Re read the question again just in case, try and put £25.50
But I got 25.5 too
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:
27,600
Step-by-step explanation:
We use the following formula:-
Number of permutations of r from n
= nPr
= n! / (n-r)!
I am assuming you don't allow repeated letters in the 4 letter codes.
Take S as the first letter. Then we have 3 letters extra out of 25 letters.
Using the above formula the possible ways of doing this is
25! / (25 - 3)!
25! / 22!
= 25*24*23
= 13800.
The same number is obtained if the first letter is a T.
So the answer is 2*13800
= 27,600
Question 1:
x - Tim`s age, y - Coach Johnson`s age:
x + 10 = y
2 * ( x - 3 ) = y - 3
-----------------------
2 x - 6 = x + 10 - 3
2 x - x = 7 + 6
x = 13
Tim is 13 years old.
Question 2:
x - 62,500 = 0.25 * 125,000
x - 62,500 = 31,250
x = 31,250 + 62,500
x = 93,750
Maya received 93,750 votes.
Answer:
m= 20 for one becouse 5×20 is 100
m= 5 because 5×2 is 10
or do 5÷100 that is 20
and 2÷10 that is 5
