| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.40 |
| Score | 0% | 68% |
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).
Simplify \( \frac{16}{68} \).
| \( \frac{4}{17} \) | |
| \( \frac{10}{13} \) | |
| \( \frac{4}{11} \) | |
| \( \frac{1}{3} \) |
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 68 are [1, 2, 4, 17, 34, 68]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{68} \) = \( \frac{\frac{16}{4}}{\frac{68}{4}} \) = \( \frac{4}{17} \)
The total water usage for a city is 5,000 gallons each day. Of that total, 23% is for personal use and 52% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 1,450 | |
| 11,700 | |
| 15,749 | |
| 750 |
52% of the water consumption is industrial use and 23% is personal use so (52% - 23%) = 29% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{29}{100} \) x 5,000 gallons = 1,450 gallons.
A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 107.8 | |
| 184 | |
| 128 | |
| 95.6 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{3}{100} \) x 6 = \( \frac{3 \times 6}{100} \) = \( \frac{18}{100} \) = 0.18 errors per hour
So, in an average hour, the machine will produce 6 - 0.18 = 5.82 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 5.82 = 128 error free parts were produced yesterday.
What is the distance in miles of a trip that takes 1 hour at an average speed of 70 miles per hour?
| 50 miles | |
| 70 miles | |
| 40 miles | |
| 45 miles |
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 distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 70mph \times 1h \)
70 miles