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.

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.

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{420mi}{60mph} \)
7 hours

The number of students taking German or Spanish is 10 + 8 = 18. Of that group of 18, 4 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 18 - 4 = 14 who are taking at least one language. 28 - 14 = 14 students who are not taking either language.

First, solve for \( \left|y + 7\right| \):

\( \left|y + 7\right| \) + 5 = 8
\( \left|y + 7\right| \) = 8 - 5
\( \left|y + 7\right| \) = 3

The value inside the absolute value brackets can be either positive or negative so (y + 7) must equal + 3 or -3 for \( \left|y + 7\right| \) to equal 3:

So, y = -10 or y = -4.