| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
A machine in a factory has an error rate of 2 parts per 100. The machine normally runs 24 hours a day and produces 6 parts per hour. Yesterday the machine was shut down for 8 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 101.5 | |
| 94.1 | |
| 99.8 | |
| 90.3 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{2}{100} \) x 6 = \( \frac{2 \times 6}{100} \) = \( \frac{12}{100} \) = 0.12 errors per hour
So, in an average hour, the machine will produce 6 - 0.12 = 5.88 error free parts.
The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 5.88 = 94.1 error free parts were produced yesterday.
What is \( \frac{7}{2} \) + \( \frac{5}{6} \)?
| 2 \( \frac{9}{6} \) | |
| 4\(\frac{1}{3}\) | |
| \( \frac{7}{6} \) | |
| \( \frac{1}{7} \) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 3}{2 x 3} \) + \( \frac{5 x 1}{6 x 1} \)
\( \frac{21}{6} \) + \( \frac{5}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{21 + 5}{6} \) = \( \frac{26}{6} \) = 4\(\frac{1}{3}\)
Which of the following is not a prime number?
2 |
|
9 |
|
7 |
|
5 |
A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.
21 members of a bridal party need transported to a wedding reception but there are only 4 4-passenger taxis available to take them. How many will need to find other transportation?
| 8 | |
| 4 | |
| 5 | |
| 7 |
There are 4 4-passenger taxis available so that's 4 x 4 = 16 total seats. There are 21 people needing transportation leaving 21 - 16 = 5 who will have to find other transportation.
Roger loaned Diane $500 at an annual interest rate of 6%. If no payments are made, what is the total amount owed at the end of the first year?
| $505 | |
| $535 | |
| $545 | |
| $530 |
The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:
interest = annual interest rate x loan amount
i = (\( \frac{6}{100} \)) x $500
i = 0.06 x $500
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $500 + $30