Answer:
25°
Step-by-step explanation:
hope it helps you solve the question
Answer: draw a straight line trough point B, same thing with the second one,for the third you must draw a straight line from the angle across to the segment. (make sure all of the intersections are 90 degrees
You can compute both the mean and second moment directly using the density function; in this case, it's
Then the mean (first moment) is
![E[X]=\displaystyle\int_{-\infty}^\infty x\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x\,\mathrm dx=710](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5C%2C%5Cmathrm%20dx%3D710)
and the second moment is
![E[X^2]=\displaystyle\int_{-\infty}^\infty x^2\,f_X(x)\,\mathrm dx=\frac1{80}\int_{670}^{750}x^2\,\mathrm dx=\frac{1,513,900}3](https://tex.z-dn.net/?f=E%5BX%5E2%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20x%5E2%5C%2Cf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cfrac1%7B80%7D%5Cint_%7B670%7D%5E%7B750%7Dx%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B1%2C513%2C900%7D3)
The second moment is useful in finding the variance, which is given by
![V[X]=E[(X-E[X])^2]=E[X^2]-E[X]^2=\dfrac{1,513,900}3-710^2=\dfrac{1600}3](https://tex.z-dn.net/?f=V%5BX%5D%3DE%5B%28X-E%5BX%5D%29%5E2%5D%3DE%5BX%5E2%5D-E%5BX%5D%5E2%3D%5Cdfrac%7B1%2C513%2C900%7D3-710%5E2%3D%5Cdfrac%7B1600%7D3)
You get the standard deviation by taking the square root of the variance, and so
![\sqrt{V[X]}=\sqrt{\dfrac{1600}3}\approx23.09](https://tex.z-dn.net/?f=%5Csqrt%7BV%5BX%5D%7D%3D%5Csqrt%7B%5Cdfrac%7B1600%7D3%7D%5Capprox23.09)
Answer:
y = 2x
Step-by-step explanation:
y=mx+b
m=2
x=2
y=4
4=2*2 + b
b = 4 - 4
b = 0
y = 2x
<h3>
Answer: Profit = 6.40 dollars</h3>
======================================================
Explanation:
Plug x = 80 into the equation to get
y = 0.12x
y = 0.12*80
y = 9.60
This means the store paid $9.60 for the rope. This amount of money is leaving the store owner's wallet or bank account. We'll keep this in mind for later.
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The graph shows the equation y = 0.20x
Note how the point (1, 0.20) is on the line to help see the slope right away. This trick only works when the line goes through the origin.
You could also use the slope formula to get this. The y intercept is 0 since the line goes through the origin.
This equation and graph show that the price per foot is $0.20, or it's 20 cents per foot.
Plug in x = 80 to find how much the store will make in revenue
y = 0.20x
y = 0.20*80
y = 16
The store makes $16 in revenue when it sells 80 ft of rope.
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The cost to the store was $9.60 found in the first section. The revenue was $16 found in section 2.
So,
profit = revenue - cost
profit = 16 - 9.60
profit = 6.40 dollars
