| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
What is \( \frac{2x^8}{3x^2} \)?
| \(\frac{2}{3}\)x\(\frac{1}{4}\) | |
| \(\frac{2}{3}\)x6 | |
| \(\frac{2}{3}\)x10 | |
| \(\frac{2}{3}\)x4 |
To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:
\( \frac{2x^8}{3x^2} \)
\( \frac{2}{3} \) x(8 - 2)
\(\frac{2}{3}\)x6
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 or a = -7 |
|
a = 7 |
|
none of these is correct |
|
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).
A circular logo is enlarged to fit the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?
| 30% | |
| 25% | |
| 27\(\frac{1}{2}\)% | |
| 20% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%
The __________ is the smallest positive integer that is a multiple of two or more integers.
least common multiple |
|
absolute value |
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least common factor |
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greatest common factor |
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 161.9 | |
| 155.5 | |
| 176.7 | |
| 126.7 |
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 6 = \( \frac{4 \times 6}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour
So, in an average hour, the machine will produce 6 - 0.24 = 5.76 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 5.76 = 126.7 error free parts were produced yesterday.