| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.41 |
| Score | 0% | 68% |
Convert z-2 to remove the negative exponent.
| \( \frac{-1}{-2z} \) | |
| \( \frac{2}{z} \) | |
| \( \frac{1}{z^2} \) | |
| \( \frac{-2}{z} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 55% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 27\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 17\(\frac{1}{2}\)% |
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 55% the radius (and, consequently, the total area) increases by \( \frac{55\text{%}}{2} \) = 27\(\frac{1}{2}\)%
What is the distance in miles of a trip that takes 2 hours at an average speed of 60 miles per hour?
| 120 miles | |
| 225 miles | |
| 300 miles | |
| 360 miles |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for distance:
distance = \( \text{speed} \times \text{time} \)
distance = \( 60mph \times 2h \)
120 miles
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).
What is \( \frac{2}{7} \) ÷ \( \frac{4}{8} \)?
| 4 | |
| 2\(\frac{2}{7}\) | |
| \(\frac{4}{7}\) | |
| \(\frac{1}{10}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{7} \) ÷ \( \frac{4}{8} \) = \( \frac{2}{7} \) x \( \frac{8}{4} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{7} \) x \( \frac{8}{4} \) = \( \frac{2 x 8}{7 x 4} \) = \( \frac{16}{28} \) = \(\frac{4}{7}\)