The answer is the last answer choice:
all the real numbers greater than or equal to -3
The range of a function is all the possible y values of a function. From the function you see on the left side, it shows that the minimum value is at (2, -3) and from there it doesn't go any lower meaning all the values will be higher than -3 for the y value.
Answer:
(a) I attached a photo with the diagram.
(b) ![f(x) = \big( \frac{1}{2} \big)^{x-1}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cbig%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbig%29%5E%7Bx-1%7D)
(c) 1/4
(d) 4
(e) ![k^2/2](https://tex.z-dn.net/?f=k%5E2%2F2)
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
![f(x) = P(X=x) = \frac{2}{2^x} = \frac{1}{2^{x-1}} = \big( \frac{1}{2} \big)^{x-1}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20P%28X%3Dx%29%20%3D%20%5Cfrac%7B2%7D%7B2%5Ex%7D%20%20%3D%20%5Cfrac%7B1%7D%7B2%5E%7Bx-1%7D%7D%20%3D%20%5Cbig%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbig%29%5E%7Bx-1%7D)
(c)
P(X = 0) = 0 because it is not possible to have two consecutive tails or heads.
![E(X > 4) = 1 - P(X \leq 3) = 1 - ( P(X = 0 ) + P(X = 1) + P(X = 2) + P(X = 3))\\= 1 - ( \frac{1}{2} + \frac{1}{4} ) = \frac{1}{4}](https://tex.z-dn.net/?f=E%28X%20%3E%204%29%20%3D%201%20-%20P%28X%20%5Cleq%203%29%20%3D%201%20-%20%28%20P%28X%20%3D%200%20%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%29%5C%5C%3D%201%20-%20%28%20%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Cfrac%7B1%7D%7B4%7D%20%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
(d)
Remember that this is a geometric distribution therefore
, in this case
so
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
![Var(X) = \frac{1-p}{p^2} = 1/2 / 1/4 = 1/2](https://tex.z-dn.net/?f=Var%28X%29%20%3D%20%5Cfrac%7B1-p%7D%7Bp%5E2%7D%20%3D%201%2F2%20%2F%201%2F4%20%3D%201%2F2)
And using properties of variance
![Var(kX - k ) = Var(kX) = k^2 var(X) = k^2 /2](https://tex.z-dn.net/?f=Var%28kX%20-%20k%20%29%20%3D%20Var%28kX%29%20%3D%20k%5E2%20var%28X%29%20%3D%20k%5E2%20%2F2)
Answer:
Well if your going 3miles per hour and it 1.5 hours than it would take about...half an hour 30mins
Step-by-step explanation:
Answer:
x=4/3
Step-by-step explanation:
transpose 3 to the lhs
hope this helps
plzz mark me brainliest
40-4x=2/3x-10
50=14/3x
150/14=x
75/7=x