Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. \
E(X)=-3 E(Y)= 7 E(Z)= -8
Var(X) = 7 Var(Y) = 20 Var(Z) = 41
Compute the values of the expressions below.
E(-4Z+5) =_____

E (-2x+4y/5) = ______

Var(-2+Y)= ______

E(-4y^2)= ________

Answer:

it should be x+12

Step-by-step explanation:

if x is bigger than -11, then the answer will always be positive

We have given a function; \(|x+12|, if x > -11\) if x is bigger than -11, then the answer will always be positive.

A function is defined as a relation between the set of inputs having exactly one output each.

We have given a function;

\(|x+12|, if x > -11\)

The modulus of any number always gives the positive term.

if x is bigger than -11, then the answer will always be positive.

Let x = 2

then we get

\(|x+12| = |2+12| \\\\= 14\)

So, we can see that the answer is positive.

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The tables in restaurants were randomly assigned to either the smiley face or control. The servers in restaurants were randomly assigned to the smiley face or control condition.  

In the given data, there are several cases involved. Firstly, the tables in the restaurants were randomly assigned to either the smiley face or control condition. This means that some tables had the smiley face icon on their receipt, while others did not. This allowed the researchers to compare the effects of the smiley face intervention versus no intervention at all.

Secondly, the servers in the restaurants were also randomly assigned to the smiley face or control condition. This means that some servers used the smiley face icon when presenting the bill, while others did not. This allowed the researchers to explore whether the effect of the smiley face intervention varied depending on who delivered it.

Thirdly, the two conditions being compared are the smiley face and control conditions. The smiley face condition involves adding a smiley face icon to the receipt, while the control condition does not involve any intervention.

Lastly, the study likely involved multiple restaurants, as the results were aggregated across a number of establishments. This means that the researchers were interested in generalizing their findings to a larger population of restaurants, rather than just one specific location.

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Answer:

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

Answer:

14

Step-by-step explanation:

In order to find the answer, you must replace all of the X's with 3, and all of the Y's with 2.

When two numbers are right next to each other, that means that they're being multiplied.

So here is the equation rewritten:

(*=times)

5*2-3+2*2-2+5.

This could also be written as:

5 x 2 - 3 + 2 x 2 - 2 + 5.

Time to solve.

Using PEMDAS.

P- Parenthesis

E- Exponents

M- Multiplication

D- Division

A- Addition

S- Subtraction

The answer will be 14.

:D

The answer is.........

25.99

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

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Answer:

Original number = 10x + y = 52

Step-by-step explanation:

To find the rate at which average cost is changing when 176 belts have been produced, we need to first find the rate at which the average cost is changing when x belts have been produced.

We know that C(x) = 720 + 37x - 0.068x²We can find the average cost by dividing the total cost by the number of units produced. Average cost = Total cost / Number of units produced Let's consider that x belts have been produced. Then the total cost of producing these x belts is C(x).

Thus, the average cost per belt can be calculated as follows: Average cost = C(x) / x The rate at which the average cost is changing when x belts have been produced is given by the derivative of the average cost with respect to the number of belts produced (x).So, we need to differentiate the equation for average cost with respect to x to find the rate at which the average cost is changing.

Thus, the derivative is given by average cost'(x) = (C(x) / x)'Now, the derivative of the cost function C(x) is given as follows:

C'(x) = 37 - 0.136xaverage cost'(x) = (C(x) / x)'= (720 + 37x - 0.068x²) / x '= [37x² - 2x(720 + 37x) - x²(0.068)] / x²= (37x - 1440 - 0.068x²) / x²Putting x = 176, we get: average cost'(176) = (37(176) - 1440 - 0.068(176²)) / 176²= 13.064

Therefore, when 176 belts have been produced, the average cost is changing at 13.064 dollars per belt for each additional belt.

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One mole of nitrogen gas at STP (standard temperature and pressure) occupies a volume of 22.4 liters.

What is gas volume?

The volume of the a system is a crucial extensive criterion for describing it's own thermodynamic state in thermodynamics. The game's volume per unit of mass is known as the fixed volume, an intensive property. Volume depends on state and on other thermodynamic characteristics like pressure and temperature. The ideal gas law, for instance, relates the volume of an ideal gas to its pressure and temperature.

A system's physical volume might or might not match the control volume used it to study the system.

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The equation describes a line that contains the point (4, -3) is y = ( -1/25 )x - 71/25 .

Given :

The point (4, -3) and is perpendicular to the line represented by the equation y = 25x +3 .

Here slope m = 25

Perpendicular slope = -1 / m

= -1 / 25

The line equation is y = mx + c

Substitute m and ( 4 , -3 ) we get

-3 = -1/25 * 4 + c

-75 = -4 + 25c

-71 = 25c

c = -71/25

y = mx + c

y = ( -1/25 )x - 71/25

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The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

The value of dy/dt at x = 4 and y = 3 is 4/9, obtained by using the relationship between the rates of change of the sides of the rectangle and substituting the given values.

To find the value of dy/dt at the instant when x = 4 and y = 3, we need to use the given relationship between the rates of change of the sides of the rectangle. We are given that dz/dt = 1 and dx/dt = 3dy/dt. We can rearrange the equation to solve for dy/dt: dx/dt = 3dy/dt, dy/dt = (dx/dt) / 3. Substituting the values x = 4 and y = 3 into the equation, we have: dy/dt = (4/3) / 3 = 4/9. Therefore, the value of dy/dt at the instant when x = 4 and y = 3 is 4/9.

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Answer:

2/3 is the porportional rate

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Rise/run = 2/3

it goes up  by 2 and to the right by three

(a) To find the probability that only one machine is in working condition after two days, we need to determine the probability of transitioning from state (1, 1) to state (1, 0) after two days.

From the transition probability matrix, we see that to transition from (1, 1) to (1, 0) in one day, both machines need to remain operational, which has a probability of (1 - p) * (1 - p) = (1 - p)^2.

Therefore, the probability of transitioning from (1, 1) to (1, 0) after two days is ((1 - p) * (1 - p))^2 = (1 - p)^4.

(b) To find the expected number of days until both machines are down, given that currently both machines are operational, we need to consider the transition probabilities from state (2, 0) to state (0, 1).

From the transition probability matrix, we see that to transition from (2, 0) to (0, 1) in one day, both machines need to fail, which has a probability of p * p = p^2.

Therefore, the expected number of days until both machines are down, given that both machines are currently operational, is 1 / (p^2).

(c) To find the steady-state probabilities, we need to solve the equation πP = π, where π is the row vector of steady-state probabilities and P is the transition probability matrix.

Solving this equation will give us the steady-state probabilities for each state (i, j). Since the given matrix is not provided, it is not possible to calculate the exact steady-state probabilities without the specific values of the transition probabilities.

(d) To determine the percentage change in the long-run average benefit per day if p changes from 0.3 to 0.2, we would need to know how the revenue R TL is related to the probability p. Without this information, it is not possible to calculate the percentage change.

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The given coins [1, 2, 5] and the value 11, the minimum number of coins needed is 2.

Here are the steps to find the minimum number of coins:

1. First, we create an array of size equal to the given value, initialized with a very large number. This array will store the minimum number of coins needed to make each value from 0 to the given value.

2. We set the first element of the array to 0, as it doesn't require any coins to make a value of 0.

3. Next, we iterate through all the coins available and for each coin, we iterate through all the values from the coin value to the given value.

4. For each value, we calculate the minimum number of coins needed by taking the minimum of the current minimum and the value obtained by subtracting the coin value from the current value and adding 1 to it.

5. Finally, we return the value stored in the last element of the array, which represents the minimum number of coins needed to make the given value.

Let's consider an example to better understand the process:

Given coins: [1, 2, 5]
Given value: 11

1. Initialize the array with [INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF] (INF represents infinity).

2. Set the first element of the array to 0, so it becomes [0, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF, INF].

3. For the first coin (1), iterate through the array from index 1 to 11.

  - For index 1, the minimum number of coins needed is 0 + 1 = 1.
  - For index 2, the minimum number of coins needed is 0 + 1 = 1.
  - For index 3, the minimum number of coins needed is 0 + 1 = 1.
  - ...
  - For index 11, the minimum number of coins needed is 0 + 1 = 1.

  The array becomes [0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

4. For the second coin (2), iterate through the array from index 2 to 11.

  - For index 2, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
  - For index 3, the minimum number of coins needed is 1 (minimum of 1 and 0 + 1 = 1).
  - For index 4, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).
  - ...
  - For index 11, the minimum number of coins needed is 1 (minimum of 1 and 1 + 1 = 2).

  The array becomes [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2].

5. For the third coin (5), iterate through the array from index 5 to 11.

  - For index 5, the minimum number of coins needed is 2 (minimum of 2 and 0 + 1 = 1).
  - For index 6, the minimum number of coins needed is 2 (minimum of 2 and 1 + 1 = 2).
  - ...
  - For index 11, the minimum number of coins needed is 2 (minimum of 2 and 2 + 1 = 3).

  The array becomes [0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2].

6. The minimum number of coins needed to make the given value (11) is 2.

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Answer:

f(-8) = -18

Step-by-step explanation:

given :

f(x) = 2(x – 3) + 4

to find f(-8), simply substitute x= -8 into the function:

f(x) = 2(x – 3) + 4

f(-8) = 2[(-8) – 3] + 4

= 2[-8 – 3] + 4

= 2[-11] + 4

= -22+4

= -18

Step-by-step explanation:

thisssss isss the answer

1. The outcomes in the sample space of this chance experiment can be listed as follows:

For the first letter (from the word SAMPLE):S, A, M, P, L, and E.

For the second letter (from the word SPACE):S, P, A,C, and E.

2. The sample space has a total of 6 × 5 = 30 outcomes.

c. The probability that the letters chosen are AA is 1/30.

In order to determine the number of outcomes in the sample space, we multiply the number of outcomes for the first letter (6) by the number of outcomes for the second letter (5).

Therefore, the sample space has a total of 6 × 5 = 30 outcomes.

The probability of choosing the letters AA can be found by considering the favorable outcome (AA) and dividing it by the total number of outcomes in the sample space. In this case, there is only one favorable outcome (AA) and a total of 30 outcomes in the sample space. Therefore, the probability is 1/30.

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As given data represents the sample so here correct choice is given by

sample mean \(\bar {x}\)  = 15.

As given in the question,

Data represents the sample :

Sample : 24 , 16, 1, 11, 23

Let \(x_{i}\) represents the each sample value of the give data where i is equals to 1 to 5:

x₁               x₂              x₃          x₄           x₅

24             16               1             11           23

It represents the sample , therefore correct choice for calculating mean is sample mean.

Sample Mean \(\bar{x}\)  = ( x₁ + x₂ + x₃ + x₄ + x₅ ) / 5

                           = ( 24 + 16 + 1 + 11 + 23 ) /5

                           = 75 /5

                           = 15

Therefore, as given data represents the sample so here correct choice is given by sample mean \(\bar {x}\)  = 15.

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Answer:

44%

Step-by-step explanation:

60%-16% the answer is up ahead.

-20

step by step explanation :

\( - 2( { - 6})^{2} - 5( - 6) + ( { - 6})^{2} + 4 + 3( - 6)\)

\( - 72 + 30 + 36 + 4 - 18 = - 20\)

Answer:

Standard Deviation

Step-by-step explanation:

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

you can reduce it to factors of degree 2 or less).

The two dice do not need to be identical. If it is possible, do it. If it is not possible, prove that it is not possible.

Some hints I got were to try to construct a pair of nonstandard dice such that the generating function for their sum matches the corresponding g.f. for a pair of standard dice and to note that the g.f. for a pair of standard dice can be factored quite a bit (you can reduce it to factors of degree 2 or less).

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Step-by-step explanation:

$1,200 divided by 251.2

hope this helps

Lets break this down.

This is pretty easy, if you just think about it, all we have to do is............. DIVIDE!

So what IS, 1200 by 251.2??

the answer is to your question 4.8

Answer:

-6A - 35b + 48c

hope it's helpful ❤❤❤❤❤❤❤

:)

THANK YOU.

only Outcome D is a Pareto efficient outcome. In this given scenario, "A and D" are Pareto efficient outcomes.What is Pareto efficiency? Pareto efficiency is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.

What are the given allocations and benefits of individuals? The net benefit for each individual in each allocation is given below: (The two numbers in each of the following brackets indicate the net benefits for individual 1 and individual 2, respectively.) Outcome A: (10, 25) Outcome B: (20, 10) Outcome C: (14, 20)Outcome D: (15, 15) Which of the outcomes are Pareto efficient?

Now, let's see which of the given outcomes are Pareto efficient: Outcome A: If we take Outcome A, then individual 1 gets 10 and individual 2 gets 25 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome B, then individual 1 gets 20 which is greater than 10 as his net benefit, and the net benefit for individual 2 would become 10 which is still greater than 25. Therefore, Outcome A isn't Pareto efficient. Outcome B: If we take Outcome B, then individual 1 gets 20 and individual 2 gets 10 as their net benefits.

But the allocation isn't Pareto efficient because if we take Outcome C, then individual 1 gets 14 which is less than 20 as his net benefit, and the net benefit for individual 2 would become 20 which is greater than 10. Therefore, Outcome B isn't Pareto efficient.Outcome C: If we take Outcome C, then individual 1 gets 14 and individual 2 gets 20 as their net benefits. But the allocation isn't Pareto efficient because if we take Outcome A, then individual 1 gets 10 which is less than 14 as his net benefit, and the net benefit for individual 2 would become 25 which is greater than 20. Therefore, Outcome C isn't Pareto efficient.

Outcome D: If we take Outcome D, then individual 1 gets 15 and individual 2 gets 15 as their net benefits. The allocation is Pareto efficient because there is no other allocation where one individual will be better off without harming the other individual.Therefore, only Outcome D is a Pareto efficient outcome.

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Total number of students = 300 (given in the question)

The number of students who prefer vanilla = 105 (given in the question)

The number of students who prefer chocolate= 93 (given in the question)

The number of students who prefer both = 56 (given in the question)

Let the total number of students = T

Let the number of students who prefer vanilla = V = 105

Let the number of students who prefer chocolate  = C = 93

Then

the number of students that prefer both = V ∩ C = 56

Number of students that prefer neither = T - (V + C - V ∩ C )

Number of students that prefer neither = 300 - ( 105 + 93 - 56)

Number of students that prefer neither = 300 -  142

Number of students that prefer neither = 158

Then, P(V) = ( V - V ∩ C )/ 300

P(V) = 105 - 56/ 300

P(V) = 49/300

P(C) = C - V ∩ C/ 300

P(C) = 93 - 56/300

P(C) = 37/300

Then the probability that the random student prefers only chocolate or only  vanilla = P(V) + P(C)

= 49/300 + 37/300

= 49 + 37/300

= 86/300

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