Using the binomial distribution, it is found that there is a 0.125 = 12.5% probability of observing exactly 3 tails.
<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.
In this problem, considering 3 tosses of a fair coin, the parameters are n = 3 and p = 0.5.
The probability of 3 tails is P(X = 3), hence:
![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 = 3) = C_{3,3}.(0.5)^{3}.(0.5)^{0} = 0.125](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B3%2C3%7D.%280.5%29%5E%7B3%7D.%280.5%29%5E%7B0%7D%20%3D%200.125)
0.125 = 12.5% probability of observing exactly 3 tails.
More can be learned about the binomial distribution at brainly.com/question/24863377
Let x be the resistance of the wire with the larger diameter.
x = (0.456 x (0.01)^2)/(0.0401)^2 = 0.0284 ohms
The answer is 0.0284 ohms.
We need an image to be able to answer this question
Answer:
Equation 1 x=-16
Equation 2 m=-3
Step-by-step explanation:
Equation 1
3x-x=-24-6
2x=-32
x=-32/2
x=-16
Equation 2
-2m=16-10
-2m=6
m=6/-2
m=-3
Answer:
![a>6](https://tex.z-dn.net/?f=a%3E6)
Step-by-step explanation:
1) Subtract 1 from both sides.
![a>7-1](https://tex.z-dn.net/?f=a%3E7-1)
2) Simplify 7 - 1 to 6.
![a>6](https://tex.z-dn.net/?f=a%3E6)
<u>Therefor, the answer is </u><u>a > 6</u>.