| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.32 |
| Score | 0% | 66% |
A machine in a factory has an error rate of 9 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 145.6 | |
| 117.2 | |
| 88.2 | |
| 211.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{9}{100} \) x 10 = \( \frac{9 \times 10}{100} \) = \( \frac{90}{100} \) = 0.9 errors per hour
So, in an average hour, the machine will produce 10 - 0.9 = 9.1 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 9.1 = 145.6 error free parts were produced yesterday.
If the ratio of home fans to visiting fans in a crowd is 2:1 and all 34,000 seats in a stadium are filled, how many home fans are in attendance?
| 35,000 | |
| 27,750 | |
| 22,667 | |
| 29,600 |
A ratio of 2:1 means that there are 2 home fans for every one visiting fan. So, of every 3 fans, 2 are home fans and \( \frac{2}{3} \) of every fan in the stadium is a home fan:
34,000 fans x \( \frac{2}{3} \) = \( \frac{68000}{3} \) = 22,667 fans.
Simplify \( \frac{16}{72} \).
| \( \frac{1}{2} \) | |
| \( \frac{3}{8} \) | |
| \( \frac{8}{15} \) | |
| \( \frac{2}{9} \) |
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 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{16}{72} \) = \( \frac{\frac{16}{8}}{\frac{72}{8}} \) = \( \frac{2}{9} \)
What is the greatest common factor of 68 and 28?
| 7 | |
| 3 | |
| 4 | |
| 19 |
The factors of 68 are [1, 2, 4, 17, 34, 68] and the factors of 28 are [1, 2, 4, 7, 14, 28]. They share 3 factors [1, 2, 4] making 4 the greatest factor 68 and 28 have in common.
Find the average of the following numbers: 17, 9, 16, 10.
| 10 | |
| 8 | |
| 16 | |
| 13 |
To find the average of these 4 numbers add them together then divide by 4:
\( \frac{17 + 9 + 16 + 10}{4} \) = \( \frac{52}{4} \) = 13