Find the differential of the function. Z = e−4x cos(4πt)

To find the steady state vector x, we must solve the equation xP = x, where P is the given transition matrix and x is the steady state vector.

P = | 0.5  0.1 |
      | 0.5  0.9 |

Let x = (x1, x2). We have two equations:

1) 0.5x1 + 0.1x2 = x1
2) 0.5x1 + 0.9x2 = x2

Also, since x is a probability vector, we have:

3) x1 + x2 = 1

Now, we can solve the system of equations:

From equation (1): 0.5x1 = 0.1x2, so x1 = 0.2x2

Substitute x1 in equation (3): 0.2x2 + x2 = 1, which gives x2 = 1/1.2 = 5/6

Now, we can find x1: x1 = 0.2x2 = 0.2(5/6) = 1/6

Thus, the steady state vector x is (1/6, 5/6).

It is important to always be factually accurate, professional, and friendly, while being concise and avoiding extraneous amounts of detail. Typos and irrelevant parts of the question should be ignored. Here is the answer to the given student question:Let P = 0.5 0.1 0.5 0.9 :] be the transition matrix for a Markov chain with two states. Let Xo = 0.5 0.5 be the initial state vector for the population.

Find the steady state vector x. (Give the steady state vector as a probability vector.) X = [0.357 0.643]Explanation:Given transition matrix, P = 0.5 0.1 0.5 0.9Given initial state vector, Xo = 0.5 0.5The steady state vector x of the transition matrix P is given by X = [x1 x2] such that PX = X or (P-I)X=0 where I is the identity matrix of order 2.The matrix (P-I) is0.5-1 0.1 0.5 0.9-1which simplifies to-0.5 0.1 0.5 -0.1Applying R2→ R2+2R1 to the matrix (P-I), we get-0.5 0.1 0.0 -0.2Now, the equations are: -0.5x1 + 0.1x2 = 0.0, 0.5x1 - 0.2x2 = 0.0, and x1 + x2 = 1.Solving these equations, we get x1 = 0.357 and x2 = 0.643.Therefore, the steady state vector as a probability vector is X = [0.357 0.643].

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Applying the leg rule, the length of LM is: 11.53 units

The leg rule is applied when finding length of the legs or hypotenuse of a right triangle that has an altitude. It is given as:

Hypotenuse/leg = leg/part.

Given the following:

Plug in the values:

17/14= 14/LM

Cross multiply:

17(LM) = (14)(14)

17(LM) = 196

Divide both sides by 17

17(LM)/17 = 196/17

LM = 11.53 units

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The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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Answer:

Independent variable: distance

Dependent variable: number of letters recognized on an eye chart

Step-by-step explanation:

Independent variables are stand-alone. This means that it does not depend on another variable but affects the dependent variable.

Dependent variables are dependent on another variable. When the independent variable changes, dependent variables are changed.

Since the hypothesis is that the distance affects the number of letters recognized,

the distance causes a change in the number of letters recognized not the other way around.

Thus, the dependent variable is the number of letters recognized on the eye chart while the independent variable is the distance.

Answer:

x and y

plz mark brainliest

Answer:

3.8 inches

Step-by-step explanation:

y = 0.2x + 2  Substitute in 9 for x

y = 0.2(9) + 2

y = 1.8 + 2

y = 3.8

The normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

Therefore, the normal curve with a mean of 0 and standard deviation of 1 is called (D)  the z-value.

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The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Answer:

600m

Step-by-step explanation:

-200 + 200 = 0, 0 to 400 need 400, 400 + 200 = 600 i guess lol

Answer:

The answer is not greater because it is a negative. If you mean less than it is exactly 400 less than 400 m.

The golden ratio between quantities 'a' and 'b' can be represented algebraically as (a+b)/a = a/b = Φ. Geometrically, it is illustrated through the construction of a golden rectangle with sides in this ratio.

The golden ratio is a mathematical constant denoted by the Greek letter phi (Φ) and is approximately equal to 1.618. It is often represented algebraically as (a+b)/a = a/b = Φ.

To illustrate the relationship geometrically, we can use a geometric construction known as the golden rectangle. A golden rectangle is a rectangle that has the property that the ratio of its longer side to its shorter side is equal to the golden ratio.

Here's how we can construct a golden rectangle:

Start with a rectangle ABCD where AB is the longer side and BC is the shorter side.

Divide the longer side AB into two segments, AC and CB, such that the ratio of AB to AC is equal to the golden ratio (Φ). This means that AB/AC = Φ.

Draw a line segment DE parallel to AD and BC, where D is the intersection point of AC and DE.

Complete the rectangle DEFG by drawing lines through points E, F, and G parallel to AB and CD.

Now, we have a golden rectangle DEFG. The longer side EF is equal to AB, and the shorter side EG is equal to BC. The ratio of EF to EG is equal to the golden ratio (Φ). Geometrically, this illustrates the relationship between the two quantities (a and b) in the golden ratio.

It's worth noting that the golden ratio is found in various aspects of art, architecture, and nature. It is considered aesthetically pleasing and has been used in design principles to create visually harmonious compositions.

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Answer:

2a2b-6ab2+9ab+5 is right answer

The area of the kite is 90 sq.m.

Calculation

Area of the kite (quadrilateral) = \(\frac{product of their diagonal}{2}\) = \(\frac{pq}{2}\)

= \(\frac{12m*15m}{2}\) = \(\frac{180 sq.m}{2}\) = 90 sq.m.

What is the geometry of a kite?

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Answer:

19/5

Step-by-step explanation:

1. multiple 3 x 5= 15

2. add 15+4

3. put it over 5: 19/5

An investigation whether smokers are more likely than non smokers to get lung cancer by grouping the class students into two groups is an example of experimental study.

Experimental Study: An experimental study is a study where the researcher has control over most of the variables. In contrast an observational study is a study where the researcher purely observes subject without controlling any variables. We have to investigate whether smokers are more likely than non-smokers to get lung cancer. Here the study is experimental study because the researcher/ we are trying to investigate the students of smokers and non-smokers. So, here control the members of the population that is students by randomly selecting them and dividing them in two groups (that is half -half) and provide one group cigarettes and not provide the other one. So, the above example of an experimental study. The following difficulties are come in study :

Hence, the given problem is an example of experimental study.

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Answer:

31 days

Step-by-step explanation:

what i did is divided it

Answer:

As a rule of thumb, a correlation greater than 0.75 is considered to be a “strong” correlation between two variables. However, this rule of thumb can vary from field to field. For example, a much lower correlation could be considered strong in a medical field compared to a technology field.

Step-by-step explanation:

The  probability that the average length of the four fish is between 51 and 60 mm is:

P(B) ≈ 0.658 .

Since the lengths of individual fish follow a normal distribution with mean 54.0 mm and standard deviation 4.5 mm, we can use the properties of the normal distribution to find the probabilities.

Let X be the length of a single fish. Then X follows a normal distribution with mean μ = 54.0 mm and standard deviation σ = 4.5 mm.

a) At least one fish in the sample is between 51 and 60 mm long:

Let A be the event that at least one fish in the sample is between 51 and 60 mm long. We want to find P(A).

The probability that a single fish is between 51 and 60 mm long is:

P(51 ≤ X ≤ 60) = P((51-54)/4.5 ≤ (X-54)/4.5 ≤ (60-54)/4.5) = P(-0.67 ≤ Z ≤ 1.11) ≈ 0.654

where Z is the standard normal variable.

Using the complement rule, the probability that none of the four fish are between 51 and 60 mm long is:

P(A') = P(no fish between 51 and 60 mm long) = (1 - 0.654)^4 ≈ 0.061

Therefore, the probability that at least one fish in the sample is between 51 and 60 mm long is:

P(A) = 1 - P(A') ≈ 0.939

b) The average length of the four fish is between 51 and 60 mm:

Let B be the event that the average length of the four fish is between 51 and 60 mm. We want to find P(B).

The distribution of the sample mean X  is also normal with mean μ_X  = μ = 54.0 mm and standard deviation σ_X  = σ/√n = 4.5/√4 = 2.25 mm.

The probability that the average length of a sample of four fish is between 51 and 60 mm is:

P(51 ≤ X  ≤ 60) = P((51-54)/(4.5/√4) ≤ (X -54)/(4.5/√4) ≤ (60-54)/(4.5/√4)) = P(-1.33 ≤ Z ≤ 0.89) ≈ 0.658

where Z is the standard normal variable.

Therefore, the probability that the average length of the four fish is between 51 and 60 mm is:

P(B) ≈ 0.658 .

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Answer:

a=99

Step-by-step explanation:

The answer is 99 square meters. I took this quiz, so I know the answers. I hope you get a good grade!!

the first four terms of the sequence represented by the expression -49 + 5n are: -49, -44, -39, -34.

The expression -49 + 5n represents a sequence where each term is obtained by substituting different values for n and evaluating the expression.

Let's substitute the first four values of n (0, 1, 2, 3) into the expression to find the corresponding terms:

For n = 0:

-49 + 5(0) = -49 + 0 = -49

For n = 1:

-49 + 5(1) = -49 + 5 = -44

For n = 2:

-49 + 5(2) = -49 + 10 = -39

For n = 3:

-49 + 5(3) = -49 + 15 = -34

Therefore, the first four terms of the sequence represented by the expression -49 + 5n are:

-49, -44, -39, -34.

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Answer:

18

Step-by-step explanation:

Answer:

13x + 11y = 212

Step-by-step explanation:

total cost of purchasing an item = unit cost x total units purchased

total cost of purchasing pepperoni pizza = 13 × x = 13x

total cost of purchasing plain pizza = 11 × y = 11y

total cost of purchasing both items = total cost of purchasing pepperoni pizza + total cost of purchasing plain pizza

- 13x + 11y = 212

The Laplace transform to the initial-value problem is y(t) = (1/3) * e^(-3t).

To solve the given initial-value problem using Laplace transform, we'll apply the Laplace transform to both sides of the differential equation.

The Laplace transform of y' is denoted as ℒ{y'}.

Using the property of the Laplace transform, ℒ{y'} = sℒ{y} - y(0), where s is the Laplace variable and y(0) is the initial condition.

Applying the Laplace transform to the differential equation, we have:

ℒ{3y} = ℒ{e^(-3t)}

Using the linearity property of the Laplace transform and the table of Laplace transforms, we can find the transforms of each term:

3ℒ{y} = ℒ{e^(-3t)}

3ℒ{y} = 1/(s+3)

Now, we can solve for ℒ{y} by dividing both sides by 3:

ℒ{y} = 1/(3(s+3))

Therefore, the Laplace transform of y is ℒ{y} = 1/(3(s+3)).

To find the actual solution, we need to inverse Laplace transform the expression

ℒ{y} = 1/(3(s+3)).

Applying the inverse Laplace transform, we obtain the solution:

y(t) = (1/3) * e^(-3t)

Therefore, the actual answer to the initial-value problem is y(t) = (1/3) * e^(-3t).

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Answer:

30 i think

Step-by-step explanation:

Answer:

(x+3)(x+3)

Step-by-step explanation:

I hopw this helps ;-)

\( \frac{vz}{zy} = \frac{vw}{wx} \ \: \\ \\ \frac{16.5 }{27.5} = \frac{vw}{36} \)

so

vw= (16.5×36)÷27.5= 21.6

vw=21.6

I hope it helps

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Answer:

  283 m

Step-by-step explanation:

The tangent relation is useful for this.

  Tan = Opposite/Adjacent

This tells us the distance from Rob's height to the ground on the other cliff is ...

  tan(60°) = CB/CA

  CB = CA·tan(60°) = 110·tan(60°)

Similarly, ...

  tan(40°) = CD/CA

  CD = CA·tan(40°) = 110·tan(40°)

Then the height of the smaller cliff is ...

  BD = CB +CD = 110·(tan(60°) +tan(40°)) ≈ 282.8 m

The height of the smaller cliff is about 283 m.

If one item is chosen from m items, a second item is chosen from n items, and a third item is chosen from p items, the total number of three-item choices is MNP.

Probability  can be regarded as a  measure of the likelihood of an event  that can take place.

It should be noted that  Many events cannot be predicted with total certainty, hence , If one item is chosen from m items, a second item is chosen from n items, and a third item is chosen from p items, the total number of three-item choices is MNP.

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Answer:

slope is 3 and y intercept of -2

Step-by-step explanation: