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

\( \frac{4}{100} \) x 8 = \( \frac{4 \times 8}{100} \) = \( \frac{32}{100} \) = 0.32 errors per hour

So, in an average hour, the machine will produce 8 - 0.32 = 7.68 error free parts.

The machine ran for 24 - 8 = 16 hours yesterday so you would expect that 16 x 7.68 = 122.9 error free parts were produced yesterday.

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{2!} \)
\( \frac{3 \times 2 \times 1}{2 \times 1} \)
\( \frac{3}{1} \)
3

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

8\( \sqrt{48} \) - 7\( \sqrt{3} \)
8\( \sqrt{16 \times 3} \) - 7\( \sqrt{3} \)
8\( \sqrt{4^2 \times 3} \) - 7\( \sqrt{3} \)
(8)(4)\( \sqrt{3} \) - 7\( \sqrt{3} \)
32\( \sqrt{3} \) - 7\( \sqrt{3} \)

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

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 = \( 45mph \times 6h \)
270 miles

The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.