
To solve this equation, we need to subtract both, 9c - 3c:

Dividing by 6 at both sides of the equation

Then

Then the answer C = 8. (Option D)
Answer:
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125
Step-by-step explanation:
Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.
To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?
Proof -
By the given information, we get the stohastic matrix
![H = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]](https://tex.z-dn.net/?f=H%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%260.25%260.25%5C%5C0.25%260.5%260.25%5C%5C0.25%260.25%260.5%5Cend%7Barray%7D%5Cright%5D)
As we know that,
The matrix is a Markov chain 
Let
The initial state vector be
![x_{0} = \left[\begin{array}{ccc}1\\0\\0\end{array}\right]](https://tex.z-dn.net/?f=x_%7B0%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
we choose this initial vector because given that If the animal chooses food #1 on an initial trial.
Now,
![x_{1} = Hx_{0} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}1\\0\\0\end{array}\right] \\= \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20Hx_%7B0%7D%20%5C%5C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%260.25%260.25%5C%5C0.25%260.5%260.25%5C%5C0.25%260.25%260.5%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C0%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%5C%5C0.25%5C%5C0.25%5Cend%7Barray%7D%5Cright%5D)
∴ we get
![x_{1} = \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]](https://tex.z-dn.net/?f=x_%7B1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%5C%5C0.25%5C%5C0.25%5Cend%7Barray%7D%5Cright%5D)
Now,
![x_{2} = Hx_{1} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right] \\= \left[\begin{array}{ccc}0.25+0.0625+0.0625\\0.125+0.125+0.0625\\0.125+0.0625+0.125\end{array}\right]\\= \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20Hx_%7B1%7D%20%5C%5C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%260.25%260.25%5C%5C0.25%260.5%260.25%5C%5C0.25%260.25%260.5%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.5%5C%5C0.25%5C%5C0.25%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.25%2B0.0625%2B0.0625%5C%5C0.125%2B0.125%2B0.0625%5C%5C0.125%2B0.0625%2B0.125%5Cend%7Barray%7D%5Cright%5D%5C%5C%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.375%5C%5C0.3125%5C%5C0.3125%5Cend%7Barray%7D%5Cright%5D)
∴ we get
![x_{2} = \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.375%5C%5C0.3125%5C%5C0.3125%5Cend%7Barray%7D%5Cright%5D)
∴ we get
The probability that it will choose food #2 on the second trial after the initial trial = 0.3125
ok is there more info about it
Answer:
X = 1
Step-by-step explanation:
X is none number but equals to 1
Rewrite
(4)(3.63) * (10^4)(10^-4)
multiply
14.52 * (10^4)(10^-4)
multiplication of the coefficient is the addition of the exponent
so 4 -4 is 0
14.52
Hope this helps :)