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 - 4 = 20 hours yesterday so you would expect that 20 x 7.68 = 153.6 error free parts were produced yesterday.

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

\( \frac{16 + 10 + 17 + 9}{4} \) = \( \frac{52}{4} \) = 13

To multiply terms with radicals, multiply the coefficients and radicands separately:

5\( \sqrt{4} \) x 5\( \sqrt{3} \)
(5 x 5)\( \sqrt{4 \times 3} \)
25\( \sqrt{12} \)

Now we need to simplify the radical:

25\( \sqrt{12} \)
25\( \sqrt{3 \times 4} \)
25\( \sqrt{3 \times 2^2} \)
(25)(2)\( \sqrt{3} \)
50\( \sqrt{3} \)

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

9\( \sqrt{8} \) - 2\( \sqrt{2} \)
9\( \sqrt{4 \times 2} \) - 2\( \sqrt{2} \)
9\( \sqrt{2^2 \times 2} \) - 2\( \sqrt{2} \)
(9)(2)\( \sqrt{2} \) - 2\( \sqrt{2} \)
18\( \sqrt{2} \) - 2\( \sqrt{2} \)

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

A number with an exponent (b^e) consists of a base (b) raised to a power (e). The exponent indicates the number of times that the base is multiplied by itself. A base with an exponent of 1 equals the base (b¹ = b) and a base with an exponent of 0 equals 1 ( (b⁰ = 1).