Answer:
(22.12, 27.48)
Step-by-step explanation:
Given : Significance level : ![\alpha: 1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3A%201-0.95%3D0.05)
Sample size : n= 8 , which is a small sample (n<30), so we use t-test.
Critical values using t-distribution: ![t_{n-1,\alpha/2}=t_{7,0.025}=2.365](https://tex.z-dn.net/?f=t_%7Bn-1%2C%5Calpha%2F2%7D%3Dt_%7B7%2C0.025%7D%3D2.365)
Sample mean : ![\overline{x}=24.8\text{ hours}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D24.8%5Ctext%7B%20hours%7D)
Standard deviation : ![\sigma=3.2\text{ hours}](https://tex.z-dn.net/?f=%5Csigma%3D3.2%5Ctext%7B%20hours%7D)
The confidence interval for population means is given by :-
![\overline{x}\pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20t_%7Bn-1%2C%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
i.e. ![24.8\pm(2.365)\dfrac{3.2}{\sqrt{8}}](https://tex.z-dn.net/?f=24.8%5Cpm%282.365%29%5Cdfrac%7B3.2%7D%7B%5Csqrt%7B8%7D%7D)
![24.8\pm2.67569206001\\\\\approx24.8\pm2.68\\\\=(24.8-2.68, 24.8+2.68)=(22.12, 27.48)](https://tex.z-dn.net/?f=24.8%5Cpm2.67569206001%5C%5C%5C%5C%5Capprox24.8%5Cpm2.68%5C%5C%5C%5C%3D%2824.8-2.68%2C%2024.8%2B2.68%29%3D%2822.12%2C%2027.48%29)
Hence, the 95% confidence interval, assuming the times are normally distributed.= (22.12, 27.48)
Answer:
25 potatoes split between 5 people would be 25÷5=5. So each person will get 5 potatoes.
Answer:
m∠1= 79
Step-by-step explanation:
What we have here is two vertical lines and one intersecting point.
The m∠1 and m∠6 are vertical angles, which means that they equal to each other. So, the equation would be: 6x+25= 10x-11.
Step 1- Subtract 6x to both sides.
6x+25= 10x-11
-6x -6x
25= 4x-11
Step 2- Add 11 to both sides.
25= 4x-11
+11 +11
36= 4x
Step 3- Divide both sides by 4.
<u>36</u>= <u>4x</u>
4 4
x= 9
Now that we know the value of the variable x, substitute it into the equation for m∠1.
m∠1= 10(9)-11
m∠1= 90-11
m∠= 79
<u>Check </u>
m∠6= 6(9)+25
m∠6= 54+25
m∠6= 79
Since m∠1 and m∠6 are vertical angles, they should equal each other.
7 would be the number cause;
25 ÷ 7 = 3 r4
hope that helps :D
<span>2m^2n^4/6m^5n^3
n
= --------
3m^3</span>