Answer: She can make 8 bracelets that are 11.43 centimeters.
Step-by-step explanation: Since one yard is equal to 91.44 centimeters you can divide this by 8, the amount of bracelets, and you get 11.43 centimeters
![$\begin{align}P&=\begin{pmatrix}0.2&0.8\\0.6&0.4\end{pmatrix} \\ &\text{So, we'll have:} \\ P_{1,1}&=0.2\\P_{1,2}&=0.8\\P_{2,1}&=0.6\\P_{2,2}&=0.4\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7DP%26%3D%5Cbegin%7Bpmatrix%7D0.2%260.8%5C%5C0.6%260.4%5Cend%7Bpmatrix%7D%20%5C%5C%20%26%5Ctext%7BSo%2C%20we%27ll%20have%3A%7D%20%5C%5C%20P_%7B1%2C1%7D%26%3D0.2%5C%5CP_%7B1%2C2%7D%26%3D0.8%5C%5CP_%7B2%2C1%7D%26%3D0.6%5C%5CP_%7B2%2C2%7D%26%3D0.4%5Cend%7Balign%7D)
(1)
![$\begin{align}\text{since }P_{1,1}=0.2,\text{ then the probability is } 0.2\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%5Ctext%7Bsince%20%7DP_%7B1%2C1%7D%3D0.2%2C%5Ctext%7B%20then%20the%20probability%20is%20%7D%200.2%5Cend%7Balign%7D)
(2)
![$\begin{align}\text{Since }P_{1,2}>P_{1,1},\text{ then the system most likely occupy state 2 because of higher probability}\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D%5Ctext%7BSince%20%7DP_%7B1%2C2%7D%3EP_%7B1%2C1%7D%2C%5Ctext%7B%20then%20the%20system%20most%20likely%20occupy%20state%202%20because%20of%20higher%20probability%7D%5Cend%7Balign%7D)
(3)
we can multiply the transition matrix (n-1) times, getting:
![$\begin{align}P^2&=\begin{pmatrix}0.2&0.8\\0.6&0.4\end{pmatrix}^2\\&=\begin{pmatrix}0.52&0.48\\0.36&0.64\end{pmatrix} \\ &\text{So,} \\ P_{1,1}&=0.52\end{align}](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7DP%5E2%26%3D%5Cbegin%7Bpmatrix%7D0.2%260.8%5C%5C0.6%260.4%5Cend%7Bpmatrix%7D%5E2%5C%5C%26%3D%5Cbegin%7Bpmatrix%7D0.52%260.48%5C%5C0.36%260.64%5Cend%7Bpmatrix%7D%20%5C%5C%20%26%5Ctext%7BSo%2C%7D%20%5C%5C%20P_%7B1%2C1%7D%26%3D0.52%5Cend%7Balign%7D)
(4)
Using the same reason as (2), the system most likely occupy state 1
Answer:
46.8 cm^3
Step-by-step explanation:
Answer:
2 (C)
Step-by-step explanation:
The "bisector" of the two sides is always equal to 1/2 of the base so...
2(3x-1) = 2x+6
Then, we simply btoh sides...
6x-2 = 2x+6
Then, we bring all the variables to one side and the numbers to the other..
4x = 8
Finally, we simplify to get our answer...
x=2 (C)