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. 37 large cakes are needed for the party so \( \frac{37}{15} \) = 2\(\frac{7}{15}\) 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. 190 small cakes are needed for the party so \( \frac{190}{60} \) = 3\(\frac{1}{6}\) 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 + 4 = 7 cooks.

First, solve for \( \left|b - 6\right| \):

\( \left|b - 6\right| \) - 6 = -4
\( \left|b - 6\right| \) = -4 + 6
\( \left|b - 6\right| \) = 2

The value inside the absolute value brackets can be either positive or negative so (b - 6) must equal + 2 or -2 for \( \left|b - 6\right| \) to equal 2:

So, b = 4 or b = 8.

To simplify a radical, factor out the perfect squares:

\( \sqrt{75} \)
\( \sqrt{25 \times 3} \)
\( \sqrt{5^2 \times 3} \)
5\( \sqrt{3} \)

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. 6 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 6 x 3 = 18 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 18 - 6 = 12 new staff for the busy season.

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 60mph \times 8h \)
480 miles