| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.32 |
| Score | 0% | 46% |
A machine in a factory has an error rate of 5 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 98.9 | |
| 88.3 | |
| 119.7 | |
| 157.3 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{5}{100} \) x 7 = \( \frac{5 \times 7}{100} \) = \( \frac{35}{100} \) = 0.35 errors per hour
So, in an average hour, the machine will produce 7 - 0.35 = 6.65 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 6.65 = 119.7 error free parts were produced yesterday.
Solve 2 + (4 + 2) ÷ 2 x 3 - 32
| 1\(\frac{2}{3}\) | |
| \(\frac{2}{9}\) | |
| 2 | |
| 1 |
Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):
2 + (4 + 2) ÷ 2 x 3 - 32
P: 2 + (6) ÷ 2 x 3 - 32
E: 2 + 6 ÷ 2 x 3 - 9
MD: 2 + \( \frac{6}{2} \) x 3 - 9
MD: 2 + \( \frac{18}{2} \) - 9
AS: \( \frac{4}{2} \) + \( \frac{18}{2} \) - 9
AS: \( \frac{22}{2} \) - 9
AS: \( \frac{22 - 18}{2} \)
\( \frac{4}{2} \)
2
What is \( 2 \)\( \sqrt{48} \) + \( 7 \)\( \sqrt{3} \)
| 9\( \sqrt{16} \) | |
| 9\( \sqrt{144} \) | |
| 14\( \sqrt{3} \) | |
| 15\( \sqrt{3} \) |
To add these radicals together their radicands must be the same:
2\( \sqrt{48} \) + 7\( \sqrt{3} \)
2\( \sqrt{16 \times 3} \) + 7\( \sqrt{3} \)
2\( \sqrt{4^2 \times 3} \) + 7\( \sqrt{3} \)
(2)(4)\( \sqrt{3} \) + 7\( \sqrt{3} \)
8\( \sqrt{3} \) + 7\( \sqrt{3} \)
Now that the radicands are identical, you can add them together:
8\( \sqrt{3} \) + 7\( \sqrt{3} \)Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 20 small cakes per hour. The kitchen is available for 3 hours and 37 large cakes and 160 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 13 | |
| 12 | |
| 11 | |
| 8 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 37 large cakes are needed for the party so \( \frac{37}{9} \) = 4\(\frac{1}{9}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 20 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 20 x 3 = 60 small cakes during that time. 160 small cakes are needed for the party so \( \frac{160}{60} \) = 2\(\frac{2}{3}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 5 + 3 = 8 cooks.
If all of a roofing company's 16 workers are required to staff 4 roofing crews, how many workers need to be added during the busy season in order to send 6 complete crews out on jobs?
| 2 | |
| 14 | |
| 18 | |
| 8 |
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 16 workers at the company now and that's enough to staff 4 crews so there are \( \frac{16}{4} \) = 4 workers on a crew. 6 crews are needed for the busy season which, at 4 workers per crew, means that the roofing company will need 6 x 4 = 24 total workers to staff the crews during the busy season. The company already employs 16 workers so they need to add 24 - 16 = 8 new staff for the busy season.