| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
How many 2\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 15 gallon tank to fill it exactly halfway?
| 5 | |
| 6 | |
| 8 | |
| 3 |
To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:
cans = \( \frac{7\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 3
A circular logo is enlarged to fit the lid of a jar. The new diameter is 70% larger than the original. By what percentage has the area of the logo increased?
| 32\(\frac{1}{2}\)% | |
| 35% | |
| 22\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% |
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 70% the radius (and, consequently, the total area) increases by \( \frac{70\text{%}}{2} \) = 35%
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 9 complete crews out on jobs?
| 15 | |
| 14 | |
| 4 | |
| 19 |
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. 9 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 9 x 3 = 27 total workers to staff the crews during the busy season. The company already employs 12 workers so they need to add 27 - 12 = 15 new staff for the busy season.
What is the greatest common factor of 28 and 48?
| 7 | |
| 16 | |
| 15 | |
| 4 |
The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]. They share 3 factors [1, 2, 4] making 4 the greatest factor 28 and 48 have in common.
What is 8c2 - 9c2?
| c-2 | |
| -c2 | |
| 17c2 | |
| 17c4 |
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:
8c2 - 9c2
(8 - 9)c2
-c2