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 7 = \( \frac{4 \times 7}{100} \) = \( \frac{28}{100} \) = 0.28 errors per hour

So, in an average hour, the machine will produce 7 - 0.28 = 6.72 error free parts.

The machine ran for 24 - 9 = 15 hours yesterday so you would expect that 15 x 6.72 = 100.8 error free parts were produced yesterday.

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.

The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 have in common.

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 $700
i = 0.03 x $700

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

To simplify a radical, factor out the perfect squares:

\( \sqrt{125} \)
\( \sqrt{25 \times 5} \)
\( \sqrt{5^2 \times 5} \)
5\( \sqrt{5} \)