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

\( \frac{2}{100} \) x 6 = \( \frac{2 \times 6}{100} \) = \( \frac{12}{100} \) = 0.12 errors per hour

So, in an average hour, the machine will produce 6 - 0.12 = 5.88 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 5.88 = 117.6 error free parts were produced yesterday.

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{36}{64}} \)
\( \frac{\sqrt{36}}{\sqrt{64}} \)
\( \frac{\sqrt{6^2}}{\sqrt{8^2}} \)
\(\frac{3}{4}\)

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

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 30mph \times 8h \)
240 miles

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

8\( \sqrt{175} \) - 7\( \sqrt{7} \)
8\( \sqrt{25 \times 7} \) - 7\( \sqrt{7} \)
8\( \sqrt{5^2 \times 7} \) - 7\( \sqrt{7} \)
(8)(5)\( \sqrt{7} \) - 7\( \sqrt{7} \)
40\( \sqrt{7} \) - 7\( \sqrt{7} \)

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

The greatest common factor (GCF) is the greatest factor that divides two integers.