In the given question, it is given that
ramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet.
And we have to find the value of tan B.
And tangent of any angle is equal to the ratio of vertical by horizontal. That is
![tan B = \frac{8}{15}](https://tex.z-dn.net/?f=tan%20B%20%3D%20%5Cfrac%7B8%7D%7B15%7D)
And that's the required missing ratio for tan B .
Solution:
First i'm going to divide the graph into 3 parts. Linear, Quadratic and Horizontal graph.
<u>Linear:</u>
![Slope=\frac{-2-0}{-4-(-2)}=1\\y=m(x-xo)+yo\\y=1x-(-2)+(-4)\\y=x-2 , x\leq-1](https://tex.z-dn.net/?f=Slope%3D%5Cfrac%7B-2-0%7D%7B-4-%28-2%29%7D%3D1%5C%5Cy%3Dm%28x-xo%29%2Byo%5C%5Cy%3D1x-%28-2%29%2B%28-4%29%5C%5Cy%3Dx-2%20%2C%20x%5Cleq-1)
<u>Quadratic:</u>
![f(x) = a(x-h)^{2} + k\\f(x)=(x-2)^{2}-7,-1\leq x\geq 6](https://tex.z-dn.net/?f=f%28x%29%20%3D%20a%28x-h%29%5E%7B2%7D%20%2B%20k%5C%5Cf%28x%29%3D%28x-2%29%5E%7B2%7D-7%2C-1%5Cleq%20x%5Cgeq%206)
<u>Horizontal:</u>
![f(x)=7,x\geq 6](https://tex.z-dn.net/?f=f%28x%29%3D7%2Cx%5Cgeq%206)
Answer:
![f(x)=x-2 , x\leq-1\\f(x)=(x-2)^{2}-7,-1\leq x\geq 6\\f(x)=7,x\geq 6](https://tex.z-dn.net/?f=f%28x%29%3Dx-2%20%2C%20x%5Cleq-1%5C%5Cf%28x%29%3D%28x-2%29%5E%7B2%7D-7%2C-1%5Cleq%20x%5Cgeq%206%5C%5Cf%28x%29%3D7%2Cx%5Cgeq%206)
<em>Hope this was helpful.</em>
<h3>
Answer: 45 degrees</h3>
Explanation:
There are n = 8 sides in a regular octagon. The smallest angle of rotational symmetry is 360/n = 360/8 = 45 degrees. Rotating this amount will not change the regular octagon. The before and after will look identical.
Answer:
![\sum X_i = 219.8](https://tex.z-dn.net/?f=%5Csum%20X_i%20%3D%20219.8)
And we can calculate the mean with the following formula:
![\bar X = \frac{\sum_{i=1}^n X_i}{n}= \frac{219.8}{27}= 8.141](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D%3D%20%5Cfrac%7B219.8%7D%7B27%7D%3D%208.141)
We can calculate the sample variance with this formula:
![s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}= 2.819](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D%3D%202.819)
And the sample deviation would be given by:
![s= \sqrt{s^2}=\sqrt{2.819}= 1.679](https://tex.z-dn.net/?f=%20s%3D%20%5Csqrt%7Bs%5E2%7D%3D%5Csqrt%7B2.819%7D%3D%201.679)
Step-by-step explanation:
For this case we have the following data given:
7.9 9.7 9.7 8.7 7.0 7.2 11.3 11.8 7.3 8.1 8.0 11.6 6.8 9.0 6.3 7.0 7.4 8.7 6.8 5.8 7.8 7.7 6.3 7.0 7.7 6.5 10.7
Our variable of interest is given by X="flexural strength (MPa) for concrete beams of a certain type"
And for this case we know that ![\sum X_i = 219.8](https://tex.z-dn.net/?f=%5Csum%20X_i%20%3D%20219.8)
And we can calculate the mean with the following formula:
![\bar X = \frac{\sum_{i=1}^n X_i}{n}= \frac{219.8}{27}= 8.141](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D%3D%20%5Cfrac%7B219.8%7D%7B27%7D%3D%208.141)
We can calculate the sample variance with this formula:
![s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}= 2.819](https://tex.z-dn.net/?f=s%5E2%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D%3D%202.819)
And the sample deviation would be given by:
![s= \sqrt{s^2}=\sqrt{2.819}= 1.679](https://tex.z-dn.net/?f=%20s%3D%20%5Csqrt%7Bs%5E2%7D%3D%5Csqrt%7B2.819%7D%3D%201.679)
My answer is p = 5,258.92
I hope this helps