| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.92 |
| Score | 0% | 58% |
Simplify \( \sqrt{8} \)
| 4\( \sqrt{4} \) | |
| 4\( \sqrt{2} \) | |
| 3\( \sqrt{4} \) | |
| 2\( \sqrt{2} \) |
To simplify a radical, factor out the perfect squares:
\( \sqrt{8} \)
\( \sqrt{4 \times 2} \)
\( \sqrt{2^2 \times 2} \)
2\( \sqrt{2} \)
What is the distance in miles of a trip that takes 5 hours at an average speed of 25 miles per hour?
| 150 miles | |
| 125 miles | |
| 600 miles | |
| 195 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 = \( 25mph \times 5h \)
125 miles
If a mayor is elected with 70% of the votes cast and 71% of a town's 27,000 voters cast a vote, how many votes did the mayor receive?
| 12,269 | |
| 13,419 | |
| 10,160 | |
| 12,461 |
If 71% of the town's 27,000 voters cast ballots the number of votes cast is:
(\( \frac{71}{100} \)) x 27,000 = \( \frac{1,917,000}{100} \) = 19,170
The mayor got 70% of the votes cast which is:
(\( \frac{70}{100} \)) x 19,170 = \( \frac{1,341,900}{100} \) = 13,419 votes.
Which of the following statements about exponents is false?
b0 = 1 |
|
b1 = b |
|
all of these are false |
|
b1 = 1 |
A number with an exponent (be) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b1 = b) and a base with an exponent of 0 equals 1 ( (b0 = 1).
A machine in a factory has an error rate of 3 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 90.2 | |
| 150.9 | |
| 174.6 | |
| 129.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{3}{100} \) x 10 = \( \frac{3 \times 10}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour
So, in an average hour, the machine will produce 10 - 0.3 = 9.7 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 9.7 = 174.6 error free parts were produced yesterday.