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 8 workers at the company now and that's enough to staff 4 crews so there are \( \frac{8}{4} \) = 2 workers on a crew. 6 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 6 x 2 = 12 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 12 - 8 = 4 new staff for the busy season.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{4!} \)
\( \frac{3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \)
\( \frac{1}{4} \)
\( \frac{1}{4} \)

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{4}{100} \) x 8 = \( \frac{4 \times 8}{100} \) = \( \frac{32}{100} \) = 0.32 errors per hour

So, in an average hour, the machine will produce 8 - 0.32 = 7.68 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 7.68 = 130.6 error free parts were produced yesterday.

By buying two shirts, Ezra will save $13 x \( \frac{40}{100} \) = \( \frac{$13 x 40}{100} \) = \( \frac{$520}{100} \) = $5.20 on the second shirt.

So, his total cost will be
$13.00 + ($13.00 - $5.20)
$13.00 + $7.80
$20.80

You have 8 out of the total of 100 raffle tickets sold so you have a (\( \frac{8}{100} \)) x 100 = \( \frac{8 \times 100}{100} \) = \( \frac{800}{100} \) = 8% chance to win the raffle.