Answer: (1.64,4.01)
Step-by-step explanation:
The confidence interval for the population variance is given by :-
![\left ( \dfrac{(n-1)s^2}{\chi^2_{n-1,\alpha/2}},\ \dfrac{(n-1)s^2}{\chi^2_{n-1,1-\alpha/2}} \ \right )](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cdfrac%7B%28n-1%29s%5E2%7D%7B%5Cchi%5E2_%7Bn-1%2C%5Calpha%2F2%7D%7D%2C%5C%20%5Cdfrac%7B%28n-1%29s%5E2%7D%7B%5Cchi%5E2_%7Bn-1%2C1-%5Calpha%2F2%7D%7D%20%5C%20%5Cright%20%29)
Given : n= 69 ; ![s^2=2.46](https://tex.z-dn.net/?f=s%5E2%3D2.46)
Significance level : ![\alpha=1-0.99=0.01](https://tex.z-dn.net/?f=%5Calpha%3D1-0.99%3D0.01)
Using Chi-square distribution table ,
[by using chi-square distribution table]
Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-
![\left ( \dfrac{(68)(2.46)}{101.77592},\ \dfrac{(68)(2.46)}{41.71347} \ \right )\\\\=\left ( 1.64361078731, 4.01021540524\right )\approx(1.64,\ 4.01)](https://tex.z-dn.net/?f=%5Cleft%20%28%20%5Cdfrac%7B%2868%29%282.46%29%7D%7B101.77592%7D%2C%5C%20%5Cdfrac%7B%2868%29%282.46%29%7D%7B41.71347%7D%20%5C%20%5Cright%20%29%5C%5C%5C%5C%3D%5Cleft%20%28%201.64361078731%2C%204.01021540524%5Cright%20%29%5Capprox%281.64%2C%5C%204.01%29)
Hence, the 99% confidence interval for the population variance of the weights of all axles in this factory is (1.64,4.01).
The change is -(1/2 + 3/4 + 3/8).
If you add the fractions, you get -(13/8).
Practical domain is "the realist" it is used in real situations
A is correct
Answer:
x = 15
Step-by-step explanation:
A full circle = 360°
Therefore,
(8x - 10)° + (6x)° + (10x + 10)° = 360°
Solve for x
8x - 10 + 6x + 10x + 10 = 360
Add like terms
24x = 360
Divide both sides by 24
x = 360/24
x = 15
Answer:
Theorem of calculus
Step-by-step explanation:
Take the integral
![\int\limits^3_4 (2x^2+9)dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E3_4%20%282x%5E2%2B9%29dx)
Integrate the sum term by term and factor out constants
![= 2 \int\limits^4_3 x^2 dx + 9 \int\limits^4_3 1 dx](https://tex.z-dn.net/?f=%3D%202%20%5Cint%5Climits%5E4_3%20x%5E2%20dx%20%2B%209%20%5Cint%5Climits%5E4_3%201%20dx)
Apply the fundamental theorem of calculus.
<em>The antiderivative of x^2 is x^3/3, while for a constat is x</em>
![= \frac{2x^3}{3} + 9x dx](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2x%5E3%7D%7B3%7D%20%2B%209x%20dx)
Evaluate the limits
![= (2*\frac{(4)^3}{3}+9*4)-(2*\frac{(3)^3}{3}+9*3)](https://tex.z-dn.net/?f=%3D%20%282%2A%5Cfrac%7B%284%29%5E3%7D%7B3%7D%2B9%2A4%29-%282%2A%5Cfrac%7B%283%29%5E3%7D%7B3%7D%2B9%2A3%29)
![=\frac{101}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B101%7D%7B3%7D)