Hi
2/3 y+y-4=31
Simplify both sides of the equation
2/3 y-4=31
Combine like terms
(2/3 y+y)+(-4)=31
5/3 y-4=31
Add 4 to both sides
5/3 y-4+4=31+4
5/3 y=35
Multiply both sides 3/5
(3/5)*(5/3 y)=(3/5)*35
y=21
I hope that's help !
The answer to the question of yours is A. Rotation Its not B. because the question is asking by turning one triangle 90 degrees. This would mean that B. is incorrect since its turning. It wouldn't be C. because it isn't translating 90 degrees left or right its turning. And it most definitely wouldn't be D. Dilation because the triangle isn't decreasing or enlarging. Hope this helped feel free to ask any more questions.
Answer:
Test statistic,
(to 3 dp)
Step-by-step explanation:
Deviation, d = x -y
Sample mean for the deviation
![\bar{d} = \frac{\sum x-y}{n}](https://tex.z-dn.net/?f=%5Cbar%7Bd%7D%20%3D%20%5Cfrac%7B%5Csum%20x-y%7D%7Bn%7D)
![\bar{d} = \frac{(28-6) + (31-27)+(20-26)+(25-25)+(28-29)+(27-32)+(33-33)+(35-34)}{8} \\\bar{d} = -0.625](https://tex.z-dn.net/?f=%5Cbar%7Bd%7D%20%3D%20%5Cfrac%7B%2828-6%29%20%2B%20%2831-27%29%2B%2820-26%29%2B%2825-25%29%2B%2828-29%29%2B%2827-32%29%2B%2833-33%29%2B%2835-34%29%7D%7B8%7D%20%5C%5C%5Cbar%7Bd%7D%20%3D%20-0.625)
Standard deviation: ![SD = \sqrt{\frac{\sum d^{2} - n \bar{d}^2}{n-1} }](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%20d%5E%7B2%7D%20-%20n%20%5Cbar%7Bd%7D%5E2%7D%7Bn-1%7D%20%20%7D)
![\sum d^{2} = (28-26)^2 + (31-27)^2 +(20-26)^2 +(25-25)^2 +(28-29)^2 +(27-32)^2 +(33-33)^2 +(35-34)^2\\\sum d^{2} = 63](https://tex.z-dn.net/?f=%5Csum%20d%5E%7B2%7D%20%20%3D%20%2828-26%29%5E2%20%2B%20%2831-27%29%5E2%20%2B%2820-26%29%5E2%20%2B%2825-25%29%5E2%20%2B%2828-29%29%5E2%20%2B%2827-32%29%5E2%20%2B%2833-33%29%5E2%20%2B%2835-34%29%5E2%5C%5C%5Csum%20d%5E%7B2%7D%20%20%3D%2063)
![SD = \sqrt{\frac{63 - 8 * (-0.625)^2}{8-1} }](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%5Cfrac%7B63%20-%208%20%2A%20%20%28-0.625%29%5E2%7D%7B8-1%7D%20%20%7D)
SD =2.93
Under the null hypothesis, the formula for the test statistics will be given by:
![t_{s} = \frac{ \bar{d}}{s_{d}/\sqrt{n} } \\t_{s} = \frac{- 0.625}{2.93/\sqrt{8} }](https://tex.z-dn.net/?f=t_%7Bs%7D%20%3D%20%5Cfrac%7B%20%5Cbar%7Bd%7D%7D%7Bs_%7Bd%7D%2F%5Csqrt%7Bn%7D%20%20%7D%20%5C%5Ct_%7Bs%7D%20%3D%20%5Cfrac%7B-%200.625%7D%7B2.93%2F%5Csqrt%7B8%7D%20%20%7D)
![t_{s} = -0.6033](https://tex.z-dn.net/?f=t_%7Bs%7D%20%3D%20-0.6033)