| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
Convert y-3 to remove the negative exponent.
| \( \frac{1}{y^3} \) | |
| \( \frac{3}{y} \) | |
| \( \frac{-1}{-3y} \) | |
| \( \frac{-3}{-y} \) |
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 60% larger than the original. By what percentage has the area of the logo increased?
| 20% | |
| 17\(\frac{1}{2}\)% | |
| 30% | |
| 25% |
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 60% the radius (and, consequently, the total area) increases by \( \frac{60\text{%}}{2} \) = 30%
If \( \left|y + 2\right| \) - 1 = -5, which of these is a possible value for y?
| -9 | |
| -2 | |
| 14 | |
| -6 |
First, solve for \( \left|y + 2\right| \):
\( \left|y + 2\right| \) - 1 = -5
\( \left|y + 2\right| \) = -5 + 1
\( \left|y + 2\right| \) = -4
The value inside the absolute value brackets can be either positive or negative so (y + 2) must equal - 4 or --4 for \( \left|y + 2\right| \) to equal -4:
| y + 2 = -4 y = -4 - 2 y = -6 | y + 2 = 4 y = 4 - 2 y = 2 |
So, y = 2 or y = -6.
How many 14-passenger vans will it take to drive all 62 members of the football team to an away game?
| 5 vans | |
| 13 vans | |
| 8 vans | |
| 9 vans |
Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:
vans = \( \frac{62}{14} \) = 4\(\frac{3}{7}\)
So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.
If a mayor is elected with 53% of the votes cast and 52% of a town's 27,000 voters cast a vote, how many votes did the mayor receive?
| 11,092 | |
| 9,547 | |
| 7,441 | |
| 8,845 |
If 52% of the town's 27,000 voters cast ballots the number of votes cast is:
(\( \frac{52}{100} \)) x 27,000 = \( \frac{1,404,000}{100} \) = 14,040
The mayor got 53% of the votes cast which is:
(\( \frac{53}{100} \)) x 14,040 = \( \frac{744,120}{100} \) = 7,441 votes.