The graph of a linear function is shown on the grid.
#6. Find the slope:
#7. Find the y-intercept:
#8. Write the equation in slope-intercept form:

a. P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]

b. P[[tex]x_{3} = 2[/tex]] = 0.18

c. p = 0.8353

d   [tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]

Given that:

{[tex]x_{n}[/tex] ; n > 0} is a Markov chain

[tex]x_{n}[/tex] denotes no of black balls in Urn A after [tex]n^{th}[/tex] round of exchange.

Clearly know that no of black balls in Urn A cannot exceed.

Hence, state space is {0, 1,2}

Transition probabilities can be

(a) [tex]P_{00}[/tex] = P [white ball is selected from A & white ball is selected from B]

          = P [white ball from A] × P [white ball from B]

           = [tex]\frac{2}{3}[/tex]

   [tex]P_{01}[/tex] = P [white ball from A & black ball from B ]

         = [tex]\frac{1}{3}[/tex]

   [tex]P_{10}[/tex] = P [black ball from A & white ball from B]

         = [tex]\frac{2}{9}[/tex]

   [tex]P_{11}[/tex] = P [black ball from A &  black ball from B]

              or P [white from A & white from B]

          [tex]= \frac{1}{3} * \frac{1}{3} + \frac{2}{3} *\frac{2}{3}\\ \\ = \frac{1}{9} + \frac{4}{9}\\ \\= \frac{5}{9}[/tex]

    [tex]P_{12}[/tex] =  P [white from A & white from B]

          = [tex]\frac{2}{9}[/tex]

    [tex]P_{21}[/tex] =  P [black ball from A & white ball from B]

          = [tex]\frac{2}{3}[/tex]

     [tex]P_{22}[/tex] =   P [white from A & white from B]

           = [tex]\frac{1}{3}[/tex]

Transition probability matrix P = [tex]\left[\begin{array}{ccc}\frac{2}{3} &\frac{1}{3} &0 \\\\\frac{2}{9} &\frac{5}{9} &\frac{2}{9}\\ \\0&\frac{2}{3} &\frac{1}{3} \end{array}\right][/tex]

(b) The probability that after 3 exchanges, there are exactly 2 black balls in Urn A.

P[[tex]x_{3} = 2[/tex]]

given initial distribution

[tex]p [x_{0} = 0] = 0 , p [x_{0} = 1] = 1 , p [x_{0} = 2] = 0[/tex]

p[tex][x_{3} = 2] =[/tex] ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex]

              = ∑ i = 0 to 2 P [tex][x_{3} = 2 , x_{0} =i ][/tex]  . P[tex][ x_{0} = i][/tex]

              =  ∑ i = 0 to 2 P [tex]i^{2^3}[/tex] P[tex][ x_{0} = i][/tex]

Transition probability matrix can be calculated by increasing power of P matrix to 3 i.e [tex]P^{3}[/tex]

P[[tex]x_{3} = 2[/tex]] = 0.18

(c) The probability that by the time we have done 3 exchanges, there has never been 2 black balls in Urn A.

[tex]P[x_{3} \neq 2 , x_{2} \neq 2, x_{1} \neq 2 | x_{0} = 1 ][/tex]

p = 0.8353

(d) Long run proportions of state 0,1,2.

[tex]\pi _{0} = \frac{2}{3} \pi _{0} + \frac{2}{3} \pi _{1}[/tex]

[tex]\pi _{1} = \frac{1}{3} \pi _{0} + \frac{5}{9} \pi _{1} + \frac{2}{3} \pi _{2}[/tex]

[tex]\pi _{2} = \frac{2}{9} \pi _{1} + \frac{1}{3} \pi _{2}[/tex]

[tex]\pi _{0} + \pi _{1} + \pi _{2} = 1[/tex]

[tex]\pi _{0} = \frac{2}{3} \pi _{1} \\[/tex]

[tex]\pi _{2} = \frac{1}{3} \pi _{1}[/tex]

[tex]\pi _{1} [\frac{1}{3} + \frac{2}{3} + 1 ] = 1[/tex]

[tex]\pi _{1} = \frac{1}{2} \\\\\pi _{2} = \frac{1}{6} \\\\\pi _{0} = \frac{2}{6}[/tex]

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The probability that the person is a woman is 40%.

P(Glasses) = P(M ∩ G) + P(W ∩ G)

P(Glasses) = 0.45 × 0.40 + 0.55 × 0.20

P(Glasses) = 0.27

P(Woman) = P(W ∩ G) / P(Glasses)

P(Woman) = 0.55 × 0.20 / 0.27

P(Woman) = 0.44

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Answer:

99 inches

Step-by-step explanation:

1 foot=12 inches

8x12=96

96+3=99

The amount allowed for housing and expenses is $2023.73.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Gross pay = $2759

Deduction:

7.65%

= 7.65/100 x 2759

= $211.06

12%

= 12/100 x 2759

= $331.08

7%

= 7/100 x 2759

= $193.13

The remaining amount.

= 2759 - 211.06 - 331.08 - 193.13

= $2023.73

Thus,

The amount allowed is $2023.73.

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As per the estimated percentage, the test statistic is 0.6167 or 61.67%

The term percentage is defined as the number or ratio that can be expressed as a fraction of 100.

Here we have given that in Arkansas than Virginia. the sample results show that, rounded to two decimal places, the estimated percentage of Arkansas residents who were born there is %. the sample results also show that, rounded to two decimal places, the estimated percentage of Virginia residents who were born there is %.

And we need to find the test statistics.

While we looking into the given situation we have identified the following values,

=> H0 : p = 0.577

=> Ha : p ≠ 0.577

Now, we have estimate the proportion of stay-at-home residents in Arkansas is calculated as,

Here the Proportion of stay-at-home residents in Arkansas is written as,

=> p = 74/120 = 0.6167

Therefore, the test statistics is 0.6167.

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For the given equation the value of n is equal to option D.

n = (s/180) + 2.

As given in the question,

Given equation is equal to  :

s = (n-2)180

Now take all the terms on one side and term n on other side of the equation we have,

Divide both the side by 180 we get,

s/ 180 =  [(n-2)180]/180

s/180 = n -2

Add 2 both the side of the equation we get,

(s/180 ) + 2 = n -2 + 2

(s/180 ) + 2 = n

so here the value is equal to

n = (s/180) +2.

Therefore, the value of n in the equation is equal to option D.

n = (s/180) + 2.

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Answer:

Divide the numerator and denominator by 45.

Step-by-step explanation:

7650/341055

Divide the numerator and denominator by 5.

1530/68211

Divide the numerator and denominator by 3.

510/22737

Divide the numerator and denominator by 3.

170/7579

The length of the vector v is approximately 4.24. A vector is a mathematical object that has both magnitude and direction

Vectors are commonly used in physics, engineering, and other fields to represent quantities that have both magnitude and direction, such as velocity, acceleration, and force. They are also important in linear algebra, where they can be used to represent lines and planes in space, and to solve systems of linear equations.

The vector v can be expressed in component form as v = <2-5, 10-7> = <-3, 3>.

To express the vector v as a linear combination of the unit vectors i and j, we can write it as v = (-3)i + 3j.

To find the length of the vector, we can use the Pythagorean theorem:

length of v = sqrt((-3)^2 + 3^2) = sqrt(9 + 9) = sqrt(18) = 3*sqrt(2) = 4.24

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The indirect proof that defines triangle RVS is not equilateral is explained below.

How triangle look like?

In math, A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices and also a polygon.

Here we need to find the indirect proof for the triangle RVS which is not equilateral.

Here we know that, We need to write an indirect proof in paragraph proof.

For, the given statement, △RVT and SVT are equilateral; 

And △RVS is not equilateral.

Then the explanation for this one is written as,

Let us assume temporarily that △RST is equilateral.

And we have given that △RVT and SVT are equilateral, then the sides of △RVT, SVT, and RST are congruent.

Therefore, RV≅VSRS which follows that △RVS is equilateral.

In contradicts the given that △RVS is not equilateral, then the temporary assumption must be false. It follows that △RST is not equilateral.

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It is said that the rural landscape has been replaced by the urban landscape because rural landscapes have been transformed into urban ones.

We have to:

At present, more and more rural spaces become urban, which is why it is indicated that the urban landscape is replacing the rural one.

¡Hope this helped!

Answer:

  see the attachment for the Venn diagram

Step-by-step explanation:

Given the numbers of students in various combinations of three courses, you want the associated Venn diagram and some numbers associated with additional combinations of courses.

It is often easiest to populate the numbers in a Venn diagram by starting with the center one: 286 are taking all three courses. (V. = 286)

Working outwards from there, the numbers taking two courses can be filled in: (II. = History & Dance - V. = 343; IV. = History & Math - V. = 319; VI. = Dance & Math - V. = 318.)

Finally, the number taking a single course can be found. (I. = History -II. -IV. -V.; III. = Dance -II. -V. -VI.; VII. = Math -IV. -V. -VI.)

Adding all the numbers found so far gives the total in History, Dance, or Math (question 4). The difference between the number surveyed and the number in courses is VIII, the number taking none of the courses (question 5).

The least arithmetic may be involved if you rewrite this expression to ...

  H ∪ D' = (H'∩D)' = 2401 -(III +VI) = 2401 -(289 +318) = 1794

This will be the sum of numbers I, IV, VII.

  226 +319 +372 = 917

This is VI alone: 318

This is all but VIIII: 2401 -248 = 2153

This is VIII alone: 248

The solution is Option D.

The value of x from the triangle is x = 31

What are similar triangles?

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ABC

The measure of side AB = 14.5

The measure of side BC = 15.5

Let the second triangle be XYZ

The measure of side XY = 29

The measure of side YZ = x

Now , if the triangle ABC is similar to triangle XYZ , then the corresponding sides of the triangles will be equal in ratio

So , the equation will be

XY / AB = YZ / BC

Substituting the values in the equation , we get

29 / 14.5 = x / 15.5

On simplifying the equation , we get

x/15.5 = 2

Multiply by 15.5 on both sides of the equation , we get

x = 2 x 15.5

x = 31

Therefore , the value of x is 31

Hence , the value of x of side YZ is 31

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Answer:

C

Step-by-step explanation:

A rational number can be written as a ratio of two integers. In decimal form, a rational number will either terminate or repeat a pattern.

Answer:

2x+9<25 or u just can say c

Answer:

t = 48 litres when full

Step-by-step explanation:

The water tank at the institution is full. A water truck begin to full the tank with water at a rate of 8 litres per minute. After 15 minutes the tank was 5/2 full. Calculate the number of litres of water that the tank can hold.

8(15) = 5/2t

120 = 5/2t

240 = 5t

t = 48 litres when full

Answer:  4

Step-by-step explanation

3^2×=6561

then think 3 raise to power what is 6561

the answer is 8

3^2×=3^8

three cancel three

2×=8

divide both sides by 2

then ×=4

Answer:

14.128

Step-by-step explanation:

you need to extract the 872g which is 0.872kg

from the 15 and that is 14.128kg

callback restricted is a function that is passed as an argument to another function

It tests whether the condition returned by the callback function holds for at least one item in array.

What is an array?

It should be noted that an array means a data structure that can store a fixed size collection of elements.

In this case, the true statement of the array is that it tests whether the condition returned by the callback function holds for at least one item in array.

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The value of f(g(2)) from the given functions f(x) and g(x) is 3.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=2x²+1 and g(x)=3x-5.

We need to find f(g(2)).

Put x=2 in the function g(x)=3x-5, we get

g(2)=3×2-5

= 6-5

= 1

So, g(2)=1

Put x=1 in the function f(x)=2x²+1, we get

f(g(2))=2(1)²+1

= 2+1

=3

Therefore, the value of f(g(2)) is 3.

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Answer:

now

Step-by-step explanation:

d= √(X2 _ X1) +(Y2 - Y1). = (5 -2 )+ (-4- 1)=

Answer:

  x ≥ 0

Step-by-step explanation:

You want to know an appropriate limit on the domain of f(x) = 3 -x² so the function is one-to-one.

A function is one-to-one if it passes the "horizontal line test." That is, a horizontal line can intersect its graph in at most one place.

The function f(x) = 3-x² has a turning point at x=0 and is symmetrical about that line. In order to make the function be one-to-one, the domain must be restricted to one of ...

or any subset of either of those domains.

Answer:

b and c

Step-by-step explanation:

When you add one-digit number to a decade number, you will notice that the ones place digit sum is interchanged in their positions

You should know the word decade means ten. so a decade number is a number with ten digits. The digits of the decade number are

1,2,3,4,5,6,7,8,9

So write the number as

12345679

A digit number is  say 9

123456789+9

= 123456798

Therefore when a digit number is added to a decade number, the last digits interchange their positions

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From the given pairs of ordered pairs {(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)} it is a function.

The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

As per the set of ordered pairs given in the question,

1.

{(-1, 3), (2, 6), (3, 9), (4, 12), (5, 20)}

It is a function because every input has a single output.

2.

{(-7, 3), (-7, 6), (-7, 12), (-7, 18)}

It is not a function because 7 corresponds to two different images like 3, 6, 12, and 18.

3.

{(9, -3), (4, -2), (1, -1), (0, 0), (1, -3)}

It is not a function because 1 corresponds to two different images, like -1 and 3.

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The solution of the system of the equations, y = 1/3x + 3 and y = 2x - 4, as shown in the graph below is: (4.2, 4.4).

A system involving two equations has a solution, which are the coordinates of the point on a graph where the two equations intersect.

Given the equation, y = 1/3x + 3, which is represented by the red line in the graph below, when y = 2x - 4 (represented as the blue line) is added, a system is formed which will make both lines intersect at the point that has the coordinates (4.2, 4.4).

Therefore, the solution of the system y = 1/3x + 3 and y = 2x - 4 is (4.2, 4.4).

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The name of this man's "small" and "final" theorems are Pierre de Fermat

He was a French mathematician who is recognized for his work on inequality and other early advances that helped pave the way for infinitesimal calculus. He is praised in particular for his work on number theory and his original invention of a technique for determining the largest and smallest ordinates of curved lines that is comparable to differential calculus, which was previously unheard of. He made important advances in probability, optics, and analytical geometry.

The Taniyama-Shimura Conjecture, commonly known as the modularity conjecture, was employed in another theorem that bears this man's name.  

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Option B  [tex]n_{1} = 27 ,n_{2} = 29[/tex]  are the two sample sizes cannot be true.

HYPOTHESIS TEST

Given that:

The degree of freedom for the test of two independent population means is 56.

Degrees of freedom for two independent populations are well known.

[tex]n_{1} + n_{2} - 2[/tex]

[tex]n_{1} + n_{2} - 2[/tex] = 56

[tex]n_{1} + n_{2}[/tex] = 54

Total sample sizes = 54

Option B (   [tex]n_{1} = 27 ,n_{2} = 29[/tex] ) cannot be true.

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The x - intercept is 40 ,which represents the number of monthly payments needed to repay the loan .

Given :

The graph models the linear relationship between the number of monthly payments made on a loan and the remaining balance in dollars left to pay on the loan.

From the graph :

Two points are ( 6 , 25500 ) and ( 25 , 11250 )

x - intercept = 40

The x - intercept gives information about the variable represented on the x - axis of a graph which is the number of monthly repayments needed to cover the loan.

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Answer:

18

Step-by-step explanation: