| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
Cooks are needed to prepare for a large party. Each cook can bake either 4 large cakes or 10 small cakes per hour. The kitchen is available for 4 hours and 39 large cakes and 290 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?
| 7 | |
| 12 | |
| 11 | |
| 10 |
If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 39 large cakes are needed for the party so \( \frac{39}{16} \) = 2\(\frac{7}{16}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 10 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 10 x 4 = 40 small cakes during that time. 290 small cakes are needed for the party so \( \frac{290}{40} \) = 7\(\frac{1}{4}\) 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 3 + 8 = 11 cooks.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 75% larger than the original. By what percentage has the area of the logo increased?
| 37\(\frac{1}{2}\)% | |
| 20% | |
| 25% | |
| 27\(\frac{1}{2}\)% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 75% the radius (and, consequently, the total area) increases by \( \frac{75\text{%}}{2} \) = 37\(\frac{1}{2}\)%
How many 14-passenger vans will it take to drive all 49 members of the football team to an away game?
| 8 vans | |
| 6 vans | |
| 7 vans | |
| 4 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{49}{14} \) = 3\(\frac{1}{2}\)
So, it will take 3 full vans and one partially full van to transport the entire team making a total of 4 vans.
Solve for \( \frac{6!}{2!} \)
| 6 | |
| 360 | |
| 3024 | |
| 4 |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{6!}{2!} \)
\( \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{6 \times 5 \times 4 \times 3}{1} \)
\( 6 \times 5 \times 4 \times 3 \)
360
If all of a roofing company's 6 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 5 complete crews out on jobs?
| 10 | |
| 13 | |
| 4 | |
| 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 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 5 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 5 x 2 = 10 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 10 - 6 = 4 new staff for the busy season.