The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 11 are [11, 22, 33, 44, 55, 66, 77, 88, 99]. The first few multiples they share are [33, 66, 99] making 33 the smallest multiple 3 and 11 have in common.

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:

6c⁵ + 7c⁵
(6 + 7)c⁵
13c⁵

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 6 = \( \frac{8 \times 6}{100} \) = \( \frac{48}{100} \) = 0.48 errors per hour

So, in an average hour, the machine will produce 6 - 0.48 = 5.52 error free parts.

The machine ran for 24 - 2 = 22 hours yesterday so you would expect that 22 x 5.52 = 121.4 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 $400
i = 0.07 x $400
i = $28

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 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80]. The first few multiples they share are [8, 16, 24, 32, 40] making 8 the smallest multiple 2 and 8 share.

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

\( \frac{9 x 4}{2 x 4} \) - \( \frac{6 x 1}{8 x 1} \)

\( \frac{36}{8} \) - \( \frac{6}{8} \)

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

\( \frac{36 - 6}{8} \) = \( \frac{30}{8} \) = 3\(\frac{3}{4}\)