56% of the water consumption is industrial use and 32% is personal use so (56% - 32%) = 24% more water is used for industrial purposes. 20,000 gallons are consumed daily so industry consumes \( \frac{24}{100} \) x 20,000 gallons = 4,800 gallons.

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 40 large cakes are needed for the party so \( \frac{40}{10} \) = 4 cooks are needed to bake the required number of large cakes.

If a single cook can bake 14 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 14 x 2 = 28 small cakes during that time. 300 small cakes are needed for the party so \( \frac{300}{28} \) = 10\(\frac{5}{7}\) 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 + 11 = 15 cooks.

To simplify a radical, factor out the perfect squares:

\( \sqrt{45} \)
\( \sqrt{9 \times 5} \)
\( \sqrt{3^2 \times 5} \)
3\( \sqrt{5} \)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [30, 60, 90] making 30 the smallest multiple 6 and 10 share.

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

\( \frac{2 x 5}{6 x 5} \) - \( \frac{8 x 3}{10 x 3} \)

\( \frac{10}{30} \) - \( \frac{24}{30} \)

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

\( \frac{10 - 24}{30} \) = \( \frac{-14}{30} \) = -\(\frac{7}{15}\)

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.