Fabrício corre diareamente em um parque perto de sua casa. Em certo dia ele deu 3,5 voltas na pista de corrida desse parque que mede 2,8 km qual foi a distância percorrida por Fabrício nesse dia?​

a)Pˣ =  \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\)  in matrix form, using eigen-values.

b)state 2 is 0.75; state 5 is 0 and ;state 6 is 0.25.

a)In order to calculate the value of Pˣ, follow the below-given steps:

Step 1: Compute the eigen-values of the matrix P.

Here, we get λ = 1, λ = 0.6, λ = 0.4, λ = 0.1, λ = 0, λ = 0.

Step 2: Compute the eigen-vectors corresponding to each eigenvalue of the matrix P.

Step 3: Compute the diagonal matrix D and the transition matrix T. \(\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\end{matrix}0.6\)

\(\begin{matrix}0.58 & 0.25 & 0.72 & 0 & 0 & 0\end{matrix}0.4.\)

\(\begin{matrix}0.07 & 0 & 0.04 & 0.7 & 0 & 0\end{matrix}0.1.\)

\(\begin{matrix}0.35 & 0.75 & 0.56 & 0 & 1 & 0\end{matrix}0.\)

\(\begin{matrix}0 & 0 & 0 & 0.3 & 0 & 1\end{matrix}\)

Pˣ = T . Dˣ . T⁻¹

We get the following matrix as a result.  

Pˣ =  \(\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}\)  

b)If the process starts in state 3,

the probability that it will be absorbed in state 2 is 0.75,

the probability that it will be absorbed in state 5 is 0, and

the probability that it will be absorbed in state 6 is 0.25.

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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The y-component of the vector, which has a magnitude of 12.1 meters and an angle of 48.4° measured from the +x axis, is approximately 9.0609 meters.

To find the y-component of the vector, we need to apply the given magnitude and angle information.

The significance of the vector is given as 12. 1 m and the angle is given as 48. 4° measured from the +x axis.

We can use trigonometry to find the y-component of the vector. The y-aspect represents the vertical displacement of the vector from its preliminary factor. Y-element = magnitude × sin(angle)

y-component = 12. 1 m × sin(48. 4°)

y-component = 9. 0609 m (rounded to 4 decimal places)

consequently, the y-component of the vector is approximately 9.0609 meters.

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Answer:

√16x/3y

Step-by-step explanation:

√4x^2 = √16x /3y = can't be simplified further

The coach made a mistake in converting the average rate from miles per hour to feet per second. To convert miles per hour to feet per second, the formula is (miles per hour) x (5280 feet/mile) / (60 minutes/hour) = (feet per second).

However, the coach used a different conversion factor, which resulted in an incorrect value. This incorrect value led the coach to conclude that Aliza was not running fast enough, when in reality, the actual rate could be higher than 8.2 feet per second.

Therefore, the coach made an error in the conversion factor used and in the conclusion based on the incorrect converted value.

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Answer:

I'm gonna estimate about 240 miles one way

Explanation:

You have a guide on the bottom right-hand corner of the map that tells you how many miles per that amount of distance. As you can see it is split off into tiles incremented by 30. What you do is take a ruler and measure that guide. For example, let's say the map is 9.5cm and the guide is 2cm per 60 miles. The next thing I would do is to measure the distance in centimeters of the physical map between point a and point b which is 8cm. Finally, I convert the centimeters into miles which is (8/2)*60 = 240.

Step-by-step explanation:

Base...from  - 7 to + 4 = 11 units

Height from  -4 to +5 = 9 units

Area of a traingle = 1/2  * base * height = 1/2 (11)(9) = 49.5   units^2

Answer:

\(\cos 2 \theta = \dfrac{119}{169}\\\\\sin2 \theta = \dfrac{120}{169}\\\\\tan 2\theta = \dfrac{120}{119}\)

Step-by-step explanation:

\(\text{Given that,} \cos \theta = \dfrac{12}{13}\\ \\\text{Now,}\\\\\cos 2 \theta = 2 \cos^2 \theta - 1\\\\\\~~~~~~~~~=2 \left( \dfrac{12}{13} \right)^2 - 1\\\\\\~~~~~~~~~=2 \left( \dfrac{144}{169} \right) - 1\\\\\\~~~~~~~~~=\dfrac{288}{169}-1\\\\\\~~~~~~~~~=\dfrac{119}{169}\)

\(\sin 2\theta = 2 \sin \theta \cos \theta\\\\\\~~~~~~~~=2\sqrt{1 -\cos^2 \theta} \cdot \cos \theta~~~~~~~~~~~;[\text{In quadrant I, all ratios are positive.}]\\\\\\~~~~~~~~=2 \sqrt{1- \left( \dfrac{12}{13} \right)^2} \cdot \left(\dfrac{12}{13} \right)\\\\\\~~~~~~~~=\left( \dfrac{24}{13} \right) \sqrt{1- \dfrac{144}{169}}\\\\\\~~~~~~~~=\dfrac{24}{13}\sqrt{\dfrac{25}{169}}\\\\\\~~~~~~~=\dfrac{24}{13} \times \dfrac{5}{13}\\\\\\~~~~~~=\dfrac{120}{169}\)

\(\tan 2 \theta = \dfrac{\sin 2\theta}{\cos 2\theta}\\\\\\~~~~~~~~~=\dfrac{\tfrac{120}{169}}{ \tfrac{119}{169}}\\\\\\~~~~~~~~~=\dfrac{120}{169} \times \dfrac{169}{119}\\\\\\~~~~~~~~~=\dfrac{120}{119}\)

A. The basis for the subspace of vectors whose components are equal in R4 is {(1, 1, 1, 1)}.

B. The basis for the subspace of vectors whose components add to zero in R4 is {(1, -1, 0, 0), (1, 0, -1, 0), (1, 0, 0, -1)}.

C. The basis for the subspace of vectors perpendicular to (1, 1, 0, 0) and (1, 0, 1, 1) in R4 is {(1, -1, 1, 0), (-1, 0, 1, -1)}.

D. The basis for the column space of U (in R2) is determined by the non-zero columns of U. The nullspace of U (in R5) is the set of vectors that satisfy the equation Ux = 0, where x is a vector. The basis for the column space and nullspace of U depends on the specific matrix U given in the problem. Without the matrix U, it is not possible to determine the basis for these subspaces.

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True. Symbolic logic, also known as formal logic or mathematical logic, encompasses three fundamental requirements.

Firstly, it involves expressing propositions, which are statements that can be either true or false. These propositions serve as the building blocks of logical reasoning.

Secondly, symbolic logic enables the expression of relationships between propositions through logical connectives such as conjunction (AND), disjunction (OR), negation (NOT), implication (IF-THEN), and biconditional (IF AND ONLY IF). These connectives allow for the construction of compound propositions and the evaluation of their truth values.

Lastly, symbolic logic provides mechanisms to describe how new propositions can be inferred from other propositions assumed to be true. This is achieved through logical rules and deduction techniques such as modus ponens, modus tollens, and proof by contradiction. These inference rules facilitate logical reasoning and allow for the derivation of new propositions based on existing ones.

In summary, symbolic logic encompasses expressing propositions, expressing relationships between propositions, and describing how new propositions can be inferred from assumed true propositions.

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Answer:

(8, -3)

Step-by-step explanation:

The coordinates of the midpoint are the average of the endpoints.

5 = (x + 2) / 2

10 = x + 2

x = 8

1 = (y + 5) / 2

2 = y + 5

y = -3

Answer:

Periodicity of 2cos(3x-2π)=

\( \frac{2\pi}{3} \)

Step-by-step explanation:

\(periodicity \: of \: 2 \cos(3x - 2\pi) \\ periodicity \: of \: a. \cos(bx + c) + d = \\ \frac{periodicity \: of \: \cos(x) }{|b|} \\ periodicity \: of \: \cos(x) \: is \: 2\pi = \frac{2\pi}{|3|} \\ simplify = \frac{2\pi}{3} \)

Answer:

\(\sf Period=\dfrac{2}{3} \pi\)

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

Standard form of a cosine function

f(x) = A cos(B(x + C)) + D

where:

Given function:

y = 2 cos (3x - 2π)

Therefore:

Period of given function:

\(\sf \implies Period=\dfrac{2 \pi}{B} = \dfrac{2 \pi}{3}\)

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Answer:

10 times

Step-by-step explanation:

7 times 10 equals 70

For the arithmetic series, The first number of the 20th line is 575, and the last number is 634 and the next two lines of the pattern are:

23 26 29

32 35 38 41 .

What is a arithmetic series?

An arithmetic series is a sequence of numbers in which each term is obtained by adding a constant value (called the common difference) to the previous term. The general form of an arithmetic series is:

a, a + d, a + 2d, a + 3d, ...

where "a" is the first term and "d" is the common difference between consecutive terms.

Now,

a) To continue the pattern, we add 3 to the first number of each line, and then add 3 to that sum to get the next number in the sequence. Therefore, the next two lines of the pattern are:

23 26 29

32 35 38 41

b) To find the first number of the 20th line, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁+ (n - 1)d

where aₙ is the nth term, a₁ is the first term, n is the number of terms, and d is the common difference between consecutive terms.

In this case, we know that the common difference is 3, and we want to find the first term of the 20th line. To do this, we need to find the number of terms in the first 19 lines of the pattern. The first line has 1 term, the second line has 2 terms, the third line has 3 terms, and so on. Therefore, the number of terms in the first 19 lines is:

1 + 2 + 3 + ... + 18 + 19 = (19/2)(1 + 19) = 190

So, the first number of the 20th line is:

a₁ = 5 + (190)(3) = 575

To find the last number of the 20th line, we can use the formula:

aₙ = a₁+ (n - 1)d

where n is the number of terms in the 20th line, and d is still the common difference of 3.

The number of terms in the 20th line is 20, so the last number is:

a₂₀ = a₁+ (n - 1)d = 575 + (20 - 1)(3) = 634

Therefore, the first number of the 20th line is 575, and the last number is 634.

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35 is 78% of 45

Sure hope this helps you

Answer:

45.00%

Step-by-step explanation:

The total answers count 40 - it's 100%, so we to get a 1% value, divide 40 by 100 to get 0.40. Next, calculate the percentage of 18: divide 18 by 1% value (0.40), and you get 45.00% - it's your percentage grade.

Please rate me brainliest

Answer:

9375

Step-by-step explanation:

If we are to test for the equality of block effects (Drivers), then we will use F2 = MSRow /MSError.

To find the test statistic:

(Consider the table for variables and given data.)

Now, we are asked to only deal with finding the value of the test statistic for testing whether the average gas mileage is the same for the four car models.

That is testing for the equality of Population means and the test statistic for the analysis of variance is:

And the hypotheses are:

Decision Rule: Reject H0 if the calculated value of F1 is its critical value F,(c-1), (c-1)(r-1) Otherwise, accept H0.

Meanwhile, if we are to test for the equality of block effects (Drivers), then we will use F2 = MSRow /MSError.

Therefore, if we are to test for the equality of block effects (Drivers), then we will use F2 = MSRow /MSError.

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The complete question is given below:

A car dealer is interested in comparing the average gas mileages of four different car models. The dealer believes that the average gas mileage of a particular car will vary depending on the person who is driving the car due to different driving styles. Because of this, he decides to use a randomized block design. He randomly selects five drivers and asks them to drive each of the cars. He then determines the average gas mileage for each car and each driver. Can the dealer conclude that there is a significant difference in average gas mileages of the four car models? The results of the study are as follows. Average Gas Mileage Driver Car A Car B Car C Car D Driver 1 29 31 20 34 Driver 2 27 37 35 39 Driver 3 24 23 31 23 Driver 4 38 24 22 38 Driver 5 20 33 37 36 ANOVA Source of Variation SS df MS Rows 190.2000 4 47.5500 Columns 114.5500 3 38.1833 Error 534.2000 12 44.5167 Total 838.9500 19 Step 1 of 3: Find the value of the test statistic for testing whether the average gas mileage is the same for the four car models. Round your answer to two decimal places, if necessary.

Answer:

Step-by-step explanation:

1. right angled (isosceles)

2. acute (equilateral or equiangular)

3. obtuse

5. acute

Answer:

Triangle number one is a right triangle. Triangle two is an equilateral triangle. Triangle three which is below triangle one is an obtuse triangle. The fourth triangle is an acute triangle.

Step-by-step explanation:

One is a right triangle because it has one right angle.

Two is an equilateral triangle because all of the three angles are 60 degrees.

Three is an obtuse triangle because one of the three angles is more than 90 degrees.

Finally, 4 is an acute triangle because all of the three angles are less than 90 degrees

Answer:

a = 9

Step-by-step explanation:

Step 1: Add 3 to both sides

2a – 3 = 15

2a – 3 + 3 = 15 + 3

Step 2: Simplify

add the numbers ( 2a = 18 )

Step 3: Divide both sides by the same factor

2a = 18

2a 18

––– = –––

2 2

Step 4: Simplify

l

Cancel the terms that are in both the numerator and the denominator

l

l

Divide the numbers

l

a = 9

Answer: a = 9

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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The expressions x + x + x + x and 4x are equivalent.

We can see this by simplifying the first expression:

x + x + x + x = 4x

So we can see that both expressions represent the same quantity, which is the total of adding x four times.

To explain this using a diagram, we can draw four boxes, each labeled with an "x".

x   x   x   x

Then, we can count the total number of "x" in the diagram, which is 4x.

Alternatively, we can also think of distributing the coefficient 4 to each term in the second expression:

4x = 4 * x

= x + x + x + x

This gives us the same expression as the first one, so they are equivalent.

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Answer:

Your answer is D.

Step-by-step explanation:

Using a Desmos Graphing calculator to graph that two equations.

Looking at the equation we look at the less/greater than or equal to shade the area.

I graph it seperately then added it together.

Answer: 29/18 or 1  11/18  

Step-by-step explanation:  When adding fractions, you need the fractions to have a common denominator. In order to get the common denominator, find the lowest common number between 9 and 6. That number is 18.

7/9 times 18 = 14/18         5/6 times 18 = 15/18     14/18 + 15/18 = 29/18

Improper fraction: 29/18        Mixed number:  1   11/18

The function f(z) is analytic.

Given u(x,y) = x⁴ - 6x²y² + y⁴ + x.

Firstly, let's check whether the given function is harmonic or not. A function u(x, y) is said to be harmonic if it satisfies the Laplace equation. i.e.,

∂²u/∂x² + ∂²u/∂y² = 0.

So, let's find the second-order partial derivatives of u to x and y.

∂u/∂x = 4x³ - 12xy² + 1

∂²u/∂x² = 12x² - 12y²

∂u/∂y = -12x²y + 4y³

∂²u/∂y² = -12x² + 12y²

Therefore,

∂²u/∂x² + ∂²u/∂y² = 12x² - 12y² - 12x² + 12y² = 0

Since f(z) is analytic, it must satisfy the Cauchy-Riemann equations:

u/∂x = ∂v/∂ and

∂u/∂y = -∂v/∂x

We have

∂u/∂x = 4x³ - 12xy² + 1.

So,

∂v/∂y = 4x³ - 12xy² + 1

∫∂v = ∫(4x³ - 12xy² + 1) dy

∂v/∂y = 4x³y - 4y³ + y

∴ v(x, y) = x⁴ - 4x²y² + y² + xy + C, where C is an arbitrary constant. So, the corresponding v(x, y) is given by v(x, y) = x⁴ - 4x²y² + y² + xy + C.

Therefore, the function f(z) is analytic.

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