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

\( \frac{8}{100} \) x 5 = \( \frac{8 \times 5}{100} \) = \( \frac{40}{100} \) = 0.4 errors per hour

So, in an average hour, the machine will produce 5 - 0.4 = 4.6 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 4.6 = 78.2 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 $900
i = 0.09 x $900

No payments were made so the total amount due is the original amount + the accumulated interest:

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.

If a single cook can bake 2 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 2 x 3 = 6 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{6} \) = 4\(\frac{2}{3}\) 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 3 hours, a single cook can bake 20 x 3 = 60 small cakes during that time. 370 small cakes are needed for the party so \( \frac{370}{60} \) = 6\(\frac{1}{6}\) 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 5 + 7 = 12 cooks.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents: