Answer:
0.0111% probability that he answers at least 10 questions correctly
Step-by-step explanation:
For each question, there are only two outcomes. Either it is answered correctly, or it is not. The probability of a question being answered correctly is independent from other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![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)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![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)
And p is the probability of X happening.
A multiple-choice examination has 15 questions, each with five answers, only one of which is correct.
This means that ![n = 15, p = \frac{1}{5} = 0.2](https://tex.z-dn.net/?f=n%20%3D%2015%2C%20p%20%3D%20%5Cfrac%7B1%7D%7B5%7D%20%3D%200.2)
What is the probability that he answers at least 10 questions correctly?
![P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2010%29%20%3D%20P%28X%20%3D%2010%29%20%2B%20P%28X%20%3D%2011%29%20%2B%20P%28X%20%3D%2012%29%20%2B%20P%28X%20%3D%2013%29%20%2B%20P%28X%20%3D%2014%29%20%2B%20P%28X%20%3D%2015%29)
![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 = 10) = C_{15,10}.(0.2)^{10}.(0.8)^{5} = 0.0001](https://tex.z-dn.net/?f=P%28X%20%3D%2010%29%20%3D%20C_%7B15%2C10%7D.%280.2%29%5E%7B10%7D.%280.8%29%5E%7B5%7D%20%3D%200.0001)
![P(X = 11) = C_{15,11}.(0.2)^{11}.(0.8)^{4} = 0.000011](https://tex.z-dn.net/?f=P%28X%20%3D%2011%29%20%3D%20C_%7B15%2C11%7D.%280.2%29%5E%7B11%7D.%280.8%29%5E%7B4%7D%20%3D%200.000011)
![P(X = 12) = C_{15,12}.(0.2)^{12}.(0.8)^{3} \cong 0](https://tex.z-dn.net/?f=P%28X%20%3D%2012%29%20%3D%20C_%7B15%2C12%7D.%280.2%29%5E%7B12%7D.%280.8%29%5E%7B3%7D%20%5Ccong%200%20)
![P(X = 13) = C_{15,13}.(0.2)^{13}.(0.8)^{2} \cong 0](https://tex.z-dn.net/?f=P%28X%20%3D%2013%29%20%3D%20C_%7B15%2C13%7D.%280.2%29%5E%7B13%7D.%280.8%29%5E%7B2%7D%20%5Ccong%200%20)
![P(X = 14) = C_{15,14}.(0.2)^{14}.(0.8)^{1} \cong 0](https://tex.z-dn.net/?f=P%28X%20%3D%2014%29%20%3D%20C_%7B15%2C14%7D.%280.2%29%5E%7B14%7D.%280.8%29%5E%7B1%7D%20%5Ccong%200%20)
![P(X = 15) = C_{15,15}.(0.2)^{15}.(0.8)^{0} \cong 0](https://tex.z-dn.net/?f=P%28X%20%3D%2015%29%20%3D%20C_%7B15%2C15%7D.%280.2%29%5E%7B15%7D.%280.8%29%5E%7B0%7D%20%5Ccong%200%20)
![P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0001 + 0.000011 = 0.000111](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2010%29%20%3D%20P%28X%20%3D%2010%29%20%2B%20P%28X%20%3D%2011%29%20%2B%20P%28X%20%3D%2012%29%20%2B%20P%28X%20%3D%2013%29%20%2B%20P%28X%20%3D%2014%29%20%2B%20P%28X%20%3D%2015%29%20%3D%200.0001%20%2B%200.000011%20%3D%200.000111)
0.0111% probability that he answers at least 10 questions correctly
Let us say that x is the real height of the original hut,
therefore we can establish the equation:
5 : x = 1.5 : 8
5 / x = 1.5 / 8
Solving for x:
x = 5 * 8 / 1.5
x = 40 / 1.5
<span>x = 26.67 ft</span>
Answer:
5
Step-by-step explanation:
The slope will be the constant amount that the cost increases by each month.
In this situation, 5 is the slope, because he has to pay $5 each month.
35 is not the slope, and is instead the y intercept. This is because this is the cost at 0 months, since it is the membership fee.
So, the correct answer is 5.
An equation of Hamid’s revenue by multiplying the book price by the number of copies sold is x = ny.
<h3>What is an equation?</h3>
The process of equating one thing with another.
Let Hamid’s revenue is $x and the price of book is $y.
If he sold n number of copies.
Then, the general equation will be x = n * y.
Therefore, an equation of Hamid's revenue will be x = ny.
Know more about equation here:
brainly.com/question/2263981
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