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
Answer:
7 minutes I'm pretty sure I'm sorry if I'm not but if I'm right can I have brainliest answer?
Answer:
14) 21.136505024965 m
15) 43.076759215619 km
Step-by-step explanation:
14)
let h be the height of the lighthouse:
tan(41.3) = 18.7/h
Then
h = 18.7÷tan(41.5)
= 21.136505024965 m
………………………………………
15)
90-71.4 =18.6
Let s be the distance that the plane flew
towards the south:
tan(90 - 71.4) = s/128
Then
tan(18.6) = s/128
Then
s = tan(18.6)×128
= 43.076759215619 km
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Formula
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Sum of all exterior numbers = 360°
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Apply Formula
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z + 45 + 55 + 78 + 74 + z = 360
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Combine likes term
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2z + 252 = 360
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Take away 252 from both sides
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2z = 360 - 252
2z = 108
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Divide by 2 on both sides
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2z = 108
z = 108 ÷ 2
z = 54
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Find z + 45
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z + 45 = 54 + 45
z + 45 = 99°
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Answer: 99°
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Answer:
Its more because 9.36 has a bigger beginning then 9.359.
Ur welcome plzzz mark this as brainlest and thank me