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

\( \frac{7}{100} \) x 10 = \( \frac{7 \times 10}{100} \) = \( \frac{70}{100} \) = 0.7 errors per hour

So, in an average hour, the machine will produce 10 - 0.7 = 9.3 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 9.3 = 176.7 error free parts were produced yesterday.

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

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

\( \frac{3}{8} \) ÷ \( \frac{3}{5} \) = \( \frac{3}{8} \) x \( \frac{5}{3} \)

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

\( \frac{3}{8} \) x \( \frac{5}{3} \) = \( \frac{3 x 5}{8 x 3} \) = \( \frac{15}{24} \) = \(\frac{5}{8}\)

To simplify this fraction, first find the greatest common factor between them. The factors of 32 are [1, 2, 4, 8, 16, 32] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 6 factors [1, 2, 4, 8, 16, 32] making 32 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{32}{64} \) = \( \frac{\frac{32}{32}}{\frac{64}{32}} \) = \( \frac{1}{2} \)

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

9\( \sqrt{75} \) - 6\( \sqrt{3} \)
9\( \sqrt{25 \times 3} \) - 6\( \sqrt{3} \)
9\( \sqrt{5^2 \times 3} \) - 6\( \sqrt{3} \)
(9)(5)\( \sqrt{3} \) - 6\( \sqrt{3} \)
45\( \sqrt{3} \) - 6\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them: