| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
Which of the following is not an integer?
\({1 \over 2}\) |
|
-1 |
|
1 |
|
0 |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
If \( \left|b + 8\right| \) + 9 = -5, which of these is a possible value for b?
| -15 | |
| -17 | |
| -22 | |
| -1 |
First, solve for \( \left|b + 8\right| \):
\( \left|b + 8\right| \) + 9 = -5
\( \left|b + 8\right| \) = -5 - 9
\( \left|b + 8\right| \) = -14
The value inside the absolute value brackets can be either positive or negative so (b + 8) must equal - 14 or --14 for \( \left|b + 8\right| \) to equal -14:
| b + 8 = -14 b = -14 - 8 b = -22 | b + 8 = 14 b = 14 - 8 b = 6 |
So, b = 6 or b = -22.
Find the average of the following numbers: 10, 6, 9, 7.
| 10 | |
| 8 | |
| 7 | |
| 11 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{10 + 6 + 9 + 7}{4} \) = \( \frac{32}{4} \) = 8
A circular logo is enlarged to fit the lid of a jar. The new diameter is 55% larger than the original. By what percentage has the area of the logo increased?
| 27\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% | |
| 15% | |
| 32\(\frac{1}{2}\)% |
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 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 192.1 | |
| 182 | |
| 193.2 | |
| 123.7 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 10 = \( \frac{9 \times 10}{100} \) = \( \frac{90}{100} \) = 0.9 errors per hour
So, in an average hour, the machine will produce 10 - 0.9 = 9.1 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 9.1 = 182 error free parts were produced yesterday.