| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 144.4 | |
| 82.4 | |
| 201.6 | |
| 81.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 10 = \( \frac{4 \times 10}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour
So, in an average hour, the machine will produce 10 - 0.4 = 9.6 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 9.6 = 201.6 error free parts were produced yesterday.
If \( \left|y + 9\right| \) + 6 = 9, which of these is a possible value for y?
| -1 | |
| 0 | |
| -6 | |
| 13 |
First, solve for \( \left|y + 9\right| \):
\( \left|y + 9\right| \) + 6 = 9
\( \left|y + 9\right| \) = 9 - 6
\( \left|y + 9\right| \) = 3
The value inside the absolute value brackets can be either positive or negative so (y + 9) must equal + 3 or -3 for \( \left|y + 9\right| \) to equal 3:
| y + 9 = 3 y = 3 - 9 y = -6 | y + 9 = -3 y = -3 - 9 y = -12 |
So, y = -12 or y = -6.
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
|
a = -7 |
|
a = 7 |
|
none of these is correct |
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).
Monica scored 90% on her final exam. If each question was worth 4 points and there were 280 possible points on the exam, how many questions did Monica answer correctly?
| 53 | |
| 55 | |
| 63 | |
| 64 |
Monica scored 90% on the test meaning she earned 90% of the possible points on the test. There were 280 possible points on the test so she earned 280 x 0.9 = 252 points. Each question is worth 4 points so she got \( \frac{252}{4} \) = 63 questions right.
Cooks are needed to prepare for a large party. Each cook can bake either 2 large cakes or 12 small cakes per hour. The kitchen is available for 4 hours and 32 large cakes and 300 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?
| 11 | |
| 8 | |
| 15 | |
| 10 |
If a single cook can bake 2 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 2 x 4 = 8 large cakes during that time. 32 large cakes are needed for the party so \( \frac{32}{8} \) = 4 cooks are needed to bake the required number of large cakes.
If a single cook can bake 12 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 12 x 4 = 48 small cakes during that time. 300 small cakes are needed for the party so \( \frac{300}{48} \) = 6\(\frac{1}{4}\) 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 4 + 7 = 11 cooks.