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 7 = \( \frac{6 \times 7}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour

So, in an average hour, the machine will produce 7 - 0.42 = 6.58 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 6.58 = 131.6 error free parts were produced yesterday.

By buying two shirts, Ezra will save $42 x \( \frac{35}{100} \) = \( \frac{$42 x 35}{100} \) = \( \frac{$1470}{100} \) = $14.70 on the second shirt.

So, his total cost will be
$42.00 + ($42.00 - $14.70)
$42.00 + $27.30
$69.30

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:

\( \frac{4!}{3!} \)
\( \frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \)
\( \frac{4}{1} \)
4

First, solve for \( \left|z + 5\right| \):

\( \left|z + 5\right| \) - 1 = 2
\( \left|z + 5\right| \) = 2 + 1
\( \left|z + 5\right| \) = 3

The value inside the absolute value brackets can be either positive or negative so (z + 5) must equal + 3 or -3 for \( \left|z + 5\right| \) to equal 3:

So, z = -8 or z = -2.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{16 + 14 + 19 + 11}{4} \) = \( \frac{60}{4} \) = 15