A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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

\( \frac{2}{100} \) x 7 = \( \frac{2 \times 7}{100} \) = \( \frac{14}{100} \) = 0.14 errors per hour

So, in an average hour, the machine will produce 7 - 0.14 = 6.86 error free parts.

The machine ran for 24 - 3 = 21 hours yesterday so you would expect that 21 x 6.86 = 144.1 error free parts were produced yesterday.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

8,953,000 in scientific notation is 8.953 x 10⁶

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 20 x \( \frac{50}{100} \) = \( \frac{50 x 20}{100} \) = \( \frac{1000}{100} \) = 10 shots

The center makes 40% 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 = \( \frac{10}{\frac{40}{100}} \) = 10 x \( \frac{100}{40} \) = \( \frac{10 x 100}{40} \) = \( \frac{1000}{40} \) = 25 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:

\( \sqrt{\frac{4}{4}} \)
\( \frac{\sqrt{4}}{\sqrt{4}} \)
\( \frac{\sqrt{2^2}}{\sqrt{2^2}} \)
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