $1,000
i = 0.09 x $1,000
i = $90
What is \( \frac{4}{2} \) + \( \frac{7}{8} \)?
| 2\(\frac{7}{8}\) | |
| \( \frac{7}{8} \) | |
| 2 \( \frac{7}{16} \) | |
| 2 \( \frac{9}{8} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{4 x 4}{2 x 4} \) + \( \frac{7 x 1}{8 x 1} \)
\( \frac{16}{8} \) + \( \frac{7}{8} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{16 + 7}{8} \) = \( \frac{23}{8} \) = 2\(\frac{7}{8}\)
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 9 to 2 and the ratio of baseball to basketball cards is 9 to 1, what is the ratio of football to basketball cards?
| 3:8 | |
| 81:2 | |
| 1:1 | |
| 1:6 |
The ratio of football cards to baseball cards is 9:2 and the ratio of baseball cards to basketball cards is 9:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 81:18 and the ratio of baseball cards to basketball cards as 18:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 81:18, 18:2 which reduces to 81:2.
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 20 small cakes per hour. The kitchen is available for 4 hours and 29 large cakes and 470 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 10 | |
| 15 | |
| 5 | |
| 11 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 29 large cakes are needed for the party so \( \frac{29}{8} \) = 3\(\frac{5}{8}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 20 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 20 x 4 = 80 small cakes during that time. 470 small cakes are needed for the party so \( \frac{470}{80} \) = 5\(\frac{7}{8}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 6 = 10 cooks.