When a slope is the steepest, the x value would be very small (in terms of fractions and decimals mostly). As the value of x is increased, the further away it starts moving from the y-axis. Therefore, the correct solution would be y=3x-16. Another way to confirm this is by graphing all the equations and comparing.
Hope I helped :)
Answer:
S = [0.2069,0.7931]
Step-by-step explanation:
Transition Matrix:
![P=\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]](https://tex.z-dn.net/?f=P%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5D)
Stationary matrix S for the transition matrix P is obtained by computing powers of the transition matrix P ( k powers ) until all the two rows of transition matrix p are equal or identical.
Transition matrix P raised to the power 2 (at k = 2)
![P^{2} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B2%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.2203%260.7797%5C%5C0.2034%260.7966%5Cend%7Barray%7D%5Cright%5D)
Transition matrix P raised to the power 3 (at k = 3)
![P^{3} =\left[\begin{array}{ccc}0.2203&0.7797\\0.2034&0.7966\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B3%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.2203%260.7797%5C%5C0.2034%260.7966%5Cend%7Barray%7D%5Cright%5D%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5D)
![P^{3} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B3%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.2086%260.7914%5C%5C0.2064%260.7936%5Cend%7Barray%7D%5Cright%5D)
Transition matrix P raised to the power 4 (at k = 4)
![P^{4} =\left[\begin{array}{ccc}0.2086&0.7914\\0.2064&0.7936\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B4%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.2086%260.7914%5C%5C0.2064%260.7936%5Cend%7Barray%7D%5Cright%5D%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5D)
![P^{4} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B4%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.2071%260.7929%5C%5C0.2068%260.7932%5Cend%7Barray%7D%5Cright%5D)
Transition matrix P raised to the power 5 (at k = 5)
![P^{5} =\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]X\left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B5%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5D%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5DX%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5DX%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5DX%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5D)
![P^{5} =\left[\begin{array}{ccc}0.2071&0.7929\\0.2068&0.7932\end{array}\right] X \left[\begin{array}{ccc}0.31&0.69\\0.18&0.82\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B5%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.2071%260.7929%5C%5C0.2068%260.7932%5Cend%7Barray%7D%5Cright%5D%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.31%260.69%5C%5C0.18%260.82%5Cend%7Barray%7D%5Cright%5D)
![P^{5} =\left[\begin{array}{ccc}0.2069&0.7931\\0.2069&0.7931\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B5%7D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.2069%260.7931%5C%5C0.2069%260.7931%5Cend%7Barray%7D%5Cright%5D)
P⁵ at k = 5 both the rows identical. Hence the stationary matrix S is:
S = [ 0.2069 , 0.7931 ]
Answer:
Its actually 100 residents who live near the proposed site for the youth center
50 children at each city's four elementary schools
100 parents of children at each of the city's four school
Step-by-step explanation:
25+N=61.
N= 36
So there is 36 numbers in Abby's cell phone.
Answer:
To find a
sin 30=a/6in
1/2=a/6in
2a=6in
a=6in/2
a=3in
To find b
cos 30=b/6in
/3/2=b/6in
2b=/3*6in
b=2/3(two radical three)
I don't get the radical sign so I use / sign on the last 3 steps on the second