Three white balls and three black balls are distributed in two urns in such a way that each contain three balls. We say that the system is in state i, i=0,1,2,3, if the first urn contains i white balls. At each step, we draw one ball from each urn and place the ball drawn from the first urn into the second, and conversely with the ball from the second urn. Let Xn denote the state of the system after the nth step. Explain why {Xn, n=0 ,1, 2} is a Markov chain and calculate its transition probability matrix.

Answer:

The answer is "0.68".

Step-by-step explanation:

Given value:

[tex]X_i \sim \frac{G_1}{2}[/tex]

[tex]E(X_i)=2 \\[/tex]

[tex]Var (X_i)= \frac{1- \frac{1}{2}}{(\frac{1}{2})^2}\\[/tex]

             [tex]= \frac{ \frac{2-1}{2}}{\frac{1}{4}}\\\\= \frac{ \frac{1}{2}}{\frac{1}{4}}\\\\= \frac{1}{2} \times \frac{4}{1}\\\\= \frac{4}{2}\\\\=2[/tex]

Now we calculate the [tex]\bar X \sim N(2, \sqrt{\frac{2}{n}})\\[/tex]

[tex]\to \frac{\bar X - 2}{\sqrt{\frac{2}{n}}} \sim N(0, 1)\\[/tex]

[tex]\to \sum^n_{i=1} \frac{X_i - 2}{n} \times\sqrt{\frac{n}{2}}} \sim N(0, 1)\\\\\to \sum^n_{i=1} \frac{X_i - 2}{\sqrt{2n}} \sim N(0, 1)\\[/tex]

[tex]\to Z_n = \frac{1}{\sqrt{n}} \sum^n_{i=1} (X_i -2) \sim N(0, 2)\\[/tex]

[tex]\to P(-1 \leq X_n \leq 2) = P(Z_n \leq Z) -P(Z_n \leq -1) \\\\[/tex]

                               [tex]= 0.92 -0.24\\\\= 0.68[/tex]

Answer:

The probability that it contains no flaws=0.585

Step-by-step explanation:

Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet.

One = 270 ft²

8*14= 112 ft²

Probability of containing flaws

So if 270 ft² = 1

112 ft² = 112/270

112ft² = 0.415

The probability that it contains no flaws= 1- probability that it contains

The probability that it contains no flaws= 1-0.415

The probability that it contains no flaws=0.585

Answer:

          N - 2 r t²

x =  -   ------------

                7x

Step-by-step explanation:

N = 2 r t² - 7 r x

solve for x

N = 2 r t² - 7 r x

N + (-2 r t²) = (2 r t²  - 7 r x) + (-2 r t²)

N - 2 r t² = 2 r t² - 7 r x - 2 r t²

N - 2 r t²  - 2 r t² +  2 r t² = - 7 r x

N - 2 r t² = 7 r x

therefore,

          N - 2 r t²

x =  -   ------------

                7x

Answer:

36,800

Step-by-step explanation:

If x < 5, we round down.

If x ≥ 5, we round up.

We are specifically looking at 8 and 1 in 36,815.

1 < 5, so we round down:

36,800

Answer:

a. H0:u1=u2

Ha:u1>u2

b. T-critical value =1.7011

c. We can conclude that relaxation training has reduced stress levels based on evidence gathered from statistical calculations

Step-by-step explanation:

Please find attachment

Answer:

This week's batch had the greater ratio of sugar to berries

Step-by-step explanation:

Last week's ratio was 2:18

This week's ratio was 4:30

Now, we can simplify both of these:

Divide last week's by 2:

1:9

Divide this week's by 2:

2:15

1:9 is equivalent to 0.11, and 2:15 is equivalent to 0.13

So, this week's batch had the greater ratio of sugar to berries

The batch with 4 cups of sugar and 30 cups of berries has a greater ratio of sugar to berries and is given by the proportion B = 4/30 = 0.1333

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion equation be represented as A and B

Now , for the last week's batch

Alec used 2 cups of sugar and 18 cups of berries

So , the ratio of sugar to berries is 2 : 18

The proportion is 2 / 18 = 0.1111

Now , for this week's batch

Alec used 4 cups of sugar and 30 cups of berries

So , the ratio of sugar to berries is 4 : 30

So , the proportion is 4 / 30 = 0.1333

Now , the proportion of 4 : 30 is greater than 2 : 18

Hence , this week's batch had a greater proportion

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Answer:

convert 13.025 to base 10

Answer:

[tex]\frac{2}{1}[/tex]

Step-by-step explanation:

Hello!

To find the slope of a line we divide how many times it goes over by the number of times it goes up

The line goes over 4 and up 2 which is shown like

[tex]\frac{4}{2}[/tex]

We can simplify this

[tex]\frac{2}{1}[/tex]

The answer is [tex]\frac{2}{1}[/tex]

Hope this helps!

Answer:

[tex]V(n) =225000*0.7^n[/tex]

Step-by-step explanation:

In this problem we are expected to model the depreciated value of the machine after some years of purchase (n years)

initial value of the machine is $225,000

after a year it reduces by 30%

Therefore the new value is now 70% of the initial value

[tex]= 225000*0.7= 157,500[/tex]

= $157,500

After another year it reduces by 30%

Hence the new value is

[tex]=225000*0.7^2\\\=225000*0.49\\\\\=110250[/tex]

= $110250

that after n years the value will be

[tex]V(n) =225000*0.7^n[/tex]

Answer:

5199

Step-by-step explanation:

Because

1 foot= 12 inches.

To convert you must have "2 fractions" to multiply.

Your first fraction must be 100in/1min. (100 inches per 1 minute).

The second should serve to convert inches to feet. It should be 1 foot/ 12 inches. (1 foot per 12 inches).

Your product should be 100ft/12 which equals 8.3 repeating or 25/3 (8 1/3) feet.

Answer:

segment AD

Step-by-step explanation:

LOD is the far side of the cube.

ABC is the left side.

So the intersection is the vertical EDGE AD, on the far-left.

The two planes ABC and LOD intersect each other at the segment AD.

A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

Given that there is a cube made of six sides. The two planes ABC and LOD intersect each other at the line segment AD or AD is the common line between the two planes. LOD is the far side of the cube. ABC is on the left side. So the intersection is the vertical EDGE AD, on the far left.

Therefore, the two planes ABC and LOD intersect each other at the segment AD.

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Answer:

$926.45

Step-by-step explanation:

$871.95 x .0625 = $54.50

$871.95 + $54.50 = $926.45

Answer:

$926.44

Step-by-step explanation:

sales tax = price*sales tax rate

sales tax = $54.49

871.95+54.49 = answer I think

Answer:

y +1 = 4/3( x-9)

Step-by-step explanation:

Point slope form of an equation is

y-y1 = m(x-x1)

where m is the slope and (x1,y1)  is a point on a line

y - -1 = 4/3( x-9)

y +1 = 4/3( x-9)

Hello, we know that

[tex]|x|=\begin{cases}x &\text{if } x \geq 0\\ -x &\text{if } x < 0 \end{cases}[/tex]

And we can write that 12x-5=0 <=> 12x =5 <=> x = 5/12

So,

[tex]|12x-5|=\begin{cases}12x-5 &\text{if } x \geq \dfrac{5}{12}\\\\ -12x+5 &\text{if } x < \dfrac{5}{12}\end{cases}[/tex]

And, we can write.

[tex]|12x-5|=11<=>\begin{cases}12x-5=11 &\text{if } x \geq \dfrac{5}{12}\\\\ -12x+5=11 &\text{if } x < \dfrac{5}{12}\end{cases}\\ \\ \\ <=>\begin{cases}12x=16 &\text{if } x \geq \dfrac{5}{12}\\\\ 12x=5-11 &\text{if } x < \dfrac{5}{12}\end{cases}\\\\<=>\begin{cases}x=\dfrac{16}{12}=\boxed{\dfrac{4}{3}} &\text{if } x \geq \dfrac{5}{12}\\\\ x=\dfrac{-6}{12}=\boxed{-\dfrac{1}{2}} &\text{if } x < \dfrac{5}{12}\end{cases}[/tex]

So the two solutions are 4/3 and -1/2.

Thank you.

Answer:

h = 10 m

Step-by-step explanation:

Area of a triangle = 1/2 * base * height

Area = 100 m²

base = 20 m

therefore,

100 m² = 1/2 * 20 m * h

h = 100 / 10

h = 10 m

The height will be 10 m.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, the area of a triangle is 100 m² and base is 20 m.

The area of a triangle = 1/2xbasexheight

100 = 1/2x20xh

h = 100/10

h = 10

Hence, The height will be 10 m.

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Answer: 11x^2

Step-by-step explanation:

I suppose that the options are:

a) 9/x

b) 11x^2

c) 20x^9-7x

d) 20x -14

First, a polynomial is something like:

aₙx^n + .... + a₂*x^2 + a₁*x^1 + a₀*x^0

Where n is the degree of the polynomial,  the therms a are the coefficients, and aₙ is the leading coefficient.

Depending on the number of terms of the polynomial, it takes different names.

If we have only one term, it is called a monomial, if it has two terms, it is called a binomial, and so on.

So if we want to find a monomial, then we need to look at the options with only one term.

The options with only one term are options a and b.

But option a is a quotient (we have a negative power of x: 9/x = 9*x^-1)

So this is not a polynomial, then the correct option is option b.

Answer:

The problems associated with choosing appropriate sampling units and frame are given below;

Step-by-step explanation:

1. The only aid available to the forester or researcher is a map of the farm.

2. Appropriate sampling units will be hard to choose because farm trees are only characterized by attributes such as

- type of crop/plant (as all trees of a certain crop are much likely to have similar width or diameter)

- height of tree (as height is closely related to width)

- location of tree on the farm (e.g. North on the map, East on the map, South on the map, West on the map)

- age of tree (as older trees are more likely to have diameters exceeding 12 inches, than the younger trees)

- etcetera.

3. Appropriate frame (size) of sample will be hard to choose because a number of trees cannot just be selected from the total number of trees, if the categorization for sampling units is uncertain.

1/2πr^2h.

1/2×3.142×3^2×2=

1/2×56.556=28.278~ 28.

Answer:

18pi

Step-by-step explanation:

I just got it right on Khan Academy

Answer:

D(x) = 4000 / x + 2

Step-by-step explanation:

Given:

marginal-demand function = d /dx[D(x )] = D'(x)= -4000/x²

Quantity of product demanded = 1002 units

Price of product per unit = $4

To find:

demand function D(x)

Solution:

D'(x)= -4000/x²

      =  -4000/x² dx

      = -4000 x⁻² dx

D(x) = -4000 x⁻¹ + C

D(x) = -4000/x + C

Since we know that the quantity of product is 1002 and price per unit is $4 so,

D(4) = 1002 = 4000/4 + C

          1002 = 4000/4 + C  

          1002 = 1000 + C  

           1002 - 1000 = C

            C = 2

Hence the demand function is:

D(x) = 4000 / x + 2

8/9 - 1/3

To subtract these two fractions, first find a common denominator.

The common denominator will be the

least common multiple for the two denominators.

In this case, the least common multiple of 9 and 3 is 9.

So to subtract, a denominator of 9 is needed in each fraction.

8/9 already has 9 in the denominator so it stays the same.

To get a 9 in the denominator of 1/3, multiply top and bottom by 3.

This gives us 3/9.

So we have 8/9 - 3/9 which is 5/9.

Answer:

Five-ninths

Step-by-step explanation:

Since the denominators are different (9 and 3) we need to change one of them.

9 is divisible by 3 therefor we do not need to change Eight-ninths.

3 times 3 = 9, nine becomes the new denominator, but remember, whatever we do to the bottom (denominator), we must also do to the top (numerator).

1 times 3 = 3

Now the equation is 8/9 - 3/9, we must only subtract the numerators. The answer is 5/9.

Answer:

A The APR is over 240%.

Step-by-step explanation:

Given:

Now options:

A The APR is over 240%.

B The fee will be paid only if Kingston makes a late payment.

C The $1,000 plus finance charges will be paid at the end of one year.

D Kingston will receive $1,200 from the loan.

Answer:

A The APR is over 240%.

Step-by-step explanation: Hope this helps ya'll

Answer:

Michaela = h

Michaela's sister = 3h

Answer = 3h

If Michaela has h hair ties and Michaela's sister has triple number of hair ties then the expression which shows the number of hair ties that Michaela's sister has is 3h.

Expression is a combination of number, symbols, variables, coefficients, indeterminants, functions, etc. It is usually not present in equal to form.

We have been given that Michaela has h number of hair ties and Michaela's sister has triple the number of hair ties that Michaela has, so if h is the expression for Michaela then 3h will be the expression for Michaela's sister.

Hence the expression which shows the number of hair ties that Michaela's sister has is 3h.

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Answer:

hello your question is incomplete below is the complete question

Case-Control Calculation Enter only numeric values into the answer line. Place a leading 0 before the decimal and remember to round to two decimal places. Note your answers for the next short essay question. Swine Influenza (SI) is a growing concern at the local Broncoville Health Department in Lawrence, Kansas. You are working for a pharmaceutical company which is developing a human vaccine against SI. You are in charge of testing the vaccine’s effectiveness. You need to determine if one or two doses of vaccine is required to provide immunity. You field test and collect the following information about the vaccine status of persons who did and did not contract SI after getting either one or two doses of vaccine. Develop a 2 x 2 table with the following information: Of the 727 cases of SI, 203 received two doses of vaccine. Of 1,239 controls, 771 received two doses of vaccine for SI. What is the likelihood of contracting SI with only one dose of vaccine?

1. Calculate the incidence of persons with one dose of vaccine for SI

2. Calculate the incidence of persons with two doses of vaccine for SI

3. Calculate the odds ratio of developing SI among those with one dose of vaccine for SI

answer : 1) ≈ 0.53 , (2)  ≈ 0.21,  (3)  ≈ 1.12

Step-by-step explanation:

cases of SI = 727

number of SI cases that received two doses of vaccine = 203

number of SI cases that received one dose of vaccine = 727 -203 = 524

controls = 1239

number of controls that received two doses of vaccine = 771

number of controls that received one dose of vaccine = 1239 - 771 = 468

I) The incidence of persons with one dose of vaccine for SI

= 524 / 992 = 0.528 ≈ 0.53

2) The incidence of persons with two doses of vaccine for SI = 203/974 = 0.208 ≈ 0.21

3) The Odds of SI in one dose group

=  524/468 = 1.119 ≈ 1.12

Answer:

answer is c

Step-by-step explanation:

i got it right

The solution of the system is unique and the solution is (2, 1). Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

If the two lines intersect, then the point of intersection represents the solution of the equations.

The solution of the system is unique and the solution is (2, 1).

The system has a unique solution at (2,1). Then the correct option is C.

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Answer:

A)Option A - To make sure that you get a straight line to bisect the line segment

B) Option D - Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.

Step-by-step explanation:

1) In bisection of a line segment, we seek to divide the line into 2 equal parts. Now, when using the bisection points of an arc, it's important to have two intersection points above and below the line segment so that we can draw a straight line that will pass through the horizontal line segment we are bisecting to make the bisected parts equal in length.

So option A is correct.

2) When bisecting a horizontal line segment using compass, usually we place one leg of the compass at one endpoint of the line and open the other leg of the compass to a length that's more than half of the horizontal line segment. Thereafter, we draw our arc from top to bottom. Without changing the distance of the opened compass, we put one of the legs at the 2nd endpoint and now draw another arc to intersect the previously drawn one.

Now, from the question we are told that the line segment has a length of approximately 10 cm and the compass is set to a width of 9 cm. Now, since 9cm is more than half of the line segment and provided this width of 9cm is maintained when moving the leg to the second endpoint, then it is possible.

Option D is correct.

Answer: The answer is C

The transformations are a horizontal translation 2 units left then a vertical translation 6 units down.