| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.01 |
| Score | 0% | 60% |
How many 14-passenger vans will it take to drive all 77 members of the football team to an away game?
| 4 vans | |
| 5 vans | |
| 6 vans | |
| 8 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{77}{14} \) = 5\(\frac{1}{2}\)
So, it will take 5 full vans and one partially full van to transport the entire team making a total of 6 vans.
If \(\left|a\right| = 7\), which of the following best describes a?
none of these is correct |
|
a = 7 or a = -7 |
|
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).
Convert z-4 to remove the negative exponent.
| \( \frac{-1}{-4z^{4}} \) | |
| \( \frac{-4}{z} \) | |
| \( \frac{1}{z^{-4}} \) | |
| \( \frac{1}{z^4} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 158.1 | |
| 182.4 | |
| 116.4 | |
| 164.2 |
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 9 = \( \frac{4 \times 9}{100} \) = \( \frac{36}{100} \) = 0.36 errors per hour
So, in an average hour, the machine will produce 9 - 0.36 = 8.64 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 8.64 = 164.2 error free parts were produced yesterday.
What is \( 3 \)\( \sqrt{18} \) + \( 6 \)\( \sqrt{2} \)
| 15\( \sqrt{2} \) | |
| 18\( \sqrt{18} \) | |
| 9\( \sqrt{18} \) | |
| 18\( \sqrt{2} \) |
To add these radicals together their radicands must be the same:
3\( \sqrt{18} \) + 6\( \sqrt{2} \)
3\( \sqrt{9 \times 2} \) + 6\( \sqrt{2} \)
3\( \sqrt{3^2 \times 2} \) + 6\( \sqrt{2} \)
(3)(3)\( \sqrt{2} \) + 6\( \sqrt{2} \)
9\( \sqrt{2} \) + 6\( \sqrt{2} \)
Now that the radicands are identical, you can add them together:
9\( \sqrt{2} \) + 6\( \sqrt{2} \)