| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
Convert c-2 to remove the negative exponent.
| \( \frac{-2}{c} \) | |
| \( \frac{-1}{-2c} \) | |
| \( \frac{-2}{-c} \) | |
| \( \frac{1}{c^2} \) |
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 9 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 3 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 139.7 | |
| 114.7 | |
| 114 | |
| 186.1 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 6 = \( \frac{9 \times 6}{100} \) = \( \frac{54}{100} \) = 0.54 errors per hour
So, in an average hour, the machine will produce 6 - 0.54 = 5.46 error free parts.
The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 5.46 = 114.7 error free parts were produced yesterday.
a(b + c) = ab + ac defines which of the following?
distributive property for division |
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commutative property for division |
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distributive property for multiplication |
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commutative property for multiplication |
The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.
If a mayor is elected with 89% of the votes cast and 42% of a town's 15,000 voters cast a vote, how many votes did the mayor receive?
| 5,607 | |
| 3,465 | |
| 3,591 | |
| 5,229 |
If 42% of the town's 15,000 voters cast ballots the number of votes cast is:
(\( \frac{42}{100} \)) x 15,000 = \( \frac{630,000}{100} \) = 6,300
The mayor got 89% of the votes cast which is:
(\( \frac{89}{100} \)) x 6,300 = \( \frac{560,700}{100} \) = 5,607 votes.
A triathlon course includes a 300m swim, a 40.5km bike ride, and a 11.9km run. What is the total length of the race course?
| 39.2km | |
| 42.8km | |
| 60.8km | |
| 52.7km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.3km + 40.5km + 11.9km
total distance = 52.7km