Answer:
Step-by-step explanation:
The main idea is that I would like to pay less than what I'm expecting to win, so in that way, I get a profit out of playing this game. Let X be the number of tosses until I get a Heads. By definition, this is a geometric random variable with parameter p = 1/2.
Let Y the amount I received for playing. So, we want to calculate the expected value of Y.
We can calculate it as follows
![E[Y] = 2 P(X=1)+ 4 P(X=2)+ 8 P(X =3) + \dots = \sum_{n=1}^infty 2^n P(X=n)](https://tex.z-dn.net/?f=E%5BY%5D%20%3D%202%20P%28X%3D1%29%2B%204%20P%28X%3D2%29%2B%208%20P%28X%20%3D3%29%20%20%2B%20%5Cdots%20%20%3D%20%5Csum_%7Bn%3D1%7D%5Einfty%202%5En%20P%28X%3Dn%29)
Since X is a geometric random variable, we have that 
Then,
![E[Y] = \sum_{n=1}^\infty 2^{n} (\frac{1}{2})^{n-1} \frac{1}{2} = \sum_{n=1}^\infty 2^{n-1} \cdot \frac{1}{2^{n-1}} = \sum_{n=1}^\infty 1 = \infty](https://tex.z-dn.net/?f=%20E%5BY%5D%20%3D%20%5Csum_%7Bn%3D1%7D%5E%5Cinfty%202%5E%7Bn%7D%20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bn-1%7D%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Csum_%7Bn%3D1%7D%5E%5Cinfty%202%5E%7Bn-1%7D%20%5Ccdot%20%5Cfrac%7B1%7D%7B2%5E%7Bn-1%7D%7D%20%3D%20%5Csum_%7Bn%3D1%7D%5E%5Cinfty%201%20%3D%20%5Cinfty)
So, we expect to have an infinite amount. Given this, we can pay as much as we want to play the game.
13 31/40
Explanation
6 3/8+7 2/5
6+7=13
Common denominator of 8 and 5=40
Use common denominator 6 15/40+7 16/40
15+16=31
Answer:
Various types of Congruency are:
1. ASA (Angle Side Angle)
2. SSS (Side Side Side)
3. SAS (Side-Angle-Side)
4. AAS (Angle-Angle-Side)
5. RHS (Right angle-Hypotenuse-Side)
As of what I had learned (class 9) this is all but I am not sure if there are more
This answer is 41
9 divided by 3
+8
x 5
-2
So, she has 550 dollars saved. If the junior season pass costs 315, you subtract that from 550. You should then have 235 dollars. Next, you divide 235 by 45 dollars per lesson, and you should get 5.22. You can't buy half a lesson, so she only has enough for 5 lessons.
