Well if she is making dinner for 10 people and each person want 2 pieces then you need to multiple 10 x 2 = 20. So she is going to need to make 20 pieces.
If each of her pumpkin pies only has 8 pieces then she is going to have to make 3 pies.
3 pies x 8 pieces = 24 pieces of pumpkin pie. So she has to make 3 pies because she needs 20 pieces since everyone wants 2.
In conclusion Mrs. Owens has to make 3 pies and she is going to have 4 pieces left over.
It's a glitch I believe (screenshot and contact your teacher)
Answer:
The steady state proportion for the U (uninvolved) fraction is 0.4.
Step-by-step explanation:
This can be modeled as a Markov chain, with two states:
U: uninvolved
M: matched
The transitions probability matrix is:

The steady state is that satisfies this product of matrixs:
![[\pi] \cdot [P]=[\pi]](https://tex.z-dn.net/?f=%5B%5Cpi%5D%20%5Ccdot%20%5BP%5D%3D%5B%5Cpi%5D)
being π the matrix of steady-state proportions and P the transition matrix.
If we multiply, we have:

Now we have to solve this equations

We choose one of the equations and solve:

Then, the steady state proportion for the U (uninvolved) fraction is 0.4.
Answer:its 10 :)
Step-by-step explanation:
A. False. Consider the identity matrix, which is diagonalizable (it's already diagonal) but all its eigenvalues are the same (1).
b. True. Suppose

is the matrix of the eigenvectors of

, and

is the diagonal matrix of the eigenvalues of

:


Then

In other words, the columns of

are

, which are identically

, and these are the columns of

.
c. False. A counterexample is the matrix

which is nonsingular, but it has only one eigenvalue.
d. False. Consider the matrix

with eigenvalue

and eigenvector

, where

. But the matrix can't be diagonalized.