Answer:
(a) The probability that both Dave and Mike will show up is 0.25.
(b) The probability that at least one of them will show up is 0.75.
(c) The probability that neither Dave nor Mike will show up is 0.25.
Step-by-step explanation:
Denote the events as follows:
<em>D</em> = Dave will show up.
<em>M</em> = Mike will show up.
Given:
It is provided that the events of Dave of Mike showing up are independent of each other.
(a)
Compute the probability that both Dave and Mike will show up as follows:
![P(D\cap M)=P(D)\times P (M)\\=[1-P(D^{c})]\times [1-P(M^{c})]\\=[1-0.55]\times[1-0.45]\\=0.2475\\\approx0.25](https://tex.z-dn.net/?f=P%28D%5Ccap%20M%29%3DP%28D%29%5Ctimes%20P%20%28M%29%5C%5C%3D%5B1-P%28D%5E%7Bc%7D%29%5D%5Ctimes%20%5B1-P%28M%5E%7Bc%7D%29%5D%5C%5C%3D%5B1-0.55%5D%5Ctimes%5B1-0.45%5D%5C%5C%3D0.2475%5C%5C%5Capprox0.25)
Thus, the probability that both Dave and Mike will show up is 0.25.
(b)
Compute the probability that at least one of them will show up as follows:
P (At least one of them will show up) = 1 - P (Neither will show up)
![=1-P(D^{c}\cup M^{c})\\=P(D\cup M)\\=P(D)+P(M)-P(D\cap M)\\=[1-P(D^{c})]+[1-P(M^{c})]-P(D\cap M)\\=[1-0.55]+[1-0.45]-0.25\\=0.75](https://tex.z-dn.net/?f=%3D1-P%28D%5E%7Bc%7D%5Ccup%20M%5E%7Bc%7D%29%5C%5C%3DP%28D%5Ccup%20M%29%5C%5C%3DP%28D%29%2BP%28M%29-P%28D%5Ccap%20M%29%5C%5C%3D%5B1-P%28D%5E%7Bc%7D%29%5D%2B%5B1-P%28M%5E%7Bc%7D%29%5D-P%28D%5Ccap%20M%29%5C%5C%3D%5B1-0.55%5D%2B%5B1-0.45%5D-0.25%5C%5C%3D0.75)
Thus, the probability that at least one of them will show up is 0.75.
(c)
Compute the probability that neither Dave nor Mike will show up as follows:
![P(D^{c}\cup M^{c})=1-P(D\cup M)\\=1-P(D)-P(M)+P(D\cap M)\\=1-[1-P(D^{c})]-[1-P(M^{c})]+P(D\cap M)\\=1-[1-0.55]-[1-0.45]+0.25\\=0.25](https://tex.z-dn.net/?f=P%28D%5E%7Bc%7D%5Ccup%20M%5E%7Bc%7D%29%3D1-P%28D%5Ccup%20M%29%5C%5C%3D1-P%28D%29-P%28M%29%2BP%28D%5Ccap%20M%29%5C%5C%3D1-%5B1-P%28D%5E%7Bc%7D%29%5D-%5B1-P%28M%5E%7Bc%7D%29%5D%2BP%28D%5Ccap%20M%29%5C%5C%3D1-%5B1-0.55%5D-%5B1-0.45%5D%2B0.25%5C%5C%3D0.25)
Thus, the probability that neither Dave nor Mike will show up is 0.25.
To find the mean (average), u add up all the numbers, then divide by how many numbers there are.
(200 + 150 + 325 + 100 + 75) / 5 = 850/5 = 170 <== the mean
These are two separate problems: in the first we will have to substitute in a new value for x into the original equation and in the second we will manipulate the preexisting equation for f(x).
To begin, we will sub in f(x/3). To do this, we will substitute each variable x in the equation (in this case there is only one) with x/3, and then simplify the resulting equation.
f(x) = 6x - 18
f(x/3) = 6(x/3) - 18
To simplify, we should distribute the 6 on the right side of the equation.
f(x/3) = 6x/3 - 18
Now, we can divide the first term on the right side to finalize our simplification.
f(x/3) = 2x -18
Secondly, we are asked to find f(x)/3. To do this, we will take our original value for f(x), and then simplify divide that entire function by 3.
f(x) = 6x - 18
f(x)/3 = (6x-18)/3
This means that we must divide each term of the binomial by 3, so we are really computing
f(x)/3 = 6x/3 - 18/3
We can simplify by dividing both of the terms.
f(x)/3 = 2x - 6
Therefore, your answer is that f(x/3) = 2x - 18, but f(x)/3 = 2x - 6. It is important to recognize that these are two similar, yet different, answers.
Hope this helps!
Answer:
1,262.5
according to the calculator lol
Think of absolute value and inverse operation, +72 to 72 and 24
