What is thirty five sixths times twenty five twelfths

The long-run proportion of time Marvin spends in room 5 is 0.214.

We can approach this problem using the concept of Markov chains, where Marvin's movements between the rooms can be represented as a sequence of states. In this case, the states are the rooms, and the probabilities of moving from one room to another are given by the fact that Marvin is equally likely to choose any available door.

We can represent this as a transition probability matrix P, where P(i,j) is the probability of moving from room i to room j. Since Marvin is equally likely to choose any available door, the probability of moving from room i to room j is 1/n(i), where n(i) is the number of doors available in room i. For example, n(5) = 2, since room 5 has two doors.

The transition probability matrix P is:

   1       2       3     4     5     6

1   0     1/2   1/2     0     0     0

2   1/3   0     1/3   1/3    0     0

3   1/2   1/2   0       0     0     0

4   0     1/3    0       0     1/3   1/3

5   0      0      0     1/2    0     1/2

6   0      0      0     1/2   1/2    0

To find the long-run proportion of time Marvin spends in room 5, we need to find the stationary distribution of the Markov chain. This is a probability distribution over the states that remains unchanged as the chain evolves over time.

The stationary distribution can be found by solving the equation πP = π, where π is the stationary distribution. This can be rewritten as (P^T - I)x = 0, where x = (π1, π2, ..., π6) and I is the identity matrix. We also need the constraint that the sum of the elements of x is 1, since x is a probability distribution.

Solving this system of equations gives us:

π1 = 9/56

π2 = 5/28

π3 = 3/28

π4 = 1/8

π5 = 3/14

π6 = 1/56

Therefore, the long-run proportion of time Marvin spends in room 5 is π5 = 3/14, or approximately 0.214.

Correct Question :

Suppose that Marvin the rat travels through a maze of 6 rooms. Doors between the rooms are depicted as breaks in the walls. At each time step, Marvin will move to a neighboring room. He is equally likely to choose from any of the available doors. What is the long-run proportion of time Marvin spends in room 5?

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For testing, if x is a significant predictor of y in simple linear regression, we need to determine if the slope is significantly different from zero.

Given,

Simple linear regression .

A statistical technique known as linear regression is used to represent the connection between a scalar answer and one or more explanatory factors. When there is just one explanatory variable, simple linear regression is employed; when there are numerous explanatory variables, multiple linear regression is utilized.

Based on the value of another variable, linear regression analysis makes predictions about the value of the first variable. The dependent variable is the one you're trying to forecast. The independent variable is the one you are utilizing to make a prediction about the value of the other variable.

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To find all of the cube roots of ii and write the answers in rectangular form, we need to first express ii in polar form. To do this, we can convert ii to its polar form by writing it as a complex number in the form r(cosθ + isinθ), where r is the magnitude and θ is the argument.

In this case, we have ii = 1(cos(π/2) + isin(π/2)).  The magnitude of ii is 1, and the argument is π/2.  Now, to find the cube roots, we need to find the numbers that, when raised to the power of 3, give us ii. To find the cube roots, we can use De Moivre's theorem, which states that for any complex number z = r(cosθ + isinθ), the nth roots of z can be found by taking the nth root of the magnitude and dividing the argument by n.

In this case, we have n = 3, r = 1, and θ = π/2.  Taking the cube root of the magnitude 1 gives us 1^(1/3) = 1. Dividing the argument π/2 by 3 gives us (π/2) / 3 = π/6. So, the first cube root is 1(cos(π/6) + isin(π/6)). To find the other cube roots, we can add multiples of 2π/3 to the argument. Adding 2π/3 to π/6 gives us π/6 + 2π/3 = π/2. So, the second cube root is 1(cos(π/2) + isin(π/2)), which is equal to ii. Adding another 2π/3 gives us π/2 + 2π/3 = 7π/6. So, the third cube root is 1(cos(7π/6) + isin(7π/6)). Therefore, the cube roots of ii in rectangular .

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volume= 16/3, A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).

limits

z= 0 to z = 4-y-2x

y= 0 to y = 4- 2x

x= 0 to x= 2

volume

v= \(\int\limits^2_0 \int\limits^4_0 \int\limits^4_0 dzdydx\)

v= \(\int\limits^2_0 \int\limits^4_0 (4-y-2x) dydx\)

v= \(\int\limits^2_0 ( 4y- y^{2} / 2 - 2xy) ^4^-^2^x _0\)

dx= \(\int\limits^2_0 [ 16-8x - 16+ 4x^2 - 16x / 2 - 8x+ 4x^2 ] dx\)

v= \(\int\limits^2_0 [ 8+ 2x^2- 8x] dx\\\)

= [ 8x + 2x^3 / 3 - 8x^2 / 2 ] ^2_0

= [16+ 16/3- 16]

v= 16/3

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Complete Question

Question: Sketch The Tetrahedron Enclosed By The Coordinate Planes And The Plane 2x+Y+Z=4. Use A Triple Integral To Find The Volume Of The tetrahedron

The graph that represents the linear equation is attached below.

A linear graph can be modelled by an equation in slope-intercept form, as: y = mx + b. Here, we have:

Given the linear equation, y = 5x + 10, it means the slope of the graph that represents this equation would be 5, while the line that intersects the y-axis would be at 10.

In the graph attached below, the slope is 5, and the y-intercept is 10.

Therefore, the graph that represents the linear equation is attached below.

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The area of the rhombus will be 96 square units. Then the correct option is B.

The missing diagram is attached below.

Let a be the length and h be the height of the rhombus.

Then the area will be

Area = a × h square units

If x = 12 units, y = 4 units, and h = 8 units.

Then the area of the rhombus will be

A = 12 × 8

A = 96 square units.

Then the correct option is B.

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Answer:

96

Step-by-step explanation:

Answer:

Roberto paid $7.43 cents.

Step-by-step explanation:

1.65 times 4.5=7.425

I rounded 7.425 to 7.43 giving you your final answer.

Answer: $7.43

Step-by-step explanation: The easy way to do this with a calculator is 1.65 times 4.5 which is 7.425, estimated to $7.43. However, if you aren't allowed to use a calculator, you can just do 1.65 times 4.5 on paper for showing work. If you don't know how to times a decimal between a decimal, you can see how much money is per pound than times that by 4.5.

Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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Answer:

After 4 hours the container left with 20 gallons of water.

Step-by-step explanation:

The container has 320 gallons of water initially.

It leaks half of its water every hour.

So, after 1 hour the container has \(\frac{320}{2}\)= 160 gallons

After 2 hours the container has \(\frac{160}{2}\) =80 gallons

After 3 hours the container has \(\frac{80}{2}\)= 40 gallons

After 4 hours the container has \(\frac{40}{2}\) =20 gallons.

So, after 4 hours the container left with 20 gallons of water.

Answer:

50.24

Step-by-step explanation:

Formula for area of a circle A= πr^2

Since the diameter os 8 yards the radius is 4 yards (radius is half of diameter)

A = (3.14) 4^2

A = (3.14) 16

A = 50.24

:p

Answer:

9√6ab² ,-5-√6ab²…2√6b²a are like radicals.

\(8^2 +B^2 = 14^2\\\\\implies B^2 = 14^2 -8^2 \\\\\implies B^2 = 132\\\\\implies B=\pm\sqrt{132} = \pm 2\sqrt{33}\)

The Simplified form of the second expression is -1/3.

The given expression, let's break it down step by step:

Expression: (-7a^3b^-3) / (21ab)

First, let's simplify the numerator:

-7a^3b^-3 = -7 * (a^3) * (1/b^3) = -7a^3/b^3

Now, let's simplify the denominator:

21ab = 3 * 7 * a * b = 3 * (7ab)

Now, let's rewrite the expression with the simplified numerator and denominator:

(-7a^3/b^3) / (3 * 7ab)

Next, let's simplify further:

The -7 in the numerator can be cancelled out with the 7 in the denominator:

(-a^3/b^3) / (3 * a * b)

We can simplify further by canceling out the common factors in the numerator and denominator:

(-1/b^3) / (3 * a)

To divide by a fraction, we can multiply by its reciprocal:

(-1/b^3) * (1 / (3 * a))

This simplifies to:

-1 / (3 * a * b^3)

Therefore, the simplified form of the expression is -1 / (3 * a * b^3).

Now let's simplify the second expression:

Expression: (-3a^2b^4) * (1 / (3a^2 / b^4)) * (1 / (3b^2))

To simplify, we can multiply the terms and divide as necessary:

(-3a^2b^4) * (b^4 / (3a^2)) * (1 / (3b^2))

Simplifying further:

-3a^2b^4 * b^4 / (3a^2 * 3b^2)

Cancelling out common factors:

-1 / 3

Therefore, the simplified form of the second expression is -1/3.

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The probability of randomly selecting a can of pink paint is P = 1/3, so the correct option is A.

Assuming that all the cans of paint have the same probability of being randomly selected, the probability that he will choose a pink can is equal to the quotient between the number of pink cans and the total number of cans.

There are 2 cans of white, 4 cans of green, and 3 cans of pink, so a total of 9 cans.

Then the probability is:

P = 3/9 = 1/3.

The correct option is A.

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Answer:

$8.69

Step-by-step explanation:

you divide 52.14 by 6

Answer:

assumption:

drinks are selected with replacement from refreshment stand

note:

i think "choosing" is poorly worded in the problem

use complement of everyone selecting a unique drink:

1-(8*7*6*5)/8^4 = 151/256 = 0.5898

answer -> D 0.59

Answer:

First of all, let us have a look at the formula for Total Surface Area of triangular prism:

TSA = B + p\times hTSA=B+p×h

Where B is the area of base

p is the perimeter of base and

h is the height of prism.

here base is a right angled triangle (because 3, 4, 5 is a triplet) Base and Height will be 3 , 4 cm or 4, 3 cm and 5 will be hypotenuse.

So formula for B:

\begin{gathered}B = \dfrac{1}{2}\times Base \times Height\\B = \dfrac{1}{2}\times 3\times 4 = 6 cm^2\end{gathered}

B=

2

1

×Base×Height

B=

2

1

×3×4=6cm

2

So, TSA = 6 + (3+4+5) \times× 10 = 6 + 120 = 126 cm^2cm

2

So, total surface area of given prism is 126cm^2cm

2

.

Answer:

3 x X - 14

Step-by-step explanation:

Is your algebra expression.

Answer:

3x-14

Step-by-step explanation:

Product of 3 and number is 3*x

For " 14 fewer than.." we simply subtract 14.

So we get 3x-14

Answer: f(x) = -1/2(x+3)

Example: g(x) = -1/2(-x-3)

This function is a dilation and a reflection of the parent function f(x) because when graphed, the two functions have the same shape but are reflected over the y-axis and are half the size of the original.

Answer:

  (a)  A two column table with five rows. ... The second column, y, has the entries, 2, 2, 2, 2

Step-by-step explanation:

You want to know which table shows a relation with zero slope.

When a graph has zero slope, it is a horizontal line. Every y-value is the same.

The table demonstrating zero slope will have all y-values the same:

  The second column, y, has the entries, 2, 2, 2, 2

Answer:

(-45,0)

Step-by-step explanation:

Answer:

(-45, 0)

Step-by-step explanation:

Question 13.

The estimated monthly cost of an energy-efficient refrigerator is $57, meaning the yearly cost is

Question 14.

The least energy-efficient refrigerator costs $72 per month, meaning the annual cost is

Therefore, the amount you will save on an energy-efficient refrigerator be

Hence, the amount saved on an energy-efficient refrigerator will be $180.

The speed of the train is 1 m/s.

A train travelled along a track for 70 s at a constant speed. What was its speed in metres per second (m/s)?The speed of the train in metres per second is the distance covered by the train in one second. Therefore, to determine the speed of the train, we must first determine the distance it covered during 70 seconds along the track.

The speed of the train can be calculated by dividing the distance covered by the train in meters by the time taken in seconds.  Therefore,Speed = Distance/TimeThe formula for distance is;Distance = Speed x TimeThe time taken by the train is 70s.The distance travelled by the train is not given, but we can calculate it using the speed of the train and time taken.

Therefore;Distance = Speed x Time Substituting the values;Distance = Speed x 70To find the speed of the train, we rearrange the formula as shown below;Speed = Distance/TimeNow we can substitute the value of distance to get the speed;Speed = (Speed x 70)/70Simplifying the expression,Speed = Speed

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The regular polygon has 18 sides.

To find the number of sides of a regular polygon given the relationship between the measures of its exterior and interior angles, we can set up an equation using the properties of polygons.

Let's assume the measure of each interior angle of the regular polygon is represented by "x" degrees. According to the given information, the measure of each exterior angle is 1/8 times the measure of the interior angle. Therefore, the measure of each exterior angle is (1/8)x degrees.

In any polygon, the sum of all exterior angles is always 360 degrees. Since our regular polygon has "n" sides, the sum of all the exterior angles will be equal to 360 degrees.

We can now set up an equation using the information:

(1/8)x * n = 360

To solve for "n," we can multiply both sides of the equation by 8 to eliminate the fraction:

x * n = 8 * 360

x * n = 2880

Since "x" represents the measure of each interior angle and "n" represents the number of sides, we know that the sum of the interior angles in any polygon is given by the formula (n-2) * 180 degrees.

Therefore, we can set up another equation using this formula:

x * n = (n-2) * 180

Substituting the value of x * n from the previous equation:

2880 = (n-2) * 180

Now, we can solve for "n" by dividing both sides of the equation by 180:

2880/180 = n - 2

16 = n - 2

Adding 2 to both sides:

16 + 2 = n

18 = n

Hence, the regular polygon has 18 sides.

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The conclusion results in a Type I error.

To determine whether the conclusion results in a Type I error, a Type II error, or a correct decision, we need to analyze the given information.

In this scenario, the test is conducted to compare a hypothesized population mean, denoted as μ, with a specific value of 58. The null hypothesis (H₀) states that μ is equal to 58, while the alternative hypothesis (H₁) suggests that μ is not equal to 58.

A significance level, denoted as α, is set at 0.05, which means that the researcher is willing to accept a 5% chance of making a Type I error - rejecting the null hypothesis when it is actually true.

The test statistic, z, is calculated to assess the likelihood of the observed data given the null hypothesis. In this case, the test statistic value is z = -2.14.

Since the test statistic is negative and falls in the rejection region of a two-tailed test, we can compare its absolute value to the critical value for a significance level of 0.05.

Looking up the critical value in the standard normal distribution table, we find that for a two-tailed test with α = 0.05, the critical value is approximately 1.96.

Since |z| = |-2.14| = 2.14 > 1.96, we have sufficient evidence to reject the null hypothesis.

Now, if the true value of μ is actually 58, and we reject the null hypothesis that μ = 58, it means we have made a Type I error - concluding that there is a difference when, in reality, there is no significant difference.

Therefore, the conclusion in this case results in a Type I error.

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The parabola's vertex is (-1,-3). The focus of the parabola is two units away from the vertex. The focus's directrix 1 unit. The point is the focus (-1,-5). The equation's directrix and focus are y = -1.

A parabola is a U-shaped curve this is drawn for a quadratic function.

The parabola (x+1)² = −8 (y+3) is given in the question.

As per the question, the required procedure would be as:

Gavin identifies that the vertex of the parabola is "(-1,-3)".

The parabola opens "down" and the focus is "2" units away from the vertex. The directrix 1 unit from the focus. The focus is the point "(-1,-5)". The directrix and the focus of the equation is "y = -1".

Thus, the required values and equation have been written as the above solution.

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Answer:

the answer is R I hope it works

Answer:

Step-by-step explanation:

The highest power of v is the fourth, so this polynomial is of the 4th degree.

The coefficient of the leading coefficient is -18.

Answer:

Degree: 4

Leading coefficient: -18

Step-by-step explanation: