| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
If all of a roofing company's 9 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
| 12 | |
| 9 | |
| 8 | |
| 15 |
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 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 7 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 7 x 3 = 21 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 21 - 9 = 12 new staff for the busy season.
What is \( \frac{2}{5} \) x \( \frac{2}{8} \)?
| \(\frac{4}{63}\) | |
| \(\frac{1}{10}\) | |
| \(\frac{1}{64}\) | |
| \(\frac{1}{2}\) |
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{5} \) x \( \frac{2}{8} \) = \( \frac{2 x 2}{5 x 8} \) = \( \frac{4}{40} \) = \(\frac{1}{10}\)
A circular logo is enlarged to fit the lid of a jar. The new diameter is 35% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 17\(\frac{1}{2}\)% | |
| 32\(\frac{1}{2}\)% | |
| 37\(\frac{1}{2}\)% |
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 35% the radius (and, consequently, the total area) increases by \( \frac{35\text{%}}{2} \) = 17\(\frac{1}{2}\)%
Which of the following statements about exponents is false?
all of these are false |
|
b1 = b |
|
b1 = 1 |
|
b0 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
What is (z4)3?
| z12 | |
| z-1 | |
| 4z3 | |
| z |
To raise a term with an exponent to another exponent, retain the base and multiply the exponents:
(z4)3