N=5
AC = 33
AC = 150
Explanation:
If two chords intersect inside a circle, the products of their segments is equal. For this circle, this means that
(n+1)(18)=(n+7)(9)
Using the distributive property on both sides,
n*18+1*18 = n*9+7*9
18n+18=9n+63
Subtract 9n from both sides:
18n+18-9n=9n+63-9n
9n+18=63
Subtract 18 from both sides:
9n+18-18=63-18
9n=45
Divide both sides by 9:
9n/9 = 45/9
n=5
The measure of an inscribed angle is equal to half of the measure of the intercepted arc. For the second image, this means that
2.5x+4=1/2(7x-2)
Using the distributive property:
2.5x+4=1/2(7x)-1/2(2)
2.5x+4=3.5x-1
Subtract 2.5x from both sides:
2.5x+4-2.5x=3.5x-1-2.5x
4=1x-1
Add 1 to both sides:
4+1=1x
5=1x
5=x
Substitute this in for x in AC:
7x-2=7*5-2=35-2=33
For the third image, we have
75=1/2(AC)
Multiplying both sides by 2:
75*2=AC
150=AC
The image is kinda blurry, but from what I can gather, the notation in the attachment means
![p_X[x_k]\equiv\mathbb P(X=k)=\begin{cases}(1-p)^{k-1}p&\text{for }k=1,2,\ldots\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=p_X%5Bx_k%5D%5Cequiv%5Cmathbb%20P%28X%3Dk%29%3D%5Cbegin%7Bcases%7D%281-p%29%5E%7Bk-1%7Dp%26%5Ctext%7Bfor%20%7Dk%3D1%2C2%2C%5Cldots%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
Then
a)
![p_X[x_k\le4]\equiv\mathbb P(X\le4)=\mathbb P(X=1)+\mathbb P(X=2)+\mathbb P(X=3)+\mathbb P(X=4)](https://tex.z-dn.net/?f=p_X%5Bx_k%5Cle4%5D%5Cequiv%5Cmathbb%20P%28X%5Cle4%29%3D%5Cmathbb%20P%28X%3D1%29%2B%5Cmathbb%20P%28X%3D2%29%2B%5Cmathbb%20P%28X%3D3%29%2B%5Cmathbb%20P%28X%3D4%29)
b)
c)
![p_X[1\le x_k\le2]\equiv\mathbb P(1\le X\le2)=\mathbb P(X=1)+\mathbb P(X=2)](https://tex.z-dn.net/?f=p_X%5B1%5Cle%20x_k%5Cle2%5D%5Cequiv%5Cmathbb%20P%281%5Cle%20X%5Cle2%29%3D%5Cmathbb%20P%28X%3D1%29%2B%5Cmathbb%20P%28X%3D2%29)
Add them all together and divide by the number of variables here there are four and the answer is 1.25 or 5/4
