Answer:
1 penny 3 nickels 2 dimes = 36 cents
quarter
Step-by-step explanation:
Answer:
wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
Step-by-step explanation:
sorry
Answer(s):
Solution:
<u>We know that:</u>
- Brookie = x dollars
- Benji = x + (20% × x)
<u>Solution:</u>
To see which expression has been used, we will need to simplify the expression.
- Benji = x + (20% × x)
- => Benji = x + (20/100 × x)
- => Benji = x + (2/10 × x)
- => Benji = x + (0.2 × x)
- => Benji = x + (0.2x)
- => Benji = x + 0.2x
- => Benji = 1.2x
Looking at the options, Option A and Option B matches with our result.
Option A and B are correct.
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 ]
If you are rolling a single six sided die numbered 1-6, you find that only 1,2,4, and 5 are factors of 20. Now the theoretical probability of an event is the ratio comparing the number of desired outcomes to the total outcomes possible.
In this case: we have 4 desired outcomes out of a total 6 outcomes possible with a single roll the die.. therefore, the probability you seek is

or approximately 67%.