Step by step solution :
standard deviation is given by :
![\sigma = \sqrt\dfrac{{\sum (x-\bar{x})^2}}{n}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%5Cdfrac%7B%7B%5Csum%20%28x-%5Cbar%7Bx%7D%29%5E2%7D%7D%7Bn%7D)
where,
is standard deviation
is mean of given data
n is number of observations
From the above data, ![\bar{x}=24.88](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D24.88)
Now, if
, then ![(x-\bar{x})^2=0.0064](https://tex.z-dn.net/?f=%28x-%5Cbar%7Bx%7D%29%5E2%3D0.0064)
If
, then ![(x-\bar{x})^2=0.9604](https://tex.z-dn.net/?f=%28x-%5Cbar%7Bx%7D%29%5E2%3D0.9604)
if
, then ![(x-\bar{x})^2=1.4884](https://tex.z-dn.net/?f=%28x-%5Cbar%7Bx%7D%29%5E2%3D1.4884)
If
, then ![(x-\bar{x})^2=0.0484](https://tex.z-dn.net/?f=%28x-%5Cbar%7Bx%7D%29%5E2%3D0.0484)
If
, then ![(x-\bar{x})^2=0.1444](https://tex.z-dn.net/?f=%28x-%5Cbar%7Bx%7D%29%5E2%3D0.1444)
so, ![\sum (x-\bar{x})^2 =\frac{0.0064+0.9604+1.4884+0.0484+0.1444}{5}](https://tex.z-dn.net/?f=%5Csum%20%28x-%5Cbar%7Bx%7D%29%5E2%20%3D%5Cfrac%7B0.0064%2B0.9604%2B1.4884%2B0.0484%2B0.1444%7D%7B5%7D)
![\sum (x-\bar{x})^2 =2.648](https://tex.z-dn.net/?f=%5Csum%20%28x-%5Cbar%7Bx%7D%29%5E2%20%3D2.648)
![\sqrt{\sum \frac{(x-\bar{x})^2}{n}}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Csum%20%5Cfrac%7B%28x-%5Cbar%7Bx%7D%29%5E2%7D%7Bn%7D%7D)
![\sigma =0.7277](https://tex.z-dn.net/?f=%5Csigma%20%3D0.7277)
No, Joe's value does not agree with the accepted value of 25.9 seconds. This shows a lots of errors.
Answer:
Staying the same unless, another force acts upon it
Explanation:
An object will stay still or keep moving at the same pace and in a straight line until acted upon by an external force that is unbalanced.
False
reason- they affect much more than physical appearance
It's like a a magnetic wave, it'll bounce off.
Answer:
- The formula its
![f(t) \ = \ - \ 352 \ \frac{\$ }{years} \ t \ + \ \$ \ 2816](https://tex.z-dn.net/?f=f%28t%29%20%5C%20%3D%20%5C%20-%20%5C%20352%20%5C%20%5Cfrac%7B%5C%24%20%7D%7Byears%7D%20%5C%20t%20%5C%20%2B%20%5C%20%5C%24%20%5C%202816%20)
- After 5 years, the computer value its $ 1056
Explanation:
<h3>
Obtaining the formula</h3>
We wish to find a formula that
- Starts at 2816.
![f(0 \ years) \ = \ \$ \ 2816](https://tex.z-dn.net/?f=f%280%20%5C%20years%29%20%5C%20%3D%20%5C%20%5C%24%20%5C%202816)
- Reach 0 at 8 years.
![f( 8 \ years) \ = \ \$ \ 0](https://tex.z-dn.net/?f=f%28%208%20%5C%20years%29%20%5C%20%3D%20%5C%20%5C%24%20%5C%200)
- Depreciates at a constant rate. m
We can cover all this requisites with a straight-line equation. (an straigh-line its the only curve that has a constant rate of change) :
,
where m its the slope of the line and b give the place where the line intercepts the <em>y</em> axis.
So, we can use this formula with the data from our problem. For the first condition:
![f ( 0 \ years ) = m \ (0 \ years) + b = \$ \ 2816](https://tex.z-dn.net/?f=f%20%28%200%20%5C%20years%20%29%20%3D%20m%20%5C%20%280%20%5C%20years%29%20%2B%20b%20%3D%20%5C%24%20%5C%202816)
![b = \$ \ 2816](https://tex.z-dn.net/?f=%20b%20%3D%20%5C%24%20%5C%202816)
So, b = $ 2816.
Now, for the second condition:
![f ( 8 \ years ) = m \ (8 \ years) + \$ \ 2816 = \$ \ 0](https://tex.z-dn.net/?f=f%20%28%208%20%5C%20years%20%29%20%3D%20m%20%5C%20%288%20%5C%20years%29%20%2B%20%5C%24%20%5C%202816%20%3D%20%5C%24%20%5C%200)
![m \ (8 \ years) = \ - \$ \ 2816](https://tex.z-dn.net/?f=%20m%20%5C%20%288%20%5C%20years%29%20%3D%20%5C%20-%20%5C%24%20%5C%202816)
![m = \frac{\ - \$ \ 2816}{8 \ years}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B%5C%20-%20%5C%24%20%5C%202816%7D%7B8%20%5C%20years%7D)
![m = \frac{\ - \$ \ 2816}{8 \ years}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B%5C%20-%20%5C%24%20%5C%202816%7D%7B8%20%5C%20years%7D)
![m = \ - \ 352 \frac{\$ }{years}](https://tex.z-dn.net/?f=%20m%20%3D%20%5C%20-%20%5C%20352%20%5Cfrac%7B%5C%24%20%7D%7Byears%7D)
So, our formula, finally, its:
![f(t) \ = \ - \ 352 \ \frac{\$ }{years} \ t \ + \ \$ \ 2816](https://tex.z-dn.net/?f=f%28t%29%20%5C%20%3D%20%5C%20-%20%5C%20352%20%5C%20%5Cfrac%7B%5C%24%20%7D%7Byears%7D%20%5C%20t%20%5C%20%2B%20%5C%20%5C%24%20%5C%202816%20)
<h3>After 5 years</h3>
Now, we just use <em>t = 5 years</em> in our formula
![f(5 \ years) \ = \ - \ 352 \ \frac{\$ }{years} \ 5 \ years \ + \ \$ \ 2816](https://tex.z-dn.net/?f=f%285%20%5C%20years%29%20%5C%20%3D%20%5C%20-%20%5C%20352%20%5C%20%5Cfrac%7B%5C%24%20%7D%7Byears%7D%20%5C%205%20%5C%20years%20%5C%20%2B%20%5C%20%5C%24%20%5C%202816%20)
![f(5 \ years) \ = \ - \$ \ 1760 + \ \$ \ 2816](https://tex.z-dn.net/?f=f%285%20%5C%20years%29%20%5C%20%3D%20%5C%20-%20%5C%24%20%5C%201760%20%2B%20%5C%20%5C%24%20%5C%202816%20)
![f(5 \ years) \ = $ \ 1056](https://tex.z-dn.net/?f=f%285%20%5C%20years%29%20%5C%20%3D%20%24%20%5C%201056%20)