| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
Convert a-5 to remove the negative exponent.
| \( \frac{-1}{-5a^{5}} \) | |
| \( \frac{-5}{a} \) | |
| \( \frac{-1}{-5a} \) | |
| \( \frac{1}{a^5} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \sqrt{\frac{64}{16}} \)?
| \(\frac{4}{7}\) | |
| 2 | |
| \(\frac{1}{2}\) | |
| 1\(\frac{1}{2}\) |
To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:
\( \sqrt{\frac{64}{16}} \)
\( \frac{\sqrt{64}}{\sqrt{16}} \)
\( \frac{\sqrt{8^2}}{\sqrt{4^2}} \)
\( \frac{8}{4} \)
2
4! = ?
4 x 3 x 2 x 1 |
|
4 x 3 |
|
5 x 4 x 3 x 2 x 1 |
|
3 x 2 x 1 |
A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 98.7 | |
| 144.1 | |
| 192.1 | |
| 72.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{2}{100} \) x 7 = \( \frac{2 \times 7}{100} \) = \( \frac{14}{100} \) = 0.14 errors per hour
So, in an average hour, the machine will produce 7 - 0.14 = 6.86 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.86 = 144.1 error free parts were produced yesterday.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Frank buys two shirts, each with a regular price of $31, how much will he pay for both shirts?
| $49.60 | |
| $32.55 | |
| $12.40 | |
| $41.85 |
By buying two shirts, Frank will save $31 x \( \frac{40}{100} \) = \( \frac{$31 x 40}{100} \) = \( \frac{$1240}{100} \) = $12.40 on the second shirt.
So, his total cost will be
$31.00 + ($31.00 - $12.40)
$31.00 + $18.60
$49.60