Question

① use substitution to match these solutions to their equations. {27, 12, 36, 7} $\frac{a}{3}=9$, a = __ $\frac{b}{6}=6$, b = $\frac{36}{c}=3$, c = ② which expression is equal to: (a • b) + (a • c) ① a(b + c) ② a • b • c ③ (a • b) • c ④ a + b + a ③ income tax rates for 7 states (%). 6, 8, 3, 5, 6, 7, 0 mean = median = mode(s) = range = __

Explanation:

Step1: Solve for a in $\frac{a}{3}=9$

Multiply both sides by 3. So $a = 9\times3=27$.

Step2: Solve for b in $\frac{b}{6}=6$

Multiply both sides by 6. So $b = 6\times6 = 36$.

Step3: Solve for c in $\frac{36}{c}=3$

Cross - multiply: $3c=36$, then $c=\frac{36}{3}=12$.

Step4: Identify the distributive property for $(a\cdot b)+(a\cdot c)$

By the distributive property of multiplication over addition, $(a\cdot b)+(a\cdot c)=a(b + c)$. So the answer is A.

Step5: Calculate the mean of the income - tax rates

The sum of the rates $6 + 8+3 + 5+6 + 7+0=35$. There are 7 data points. The mean is $\frac{35}{7}=5$.

Step6: Calculate the median of the income - tax rates

Arrange the data in ascending order: $0,3,5,6,6,7,8$. The middle value (since $n = 7$) is the 4th value, so the median is 6.

Step7: Calculate the mode of the income - tax rates

The number 6 appears twice, more frequently than other numbers, so the mode is 6.

Step8: Calculate the range of the income - tax rates

The range is the difference between the largest and the smallest values. $8−0 = 8$.

Answer:

1. a = 27, b = 36, c = 12
2. A. a(b + c)
3. mean = 5, median = 6, mode(s) = 6, range = 8