MATHEMATICS COLLEGE

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

Answers

Answer 1

Answer:

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:

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

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:

$(\pi_U,\pi_M)*\begin{pmatrix}0.85&0.15\n0.10&0.90\end{pmatrix}=(\pi_U,\pi_M)$

Now we have to solve this equations

$0.85\pi_U+0.10\pi_M=\pi_U\n\n0.15\pi_U+0.90\pi_M=\pi_M$

We choose one of the equations and solve:

$0.85\pi_U+0.10\pi_M=\pi_U\n\n\pi_M=((1-0.85)/0.10)\pi_U=1.5\pi_U\n\n\n\pi_M+\pi_U=1\n\n1.5\pi_U+\pi_U=1\n\n\pi_U=1/2.5=0.4 \n\n \pi_M=1.5\pi_U=1.5*0.4=0.6$

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

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Line l passes through the points (- 4, 3) and (2, 1) What is the slope of a line that is perpendicular l

Answers

Answer:

m=1

Step-by-step explanation:

The plots (-4,3) and (2,1) have a slope of -1. Perpendicular lines would mirror that, making it a positive 1

Which equation represents the polar form of x2 + (y + 4)2 = 16?

Answers

The polar form of equation is r = -8sinθ.

What is polar form of complex number?

The combination of the complex number's modulus r and argument is how complex numbers are shown in polar form z = r cosθ + i r sinθ = r (cosθ + i sinθ), is the polar form of a complex number with coordinates (x, y). In the coordinate system, polar coordinates of real and imaginary numbers are used to represent the polar form.

Given x² + (y + 4)² = 16

here The following is the relationship between (r, θ) and (x, y) if they are in Cartesian form:

x = rcosθ, y = rsinθ and r² = x² + y² ad tanθ = y/x

x² + (y + 4)² = 16

x² + y² + 16 + 8y = 16

x² + y² + 8y = 0

r² + 8rsinθ = 0

r(r + 8sinθ) = 0

r =0 and r = -8sinθ

Hence the polar form of equation is r = -8sinθ.

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Answer:

c. r=-8sin(theta)

Step-by-step explanation:

edge 2021

Help!! Is anyone good at algebra??

Answers

Answer:

h = 20 m

Step-by-step explanation:

So you know volume of a cylinder = π*(r^2) * h

and you also know volume of this cylinder = 180π

(volume is also in meters^3)

you can set these volumes equal to one another

180π = π*(r^2) * h

by dividing by π you get this:

180 = (r^2) * h

you need h so you can divide by r^2 to get this

h = 180 / (r^2)

now you just need to plug in the radius you are given which was 3 meters

h = 180 m^3 / (3 m^2)

h = 180 m^ 3 / 9 m^2

h = 20 m

What is the length of AC?

Answers

The length of AC found using the Pythagorean Theorem is C) 120.

The length of AC can be found using the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is AC, and the other two sides are AB and BC.

AB = 60 units

BC = 80 units

Plugging these values into the Pythagorean Theorem, we get:

$AC^2$ = $AB^2$ + $BC^2$

$AC^2$ = $60^2$ + $80^2$

$AC^2$ = 3600 + 6400

$AC^2$ = 10000

AC = $\sqrt{$ (10000)

AC = 100 * $\sqrt{$ (10)

AC = 120 units

Therefore, the length of AC is C) 120.

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B I think and I hope it’s right!

PLEASE HELP!Which is the correct classification of square root of 18?

A. irrational number, non-repeating decimal
B. irrational number, terminating decimal
C. rational number, terminating decimal
D .rational number, non-repeating decimal

Answers

The correct classification of the square root of 18 is: A. irrational number, non-repeating decimal.

To determine the classification of the square root of 18, let's break down the steps:

1. Calculate the square root of 18:

$√(18) \approx 4.24264068712$

2. Rational or Irrational?

The square root of 18 is an irrational number because it cannot be expressed as a fraction of two integers, and it is non-terminating, non-repeating decimal.

Rational numbers can be expressed as fractions, and their decimal representation either terminates (e.g., 1/4 = 0.25) or repeats in a pattern (e.g., 1/3 = 0.333...).

Since $√(18)$ cannot be expressed as a simple fraction, and its decimal representation continues infinitely without repeating, it is classified as an irrational number, non-repeating decimal.