Answer:
(a) I attached a photo with the diagram.
(b) 
(c) 1/4
(d) 4
(e) 
Step-by-step explanation:
(a) I attached a photo with the diagram.
(b) The easiest way to think about this part is in terms of combinatorics. Think about it like this.
To begin with, look at the three each level of the three represents a possible outcome of throwing the coin n-times. If you throw the coin 3 times at the end in total there are 8 possible outcomes. But The favorable outcomes are just 2.
1 - Your first outcome is HEADS and all the others are different except the last one.
2 - Your first outcome is TAILS and all the others are different except the last one.
Therefore the probability of the event is
(c)
P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.
(d)
Remember that this is a geometric distribution therefore
![E[X] = p/(1-p)](https://tex.z-dn.net/?f=E%5BX%5D%20%3D%20p%2F%281-p%29)
, in this case 
so ![E[X] = 1](https://tex.z-dn.net/?f=E%5BX%5D%20%3D%201)
and
![E[X+1]^2 = ( E[X] +1 )^2 = (1+1)^2 = 2^2 = 4](https://tex.z-dn.net/?f=E%5BX%2B1%5D%5E2%20%3D%20%28%20E%5BX%5D%20%2B1%20%29%5E2%20%20%3D%20%281%2B1%29%5E2%20%3D%202%5E2%20%3D%204)
Also
(e)
This is a geometric distribution so its variance is
And using properties of variance
If the transformed equation is g (x) = (1/x + 4) - 6, then the equation was shifted 4 units left, and translated 6 units down.
Easy One way to solve this system of equations would be by substitution. It would helpful to write these equation in the form y=mx + b in order to substitute one equation to the other. We do as follows:
1.) x - 2y = 6
y = x/2 -3
2.) 2x - 4y = 10
y = x/2 - 5/2
As we look at the rearranged equations, we see that their slopes are equal which means they are parallel lines so they do not intersect at one point. There is no solution for this system of equations.
Answer:
There would be 63 grams of protein in 9 ounces of tuna.
Step-by-step explanation:
Equivalent ratios compare two different quantities the have the same rate regardless of the amount. In this example, for every 3 ounces of tuna, there are 21 grams of protein. We can write this as a ratio of: 3/21. Like fractions, we can simplify ratios by dividing the numerator and denominator by the same greatest common factor. In this case, we would divide both the numerator and denominator by 3: (3÷3)/(21÷3) = 1/7. So, our new ratio is for every ounce of tuna, we have 7 grams of protein. Using equivalent ratios, we can set up our ratios to solve for the grams of protein in 9 ounces of tuna: 1/7 = 9/x. Since we have to multiply both the numerator and denominator by the same factor, in this case 9, then our x = 63 grams of protein.
