The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

42% of the water consumption is industrial use and 21% is personal use so (42% - 21%) = 21% more water is used for industrial purposes. 35,000 gallons are consumed daily so industry consumes \( \frac{21}{100} \) x 35,000 gallons = 7,350 gallons.

If a single cook can bake 4 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 4 x 4 = 16 large cakes during that time. 31 large cakes are needed for the party so \( \frac{31}{16} \) = 1\(\frac{15}{16}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 20 x 4 = 80 small cakes during that time. 480 small cakes are needed for the party so \( \frac{480}{80} \) = 6 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 2 + 6 = 8 cooks.

To simplify a radical, factor out the perfect squares:

\( \sqrt{50} \)
\( \sqrt{25 \times 2} \)
\( \sqrt{5^2 \times 2} \)
5\( \sqrt{2} \)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{4}{49}} \)
\( \frac{\sqrt{4}}{\sqrt{49}} \)
\( \frac{\sqrt{2^2}}{\sqrt{7^2}} \)
\(\frac{2}{7}\)