| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.05 |
| Score | 0% | 61% |
If a mayor is elected with 59% of the votes cast and 56% of a town's 49,000 voters cast a vote, how many votes did the mayor receive?
| 19,482 | |
| 19,208 | |
| 16,190 | |
| 18,659 |
If 56% of the town's 49,000 voters cast ballots the number of votes cast is:
(\( \frac{56}{100} \)) x 49,000 = \( \frac{2,744,000}{100} \) = 27,440
The mayor got 59% of the votes cast which is:
(\( \frac{59}{100} \)) x 27,440 = \( \frac{1,618,960}{100} \) = 16,190 votes.
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 65 | |
| 61 | |
| 68 | |
| 53 |
The equation for this sequence is:
an = an-1 + 4(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61
What is \( \frac{4}{6} \) ÷ \( \frac{3}{5} \)?
| 3\(\frac{1}{3}\) | |
| 1\(\frac{1}{9}\) | |
| \(\frac{1}{18}\) | |
| \(\frac{2}{25}\) |
To divide fractions, invert the second fraction and then multiply:
\( \frac{4}{6} \) ÷ \( \frac{3}{5} \) = \( \frac{4}{6} \) x \( \frac{5}{3} \)
To multiply fractions, multiply the numerators together and then multiply the denominators together:
\( \frac{4}{6} \) x \( \frac{5}{3} \) = \( \frac{4 x 5}{6 x 3} \) = \( \frac{20}{18} \) = 1\(\frac{1}{9}\)
Convert z-5 to remove the negative exponent.
| \( \frac{-5}{-z} \) | |
| \( \frac{-1}{z^{-5}} \) | |
| \( \frac{-5}{z} \) | |
| \( \frac{1}{z^5} \) |
To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal.
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 9 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 102.3 | |
| 98.7 | |
| 153.9 | |
| 165.9 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 9 = \( \frac{5 \times 9}{100} \) = \( \frac{45}{100} \) = 0.45 errors per hour
So, in an average hour, the machine will produce 9 - 0.45 = 8.55 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 8.55 = 153.9 error free parts were produced yesterday.