To fill a 25 gallon tank exactly halfway you'll need 12\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{12\frac{1}{2} \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 5

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 12 workers at the company now and that's enough to staff 4 crews so there are \( \frac{12}{4} \) = 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 12 workers so they need to add 18 - 12 = 6 new staff for the busy season.

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

First, solve for \( \left|z - 7\right| \):

\( \left|z - 7\right| \) - 5 = -1
\( \left|z - 7\right| \) = -1 + 5
\( \left|z - 7\right| \) = 4

The value inside the absolute value brackets can be either positive or negative so (z - 7) must equal + 4 or -4 for \( \left|z - 7\right| \) to equal 4:

So, z = 3 or z = 11.

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).