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 $1,400
i = 0.08 x $1,400

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

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

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

3\( \sqrt{18} \) + 7\( \sqrt{2} \)
3\( \sqrt{9 \times 2} \) + 7\( \sqrt{2} \)
3\( \sqrt{3^2 \times 2} \) + 7\( \sqrt{2} \)
(3)(3)\( \sqrt{2} \) + 7\( \sqrt{2} \)
9\( \sqrt{2} \) + 7\( \sqrt{2} \)

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

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 10 = \( \frac{8 \times 10}{100} \) = \( \frac{80}{100} \) = 0.8 errors per hour

So, in an average hour, the machine will produce 10 - 0.8 = 9.2 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 9.2 = 156.4 error free parts were produced yesterday.

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, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).