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 5 = \( \frac{3 \times 5}{100} \) = \( \frac{15}{100} \) = 0.15 errors per hour

So, in an average hour, the machine will produce 5 - 0.15 = 4.85 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 4.85 = 97 error free parts were produced yesterday.

The distributive property for multiplication helps in solving expressions like a(b + c). It specifies that the result of multiplying one number by the sum or difference of two numbers can be obtained by multiplying each number individually and then totaling the results: a(b + c) = ab + ac. For example, 4(10-5) = (4 x 10) - (4 x 5) = 40 - 20 = 20.

If 66% of the town's 11,000 voters cast ballots the number of votes cast is:

(\( \frac{66}{100} \)) x 11,000 = \( \frac{726,000}{100} \) = 7,260

The mayor got 67% of the votes cast which is:

(\( \frac{67}{100} \)) x 7,260 = \( \frac{486,420}{100} \) = 4,864 votes.

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-9b⁷ - 4b⁷
(-9 - 4)b⁷
-13b⁷

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{45}{100} \) = \( \frac{45 x 25}{100} \) = \( \frac{1125}{100} \) = 11 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 = \( \frac{11}{\frac{25}{100}} \) = 11 x \( \frac{100}{25} \) = \( \frac{11 x 100}{25} \) = \( \frac{1100}{25} \) = 44 shots

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