36% of the water consumption is industrial use and 21% is personal use so (36% - 21%) = 15% more water is used for industrial purposes. 50,000 gallons are consumed daily so industry consumes \( \frac{15}{100} \) x 50,000 gallons = 7,500 gallons.

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

The area of a circle is given by the formula A = πr² where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))². If the diameter of the logo increases by 30% the radius (and, consequently, the total area) increases by \( \frac{30\text{%}}{2} \) = 15%

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.

To add these radicals together their radicands must be the same:

3\( \sqrt{8} \) + 4\( \sqrt{2} \)
3\( \sqrt{4 \times 2} \) + 4\( \sqrt{2} \)
3\( \sqrt{2^2 \times 2} \) + 4\( \sqrt{2} \)
(3)(2)\( \sqrt{2} \) + 4\( \sqrt{2} \)
6\( \sqrt{2} \) + 4\( \sqrt{2} \)

Now that the radicands are identical, you can add them together: