Average speed in miles per hour is the number of miles traveled divided by the number of hours:

You have 9 out of the total of 100 raffle tickets sold so you have a (\( \frac{9}{100} \)) x 100 = \( \frac{9 \times 100}{100} \) = \( \frac{900}{100} \) = 9% chance to win the raffle.

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 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 5 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 5 x 3 = 15 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 15 - 9 = 6 new staff for the busy season.

The equation for this sequence is:

a_n = a_n-1 + 9

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 9
a₆ = 37 + 9
a₆ = 46

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 9 are [9, 18, 27, 36, 45, 54, 63, 72, 81, 90] and the first few multiples of 15 are [15, 30, 45, 60, 75, 90]. The first few multiples they share are [45, 90] making 45 the smallest multiple 9 and 15 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{9 x 5}{9 x 5} \) - \( \frac{9 x 3}{15 x 3} \)

\( \frac{45}{45} \) - \( \frac{27}{45} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{45 - 27}{45} \) = \( \frac{18}{45} \) = \(\frac{2}{5}\)