Slope = 0.2 and y-intercept = 0.3
The slope intercept form of line is
y=mx + b where m is the slope and b is the y intercept
So equation becomes y = 0.2 x + 0.3
To find coordinates of 4 points , we plug in some number for x and find out y
x y = 0.2 x + 0.3
0 y = 0.2 (0) + 0.3= 0.3
1 y = 0.2 (1) + 0.3= 0.5
2 y = 0.2 (2) + 0.3= 0.7
3 y = 0.2 (3) + 0.3= 0.9
Four coordinates are (0,0.3) (1,0.5) (2,0.7) (3,0.9)
A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459 , 24.8293 ) .
What is population mean?
A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.
Data: 18
for given data
![$$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%5Cbar%7BX%7D%20%26%20%3D%5Cfrac%7B%5Csum%20X%20i%7D%7Bn%7D%20%5C%5C%26%20%3D2448%20%2F%20101%20%5C%5C%26%20%3D24.2376%5Cend%7Baligned%7D%24%24)
as population variance is unknown so we used sample variance
![$$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7DS%5E2%20%26%20%3D%5Cfrac%7B1%7D%7Bn-1%7D%5Cleft%28%5Csum%20X%20i%5E2-n%20%5Ctimes%20%5Cbar%7BX%7D%5E2%5Cright%29%20%5C%5CS%5E2%20%26%20%3D%5Cfrac%7B1%7D%7B100%7D%5Cleft%2860232-101%20%5Ctimes%2024.2376%5E2%5Cright%29%20%5C%5C%26%20%3D8.9830%5Cend%7Baligned%7D%24%24)
Now
![\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cbar%7BX%7D-%5Cmu%7D%7BS%20%2F%20%5Csqrt%7Bn%7D%7D%20%5Csim%20t_%7Bn-1%7D%24%24)
hence 95 % of population mean is
As n=101 which is large so critical value is 1.98397
![$$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$](https://tex.z-dn.net/?f=%24%24%5Cbegin%7Baligned%7D%26%20%3D%5Cleft%28%5Cbar%7BX%7D-%5Csqrt%7B%5Cfrac%7BS%7D%7Bn%7D%7D%20%5Ctimes%20t_%7B%28n-1%2C%20%5Calpha%20%2F%202%29%7D%2C%20%5Cbar%7BX%7D%2B%5Csqrt%7B%5Cfrac%7BS%7D%7Bn%7D%7D%20%5Ctimes%20t_%7B%28n-1%2C%20%5Calpha%20%2F%202%29%7D%5Cright%29%20%5C%5C%26%20%3D%5Cleft%2824.2376-%5Csqrt%7B%5Cfrac%7B8.9830%7D%7B101%7D%7D%20%5Ctimes%201.98397%2C24.2376%2B%5Csqrt%7B%5Cfrac%7B8.9830%7D%7B101%7D%7D%20%5Ctimes%201.98397%5Cright%29%20%5C%5C%26%20%3D%2823.6459%2C24.8293%29%5Cend%7Baligned%7D%24%24)
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5x^2+3x-4=0
<span>x^2+3x/5-4/5=0 </span>
<span>x^2+3x/5=4/5 </span>
<span>x^2+3x/5+9/100=89/100 </span>
<span>(x+3/10)^2=89/100 </span>
<span>x+3/10=±(√89)/10 </span>
<span>x=-3/10±√89/100 </span>
<span>x=-3±(√89/10)</span>
A= 42in²
P = 2l + 2w so
(21 x 2) + (2 x 2)
42 + 4 = 46
46 = 21 by 2
Now let's do 6 and 7
(6 x 2) + (7 x 2)
12 + 14 = 26
46 > 26
so 21 by 2 has greater P (perimeter)