When we reject the null and the null is true, we have a made a type I error
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.
null hypothesis is denoted as H₀
Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. When you can reject the null hypothesis, your results are statistically significant.
when the p-value is greater than your significance level, you fail to reject the null hypothesis.
Sometimes , we reject our null hypothesis even when its true
there we made a type I error in hypothesis
To know more about null hypothesis here
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Answer:
option a) 30 : 19
Step-by-step explanation:

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Answer:
Step-by-step explanation:
The horizontal asymtote is when there are no solutions for x, so it is when y = -10.
This is because when y = -10, 0.8^x must be 0, but this is impossible. You can test this by trying 4^x/5^x. It will get super small, but never 0.
Given a solution

, we can attempt to find a solution of the form

. We have derivatives



Substituting into the ODE, we get


Setting

, we end up with the linear ODE

Multiplying both sides by

, we have

and noting that
![\dfrac{\mathrm d}{\mathrm dx}\left[x(\ln x)^2\right]=(\ln x)^2+\dfrac{2x\ln x}x=(\ln x)^2+2\ln x](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5Bx%28%5Cln%20x%29%5E2%5Cright%5D%3D%28%5Cln%20x%29%5E2%2B%5Cdfrac%7B2x%5Cln%20x%7Dx%3D%28%5Cln%20x%29%5E2%2B2%5Cln%20x)
we can write the ODE as
![\dfrac{\mathrm d}{\mathrm dx}\left[wx(\ln x)^2\right]=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cleft%5Bwx%28%5Cln%20x%29%5E2%5Cright%5D%3D0)
Integrating both sides with respect to

, we get


Now solve for

:


So you have

and given that

, the second term in

is already taken into account in the solution set, which means that

, i.e. any constant solution is in the solution set.
X=popcorn
x - 3.50=drink
2x+ 4(x-3.50)=32.50
2x+4x-14=32.50
solve for x