To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{7} \) ÷ \( \frac{1}{7} \) = \( \frac{2}{7} \) x \( \frac{7}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{7} \) x \( \frac{7}{1} \) = \( \frac{2 x 7}{7 x 1} \) = \( \frac{14}{7} \) = 2

The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 32 are [1, 2, 4, 8, 16, 32]. They share 4 factors [1, 2, 4, 8] making 8 the greatest factor 24 and 32 have in common.

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

\( \frac{3}{100} \) x 5 = \( \frac{3 \times 5}{100} \) = \( \frac{15}{100} \) = 0.15 errors per hour

So, in an average hour, the machine will produce 5 - 0.15 = 4.85 error free parts.

The machine ran for 24 - 7 = 17 hours yesterday so you would expect that 17 x 4.85 = 82.4 error free parts were produced yesterday.

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

2\( \sqrt{32} \) + 5\( \sqrt{2} \)
2\( \sqrt{16 \times 2} \) + 5\( \sqrt{2} \)
2\( \sqrt{4^2 \times 2} \) + 5\( \sqrt{2} \)
(2)(4)\( \sqrt{2} \) + 5\( \sqrt{2} \)
8\( \sqrt{2} \) + 5\( \sqrt{2} \)

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

There are 3 2-passenger taxis available so that's 3 x 2 = 6 total seats. There are 9 people needing transportation leaving 9 - 6 = 3 who will have to find other transportation.