| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 5 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 | |
| 96 | |
| 70.5 | |
| 114 |
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 5 = \( \frac{4 \times 5}{100} \) = \( \frac{20}{100} \) = 0.2 errors per hour
So, in an average hour, the machine will produce 5 - 0.2 = 4.8 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 4.8 = 96 error free parts were produced yesterday.
The total water usage for a city is 10,000 gallons each day. Of that total, 35% is for personal use and 59% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 2,400 | |
| 10,500 | |
| 8,000 | |
| 2,850 |
59% of the water consumption is industrial use and 35% is personal use so (59% - 35%) = 24% more water is used for industrial purposes. 10,000 gallons are consumed daily so industry consumes \( \frac{24}{100} \) x 10,000 gallons = 2,400 gallons.
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
|
a = 7 |
|
none of these is correct |
|
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).
What is \( \frac{3}{5} \) ÷ \( \frac{1}{5} \)?
| \(\frac{4}{81}\) | |
| 3 | |
| \(\frac{1}{48}\) | |
| \(\frac{2}{63}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{3}{5} \) ÷ \( \frac{1}{5} \) = \( \frac{3}{5} \) x \( \frac{5}{1} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{3}{5} \) x \( \frac{5}{1} \) = \( \frac{3 x 5}{5 x 1} \) = \( \frac{15}{5} \) = 3
The __________ is the greatest factor that divides two integers.
absolute value |
|
greatest common multiple |
|
greatest common factor |
|
least common multiple |
The greatest common factor (GCF) is the greatest factor that divides two integers.