| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.92 |
| Score | 0% | 58% |
A machine in a factory has an error rate of 7 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 163.7 | |
| 97.7 | |
| 147 | |
| 79.9 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{7}{100} \) x 8 = \( \frac{7 \times 8}{100} \) = \( \frac{56}{100} \) = 0.56 errors per hour
So, in an average hour, the machine will produce 8 - 0.56 = 7.4399999999999995 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 7.4399999999999995 = 163.7 error free parts were produced yesterday.
Which of the following is not a prime number?
5 |
|
9 |
|
7 |
|
2 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
What is 7\( \sqrt{4} \) x 8\( \sqrt{4} \)?
| 56\( \sqrt{4} \) | |
| 15\( \sqrt{4} \) | |
| 15\( \sqrt{16} \) | |
| 224 |
To multiply terms with radicals, multiply the coefficients and radicands separately:
7\( \sqrt{4} \) x 8\( \sqrt{4} \)
(7 x 8)\( \sqrt{4 \times 4} \)
56\( \sqrt{16} \)
Now we need to simplify the radical:
56\( \sqrt{16} \)
56\( \sqrt{4^2} \)
(56)(4)
224
Convert b-4 to remove the negative exponent.
| \( \frac{1}{b^4} \) | |
| \( \frac{-1}{-4b} \) | |
| \( \frac{-1}{-4b^{4}} \) | |
| \( \frac{-4}{-b} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{4}{5} \) ÷ \( \frac{2}{8} \)?
| 3\(\frac{1}{5}\) | |
| \(\frac{1}{7}\) | |
| \(\frac{2}{49}\) | |
| 16 |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{5} \) ÷ \( \frac{2}{8} \) = \( \frac{4}{5} \) x \( \frac{8}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{5} \) x \( \frac{8}{2} \) = \( \frac{4 x 8}{5 x 2} \) = \( \frac{32}{10} \) = 3\(\frac{1}{5}\)