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

\( \frac{3}{100} \) x 8 = \( \frac{3 \times 8}{100} \) = \( \frac{24}{100} \) = 0.24 errors per hour

So, in an average hour, the machine will produce 8 - 0.24 = 7.76 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 7.76 = 124.2 error free parts were produced yesterday.

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 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 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.

You have 10 out of the total of 200 raffle tickets sold so you have a (\( \frac{10}{200} \)) x 100 = \( \frac{10 \times 100}{200} \) = \( \frac{1000}{200} \) = 5% chance to win the raffle.