The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $100
i = 0.05 x $100
i = $5

33% of the water consumption is industrial use and 10% is personal use so (33% - 10%) = 23% more water is used for industrial purposes. 5,000 gallons are consumed daily so industry consumes \( \frac{23}{100} \) x 5,000 gallons = 1,150 gallons.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

-7y⁴ + 8y⁴
(-7 + 8)y⁴
y⁴

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

\( \frac{2}{5} \) ÷ \( \frac{1}{7} \) = \( \frac{2}{5} \) x \( \frac{7}{1} \)

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

\( \frac{2}{5} \) x \( \frac{7}{1} \) = \( \frac{2 x 7}{5 x 1} \) = \( \frac{14}{5} \) = 2\(\frac{4}{5}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

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

\( \frac{2 x 2}{2 x 2} \) - \( \frac{2 x 1}{4 x 1} \)

\( \frac{4}{4} \) - \( \frac{2}{4} \)

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

\( \frac{4 - 2}{4} \) = \( \frac{2}{4} \) = \(\frac{1}{2}\)