| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 135.4 | |
| 143.2 | |
| 139.7 | |
| 99.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 5 = \( \frac{5 \times 5}{100} \) = \( \frac{25}{100} \) = 0.25 errors per hour
So, in an average hour, the machine will produce 5 - 0.25 = 4.75 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 4.75 = 99.8 error free parts were produced yesterday.
Simplify \( \sqrt{48} \)
| 7\( \sqrt{6} \) | |
| 4\( \sqrt{3} \) | |
| 3\( \sqrt{3} \) | |
| 6\( \sqrt{6} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)
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).
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
|
absolute value |
|
greatest common factor |
|
least common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?
| 26 | |
| 29 | |
| 31 | |
| 28 |
The equation for this sequence is:
an = an-1 + 2(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31