Which table represents a linear function?

To determine if X and Y are uncorrelated or independent, calculate their expected values, variances, and covariances. If X and Y are uncorrelated, Cov(X, Y) = 0, while if they are independent, P(X,Y) = P(X).P(Y). However, P(Y/X) is not independent, indicating X and Y are not independent.

Suppose X is uniform over (-1,1) and Y=X2. Are X and Y uncorrelated? Are X and Y independent?The answer to this question can be determined with a step by step approach. First, we will calculate E(X), E(Y), E(XY) and Var(X), Var(Y) and Cov(X, Y). Let us start:Calculation of E(X)E(X) is defined as the expected value of the probability density function of X over the interval (-1, 1). Therefore,

E(X) = ∫X.P(X)dX over (-1,1)

Here, P(X) = 1/(1-(-1))

= 1/2

Thus,

E(X) = ∫X.1/2dX over (-1,1)

= [(1/2)*X^2] over (-1,1)= (1/2)[1-(-1)] = 0

Therefore, E(X) = 0Calculation of E(Y)E(Y) is defined as the expected value of the probability density function of Y over the interval (0, 1). Therefore,

E(Y) = ∫Y.P(Y)dY over (0,1)

Here, P(Y) = 1/(1-0) = 1

Thus, E(Y) = ∫Y.1dY over (0,1)

= [(1/3)*Y^3] over (0,1)= 1/3

Therefore, E(Y) = 1/3

Calculation of E(XY)E(XY) is defined as the expected value of the probability density function of XY over the interval (-1, 1).

Therefore, E(XY) = ∫∫XY.P(XY)dXdY over (-1,1)

Here, P(XY) = P(X)P(Y/X)

Therefore, P(Y/X) = δ(X^2-Y) over (-1,1) = δ(X-√Y) + δ(X+√Y)

Then, E(XY) = ∫∫XY.[1/2].δ(X-√Y) + δ(X+√Y) dXdY

over (-1,1)= ∫0^1∫-√y^√yX.[1/2].δ(X-√Y) + δ(X+√Y) dXdY

= ∫0^1[√y/2 + (-√y)/2] dy= 0

Therefore, E(XY) = 0Calculation of Var(X)Var(X) is defined as the variance of X.

Therefore,

Var(X) = E(X^2) - [E(X)]^2

Here, E(X) = 0T

herefore, Var(X) = E(X^2)

Now, E(X^2) = ∫X^2.P(X)dX

over (-1,1)Here, P(X)

= 1/(1-(-1))

= 1/2

Thus, E(X^2) = ∫X^2.1/2 dX over (-1,1)

= [(1/3)*X^3] over (-1,1)= (1/3)[1-(-1)] = 2/3

Therefore, Var(X) = 2/3Calculation of Var(Y)Var(Y) is defined as the variance of Y. Therefore,

Var(Y) = E(Y^2) - [E(Y)]^2

Here, E(Y) = 1/3Therefore, Var(Y) = E(Y^2) - [1/3]^2

Now, E(Y^2) = ∫Y^2.P(Y)dY over (0,1)Here, P(Y) = 1/(1-0) = 1

Thus, E(Y^2) = ∫Y^2.1 dY over (0,1)= [(1/4)*Y^4] over (0,1)= 1/4

Therefore, Var(Y) = 1/4 - [1/3]^2

Calculation of Cov(X, Y)Cov(X, Y) is defined as the covariance of X and Y. Therefore,

Cov(X, Y) = E(XY) - E(X).E(Y)Here, E(X) = 0 and E(XY) = 0

Therefore, Cov(X, Y) = -E(X).E(Y)

Now, E(Y) = 1/3Therefore, Cov(X, Y) = 0

Thus, we have:E(X) = 0E(Y) = 1/3E(XY) = 0Var(X) = 2/3Var(Y) = 1/4 - [1/3]^2Cov(X, Y) = 0

Now, we can proceed to determine whether X and Y are uncorrelated or independent.If X and Y are uncorrelated, then Cov(X, Y) = 0, which is the case here.

Therefore, X and Y are uncorrelated .If X and Y are independent, then P(X,Y) = P(X).P(Y)

Here, P(X) = 1/(1-(-1)) = 1/2 and P(Y) = 1/(1-0) = 1

Therefore, P(X,Y) = 1/2.1 = 1/2

However, P(Y/X) = δ(X^2-Y) over (-1,1) = δ(X-√Y) + δ(X+√Y)Therefore, P(X,Y) ≠ P(X).P(Y)Hence, X and Y are not independent.

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The area of the square t inscribed in square s of perimeter 40 cm is 50 sq cm.

If a square is inscribed in a square then the square is formed by joining the midpoints of the square of edges. This is the only square thus the square with the minimum possible area that can be inscribed in a square. Thus we can calculate the side of the inscribed square t as we following:

In right-angled triangle APS, right-angled at A,

By Pythagoras' theorem,

\(a^2=b^2+c^2\)

where a is the hypotenuse

b is the base

c is the height

\(PS^2=AP^2+AS^2\)

Since P is the midpoint, the length of AP and AS is 5 cm.

\(PS^2\) = 25 + 25

PS = \(5\sqrt{2}\) cm

Thus, the side of the square t is \(5\sqrt{2}\) cm

The area of square t is \(side^2\)

= \((5\sqrt{2})^2\)

= 50 sq cm.

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Answer:

x = - 10

Step-by-step explanation:

2(x + 3) = x - 4 ← distribute parenthesis on left side

2x + 6 = x - 4 ( subtract x from both sides )

x + 6 = - 4 ( subtract 6 from both sides )

x = - 10

Answer:

-10

Step-by-step explanation:

2(x+3)=x-4

2x+6=x-4

2x-x=(-4)-6

x=-10

Hence the answer is -10

Answer:

it is 750 ml of flour this is the answer

Answer:

Step-by-step explanation:

Given

Ratio as per given

74. 94×10³= 74940 because the number 10³ has zeros when it is written without an exponent.

Using scientific notation, it's found that the number in standard notation is represented by:

74. 94 × 10³= 74940

Using scientific notation, you can write extremely large or extremely small numbers. When a number between 1 and 10 is multiplied by a power of 10, the result is expressed in scientific notation as variety.

Scientific notation for the following number is:

\(a \times 10^{b}\)

In this problem, the amount is given by:

= 74. 94 × 10³

Hence, applying the multiplication, we have that:

74. 94 × 10³ = 74. 94 × 1000 = 74940

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Answer:

It depends on your situation

Step-by-step explanation:

If you have a mixed fraction, for example: 5 23/3000 + 101 777/3000 you would have to make them irrational numbers and add them. Like so: 3000x5 = 15000. 15000+23 = 15023.  15023/3000. Same process but this time you get 303777/3000. You then add the numerators (top numbers) and you'll get the sum over 3000.

For regular fractions you simply add the numerators. If your denominators are not the same, you need to find a common term that both can fit into. If the denominators are not the same, no matter the size of the fraction, you cannot add it.

To get x, we will use the Pythagoras theorem

With the hypotenuse equal to 12m

Answer:

Read this passage from "The American Dream."

One of the first things we notice in this dream is an amazing universalism. It does not say some men, but it says all men. It does not say all white men, but it says all men, which includes black men. It does not say all Gentiles, but it says all men, which includes Jews. It does not say all Protestants, but it says all men, which includes Catholics.

How does the use of rhythm contribute to the ideas in the passage?

It supports key points by connecting them.

It states rational ideas to support a claim.

It convinces people that the ideas are true.

It connects the ideas to people in a specific place.

Step-by-step explanation:

Answer:

Green parachute

Explanation:

Orange parachute

• Distance = 12 feet

• Time = 5 seconds

Rate of descent = 12/5 =2.4 feet/seconds

Green parachute

• Distance = 14 feet

• Time = 7 seconds

Rate of descent = 14/7 =2 feet/seconds

Since 2 is less than 2.4, the green parachute has a slower descent.

The feasible solution space for an integer programming model is smaller than that for a linear programming model, as stated in the statement.

The feasible solution space for an integer programming model is smaller than the feasible solution space for a linear programming version of the same model.What is integer programming?Integer programming is a mathematical approach that solves optimization problems that include integer decision variables. It includes optimization methods such as branch and bound, branch and cut, and cutting planes, among others, to obtain the optimal solution. Linear programming is a subset of integer programming.

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1.a. The total resistance is 8 ohms, total voltage is 40 volts.

 b. The voltage drop across the 10-ohm resistor is 50 volts.

 c. The current flowing through the 2-ohm resistors is 2.5 amperes.

2.a. The current flowing in the circuit is 0.0417 amperes.

  b. The source voltage is 100 volts.

  c. The values of the resistors are: 300 ohms, 600 ohms, and 1200 ohms.

3.a. The resistance of B is 24 ohms.

  b. The equivalent resistance of the circuit is 136 ohms.

  c. The voltages across resistors A, C, and D are 12 volts, 16 volts, and 20 volts respectively.

  d. The total power is 1320 watts.

  e. The power in resistors A, B, C, and D is 528 watts, 264 watts, 440 watts, and 88 watts respectively.

4.a. The resistance of D is 16 ohms.

  b. The total resistance of the combination is 12 ohms.

  c. The currents through resistors A, B, and C are 3 amperes, 3.6 amperes, and 4.5 amperes respectively.

In the first problem, we have a circuit with a total current of 5 amperes. Using Ohm's Law (V = I * R), we can find that the total voltage is 25 volts. To find the total resistance, we use the formula R = V / I, which gives us a total resistance of 5 ohms. The voltage drop across the 10-ohm resistor is calculated by multiplying the resistance by the current, resulting in 50 volts. Finally, since the circuit is in series, the current flowing through the 2-ohm resistors will be the same as the total current, which is 2.5 amperes.

In the second problem, we are given the power ratings of three resistors and the total resistance of the circuit. Since each resistor operates at its maximum power dissipation, we can use the formula P = V^2 / R to calculate the power dissipated by each resistor. From the power ratings, we can determine the voltage across each resistor. Using Ohm's Law (V = I * R), we can find the current flowing in the circuit. The source voltage is obtained by multiplying the current by the total resistance. Finally, we can use Ohm's Law again to find the value of each resistor by dividing the voltage across each resistor by the current flowing through it.

In the third problem, resistors A, B, C, and D are connected in series. We are given the resistances of A, C, and D, as well as the voltage across resistor B and the total voltage in the system. Using Ohm's Law, we can find the resistance of B by dividing the voltage by the current. The equivalent resistance of the circuit is obtained by summing up the resistances of all the resistors. The voltage in resistors A, C, and D can be determined using Ohm's Law. The total power dissipated in the circuit is calculated using the formula P = V * I. The power in each resistor is obtained by using the formula P = V^2 / R.

In the fourth problem, we have a parallel circuit with resistors A, B, C, and D. The current in D and the total current in the circuit

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If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.

Here,

4 is a root/zero of polynomial

P(x)  =   (k-2) x²  - 2 x  - (k+5)

P(4) = 0

(k - 2) 4²  - 2 * 4 - (k+5)  = 0

15 k - 45 = 0  

k = 3

The value of k if 4 is one of the zeros of the quadratic polynomial is 3.

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Complete question:

If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.

Display ads sold on a cost per thousand impressions (CPM) basis often focus on reaching a large audience or maximizing brand exposure.

Cost per thousand impressions (CPM) is a common pricing model used in digital advertising, where advertisers pay for every one thousand times their ad is displayed to users.

In this model, the focus is on the number of impressions or views rather than the actual performance or engagement with the ad. As a result, display ads sold on a CPM basis often prioritize reaching a large audience and maximizing brand exposure.

By selecting a CPM pricing model, advertisers aim to increase their ad's visibility and generate brand awareness among a wide range of users.

They are interested in getting their message in front of as many people as possible, regardless of whether those users interact with the ad or take any specific action.

CPM-based display ads are commonly used for branding campaigns, where the primary goal is to create brand recognition, increase visibility, and establish a presence in the minds of potential customers.

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Answer:

y=1.5x-5

Step-by-step explanation:

1 pound is equivalent to 16oz

Answer:0.5j^27+3j+168.45

Step-by-step explanation: I used a calculator

The person is required to select a three-digit number, and if they guess the right number, they will be paid $700 for each dollar they bet. Each day, there is a new winning number.

The person bets $1 each day for one year.To get the possible win or loss from the game, the following formula can be used:Expected win or loss = (Probability of winning × Amount won) − (Probability of losing × Amount lost)From the question, we know that the person is betting $1 every day for a year. Therefore, the total amount of money spent by the person in a year is: Amount spent in a year = $1 × 365 = $365Let's calculate the probability of winning: There are 1000 possible three-digit numbers that can be selected. Only one of them is the winning number.Therefore,

The probability of winning the game is:P(win) = 1/1000Let's calculate the probability of losing the game:There are 999 three-digit numbers left after selecting the winning number.  This means that the person can expect to lose about $0.299 every day. Therefore, the person can expect to lose $109.14 in a year (365 days). Answer: $109.14

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Answer:

Step-by-step explanation:

This equation is in slop-intercept form. This means that the y-int is in the equation, it will always be the constant, so y is -18.

To find x, set y to 0.

0 = 8x - 18

18 = 8x

18/8 = x

9/4 = x

Answer:

Factor {x}^{2}-4x-5x

​2

​​ −4x−5.

(x-5)(x+1)=0(x−5)(x+1)=0

2 Solve for x.

x=5,-1x=5,−1

Step-by-step explanation:

Answer:

x=2+i or x=2-i

Step-by-step explanation:

The differential equation is equivalent to

                           \(\frac{dy}{dx} -\frac{3x(1-y)}{x^{2} +1}\)

If y denotes the fraction of the population who have heard the rumor, then 1 −y represents the fraction of the population who haven’t heard the rumor.

The rate of spread of the rumor (y'(t)) being proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor can then be rewritten as:

\(\frac{dy}{dt} =ky(1-y)\)

for some positive constant k. This is a separable differential equation, so to solve it we separate the variables

\(\frac{dy}{y(1-y)} =kdt\)

and integrate

\(\int\ \frac{dy}{y(1-y)} =\int k dt < = > ln |\frac{y}{1-y} |=kt+c\)

Exponentiating, we get

\(|\frac{y}{1-y}|=e^{kt+c}\)

Denoting ec by A, and taking into account that y ∈ (0, 1) we get

\(\frac{y}1-{y} =Ae^{kt} =\frac{Ae^{kt} }{1}\)

Adding the numerators to the denominators in the above equality of fractions we obtain

\(y=\frac{y}{(1-y)+y} =\frac{Ae^{kt} }{1+Ae^{kt} }\)

The Initial value:

\((x^{2}+1) \frac{dy}{dx} +3y(y-1)=0,y(0)=1\)

The differential equation is equal to

\(\frac{dy}{dx} -\frac{3x(1-y)}{x^2+1}\)

the initial condition of our problem is y(0) = 1, the solution must be y ≡ 1

The differential equation is equivalent to

\(\frac{dy}{dx} +\frac{3x}{x^2+1} y=\frac{3x}{x^2+1}\)

which is a linear equation, with P(x) = Q(x) =\(\frac{3x}{x^2+1}\) we have

\(\int P(x)=\frac{3}{2}\int \frac{2x}{x^2+1} dx=\frac{3}{2} ln(x^2+1)\)

It follows that the integrating factor I(x) is then

\(I(x)e^{\int P(x)dx} =e^{\frac{3}{2} ln(x^2+1)} =(x^2+1)^{\frac{3}{2} }\)

The general technique for solving linear differential equations yields

\(yI(x)=\int Q(x)I(x)dx=\int \frac{3x}{x^2+1} (x^2+1)^{\frac{3}{2} } \\\\=\int 3x(x^2+1)^{\frac{1}{2} } =(x^2+1)^{\frac{3}{2} } +C\)

Dividing by I(x) we get

\(y=1+\frac{C}{(x^2+1)^{\frac{3}{2} } }\)

The initial condition y(0) = 1 yields 1 = 1 + c, i.e. c = 0. Therefore y ≡ 1.

The differential equation is separable. We get this by separating the variables

\(\frac{dy}{y-1} -\frac{-3x}{x^2+1}\)

Integrating, we obtain

\(ln|y-1|=\frac{-3}{2} ln(x^2+1)+c\)

which yields by exponentiation

\(|y-1|=\frac{e^c}{(X^2+1)^\frac{3}{2} }\)

substituting ec by a constant A, and allowing A to also be negative or 0, we get

\(y-1=\frac{A}{(x^2+1)^\frac{3}{2} }\)

The initial condition y(0) = 1 implies that 1 − 1 = A/1 = A, hence A = 0 and          y ≡ 1

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The answer for $b c$ given that both are positive integers is $11$.

To explain, the result of $b^2$ written in base $c$ is $121 c$, which means that $b^2$ is equal to $121 c$ multiplied by the base $c$. Similarly, the result of $c^2$ written in base $b$ is $71b$, which means that $c^2$ is equal to $71b$ multiplied by the base $b$.

Since both of these equations are equal to each other, $b^2 = c^2$, we can solve for $b$ and $c$ by dividing both sides by their respective bases, giving us $bc = \frac{121c}{71b} = \frac{121}{71} = 11$. Thus, $b$ and $c$ are both equal to 11.

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Answer:

There is no solution

Step-by-step explanation:

Simplifying

b + 25 = b + -25

Reorder the terms:

25 + b = b + -25

Reorder the terms:

25 + b = -25 + b

Add '-1b' to each side of the equation.

25 + b + -1b = -25 + b + -1b

Combine like terms: b + -1b = 0

25 + 0 = -25 + b + -1b

25 = -25 + b + -1b

Combine like terms: b + -1b = 0

25 = -25 + 0

25 = -25

Solving

25 = -25

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

Answer:

There are no values of b no solution that makes the equation true.

Step-by-step explanation:

If the balloon is 5,000 feet above the ground, then the Harrison is 7100 feet away (option c)

To solve for the adjacent side, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle to the angle between them.

Tangent of an angle = opposite side / adjacent side

In this case, the tangent of 35° can be written as:

tan(35°) = height of balloon / distance between Harrison and balloon

We can rearrange this equation to solve for the distance between Harrison and the balloon:

distance between Harrison and balloon = height of balloon / tan(35°)

Substituting the given values, we get:

distance between Harrison and balloon = 5000 / tan(35°)

Using a calculator, we can find that the tangent of 35° is approximately 0.7002. Substituting this value, we get:

distance between Harrison and balloon = 5000 / 0.7002

Simplifying this expression, we get:

distance between Harrison and balloon ≈ 7,100 feet

Therefore, the answer is (C) 7,100 feet.

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Answer:

b) -9.9

Step-by-step explanation:

since its a negative its automatically smaller than any whole

hope this helps plz give brainliest

Answer:

10

Step-by-step explanation:

Answer:f and h

Step-by-step explanation:the answer I gave is because if you read the question carefully enough you can see what the answer would be

Answer:

perseveration

Step-by-step explanation:

The term you are looking for is "perseveration."