13/15 = 87%
This is because 13 divided by 15 is 87, so 13 is 87% of 15:)
Answer: √5
2.7 is a rational number because it's a terminating decimal which means that the decimal does end and all terminating decimals are rational numbers.
-3 is a rational number because it's an
integer and all integers are rational.
√4 is rational because it's a perfect square which means that a number can be multiplied by itself to get 4 and that number is 2.
√5 is no rational! It's impossible to find a whole number multiplied by itself to give us 5 which means that it's
non-terminating and non-repeating.
Answer:
7^22
Step-by-step explanation
Given the expression
7^8 × 7^3 × 7^4 × 7^7
In indices
a^m × a^n = a^{m+n}
The powers are added since the base are the same
We ate going to add all the powers of the expression given since they have the same base which is 7
7^8 × 7^3 × 7^4 × 7^7
= 7^{8+3+4+7}
= 7^22
= 3.91×10^18
Answer:
![f_{avg}=\frac{1}{e-1}](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D)
Step-by-step explanation:
We are given that a function
![f(x)=2lnx](https://tex.z-dn.net/?f=f%28x%29%3D2lnx)
We have to find the average value of function on the given interval [1,e]
Average value of function on interval [a,b] is given by
![\frac{1}{b-a}\int_{a}^{b}f(x)dx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bb-a%7D%5Cint_%7Ba%7D%5E%7Bb%7Df%28x%29dx)
Using the formula
![f_{avg}=\frac{1}{e-1}\int_{1}^{e}lnx dx](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%5Cint_%7B1%7D%5E%7Be%7Dlnx%20dx)
By Parts integration formula
![\int(uv)dx=u\int vdx-\int(\frac{du}{dx}\int vdx)dx](https://tex.z-dn.net/?f=%5Cint%28uv%29dx%3Du%5Cint%20vdx-%5Cint%28%5Cfrac%7Bdu%7D%7Bdx%7D%5Cint%20vdx%29dx)
u=ln x and v=dx
Apply by parts integration
![f_{avg}=\frac{1}{e-1}([xlnx]^{e}_{1}-\int_{1}^{e}(\frac{1}{x}\times xdx))](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%28%5Bxlnx%5D%5E%7Be%7D_%7B1%7D-%5Cint_%7B1%7D%5E%7Be%7D%28%5Cfrac%7B1%7D%7Bx%7D%5Ctimes%20xdx%29%29)
![f_{avg}=\frac{1}{e-1}(elne-ln1-[x]^{e}_{1})](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%28elne-ln1-%5Bx%5D%5E%7Be%7D_%7B1%7D%29)
![f_{avg}=\frac{1}{e-1}(e-0-e+1)=\frac{1}{e-1}](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D%28e-0-e%2B1%29%3D%5Cfrac%7B1%7D%7Be-1%7D)
By using property lne=1,ln 1=0
![f_{avg}=\frac{1}{e-1}](https://tex.z-dn.net/?f=f_%7Bavg%7D%3D%5Cfrac%7B1%7D%7Be-1%7D)
Answer:
The degrees of freedom are given by:
![df =n-1= 15-1=14](https://tex.z-dn.net/?f=%20df%20%3Dn-1%3D%2015-1%3D14)
And if we look in the chi square distribution with 14 degrees of freedom and if we find a quantile who accumulates 0.1 of the area in the left we got:
![\chi^2 = 7.790](https://tex.z-dn.net/?f=%20%5Cchi%5E2%20%3D%207.790)
And then the best answer would be:
c. 7.790
Step-by-step explanation:
For this case we know that we are using a one tailed (lower tail) critical value using a significance level of
and for this case we know that the ample size is n=15. The degrees of freedom are given by:
![df =n-1= 15-1=14](https://tex.z-dn.net/?f=%20df%20%3Dn-1%3D%2015-1%3D14)
And if we look in the chi square distribution with 14 degrees of freedom and if we find a quantile who accumulates 0.1 of the area in the left we got:
![\chi^2 = 7.790](https://tex.z-dn.net/?f=%20%5Cchi%5E2%20%3D%207.790)
And then the best answer would be:
c. 7.790