| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.14 |
| Score | 0% | 63% |
A machine in a factory has an error rate of 8 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 4 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 148.8 | |
| 92 | |
| 108.3 | |
| 128.3 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{8}{100} \) x 5 = \( \frac{8 \times 5}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour
So, in an average hour, the machine will produce 5 - 0.4 = 4.6 error free parts.
The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 4.6 = 92 error free parts were produced yesterday.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 30% off." If Roger buys two shirts, each with a regular price of $18, how much will he pay for both shirts?
| $30.60 | |
| $12.60 | |
| $20.70 | |
| $5.40 |
By buying two shirts, Roger will save $18 x \( \frac{30}{100} \) = \( \frac{$18 x 30}{100} \) = \( \frac{$540}{100} \) = $5.40 on the second shirt.
So, his total cost will be
$18.00 + ($18.00 - $5.40)
$18.00 + $12.60
$30.60
What is the greatest common factor of 52 and 52?
| 49 | |
| 52 | |
| 14 | |
| 2 |
The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 52 are [1, 2, 4, 13, 26, 52]. They share 6 factors [1, 2, 4, 13, 26, 52] making 52 the greatest factor 52 and 52 have in common.
How many 2\(\frac{1}{2}\) gallon cans worth of fuel would you need to pour into an empty 25 gallon tank to fill it exactly halfway?
| 5 | |
| 6 | |
| 10 | |
| 5 |
To fill a 25 gallon tank exactly halfway you'll need 12\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:
cans = \( \frac{12\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 5
Simplify \( \frac{16}{76} \).
| \( \frac{4}{7} \) | |
| \( \frac{4}{19} \) | |
| \( \frac{1}{3} \) | |
| \( \frac{3}{4} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{76} \) = \( \frac{\frac{16}{4}}{\frac{76}{4}} \) = \( \frac{4}{19} \)