The populations is all of the beavers at the park and the sample is the 10 that he randomly chose. A population means the total amount, so it wouldn’t make sense that it would be 10. A sample is a portion of the entire population, so 10 would be the right answer since it is only a portion of the entire population. 31 does not work because it is the data that is found using the sample of 10 beavers.
Answer:
.
Step-by-step explanation:
Let the 
-coordinate of 
be 
. For 
to be on the graph of the function 
, the 
-coordinate of 
would need to be 
. Therefore, the coordinate of 
would be 
.
The Euclidean Distance between and 
is:
.
The goal is to find the a that minimizes this distance. However, 
is non-negative for all real 
. Hence, the 
that minimizes the square of this expression, 
, would also minimize 
.
Differentiate with respect to :
![\displaystyle \frac{d}{dt}\left[t^2 - 17 \, t + 81\right] = 2\, t - 17](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5Bt%5E2%20-%2017%20%5C%2C%20t%20%2B%2081%5Cright%5D%20%3D%202%5C%2C%20t%20-%2017)
.
![\displaystyle \frac{d^{2}}{dt^{2}}\left[t^2 - 17 \, t + 81\right] = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%5E%7B2%7D%7D%7Bdt%5E%7B2%7D%7D%5Cleft%5Bt%5E2%20-%2017%20%5C%2C%20t%20%2B%2081%5Cright%5D%20%3D%202)
.
Set the first derivative, 
, to 
and solve for :
.
.
Notice that the second derivative is greater than for this . Hence, would indeed minimize . This value would also minimize , the distance between and .
Therefore, the point would be closest to when the -coordinate of is .
Operate your equation with respect to your variable. Add, subtract or multiply, anything but equally for all the sides of the equation.
[ You can post particular question, for practical understanding ]
Hope this helps!
