Answer:
There is a linear correlation between the chest size and weight
Proportion of the variation in weight can be explained by the linear relationship between weight and chest size is 0.006724 .
Step-by-step explanation:
Null Hypothesis:
= There is no linear correlation between the chest size and weight
Alternative Hypothesis :
=There is a linear correlation between the chest size and weight
The value of the linear correlation coefficient is r=0.882.
n = 8
Formula : ![t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Br%5Csqrt%7Bn-2%7D%7D%7B%5Csqrt%7B1-r%5E2%7D%7D)
![t=\frac{0.882\sqrt{8-2}}{\sqrt{1-(0.882)^2}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B0.882%5Csqrt%7B8-2%7D%7D%7B%5Csqrt%7B1-%280.882%29%5E2%7D%7D)
![t=4.584](https://tex.z-dn.net/?f=t%3D4.584)
Degree of freedom = n-1 = 8-1 = 7
α =0.05
so, p value is 2.365
t calculated > t critical
So, we reject the null hypothesis
So, There is a linear correlation between the chest size and weight
The proportion of the variation in weight can be explained by the linear relationship between weight and chest size = ![r^2 = (0.082)^2=0.006724](https://tex.z-dn.net/?f=r%5E2%20%3D%20%280.082%29%5E2%3D0.006724)
Hence proportion of the variation in weight can be explained by the linear relationship between weight and chest size is 0.006724 and There is a linear correlation between the chest size and weight
My brain is going to explode
Given equation is ![y= 2x^2 + 8x - 5](https://tex.z-dn.net/?f=y%3D%202x%5E2%20%2B%208x%20-%205)
To find the x coordinate of vertex we use formula
![x=\frac{-b}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%7D%7B2a%7D)
From the given equation a= 2, b= 8 and c= -5
Plug in all the values
![x=\frac{-8}{2*2}=-2](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-8%7D%7B2%2A2%7D%3D-2)
The x coordinate of vertex is x=-2
To find y coordinate of vertex we plug in -2 for x in the given equation
![y= 2x^2 + 8x - 5](https://tex.z-dn.net/?f=y%3D%202x%5E2%20%2B%208x%20-%205)
![y= 2(-2)^2 + 8(-2) - 5= 8-16-5=-13](https://tex.z-dn.net/?f=y%3D%202%28-2%29%5E2%20%2B%208%28-2%29%20-%205%3D%208-16-5%3D-13)
So vertex is (-2,-13)
Answer:
x = 8 + sqrt(3)/2 or x = 8 - sqrt(3)/2
Step-by-step explanation by completing the square:
Solve for x:
3 - 4 (x - 8)^2 = 0
Subtract 3 from both sides:
-4 (x - 8)^2 = -3
Divide both sides by -4:
(x - 8)^2 = 3/4
Take the square root of both sides:
x - 8 = sqrt(3)/2 or x - 8 = -sqrt(3)/2
Add 8 to both sides:
x = 8 + sqrt(3)/2 or x - 8 = -sqrt(3)/2
Add 8 to both sides:
Answer: x = 8 + sqrt(3)/2 or x = 8 - sqrt(3)/2