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

\( \frac{3}{100} \) x 9 = \( \frac{3 \times 9}{100} \) = \( \frac{27}{100} \) = 0.27 errors per hour

So, in an average hour, the machine will produce 9 - 0.27 = 8.73 error free parts.

The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 8.73 = 157.1 error free parts were produced yesterday.

You have 3 out of the total of 100 raffle tickets sold so you have a (\( \frac{3}{100} \)) x 100 = \( \frac{3 \times 100}{100} \) = \( \frac{300}{100} \) = 3% chance to win the raffle.

A factorial has the form n! and is the product of the integer (n) and all the positive integers below it. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

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

9\( \sqrt{9} \) x 9\( \sqrt{2} \)
(9 x 9)\( \sqrt{9 \times 2} \)
81\( \sqrt{18} \)

Now we need to simplify the radical:

81\( \sqrt{18} \)
81\( \sqrt{2 \times 9} \)
81\( \sqrt{2 \times 3^2} \)
(81)(3)\( \sqrt{2} \)
243\( \sqrt{2} \)

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).