If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 38 large cakes are needed for the party so \( \frac{38}{15} \) = 2\(\frac{8}{15}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 10 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 10 x 3 = 30 small cakes during that time. 180 small cakes are needed for the party so \( \frac{180}{30} \) = 6 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 3 + 6 = 9 cooks.

A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{7} \) x \( \frac{2}{9} \) = \( \frac{3 x 2}{7 x 9} \) = \( \frac{6}{63} \) = \(\frac{2}{21}\)

The equation for this sequence is:

a_n = a_n-1 + 4(n - 1)

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 + 4(6 - 1)
a₆ = 41 + 4(5)
a₆ = 61

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 6 workers at the company now and that's enough to staff 2 crews so there are \( \frac{6}{2} \) = 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 6 workers so they need to add 15 - 6 = 9 new staff for the busy season.