To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 8 are [8, 16, 24, 32, 40, 48, 56, 64, 72, 80] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [40, 80] making 40 the smallest multiple 8 and 10 share.

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

\( \frac{8 x 5}{8 x 5} \) - \( \frac{9 x 4}{10 x 4} \)

\( \frac{40}{40} \) - \( \frac{36}{40} \)

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

\( \frac{40 - 36}{40} \) = \( \frac{4}{40} \) = \(\frac{1}{10}\)

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

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

So, in an average hour, the machine will produce 8 - 0.48 = 7.52 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 7.52 = 150.4 error free parts were produced yesterday.

The number of students taking German or Spanish is 8 + 13 = 21. Of that group of 21, 7 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 21 - 7 = 14 who are taking at least one language. 29 - 14 = 15 students who are not taking either language.

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.