| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
none of these is correct |
|
a = 7 or a = -7 |
|
a = -7 |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
If all of a roofing company's 16 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?
| 16 | |
| 14 | |
| 3 | |
| 8 |
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 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 6 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 6 x 4 = 24 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 24 - 16 = 8 new staff for the busy season.
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?
| 15% | |
| 30% | |
| 37\(\frac{1}{2}\)% | |
| 35% |
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\(\frac{1}{2}\)%
Which of the following is not an integer?
1 |
|
0 |
|
-1 |
|
\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 7 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 111.9 | |
| 146.9 | |
| 186.1 | |
| 174.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 7 = \( \frac{6 \times 7}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour
So, in an average hour, the machine will produce 7 - 0.42 = 6.58 error free parts.
The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 6.58 = 111.9 error free parts were produced yesterday.