Mathematics: Ms. Mosher recorded the math test scores of six students in the table below. Student Student Score 72 Andrew John 80 85 George Amber 93 78 Betty Roberto 80 Determine the mean of the student scores, to the nearest tenth. Determine the median of the student scores. Describe the effect on the mean and the median if Ms. Mosher adds 5 bonus points to each of the six students scores.

1. 2. The excluded values are x = 0 (not removable), x = -2 (not removable), and x = 2 (removable)Explanation:The excluded values are those that make any denominator 0.1. Excluded values for 2. Excluded values for 3. Join both setsThe excluded values are x = 0, x = -2, and x = 24. Simplify At the end, the factor x - 2 was canceled, meaning that the excluded value x = 2 is removable.x...

Ms. Mosher recorded the math test scores of six

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greg777

07.10.2021

Mathematics

1. $\dfrac{x+1}{x(x+2)}$

2. The excluded values are x = 0 (not removable), x = -2 (not removable), and x = 2 (removable)

Explanation:

The excluded values are those that make any denominator 0.

1. Excluded values for

$-\dfrac{2}{x^2-4}$

$x^2-4=0\implies x^2=4\implies x=\pm2$

2. Excluded values for

$\dfrac{x-1}{x^2-2x}$

$x^2-2x=0\implies x(x-2)\implies x=0\text{ }and\text{ } x=2$

3. Join both sets

The excluded values are x = 0, x = -2, and x = 2

4. Simplify

$-\dfrac{2}{x^2-4}+\dfrac{x-1}{x^2-2x}=-\dfrac{2}{(x+2)(x-2)}+\dfrac{x-1}{x(x-2)}=\\ \\ \\ \dfrac{-2x+(x+2)(x-1)}{(x+2)(x-2)x}=\\ \\ \\ \dfrac{-2x+x^2+x-2}{(x+2)(x-2)x}=\dfrac{x^2-x-2}{(x+2)(x-2)x}=\dfrac{(x-2)(x+1)}{(x+2)(x-2)x}=\\ \\ \\ \dfrac{x+1}{(x+2)x}$

At the end, the factor x - 2 was canceled, meaning that the excluded value x = 2 is removable.x = -2 and x = 0 yet make the final expression undefined, thus they are not removable.

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