| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.51 |
| Score | 0% | 70% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 35% larger than the original. By what percentage has the area of the logo increased?
| 35% | |
| 17\(\frac{1}{2}\)% | |
| 32\(\frac{1}{2}\)% | |
| 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 35% the radius (and, consequently, the total area) increases by \( \frac{35\text{%}}{2} \) = 17\(\frac{1}{2}\)%
Convert z-3 to remove the negative exponent.
| \( \frac{1}{z^3} \) | |
| \( \frac{-1}{z^{-3}} \) | |
| \( \frac{-3}{z} \) | |
| \( \frac{-1}{-3z^{3}} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
What is \( \frac{2}{7} \) ÷ \( \frac{2}{9} \)?
| \(\frac{4}{27}\) | |
| 1\(\frac{2}{7}\) | |
| \(\frac{1}{12}\) | |
| \(\frac{8}{35}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{2}{7} \) ÷ \( \frac{2}{9} \) = \( \frac{2}{7} \) x \( \frac{9}{2} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{2}{7} \) x \( \frac{9}{2} \) = \( \frac{2 x 9}{7 x 2} \) = \( \frac{18}{14} \) = 1\(\frac{2}{7}\)
A factor is a positive __________ that divides evenly into a given number.
integer |
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fraction |
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improper fraction |
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mixed number |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
What is the distance in miles of a trip that takes 7 hours at an average speed of 25 miles per hour?
| 390 miles | |
| 100 miles | |
| 70 miles | |
| 175 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 = \( 25mph \times 7h \)
175 miles