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. 9 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 9 x 2 = 18 total workers to staff the crews during the busy season. The company already employs 8 workers so they need to add 18 - 8 = 10 new staff for the busy season.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 4 and 6 share.

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

\( \frac{3 x 3}{4 x 3} \) + \( \frac{3 x 2}{6 x 2} \)

\( \frac{9}{12} \) + \( \frac{6}{12} \)

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

\( \frac{9 + 6}{12} \) = \( \frac{15}{12} \) = 1\(\frac{1}{4}\)

66% of the water consumption is industrial use and 35% is personal use so (66% - 35%) = 31% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{31}{100} \) x 40,000 gallons = 12,400 gallons.

There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 9 people needing transportation leaving 9 - 8 = 1 who will have to find other transportation.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-5b⁶ - 7b⁶
(-5 - 7)b⁶
-12b⁶