| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.36 |
| Score | 0% | 67% |
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 8 parts per hour. Yesterday the machine was shut down for 9 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 111.6 | |
| 109.2 | |
| 74.4 | |
| 143.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 8 = \( \frac{9 \times 8}{100} \) = \( \frac{72}{100} \) = 0.72 errors per hour
So, in an average hour, the machine will produce 8 - 0.72 = 7.28 error free parts.
The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 7.28 = 109.2 error free parts were produced yesterday.
4! = ?
3 x 2 x 1 |
|
4 x 3 |
|
4 x 3 x 2 x 1 |
|
5 x 4 x 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.
This property states taht the order of addition or multiplication does not mater. For example, 2 + 5 and 5 + 2 are equivalent.
PEDMAS |
|
commutative |
|
associative |
|
distributive |
The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.
Simplify \( \sqrt{80} \)
| 5\( \sqrt{5} \) | |
| 3\( \sqrt{5} \) | |
| 3\( \sqrt{10} \) | |
| 4\( \sqrt{5} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{80} \)
\( \sqrt{16 \times 5} \)
\( \sqrt{4^2 \times 5} \)
4\( \sqrt{5} \)
Simplify \( \frac{36}{52} \).
| \( \frac{1}{3} \) | |
| \( \frac{4}{9} \) | |
| \( \frac{9}{13} \) | |
| \( \frac{9}{20} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 36 are [1, 2, 3, 4, 6, 9, 12, 18, 36] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{36}{52} \) = \( \frac{\frac{36}{4}}{\frac{52}{4}} \) = \( \frac{9}{13} \)