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.

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

\( \frac{8}{100} \) x 9 = \( \frac{8 \times 9}{100} \) = \( \frac{72}{100} \) = 0.72 errors per hour

So, in an average hour, the machine will produce 9 - 0.72 = 8.28 error free parts.

The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 8.28 = 157.3 error free parts were produced yesterday.

Calculate the number of vans needed by dividing the number of people that need transported by the capacity of one van:

vans = \( \frac{37}{8} \) = 4\(\frac{5}{8}\)

So, it will take 4 full vans and one partially full van to transport the entire team making a total of 5 vans.

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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.