Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

4 + (2 + 4) ÷ 3 x 3 - 3²
P: 4 + (6) ÷ 3 x 3 - 3²
E: 4 + 6 ÷ 3 x 3 - 9
MD: 4 + \( \frac{6}{3} \) x 3 - 9
MD: 4 + \( \frac{18}{3} \) - 9
AS: \( \frac{12}{3} \) + \( \frac{18}{3} \) - 9
AS: \( \frac{30}{3} \) - 9
AS: \( \frac{30 - 27}{3} \)
\( \frac{3}{3} \)
1

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

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

\( \frac{7}{100} \) x 8 = \( \frac{7 \times 8}{100} \) = \( \frac{56}{100} \) = 0.56 errors per hour

So, in an average hour, the machine will produce 8 - 0.56 = 7.4399999999999995 error free parts.

The machine ran for 24 - 4 = 20 hours yesterday so you would expect that 20 x 7.4399999999999995 = 148.8 error free parts were produced yesterday.

The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{14 + 12 + 16 + 10}{4} \) = \( \frac{52}{4} \) = 13