| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 13 small cakes per hour. The kitchen is available for 3 hours and 38 large cakes and 170 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 | |
| 7 | |
| 13 | |
| 5 |
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. 38 large cakes are needed for the party so \( \frac{38}{9} \) = 4\(\frac{2}{9}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 13 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 13 x 3 = 39 small cakes during that time. 170 small cakes are needed for the party so \( \frac{170}{39} \) = 4\(\frac{14}{39}\) 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 5 + 5 = 10 cooks.
Which of the following is an improper fraction?
\({7 \over 5} \) |
|
\({2 \over 5} \) |
|
\(1 {2 \over 5} \) |
|
\({a \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
What is -8z2 + 7z2?
| 15z-2 | |
| -15z2 | |
| -z-4 | |
| -z2 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-8z2 + 7z2
(-8 + 7)z2
-z2
On average, the center for a basketball team hits 40% of his shots while a guard on the same team hits 45% of his shots. If the guard takes 10 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 10 | |
| 8 | |
| 9 | |
| 7 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 10 x \( \frac{45}{100} \) = \( \frac{45 x 10}{100} \) = \( \frac{450}{100} \) = 4 shots
The center makes 40% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{4}{\frac{40}{100}} \) = 4 x \( \frac{100}{40} \) = \( \frac{4 x 100}{40} \) = \( \frac{400}{40} \) = 10 shots
to make the same number of shots as the guard and thus score the same number of points.
If all of a roofing company's 12 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 12 | |
| 4 | |
| 3 | |
| 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 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 3 workers on a crew. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 18 - 12 = 6 new staff for the busy season.