| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
| 7.2 | |
| 1 | |
| 4.8 | |
| 1.4 |
1
What is the greatest common factor of 40 and 32?
| 6 | |
| 14 | |
| 26 | |
| 8 |
The factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40] and the factors of 32 are [1, 2, 4, 8, 16, 32]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 40 and 32 have in common.
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 10 parts per hour. Yesterday the machine was shut down for 2 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 105.6 | |
| 121 | |
| 99.4 | |
| 206.8 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 10 = \( \frac{6 \times 10}{100} \) = \( \frac{60}{100} \) = 0.6 errors per hour
So, in an average hour, the machine will produce 10 - 0.6 = 9.4 error free parts.
The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 9.4 = 206.8 error free parts were produced yesterday.
If \( \left|a + 2\right| \) + 0 = -4, which of these is a possible value for a?
| 2 | |
| -11 | |
| -5 | |
| 9 |
First, solve for \( \left|a + 2\right| \):
\( \left|a + 2\right| \) + 0 = -4
\( \left|a + 2\right| \) = -4 + 0
\( \left|a + 2\right| \) = -4
The value inside the absolute value brackets can be either positive or negative so (a + 2) must equal - 4 or --4 for \( \left|a + 2\right| \) to equal -4:
| a + 2 = -4 a = -4 - 2 a = -6 | a + 2 = 4 a = 4 - 2 a = 2 |
So, a = 2 or a = -6.
Alex loaned Jennifer $100 at an annual interest rate of 9%. If no payments are made, what is the total amount owed at the end of the first year?
| $107 | |
| $104 | |
| $106 | |
| $109 |
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 $100
i = 0.09 x $100
No payments were made so the total amount due is the original amount + the accumulated interest:
total = $100 + $9