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

3y² - 9y²
(3 - 9)y²
-6y²

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

The amount of flour you need is (1\(\frac{7}{8}\) - 1) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{15}{8} \) - \( \frac{8}{8} \)) cups
\( \frac{7}{8} \) cups
\(\frac{7}{8}\) cups

The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:

\( \frac{4}{100} \) x 8 = \( \frac{4 \times 8}{100} \) = \( \frac{32}{100} \) = 0.32 errors per hour

So, in an average hour, the machine will produce 8 - 0.32 = 7.68 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 7.68 = 115.2 error free parts were produced yesterday.

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 $300
i = 0.01 x $300
i = $3