What’s the correct answer I have to get this correct ... ASAP ..

a. The expected value of g(X) is 2π.
b. The variance of g(X) is 4π – 4π^2.


a. To calculate the expected value of g(X), we need to compute the sum of g(xi) multiplied by the probability of X taking the value xi. In this case, g(X) = 2X.
The possible values of X are 0 and 1, and their corresponding probabilities are (1 – π) and π, respectively.
So, the expected value can be calculated as follows:
E(g(X)) = g(0) * P(X = 0) + g(1) * P(X = 1)
       = 2 * 0 * (1 – π) + 2 * 1 * π
       = 0 + 2π
       = 2π
Therefore, the expected value of g(X) is 2π.

b. To calculate the variance of g(X), we need to compute the sum of (g(xi) – E(g(X)))^2 multiplied by the probability of X taking the value xi.
The possible values of X are 0 and 1, and their corresponding probabilities are (1 – π) and π, respectively.
The variance can be calculated as follows:
Var(g(X)) = (g(0) – E(g(X)))^2 * P(X = 0) + (g(1) – E(g(X)))^2 * P(X = 1)
         = (2 * 0 – 2π)^2 * (1 – π) + (2 * 1 – 2π)^2 * π
         = (-2π)^2 * (1 – π) + (2 – 2π)^2 * π
         = 4π^2 * (1 – π) + (4 – 8π + 4π^2) * π
         = 4π^2 – 4π^3 + 4π – 8π^2 + 4π^3
         = 4π – 4π^2
Therefore, the variance of g(X) is 4π – 4π^2.

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Thus, option A is the correct answer choice which shows the quotient of the given division problem as a simplified fraction in 250 words.

To solve the given division problem and show the quotient as a simplified fraction, we need to follow the steps given below:

Step 1: We need to perform the division of 8/21 ÷ 6/7 by multiplying the dividend with the reciprocal of the divisor.8/21 ÷ 6/7 = 8/21 × 7/6Step 2: We simplify the obtained fraction by cancelling out the common factors.8/21 × 7/6= (2×2×2)/ (3×7) × (7/2×3) = 8/21 × 7/6 = 56/126

Step 3: We reduce the obtained fraction by dividing both the numerator and denominator by the highest common factor (HCF) of 56 and 126.HCF of 56 and 126 = 14

Therefore, the simplified fraction of the quotient is:56/126 = 4/9

Thus, option A is the correct answer choice which shows the quotient of the given division problem as a simplified fraction in 250 words.

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Answer:

In this algebraic expression, "Negative x" represents a term with a coefficient of -1, and "x" represents a variable. "10.2" represents a constant term. The "+" sign represents addition.

Step-by-step explanation:

"minus one-half x" represents a term with a coefficient of -0.5 and variable "x". "+ y" represents a term with variable "y" and a coefficient of 1.

Simplifying the expression by combining like terms:

-x - 0.5x = -1.5x

Negative x + 10.2 - one-half x + y = 10.2 - 1.5x + y

The solution to the system of equations is (m, n) = (7.5, 8). This represents a unique solution (A.) to the system. Option A

To solve the system of equations using elimination by addition, we need to eliminate one variable by adding the two equations together. Let's consider the system:

4m - n = 22

2m - 4n = -17

To eliminate the variable "n," we can multiply the first equation by 4 and the second equation by 1:

(4)(4m - n) = (4)(22)

(1)(2m - 4n) = (1)(-17)

Simplifying these equations gives us:

16m - 4n = 88

2m - 4n = -17

Now, we can subtract the second equation from the first equation:

(16m - 4n) - (2m - 4n) = 88 - (-17)

This simplifies to:

14m = 105

Dividing both sides of the equation by 14 gives us:

m = 105 / 14

m = 7.5

Now that we have the value of "m," we can substitute it back into one of the original equations to solve for "n." Let's use the first equation:

4m - n = 22

Substituting m = 7.5:

4(7.5) - n = 22

30 - n = 22

Solving for "n," we subtract 22 from both sides:

-n = 22 - 30

-n = -8

Multiplying both sides by -1 gives us:

n = 8

Option A

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Answer:

4 ) {2,3}

5) {0,1,2,3,4,5}

6) { }

Answer:

\(a_{n}\) = \(a_{n-1}\) - 3

Step-by-step explanation:

The recursive formula lets us find a term in the sequence by adding the common difference d to the previous term.

Here d = a₂ - a₁ = - 9 - (- 6) = - 9 + 6 = - 3 , thus

\(a_{n}\) = \(a_{n-1}\) - 3 with a₁ = - 6

Answer:

slope: -3

y-intercept: 5

Step-by-step explanation:

y=mx+b, where m=slope and b=y-intercept

Answer:

The slope is -3 and y is 5. hope that helped

Answer:

  7 units

Step-by-step explanation:

You want the length of the longer side of the rectangle defined by the coordinates (−4, 2), (3, 2), (3, −2), and (−4, −2).

When you plot the points, or simply consider the coordinates, you see the sides of the rectangle are vertical and horizontal line segments.

The length of a vertical segment is the difference of its endpoint y-coordinates:

  2 -(-2) = 4

The length of a horizontal segment is the difference of the x-coordinates of its endpoints:

  3 -(-4) = 7

The longer side is 7 units long.

Answer:

its 18

Step-by-step explanation:

i took this testtttttttttttt

Answer:

18

Step-by-step explanation:

(a) A motor is the device that converts electrical energy to mechanical energy. (b) The kinetic energy of the antelope is nine times greater than before.

(a)A motor is an electrical device that uses the principle of electromagnetic induction to convert electrical energy into mechanical energy. It consists of coils, magnets, and a rotating shaft. When an electric current is passed through the coils, it creates a magnetic field that interacts with the magnetic field of the permanent magnets, causing the shaft to rotate and thus converting electrical energy to mechanical energy. Motors are commonly used in various applications such as appliances, vehicles, and industrial machinery.

(b)The kinetic energy of an object is given by the equation KE = (1/2)mv^2, where KE represents kinetic energy, m represents mass, and v represents velocity. When an object's speed is tripled, the new kinetic energy is calculated by substituting the new velocity into the equation. Since the velocity is squared, tripling the velocity results in a nine-fold increase in the kinetic energy. Therefore, the kinetic energy of the antelope is nine times greater than before when its speed is tripled.

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Answer:

a.) 4x = 2(x + 14)

b.) Measure of A = 56°

    Measure of B = 56°

Step-by-step explanation:

We know that,

When two lines are crossed by another line transversal line , the angles in matching corners are called corresponding angles.

Also,

When two lines are parallel then the Corresponding Angles are equal.

Given that,

A = 4x and B = 2(x+14).

i.e.

∠A = 4x and ∠B = 2(x+14)

a.)

Now,

As A and B are parallel

So,

∠A = ∠B

⇒4x = 2(x + 14)                  

(This is the equation that represent the corresponding angle relationship between A and B.)

b.)

Now,

⇒4x = 2x + 2(14)

⇒4x = 2x + 28

⇒4x - 2x = 28

⇒2x = 28

⇒x = 14

So,

we get

∠A = 4(14)

      = 56

⇒∠A = 56°

and

∠B = 2(14 + 14)

     = 2(28)

     = 56°

⇒∠B = 56°

∴ we get

Measure of A = 56°

Measure of B = 56°

Answer:

1 /30

Step-by-step explanation:

25 marbles in total

P(B,B) = 5/25 x 4/24

          = 1/5 x 1/6

Answer:

14 or 0.14

Step-by-step explanation:

3 1/2 ÷ 1/4

1/4 = 25

3 1/2 ÷ 25 = 0.14 or 14

This is correct answer can you mark me brainliest

Answer:

Two sets of dimensions are possible:

              L(m)   W(m)   Area(m^2)   Fence (m) Perimeter

Set 1         19        16       304              51

Set 2         32      9.5      304              51

Step-by-step explanation:

Let's set L and W for the Length and Width of the perimeter.  We know that:

Area = L*W

Area = 304 m^2

Perimeter = 51 m

Let's say that the side bounded by the river is the length side.   No fence is required for that portion, so the fencing for the perimeter is given by:

Perimeter, P = L + 2W

P = 51 m

We can write:   L+2W=51 m

Rearrange to isolate one of the two variables.  Lets pick L:

 L+2W=51

 L=51-2W

L = (51-2W)

Now use this in the area equation:

304 m^2 = L*W

304 m^2 = (51-2W)*W

304 m^2 = (51-2W)*W

304 m^2 = 51W-2W^2

Arrange this in the standard form of a quadratice equation and solve:

-2W^2+51W-304 m^2 = 0

W = 16 and 9.5 meters

W = 16 m

Since L=51-2W

 L=51-2*(16)

L = 51-32

L = 19 m

Area = L*W

L*W = 304 m^2

(19m)W = 304 m^2

W =  16 m

Check:

Does a length (L) of 19 m and a width (W) of 16 m give an area of 304 m^2 and a fencing perimeter of 51 m if one of the L sides is the river?

Area = (19 m)*(16 m) = 304 m^2  YES

Per.  = 2*(16)+ 19 = 51 m  YES

W = 9.5 m

Ding the same calculation for a width of 9.5 m also satisfies all the equations, as per above.  

Both values of W are valid, so the twos sets of possible dimensions are:

                   L(m)    W(m)   Area(m^2)   Fence (m) Perimeter

Set 1          19      16       304              51

Set 2          32      9.5      304              51

Answer:

My age is 94. Ouch.

Step-by-step explanation:

Let X be "my" age.

500 - 3X = 218 [500 reduced by 3 times my age is 218]

-3X = -282

X = 94

===

CHECK:  Will subtracting 3 times my age of 94 from 500 equal 218?

3*(94) = 282

500 - 282 = 218  YES

23 kg is equivalent to 50.7098 pounds.

When converting between units of weight, it is important to understand the relationship between the units. Kilograms (kg) and pounds (lbs) are both units of weight, but they are not equivalent. One kilogram is equal to 2.20462 pounds.

To convert kilograms (kg) to pounds (lbs), you can use the conversion factor of 2.20462. The formula to convert kg to lbs is:

lbs = kg x 2.20462

So, to convert 23 kg to pounds, we can plug in the value of 23 for kg and multiply it by 2.20462:

lbs = 23 x 2.20462

lbs = 50.7098

It's worth noting that when dealing with such calculations, you need to take care of the precision of the result.

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The probability that a shutdown is due to hardware failure given that there is a shutdown is 0.346.

To find the probability that the shutdown is due to hardware failure given that there is a shutdown, we need to use Bayes' theorem.

Let H be the event that the shutdown is due to hardware failure, and S be the event that there is a shutdown. Then we need to find P(H|S).

Using the formula for Bayes' theorem:

P(H|S) = P(S|H) * P(H) / P(S)

We already have P(H) = 0.45, and P(S|H) = 0.43, the probability of a shutdown given hardware failure.

To find P(S), we need to use the law of total probability:

P(S) = P(S|H) * P(H) + P(S|E) * P(E) + P(S|S) * P(S)

where E is the event of electronic failure, and S is the event of software failure.

We are given P(S|E) = 0.95, P(E) = 0.30, P(S|S) = 0.09, and P(S|H), P(H) as calculated above.

Substituting the values:

P(S) = 0.43 * 0.45 + 0.95 * 0.30 + 0.09 * 0.25 = 0.558

Finally, substituting all values into Bayes' theorem:

P(H|S) = 0.43 * 0.45 / 0.558 = 0.346

Therefore, the probability that a shutdown is due to hardware failure given that there is a shutdown is 0.346.

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Answer:

LM ≈ 7.1 in

Step-by-step explanation:

using the Sine rule in Δ LMN

\(\frac{l}{sinL}\) = \(\frac{n}{sinN}\)

where l is the side opposite ∠ L , that is MN

n is the side opposite ∠ N , that is LM

\(\frac{LM}{sin24}\) = \(\frac{MN}{sin67}\) , that is

\(\frac{LM}{sin24}\) = \(\frac{16}{sin67}\) ( cross- multiply )

LM × sin67° = 16 × sin24° ( divide both sides by sin67° )

LM = \(\frac{16sin24}{sin67}\) ≈ 7.1 in ( to the nearest tenth )

The author would have sold  12,699 books over the first 6 months.

To find the total number of books the author would have sold over the first 6 months

we can use the formula for the sum of a geometric series.

The first term (a) is 27500, and the common ratio (r) is 0.9 (since the sales decline by 10% each month).

The sum of a geometric series is given by the formula:

S = a(1 - rⁿ) / (1 - r),

where S is the sum, n is the number of terms.

Plugging in the values, we have:

S = 27500 × (1 - 0.9⁶) / (1 - 0.9).

Calculating this expression:

S = 27500(1 - 0.531441) / (1 - 0.9)

= 27500×0.468559 / 0.1

= 12698.647

= 12699.

Hence,  the author would have sold 12,699 books over the first 6 months.

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2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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The conclusion is that the cross product is not associative, which means that (i×j)×j is not equal to i×(j×j).

To compute (i×j)×j, we first need to find i×j, which is the cross product of i and j. The cross product of i and j is a vector perpendicular to both i and j, and its direction can be determined using the right-hand rule. Since i and j are perpendicular unit vectors in the x-y plane, their cross product i×j is a vector pointing in the z direction, which can be written as k.

Now, we can compute (i×j)×j by taking the cross product of k and j. Since k is perpendicular to j, the cross product of k and j will be perpendicular to both k and j, which means it will be in the i direction. Therefore, (i×j)×j equals the vector i.

To compute i×(j×j), we first need to find j×j, which is the cross product of j with itself. Since the cross product of any vector with itself is the zero vector, j×j equals 0. Therefore, i×(j×j) equals the zero vector.

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Answer:

Its b

Step-by-step explanation:

I had to use multiple apps to get this but im pretty sure its b, its definitly not A c or D. I have this exact same test.

Answer:

80 + 15x ≤ 300

Step-by-step explanation:

max amount = $300

already spent = $80

$300 - 80 = $220

shirts = $15 each

80 + 15x ≤ 300

$80 that is already spent + $15x ≤ $300 maximum

x = number of shirts

According to the model, 18% of gross domestic product will go toward health care in the year 2026.

To find the year when 18% of gross domestic product (GDP) will go toward health care according to the given model, we need to solve the equation:

f(x) = 18

where f(x) represents the percentage of GDP going toward health care x years after 2006.

Given the model f(x) = 1.4 ln(x) + 13.8, we can substitute 18 for f(x):

1.4 ln(x) + 13.8 = 18

Subtracting 13.8 from both sides:

1.4 ln(x) = 4.2

Dividing both sides by 1.4:

ln(x) = 3

To solve for x, we can exponentiate both sides using the base e (natural logarithm):

e^(ln(x)) = e^3

x = e^3

Using a calculator, the approximate value of e^3 is 20.0855.

Therefore, according to the model, 18% of GDP will go toward health care in the year 2006 + x = 2006 + 20.0855 ≈ 2026 (rounded to the nearest year).

According to the model, 18% of gross domestic product will go toward health care in the year 2026.

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Complete question is below

The percentage of gross domestic product (GDP) in a state going toward health care from 2007 through 2010, with projections for 2014 and 2019 is modeled by the function f(x) = 1.4 In x + 13.8, where f(x) is the percentage of gross domestic product going toward health care x years after 2006. According to the model, when will 18% of gross domestic product go toward health care?

According to the model, 18% of gross domestic product will go toward health care in the year (Round to the nearest year as needed.)

One product/service that is currently in the decline stage is DVD rentals. The decline can be attributed to the rapid rise of digital streaming platforms and the decreasing popularity of physical media. Companies competing in a declining market have strategic options such as harvesting and divesting. Harvesting involves maximizing profits from the declining product/service by reducing costs and maintaining a loyal customer base, while divesting involves exiting the market and reallocating resources to more profitable ventures.

DVD rentals are in the decline stage of the product lifecycle due to several factors. The advent of digital streaming platforms like Netflix, Hulu, and Amazon Prime Video has revolutionized the way people consume media. The convenience and vast content libraries offered by these platforms have led to a significant decline in DVD rentals. Moreover, the proliferation of high-speed internet connections and the increasing availability of streaming devices have made it easier for consumers to access digital content.

In a declining market, companies have strategic options to consider. One option is harvesting, which involves maximizing profits from the declining product/service. Companies can achieve this by reducing costs associated with production, distribution, and marketing, as the demand for the product/service diminishes. They may also focus on retaining their loyal customer base by providing incentives, discounts, or exclusive offers. For example, DVD rental companies may lower rental fees, offer bundle deals, or introduce loyalty programs to retain their remaining customers.

Another strategic option is divesting, which involves exiting the declining market altogether. Companies may choose to reallocate their resources to more profitable ventures or invest in emerging technologies or industries. In the case of DVD rentals, companies could divest by shutting down physical rental stores and selling off their DVD inventory. They could then shift their focus to digital streaming services or invest in other areas with growth potential, such as content production or streaming device manufacturing.

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There are 5.5 × 10¹⁰ grains of sand in a sandbox that is 1.0 m wide, 1.0 m long and 10 cm deep.

In this problem we need to estimate the number of grains of sand contained in the sandbox (N), in grains, which is equal to the product of the volume occupied by the sandbox (V), in cubic milimeters, and the average grain concentration (c), in grains per cubic milimeters. Then, the volume is defined by the following formula:

N = c · V

N = c · w · h · l

N = (55 grains / mm³) · (1000 mm) · (1000 mm) · (100 mm)

N = 5.5 × 10¹⁰ grains

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Answer:

Irrational

Step-by-step explanation:

It has an infinite number of digits after the decimal point

A 95% confidence interval for μ is (15.5, 18.3). If we were to take many different samples from the same population and calculate a confidence interval for each sample, approximately 95% of those intervals would contain the true population mean.

We first need to understand the concept of a confidence interval. A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. In this case, we are trying to construct a confidence interval for the population mean μ, with a confidence level of 0.95 (or 95%).

To construct the confidence interval, we use the formula:

CI = x ± z*(σ/√n)

where x is the sample mean, σ is the population standard deviation, n is the sample size, and z is the z-score associated with the desired confidence level (0.95 in this case).

Plugging in the given values, we get:

CI = 16.9 ± 1.96*(9/√85)

Simplifying, we get:

CI = (15.5, 18.3)

This means that we can be 95% confident that the true population mean μ falls within the range of 15.5 to 18.3.

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Answer:

c(x) = 5x + 20

Step-by-step explanation:

there is a fixed membership fee of 20$ and each day cost 5$

The value of the constant of proportionality is, 20

We have to given that;

the point (4, 80) represent he bicyclist rides 80 miles in 4 hours.

Hence, We can conclude that;

The equation for constant of proportionality is,

y = kx

80 = 4k

k = 80 / 4

k = 20

Thus, The value of the constant of proportionality is, 20

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