Question

1. what is the sum of the solutions of the 2 equations below?

8x = 12
2y + 10 = 22
a. 2\frac{2}{5}
b. 7\frac{1}{2}
c. 9
d. 10
e. 17\frac{1}{2}

1. the average of 5 distinct scores has the same value as the median of the 5 scores. the sum of the 5 scores is 420. what is the sum of the 4 scores that are not the median?

f. 315
g. 320
h. 336
j. 350
k. 360

1. what is the value of the expression below?

- 8 + 4

-

3 - 9

a. - 18
b. - 2
c. 0
d. 2
e. 18

1. which of the following expressions is equivalent to x^{\frac{2}{3}}?

f. \frac{x^{2}}{3}
g. \frac{x(2)}{3}
h. \sqrt{x^{3}}
j. \sqrt3{x}
k. \sqrt3{x^{2}}
go on to the next page.

Explanation:

Step1: Solve the first equation

For \(8x = 12\), divide both sides by \(8\).
\(x=\frac{12}{8}=\frac{3}{2}\)

Step2: Solve the second equation

For \(2y + 10=22\), first subtract \(10\) from both sides: \(2y=22 - 10=12\). Then divide both sides by \(2\), \(y = 6\)

Step3: Find the sum of the solutions

The sum of \(x\) and \(y\) is \(\frac{3}{2}+6=\frac{3 + 12}{2}=\frac{15}{2}=7\frac{1}{2}\)

Step1: Use the average formula

The average of \(n\) numbers is \(\text{Average}=\frac{\text{Sum of numbers}}{n}\). Given \(n = 5\) and \(\text{Sum}=420\), the average \(\bar{x}=\frac{420}{5}=84\)

Step2: Relate average and median

Since the average is equal to the median, the median \(m = 84\)

Step3: Find the sum of non - median scores

The sum of the \(4\) non - median scores is \(420-84 = 336\)

Step1: Simplify the inner absolute values

First, \(\vert-8 + 4\vert=\vert-4\vert = 4\) and \(\vert3-9\vert=\vert-6\vert = 6\)

Step2: Simplify the outer absolute value

\(\vert\vert-8 + 4\vert-\vert3 - 9\vert\vert=\vert4 - 6\vert=\vert-2\vert=2\)

Step1: Use the rule of exponents \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\)

For \(x^{\frac{2}{3}}\), by the rule \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) (where \(a=x\), \(m = 2\), \(n = 3\)), we have \(x^{\frac{2}{3}}=\sqrt[3]{x^{2}}\)

Answer:

B. \(7\frac{1}{2}\)