Answer:
-30
Step-by-step explanation:
Answer:1/3 divided by 6 equals 18
Step-by-step explanation: If you have a cloth that is 1/3 long then divide it by 6 it would look like 1/3 divided by 1/6 which would then equal 1/18.
first subtract the last equation from the first. this gives:-
-x + y = -8 .....................(1)
Then multiply the first equation by 2 and add it to the 2nd equations This gives
9x = 18
so x = 2
and from equation (1) y = -8 + 2 = -6
Substituting for x and y in the second equation
z = (24 -5(2) -12) / 2 = 1
Answer is choice b.
Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the <em>binomial distribution</em> is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- There are 9 rolls, hence
.
- Of the six sides, 2 are 3 or 4, hence
![p = \frac{2}{6} = 0.3333](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B2%7D%7B6%7D%20%3D%200.3333)
The desired probability is:
![P(X \geq 2) = 1 - P(X < 2)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%202%29%20%3D%201%20-%20P%28X%20%3C%202%29)
In which:
![P(X < 2) = P(X = 0) + P(X = 1)](https://tex.z-dn.net/?f=P%28X%20%3C%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29)
Then
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{9,0}.(0.3333)^{0}.(0.6667)^{9} = 0.026](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B9%2C0%7D.%280.3333%29%5E%7B0%7D.%280.6667%29%5E%7B9%7D%20%3D%200.026)
![P(X = 1) = C_{9,1}.(0.3333)^{1}.(0.6667)^{8} = 0.117](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20C_%7B9%2C1%7D.%280.3333%29%5E%7B1%7D.%280.6667%29%5E%7B8%7D%20%3D%200.117)
Then:
![P(X < 2) = P(X = 0) + P(X = 1) = 0.026 + 0.117 = 0.143](https://tex.z-dn.net/?f=P%28X%20%3C%202%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%3D%200.026%20%2B%200.117%20%3D%200.143)
![P(X \geq 2) = 1 - P(X < 2) = 1 - 0.143 = 0.857](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%202%29%20%3D%201%20-%20P%28X%20%3C%202%29%20%3D%201%20-%200.143%20%3D%200.857)
0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For more on the binomial distribution, you can check brainly.com/question/24863377
Answer:
$42.09
Step-by-step explanation:
1. multiply the cost per gallon (3.45) by the gallons purchased (12.2)
3.45*12.2 = 42.09