Answer:
Ste-by-step explanation:bf=7x-10 bc=4x-29
Answer:
The function will be: f(n) = 2n
Step-by-step explanation:
An arithmetic sequence is a sequence where the common difference between consecutive terms is same
The sequence according to given information is:
2,4,6...
Here
a_1 = 2
a_2 = 4
a_3 = 6
the common difference will be:
![d = a_2-a_1 = 4-2 = 2\\d = a_3-a_2 = 6-4 = 2](https://tex.z-dn.net/?f=d%20%3D%20a_2-a_1%20%3D%204-2%20%3D%202%5C%5Cd%20%3D%20a_3-a_2%20%3D%206-4%20%3D%202)
The arithmetic sequence is given by:
![a_n = a_1+(n-1)d](https://tex.z-dn.net/?f=a_n%20%3D%20a_1%2B%28n-1%29d)
Putting the values
![a_n = 2+(n-1)(2)\\a_n = 2+2n-2\\a_n = 2n](https://tex.z-dn.net/?f=a_n%20%3D%202%2B%28n-1%29%282%29%5C%5Ca_n%20%3D%202%2B2n-2%5C%5Ca_n%20%3D%202n)
Hence,
The function will be: f(n) = 2n
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
Vertical line has no slope. so only look at the x value. x=-4.