| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.66 |
| Score | 0% | 53% |
If a mayor is elected with 68% of the votes cast and 34% of a town's 41,000 voters cast a vote, how many votes did the mayor receive?
| 10,594 | |
| 9,479 | |
| 11,849 | |
| 10,176 |
If 34% of the town's 41,000 voters cast ballots the number of votes cast is:
(\( \frac{34}{100} \)) x 41,000 = \( \frac{1,394,000}{100} \) = 13,940
The mayor got 68% of the votes cast which is:
(\( \frac{68}{100} \)) x 13,940 = \( \frac{947,920}{100} \) = 9,479 votes.
Convert 0.0003107 to scientific notation.
| 3.107 x 105 | |
| 3.107 x 10-4 | |
| 31.07 x 10-5 | |
| 3.107 x 10-3 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0003107 in scientific notation is 3.107 x 10-4
On average, the center for a basketball team hits 25% of his shots while a guard on the same team hits 35% of his shots. If the guard takes 20 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?
| 28 | |
| 19 | |
| 33 | |
| 20 |
guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{35}{100} \) = \( \frac{35 x 20}{100} \) = \( \frac{700}{100} \) = 7 shots
The center makes 25% of his shots so he'll have to take:
shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)
to make as many shots as the guard. Plugging in values for the center gives us:
center shots taken = \( \frac{7}{\frac{25}{100}} \) = 7 x \( \frac{100}{25} \) = \( \frac{7 x 100}{25} \) = \( \frac{700}{25} \) = 28 shots
to make the same number of shots as the guard and thus score the same number of points.
A machine in a factory has an error rate of 4 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 7 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 107.2 | |
| 106.7 | |
| 114.2 | |
| 159.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{4}{100} \) x 7 = \( \frac{4 \times 7}{100} \) = \( \frac{28}{100} \) = 0.28 errors per hour
So, in an average hour, the machine will produce 7 - 0.28 = 6.72 error free parts.
The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 6.72 = 114.2 error free parts were produced yesterday.
Simplify \( \sqrt{18} \)
| 4\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) | |
| 6\( \sqrt{4} \) | |
| 6\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{18} \)
\( \sqrt{9 \times 2} \)
\( \sqrt{3^2 \times 2} \)
3\( \sqrt{2} \)