Random variables X and Y have the joint pdf
fX,Y (x, y) = 2 0≤ y ≤ x ≤ 1,
0 otherwise.
(a) Find E(X) and V ar(Y ).
(b) Find E(Y ) and V ar(Y ).
(c) Find Cov(X, Y ).

The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

55%

Step-by-step explanation:

33 is 55% of 60

and 11/20 = 33/60=0.55

Answer:

7x(3y - 2z - 4w)

Step-by-step explanation:

21xy - 14xz - 28wx ← factor out 7x from each term

= 7x(3y - 2z - 4w)

Answer:

7 x . (3y - 2z - 4w

Step-by-step explanation:

The Volume of the given Hemisphere is  1071.8 cm³ rounded to 1 decimal place whose radius is 8cm

The Volume of the sphere  is given by the formula 4/3 πr³

The volume of hemisphere is half of sphere

So, The volume of hemisphere is 2/3 πr³

From the given figure it is clear that the radius of the hemisphere is 8cm

Here, we will use the value of π as 3.14 and not 22/7

So, Substituting the values in the formula of Volume of hemisphere

the Volume of hemisphere =2/3 π (8)³

                                      =2/ 3× 3.14 × 512

                                     = 1071.7867 cm³

Hence, the Volume of hemisphere 1071.7867 cm² or 1071.8 cm² rounded to 1 decimal place whose radius is 8cm

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Answer: Slope intercept from is y= 4/13x-5/13

Step-by-step explanation:

Stress fracturing is a term used in the fire investigation community to describe a complicated pattern of short cracks in glass arising from this condition.

When a flame comes into contact with one side of a glass pane, it heats that side, causing it to expand. At the same time, the unexposed side of the glass remains relatively cool and does not expand as much. This temperature gradient creates non-uniform expansion and differential stresses within the glass. As a result, the glass may fracture between the faces, forming a complex pattern of short cracks.

Stress fracturing is a phenomenon commonly observed in fire investigations, particularly in situations where rapid heating or cooling of glass occurs. It is important to understand and analyze these patterns to gain insights into the behavior of glass under fire conditions and to help determine the sequence of events during a fire incident.

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Answer:

A. 2086 yd²

Step-by-step explanation:

SA = 2lw + 2wh + 2lh
SA = 2*17*20 + 2*20*19 + 2*17*19
SA = 680 + 760 + 646
SA = 2086
Hope this helps :)

The completed statement based on two-dimensional motion in the x-y plane can be presented as follows;

The two-dimensional motion in the x-y plane, the x part of the motion and the y part of the motion are independent, whether or not there is an acceleration in any direction. The correct option is therefore;

D) Whether or not there is an acceleration in any direction

Two-dimensional motion in the x-y plane can be analyzed by separating them into its horizontal (x) and vertical (y) components, and analyze each component using the one dimensional equations of motion.

The meaning of the motion on the x-y plane is that the x-direction motion of an object exclusive or excludes the effect of the motion of the object in the y-direction, vis a vis, the y-direction motion.

The horizontal and vertical components of the motion can be analyzes individually or by themselves, by making use of the equations of motion for a one-dimensional motion, whether or not there is an acceleration in any direction as the acceleration are also evaluated using one dimensional equations.

The possible options in the question from a similar question on the internet are;

A) When there is no acceleration in any direction

B) When there is no acceleration in one direction

C) Only when an acceleration is present in both directions

D) Whether or not there is an acceleration in either direction

E) Only when the acceleration is in the y-direction

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Answer:

The volume of the cylinder is 163.3 m³.

Step-by-step explanation:

Given that,

Height = 13 cm

Base = 4 cm

So, radius = 2 cm

We need to calculate the volume of the cylinder

Using formula of cylinder

\(V=\pi r^2h\)

Where, r = radius

h = height

Put the value into the formula

\(V=\pi\times(2)^2\times13\)

\(V=163.3\ cm^3\)

Hence, The volume of the cylinder is 163.3 cm³.

Answer:

sin θ = (√119)/12

tan θ = (√119)/5

csc θ = 12/(√119)

cot θ = 5/(√119)

Five trigonometric functions of θ are

sinθ = \(\frac{\sqrt{119} }{12}\)cosθ = \(\frac{5}{12}\)tanθ = \(\frac{\sqrt{119} }{5}\)cosecθ = \(\frac{12}{\sqrt{119} }\)secθ = \(\frac{12}{5}\)cotθ = \(\frac{5}{\sqrt{119} }\)

"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."

Let θ be an acute angle of a right angle triangle

"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."

"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).

"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."

"An 'opposite' side is the one across from a given angle."

"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."

we have,

cosθ = \(\frac{5}{12}\)

secθ = \(\frac{12}{5}\)

Hypotenuse side = 12

Adjacent side = 5

∴ Opposite side = \(\sqrt{hyp^{2}-adj^{2} }\)= \(\sqrt{12^{2}-5^{2} }\) = \(\sqrt{119}\)

sinθ = \(\frac{opp}{hyp}\) = \(\frac{\sqrt{119} }{12}\)

tanθ = \(\frac{opp}{adj}\) = \(\frac{\sqrt{119} }{5}\)

cosecθ = \(\frac{hyp}{opp}\) = \(\frac{12}{\sqrt{119} }\)

cotθ  = \(\frac{adj}{opp}\) = \(\frac{5}{\sqrt{119} }\)

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Given the expression;

19 - x = 14

subtract 19 from both sides;

19 - x - 19 = 14 - 19

-x = -5

multiply both sides by -1

-(-x) = -(-5)

x = 5

Hence x = 5 is a solution to the equation

Answer:

  ∠ABD = 19.5°

  ∠ABE = 160.5°

Step-by-step explanation:

Given angle ABC = 39° and its bisector BD, you want the measures of angle ABD and ABE, its supplement.

An angle bisector divides an angle into two equal parts, each with half the measure of the whole.

  ∠ABD = 1/2∠ABC

  ∠ABD = 1/2(39°)

  ∠ABD = 19.5°

The angles of a linear pair are supplementary: they total 180°. Angles ABD and ABE form a linear pair.

  ∠ABE = 180° -∠ABD

  ∠ABE = 180° -19.5°

  ∠ABE = 160.5°

Answer:

\(25\%\)

Step-by-step explanation:

\(10\dfrac{1}{2}\cdot 8=84\)

\(\dfrac{21}{84}=\dfrac{1}{4}=25\%\)

Answer:

The answer is d

Step-by-step explanation:

0.09

Answer:

\(\boxed{\sf D. \ 0.09}\)

Step-by-step explanation:

\(\sf y = 0.3^x\)

\(\sf Plug \ x \ as \ 2.\)

\(\sf y = 0.3^2\)

\(\sf y =( \frac{3}{10} )^2\)

\(\sf y =\frac{3^2 }{10^2 }\)

\(\sf y =\frac{9}{100 }\)

\(\sf y =0.09\)

The degrees of freedom for the t statistic of 2.3 with 22 observations is 21.

The degrees of freedom for the t-statistic can be calculated using the sample size. In this case, the sample size is 22. For a one-sample t-test, the degrees of freedom (df) is equal to the sample size minus 1.

Degrees of freedom (df) = Sample size - 1

df = 22 - 1

df = 21

This can be determined using a t-distribution table or a calculator. The degrees of freedom represent the number of independent pieces of information available to estimate the population variance, which affects the shape of the t-distribution.

In this case, the sample size of 22 allows for a relatively accurate estimation of the population variance, resulting in a higher degree of freedom.

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The volume of the cone is (5/3)π(9²) cubic units ≈ 381.7 cubic units.

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the circular base and h is the height of the cone. However, we are given the base area B instead of the radius, so we need to find the radius first.

We know that the area of a circle is A = πr², so if the base area of the cone is B = 5π square units, then πr² = 5π, which means r² = 5. Solving for r, we get r = √5.

Now that we have the height h = 9 units and the radius r = √5 units,

we can use the formula for the volume of a cone:

V = (1/3)πr²h.

Substituting the values, we get

V = (1/3)π(√5)²(9) = (5/3)π(9²) cubic units, which simplifies to ≈ 381.7 cubic units.

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To determine the order in which Harry Potter should visit the 4 places and return to Gryffindor in the least amount of time, we need to look at the graph provided by Hermione.

We can start by looking for the shortest distances between each location. Once we have identified the shortest distances, we can then use this information to determine the most efficient order for Harry to visit each place.
It's important to note that there may be multiple routes that Harry can take to visit all 4 places, but we want to find the one that will take the least amount of time. To do this, we can start by identifying the shortest distance between two locations and continue to do this until we have identified the shortest path to all 4 locations.
Once we have determined the order in which Harry should visit each location, we can then calculate the amount of time it will take for him to travel between each place and return to Gryffindor. This will give us a total time for the entire journey.
We can say that determining the most efficient route for Harry to visit the 4 places and return to Gryffindor in the least amount of time requires careful analysis of the graph provided by Hermione. By identifying the shortest distance between each location and using this information to create the most efficient route, we can minimize the amount of time Harry spends traveling between each place. Once we have identified the order in which Harry should visit each location, we can then calculate the amount of time it will take him to travel between each place and return to Gryffindor. By doing this, we can determine the total amount of time it will take for Harry to complete his journey.

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let's first convert this to number form.

3^6 / 3^3= what?

to divide a number with the same base but different exponent, we simply subtract the second exponent by the first exponent.

3^6 / 3^3 = 3^6-3=3^3

Answer:

Step-by-step explanation:

Let the number be x

5/9 of the number is 90

Which is

5/9 of x = 90

5/9 × x = 90

5/9x = 90

Multiply through by 9

That's

5x = 810

Divide both sides by 5

5x/5 = 810/5

x = 162

Therefore the number is 162

Hope this helps you

Answer:

12/5

Step-by-step explanation:

tangent is opposite over adjacent... 24/10 reduces to 12/5

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Answer:tan(Z)=24/10=12/5

Step-by-step explanation:

Tangent of an angle is dividing opposite side by adjacent side

Answer:

c = 4,9

d = 4,6

Answer:

29

Step-by-step explanation:

3² + 4 × 5 ← first evaluate the exponent

= 9 + 4 × 5 ← second evaluate the product

= 9 + 20 ← third add the values

= 29

Answer:

point j is .55 because its .55

Step-by-step explanation:

The x-intercepts -2 and 6 are called the "zeros" or "roots" of the function.

The x-intercepts of a function represent the values of x for which the function equals zero. In this case, the x-intercepts are -2 and 6. When a function equals zero at a specific x-value, it means that the function's output or y-value is zero at that point.The values f(-2) and f(6) represent the function evaluated at those specific x-values. Since the x-intercepts are the points where the function equals zero, we can conclude that:

f(-2) = 0

f(6) = 0

Therefore, the x-intercepts -2 and 6 are called the "zeros" or "roots" of the function.The x-intercepts of a function are the values of x for which the function equals zero. Geometrically, they represent the points where the graph of the function intersects the x-axis. At these points, the y-coordinate is zero.

In the given scenario, the x-intercepts of the function are -2 and 6. This means that when we substitute these values into the function, the result will be zero:

f(-2) = 0

f(6) = 0

When we evaluate the function at x = -2 and x = 6, we find that the corresponding y-values are both zero. This indicates that the function crosses the x-axis at those points.

The notation f(x) represents the output or value of the function at a specific x-value. So, f(-2) represents the value of the function when x = -2, and f(6) represents the value of the function when x = 6.

Since the y-values at these x-intercepts are both zero, we can conclude that f(-2) = 0 and f(6) = 0.

In summary, the x-intercepts, in this case, -2 and 6, are called the "zeros" or "roots" of the function because they are the points where the function equals zero. These points indicate where the graph of the function intersects the x-axis.

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The predicted selling price for an observed selling price of 233.1 and square footage of 1385 is $235.96 (thousands of dollars). The error is 1.24 and the squared error is 1.5376.

Selling price is the amount of money that a seller charges for a product or service. It is usually determined by factors such as the cost of materials, labor costs, overhead, and the desired profit margin. In some cases, the selling price may also be affected by factors such as the product's demand, competitive pricing, and market conditions.

The equation used to predict the selling price is Predicted Selling Price (Thousands of Dollars)=23.11 +0.15 Square Footage.
For the given data, we have
Observed Selling Price = 233.1
Square Footage = 1385

Therefore,
Predicted Selling Price (Thousands of Dollars) = 23.11 + 0.15*1385
= 23.11 + 207.75
= 230.86.

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Answer:

If it says working for 23hrs then the answer is €204

Step-by-step explanation:

8×23=204