Answer:
38%
Step-by-step explanation:
3/8=0.375 move decimal twice right, round the 7 to an eight (8)
Answer:
3x+15
Step-by-step explanation:
Using the binomial distribution, it is found that the probabilities are:
<h3>What is the binomial distribution formula?</h3>
The formula is:
![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)
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
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.
Exercise 1:
The parameters are:
n = 15, p = 0.4, x = 4.
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 = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228](https://tex.z-dn.net/?f=P%28X%20%3D%204%29%20%3D%20C_%7B15%2C4%7D.%280.4%29%5E%7B4%7D.%280.6%29%5E%7B11%7D%20%3D%200.1228)
Exercise 2:
The parameters are:
n = 12, p = 0.2, x = 2.
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 = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B12%2C2%7D.%280.2%29%5E%7B2%7D.%280.8%29%5E%7B10%7D%20%3D%200.2835)
Exercise 3:
The parameters are:
n = 20, p = 0.05.
The probability is:
![P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%203%29%20%3D%20P%28X%20%3D%200%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)
Using the binomial formula for each value and adding them:
![P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841](https://tex.z-dn.net/?f=P%28X%20%5Cleq%203%29%20%3D%20P%28X%20%3D%200%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%20%3D%200.3585%20%2B%200.3774%20%2B%200.1887%20%2B%200.0596%20%3D%200.9841)
More can be learned about the binomial distribution at brainly.com/question/24863377
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<span>Orthocenter of a triangle is the point of intersection of all the altitudes of the triangle.
in this case, the altitude of XY is XZ, and the altitude of XZ is XY, and the two altitudes meet at the origin.
so in this case, X(0,0) is the orthocenter</span>