If 48% of the town's 12,000 voters cast ballots the number of votes cast is:

(\( \frac{48}{100} \)) x 12,000 = \( \frac{576,000}{100} \) = 5,760

The mayor got 58% of the votes cast which is:

(\( \frac{58}{100} \)) x 5,760 = \( \frac{334,080}{100} \) = 3,341 votes.

If a single cook can bake 3 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 3 x 3 = 9 large cakes during that time. 30 large cakes are needed for the party so \( \frac{30}{9} \) = 3\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 13 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 13 x 3 = 39 small cakes during that time. 350 small cakes are needed for the party so \( \frac{350}{39} \) = 8\(\frac{38}{39}\) cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 4 + 9 = 13 cooks.

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:

\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)

The greatest common factor (GCF) is the greatest factor that divides two integers.

38% of the water consumption is industrial use and 19% is personal use so (38% - 19%) = 19% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{19}{100} \) x 5,000 gallons = 950 gallons.