Answer:
if f(10) was shown if the graph, f(n) would be -20
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
X= 4/5
Because...
You turn all the missed numbers in to improper fractions, then after you add all the ones with x’s after that you should get 7 then divide 7 by 28/5. Which equals 4/5
Answer:
$0.80
Step-by-step explanation:
percent times the original number equals the part
(%)(start or total cost)= (part of the total cost). you need to know the total cost, so you would fill in the part and the percent. 0.9x=0.72. you use x because you don't know what the total cost is. then you divide both sides by 0.9 to get x by itself and you get that x = 0.8, meaning that the present costs $0.80.
Answer:
If Avery decides to deposit $7,000 for 5 years, the bank would be the better deal would be bank is offering a rate of 3%
compounded annually
Step-by-step explanation:
In order to calculate which bank would be the better deal If Avery decides to deposit $7,000 for 5 years, we would have to make the following calculation:
simple interest rate of 32%.
Therefore, I= P*r*t
=$7,000*32%*5
=$11,200.
compound interest rate of 3%
Therefore, FV=PV(1+r)∧n
FV=$7,000(1+0.03)∧5
FV=$8,114.
If Avery decides to deposit $7,000 for 5 years, the bank would be the better deal would be bank is offering a rate of 3%
compounded annually