The value of K for which f(x) is a valid probability density function is 1/4.
<h3>How to solve for the value of K</h3>
![K[\frac{2^2}{2} -0]+[K[4(4-2)-(\frac{4^2}{2} -\frac{2^2}{2} )]=1](https://tex.z-dn.net/?f=K%5B%5Cfrac%7B2%5E2%7D%7B2%7D%20-0%5D%2B%5BK%5B4%284-2%29-%28%5Cfrac%7B4%5E2%7D%7B2%7D%20-%5Cfrac%7B2%5E2%7D%7B2%7D%20%29%5D%3D1)
open the equation
![K\frac{4}{2}+K[8 - (\frac{16}{2} -\frac{4}{2} )] = 1\\](https://tex.z-dn.net/?f=K%5Cfrac%7B4%7D%7B2%7D%2BK%5B8%20-%20%28%5Cfrac%7B16%7D%7B2%7D%20%20-%5Cfrac%7B4%7D%7B2%7D%20%29%5D%20%3D%201%5C%5C)
![2K+K[\frac{4}{2} ]=1](https://tex.z-dn.net/?f=2K%2BK%5B%5Cfrac%7B4%7D%7B2%7D%20%5D%3D1)
2K + 2K = 1
4K = 1
divide through by 4
K = 1/4
Read more on probability density function here
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Answer:
Huw spends £48 on his social life
25% 6 divided by 24 will give you the percentage of copper in the bar
So first do 3(x+1) which is 3x+3 because you have to multiply the outside number by the stuff in side the parentheses. Then you do the 5(x-2)+7 and it should be 5x-10+7 so now your equation should be 3x+3=5x-10+7 now subtract the 3x from the 5x and now your equation should look like this: 3=2x-10+7. Then you add the 10 and the 7 so now your equation should look like this: 3=2x-3 because it's a -10 and a positive 7 it would be -3. So then you have to add the -3( which now becomes positive to the other 3 in front of the = sign. So now your equation should look like this: 6=2x. Now divide by 2 to get x by its self and now your answer should be 3=x or x=3.
