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

7\( \sqrt{80} \) - 3\( \sqrt{5} \)
7\( \sqrt{16 \times 5} \) - 3\( \sqrt{5} \)
7\( \sqrt{4^2 \times 5} \) - 3\( \sqrt{5} \)
(7)(4)\( \sqrt{5} \) - 3\( \sqrt{5} \)
28\( \sqrt{5} \) - 3\( \sqrt{5} \)

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

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{35}{100} \) = \( \frac{35 x 25}{100} \) = \( \frac{875}{100} \) = 8 shots

The center makes 25% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{8}{\frac{25}{100}} \) = 8 x \( \frac{100}{25} \) = \( \frac{8 x 100}{25} \) = \( \frac{800}{25} \) = 32 shots

to make the same number of shots as the guard and thus score the same number of points.

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:

\( \sqrt{\frac{16}{64}} \)
\( \frac{\sqrt{16}}{\sqrt{64}} \)
\( \frac{\sqrt{4^2}}{\sqrt{8^2}} \)
\(\frac{1}{2}\)

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

\( \frac{9}{100} \) x 7 = \( \frac{9 \times 7}{100} \) = \( \frac{63}{100} \) = 0.63 errors per hour

So, in an average hour, the machine will produce 7 - 0.63 = 6.37 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.37 = 133.8 error free parts were produced yesterday.

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