1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Valentin [98]
3 years ago
15

The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either

involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 15 percent will enter into a relationship every month. What is the steady-state fraction of residents who are uninvolved
Mathematics
1 answer:
Ad libitum [116K]3 years ago
4 0

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:

\begin{pmatrix} &U&M\\U&0.85&0.15\\M&0.10&0.90\end{pmatrix}

The steady state is that satisfies this product of matrixs:

[\pi] \cdot [P]=[\pi]

being π the matrix of steady-state proportions and P the transition matrix.

If we multiply, we have:

(\pi_U,\pi_M)*\begin{pmatrix}0.85&0.15\\0.10&0.90\end{pmatrix}=(\pi_U,\pi_M)

Now we have to solve this equations

0.85\pi_U+0.10\pi_M=\pi_U\\\\0.15\pi_U+0.90\pi_M=\pi_M

We choose one of the equations and solve:

0.85\pi_U+0.10\pi_M=\pi_U\\\\\pi_M=((1-0.85)/0.10)\pi_U=1.5\pi_U\\\\\\\pi_M+\pi_U=1\\\\1.5\pi_U+\pi_U=1\\\\\pi_U=1/2.5=0.4 \\\\ \pi_M=1.5\pi_U=1.5*0.4=0.6

Then, the steady state proportion for the U (uninvolved) fraction is 0.4.

You might be interested in
Find the surface area of the tin game case
butalik [34]
To find the surface area you will need to find the area of all 5 surfaces (faces) on the prism.  On a triangular prism there are 2 triangular faces and 3 rectangular faces.  All 3 rectangular faces are the same and the 2 triangular faces are also the same.

To find the area of the triangular faces, you will use the formula for finding the area of a triangle:

A = 1/2bh
     1/2 x 10 x 8.7
A = 43.5 in^2 

To find the area of the rectangular faces, you will use the formula for finding the area of a rectangle:

A = bh
    10 x 3
A = 30 in ^2

30 + 30 + 30 + 43.5 + 43.5 = 177

The minimum amount of wrapping paper needed for the gift is 177 square inches.
8 0
3 years ago
- Which is greater?<br> 5 2<br> a) or<br> 16 9
azamat

Answer:

5/2

Step-by-step explanation:

5/2= 2 1/2

while 16/9=1 7/9

6 0
3 years ago
A ball is kicked 4 feet above the ground with an initial vertical velocity of 55 feet per second. The function h(t)=-16t^2+55t+4
Shalnov [3]

Answer:

Time in seconds when the ball is 4 feet above the ground is:

t= 0.6 and 2.9.

6 0
3 years ago
What is the discriminant of 3x^2 - 10 = -2?
Tatiana [17]
The formula for the discriminant is b^2-4ac. The formula you wote is in the form of 
ax^2+c=0, so first, you need to bring that -2 to the left. When you do that, you get (the original equation would be ax^2+bx+c but you have no bx.)

3x^2-8

So, since there's no b, it would be
b^2-4ac
0^2-4(3)(-8
-12 x -8
96

7 0
3 years ago
Nathaly lost 29 cups of sugar by accidentally spilling it all over the floor after she cleaned it up,she asked her neighbor she
Taya2010 [7]

She needs 3 3/4 cups more

Step-by-step explanation:

(I think you accidently put the 18 3/4 part twice) but anyways if you add 3/4 and 1/2 you get 1 and 1/4 that will be important later then you do 18 + 6 = 24 and then add your 1 and 1/4 to get a total of 25 1/4 then you just minus that from 29 and get 3 and 3/4

Hope this Helps!

7 0
2 years ago
Other questions:
  • What is the median of the following numbers: 120, 35, 42, 119, 120.5, 99, 72 ? *
    5·1 answer
  • Hi, can someone help me on these 2 as quick as possible please, ty!!
    8·2 answers
  • Solve by factoring or finding square roots x^2-6x-7=0
    15·2 answers
  • The blue M&amp;M was introduced in 1995. Before then, the color mix in a bag of plain M&amp;Ms was (30% Brown, 20% Yellow, 20% R
    7·1 answer
  • Draw algebra tile models to prove that 4+8x and 4 (2x+1) are equivalent
    6·1 answer
  • State whether the number 97 is prime, composite, or neither
    15·1 answer
  • Look at the picture above. need help ASAP ​
    7·1 answer
  • Mrs. Masinick is interested in buying a notebook computer. If she buys the computer this week, she will save $150.00 while it is
    5·1 answer
  • ANSWER PART B
    8·2 answers
  • Triangles IJK and LMN are similar. Find y using proportions. Explain and show all your steps.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!