| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.65 |
| Score | 0% | 53% |
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 12 small cakes per hour. The kitchen is available for 3 hours and 35 large cakes and 280 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 | |
| 14 | |
| 12 | |
| 15 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 35 large cakes are needed for the party so \( \frac{35}{9} \) = 3\(\frac{8}{9}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 12 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 12 x 3 = 36 small cakes during that time. 280 small cakes are needed for the party so \( \frac{280}{36} \) = 7\(\frac{7}{9}\) 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 + 8 = 12 cooks.
What is \( \frac{-4b^7}{4b^3} \)?
| -b\(\frac{3}{7}\) | |
| -b-4 | |
| -b2\(\frac{1}{3}\) | |
| -b4 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{-4b^7}{4b^3} \)
\( \frac{-4}{4} \) b(7 - 3)
-b4
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 7 to 2 and the ratio of baseball to basketball cards is 7 to 1, what is the ratio of football to basketball cards?
| 7:4 | |
| 5:2 | |
| 3:4 | |
| 49:2 |
The ratio of football cards to baseball cards is 7:2 and the ratio of baseball cards to basketball cards is 7:1. 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 49:14 and the ratio of baseball cards to basketball cards as 14:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 49:14, 14:2 which reduces to 49:2.
Roger loaned Ezra $200 at an annual interest rate of 1%. If no payments are made, what is the interest owed on this loan at the end of the first year?
| $2 | |
| $75 | |
| $30 | |
| $9 |
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 $200
i = 0.01 x $200
i = $2
What is \( 9 \)\( \sqrt{50} \) - \( 3 \)\( \sqrt{2} \)
| 6\( \sqrt{2} \) | |
| 27\( \sqrt{100} \) | |
| 27\( \sqrt{50} \) | |
| 42\( \sqrt{2} \) |
To subtract these radicals together their radicands must be the same:
9\( \sqrt{50} \) - 3\( \sqrt{2} \)
9\( \sqrt{25 \times 2} \) - 3\( \sqrt{2} \)
9\( \sqrt{5^2 \times 2} \) - 3\( \sqrt{2} \)
(9)(5)\( \sqrt{2} \) - 3\( \sqrt{2} \)
45\( \sqrt{2} \) - 3\( \sqrt{2} \)
Now that the radicands are identical, you can subtract them:
45\( \sqrt{2} \) - 3\( \sqrt{2} \)