Distributive property says 4 * a and 4 * -1 so 4a - 4 - 5 = 3a + 7
Now do the simple subtraction
-4 - 5 = -9
Then add 9 and subtract 3a <span>Remember: Always do the opposite operation to <span><em>both
</em><em />sides. So you have a = 16<em>
</em></span></span>
Your answer is option d. (3,-1)
Answer:
(a) -1.0133
(b) 2.32
(c) -2
(d) 0.9867
(e) 2.9867
Step-by-step explanation:
The <em>z</em>-score of a raw score <em>X</em> is a standardized score that follows a normal distribution with mean 0 and standard deviation 1.
The formula to compute the <em>z</em>-score is:
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
<u>Given</u>:
Mean (<em>μ</em>) = $775
Standard deviation (<em>σ</em>) = $75
(a)
For <em>X</em> = $699 the <em>z</em>-score is:
![z=\frac{x-\mu}{\sigma}\\=\frac{699-775}{75} \\=-1.0133](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5C%5C%3D%5Cfrac%7B699-775%7D%7B75%7D%20%5C%5C%3D-1.0133)
(b)
For <em>X</em> = $949 the <em>z</em>-score is:
![z=\frac{x-\mu}{\sigma}\\=\frac{949-775}{75} \\=2.32](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5C%5C%3D%5Cfrac%7B949-775%7D%7B75%7D%20%5C%5C%3D2.32)
(c)
For <em>X</em> = $625 the <em>z</em>-score is:
![z=\frac{x-\mu}{\sigma}\\=\frac{625-775}{75} \\=-2](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5C%5C%3D%5Cfrac%7B625-775%7D%7B75%7D%20%5C%5C%3D-2)
(d)
For <em>X</em> = $849 the <em>z</em>-score is:
![z=\frac{x-\mu}{\sigma}\\=\frac{849-775}{75} \\=0.9867](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5C%5C%3D%5Cfrac%7B849-775%7D%7B75%7D%20%5C%5C%3D0.9867)
(e)
For <em>X</em> = $999 the <em>z</em>-score is:
![z=\frac{x-\mu}{\sigma}\\=\frac{999-775}{75} \\=2.9867](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5C%5C%3D%5Cfrac%7B999-775%7D%7B75%7D%20%5C%5C%3D2.9867)
Distribute on the left
-4x+6=2x
Get x onto one side. Add 4x to both sides
6=6x
Divide both sides by 6
1=x
Final answer: x=1