54% of the water consumption is industrial use and 23% is personal use so (54% - 23%) = 31% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{31}{100} \) x 20,000 gallons = 6,200 gallons.

To fill a 6 gallon tank exactly halfway you'll need 3 gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{3 \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 2

The equation for this sequence is:

a_n = a_n-1 + 4

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 4
a₆ = 17 + 4
a₆ = 21

To divide fractions, invert the second fraction and then multiply:

\( \frac{3}{7} \) ÷ \( \frac{4}{5} \) = \( \frac{3}{7} \) x \( \frac{5}{4} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{3}{7} \) x \( \frac{5}{4} \) = \( \frac{3 x 5}{7 x 4} \) = \( \frac{15}{28} \) = \(\frac{15}{28}\)

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:

\( \frac{3!}{5!} \)
\( \frac{3 \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{5 \times 4} \)
\( \frac{1}{20} \)