64% of the water consumption is industrial use and 29% is personal use so (64% - 29%) = 35% more water is used for industrial purposes. 40,000 gallons are consumed daily so industry consumes \( \frac{35}{100} \) x 40,000 gallons = 14,000 gallons.

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 = \( 60mph \times 5h \)
300 miles

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{2!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} \)
\( \frac{5 \times 4 \times 3}{1} \)
\( 5 \times 4 \times 3 \)
60

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

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

\( \frac{7 x 5}{3 x 5} \) - \( \frac{6 x 3}{5 x 3} \)

\( \frac{35}{15} \) - \( \frac{18}{15} \)

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

\( \frac{35 - 18}{15} \) = \( \frac{17}{15} \) = 1\(\frac{2}{15}\)