| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.53 |
| Score | 0% | 71% |
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 101.5 | |
| 163.8 | |
| 209 | |
| 128.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 9 = \( \frac{9 \times 9}{100} \) = \( \frac{81}{100} \) = 0.81 errors per hour
So, in an average hour, the machine will produce 9 - 0.81 = 8.19 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 8.19 = 163.8 error free parts were produced yesterday.
How many hours does it take a car to travel 90 miles at an average speed of 45 miles per hour?
| 7 hours | |
| 2 hours | |
| 4 hours | |
| 6 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{90mi}{45mph} \)
2 hours
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = -7 |
|
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).
Find the average of the following numbers: 9, 3, 8, 4.
| 3 | |
| 1 | |
| 6 | |
| 7 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{9 + 3 + 8 + 4}{4} \) = \( \frac{24}{4} \) = 6
Simplify \( \frac{16}{76} \).
| \( \frac{9}{20} \) | |
| \( \frac{4}{19} \) | |
| \( \frac{7}{12} \) | |
| \( \frac{1}{2} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{76} \) = \( \frac{\frac{16}{4}}{\frac{76}{4}} \) = \( \frac{4}{19} \)