Answer to Solved The pdf of a random variable X is given by: f(x) = 8x. ... X is given by: f(x) = 8x for 0≤x≤ 0.5 Please find out the expectation of X. O ...

Answer:

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

I hope I helped you^_^

To calculate the cost using data from watts produced and watts per unit cost, you can follow these steps:

Determine the total watts produced: Multiply the watts produced by the number of units. Total Watts = Watts Produced × Number of Units

Calculate the cost per unit of electricity: Divide the total watts by the watts per unit cost. Cost per Unit = Total Watts / Watts per Unit Cost

Calculate the total cost: Multiply the cost per unit by the number of units. Total Cost = Cost per Unit × Number of Units

Here's an example to illustrate the calculation:

Let's say you have 10 solar panels, and each panel produces 200 watts. The cost per unit of electricity is $0.15 per watt.

Total Watts = 200 watts/panel × 10 panels = 2000 watts

Cost per Unit = 2000 watts / $0.15 per watt = $13.33 per unit

Total Cost = $13.33 per unit × 10 units = $133.33

Therefore, the total cost of electricity generated by the 10 solar panels would be $133.33.

By multiplying the watts produced by the number of units and dividing it by the watts per unit cost, you can determine the cost per unit. Multiplying the cost per unit by the number of units gives you the total cost.

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3. The current price of the common stock is $40.

4. The stock price considering the company quitting business after 25 years is $46.81.

5. The stock price assuming constant dividends is $26.67.

6. The stock price assuming constant dividends and the company quitting business after 25 years is $25.88.

3. The current price of the common stock can be calculated using the dividend discount model. The formula for the stock price is P = D / (r - g), where P is the stock price, D is the dividend, r is the required return, and g is the growth rate. In this case, the dividend is $4, the required return is 15% (0.15), and the growth rate is 5% (0.05). Plugging these values into the formula, we get P = 4 / (0.15 - 0.05) = $40.

4. If the company quits business after 25 years, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / (r - g) * (1 - (1 + g)^-n), where PV is the present value, D is the dividend, r is the required return, g is the growth rate, and n is the number of years. In this case, D = $4, r = 15% (0.15), g = 5% (0.05), and n = 25. Plugging these values into the formula, we get PV = 4 / (0.15 - 0.05) * (1 - (1 + 0.05)^-25) = $46.81. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $46.81 + $0 = $46.81.

5. Assuming constant dividends, the stock price can be calculated using the formula P = D / r, where P is the stock price, D is the dividend, and r is the required return. In this case, the dividend is $4 and the required return is 15% (0.15). Plugging these values into the formula, we get P = 4 / 0.15 = $26.67.

6. If the company quits business after 25 years and assuming constant dividends, we need to calculate the present value of the dividends for those 25 years and add it to the final liquidation value. The present value of the dividends can be calculated using the formula PV = D / r * (1 - (1 + r)^-n), where PV is the present value, D is the dividend, r is the required return, and n is the number of years. In this case, D = $4, r = 15% (0.15), and n = 25. Plugging these values into the formula, we get PV = 4 / 0.15 * (1 - (1 + 0.15)^-25) = $25.88. Adding the final liquidation value, which is the future value of the stock price after 25 years, we get $25.88 + $0 = $25.88.

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Answer:

9.36kg

Step-by-step explanation:

Given That:

Mass of her Packages = 8.7 kg

Mass of bag = 660g = 0.66 kg

Total Mass = ?

To find the total mass, add the 2 weight together :"

8.7 + 0.66 = 9.36kg.

Hope this helps.

Good Luck

Answer:

Mass of the things=8.7kg

Mass of the bag=660g=0.66kg

Total mass=mass of the bag+mass of the things

Total mass=8.7kg+0.66kg

Total mass=9.36kg≈9kg

Step-by-step explanation:

i hope this will help you :)

Answer:

7.5

Step-by-step explanation:

➢ Calculating for diameter :-

➢ Calculating Diameter :-

__________________________________

To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

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Answer:

question 1: answer is 4

question 2: answer is 1

Step-by-step explanation:

To compare the motion of the mass in oil and air, you can comment/uncomment the appropriate damping coefficients in the code (as indicated) and run the script.

The MATLAB code to solve the given differential equation and plot the response for 10 seconds using a time interval of 0.1 seconds:

```MATLAB

% Constants

m = 1;

k = 5;

b_air = 1;

b_oil = 3;

% Initial conditions

y0 = 1;

y_dot0 = 2;

% Time parameters

t_start = 0;

t_end = 10;

dt = 0.1;

t = t_start:dt:t_end;

% System of difference recurrence equations

y = zeros(size(t));

y_dot = zeros(size(t));

y(1) = y0;

y_dot(1) = y_dot0;

for i = 1:length(t)-1

   y_ddot = -(b_air/m)*y_dot(i) - (k/m)*y(i); % Air damping

   %y_ddot = -(b_oil/m)*y_dot(i) - (k/m)*y(i); % Oil damping

   y_dot(i+1) = y_dot(i) + dt * y_ddot;

   y(i+1) = y(i) + dt * y_dot(i);

end

% Plotting the response

figure;

plot(t, y);

xlabel('Time (seconds)');

ylabel('Position (y)');

title('Mass Oscillation with Air Damping');

%title('Mass Oscillation with Oil Damping');

```

To compare the motion of the mass in oil and air, you can comment/uncomment the appropriate damping coefficients in the code (as indicated) and run the script.

To determine how many seconds sooner the motion ceases in oil compared to air, you can observe the graphs of the mass oscillation with air damping and oil damping. The motion ceases when the position (y) becomes close to zero and remains near zero. Compare the time at which this occurs in both cases to find the difference in time.

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Answer:

6

Step-by-step explanation:

x = 216^(1/3)

x = 6

Answer:

you didnt put a question

Step-by-step explanation:

The probability that a randomly selected hot water heater has a life span of between 12 and 15 years is about 65.62%.

A Z-score is a numerical measurement that describes a cost's relationship to the suggestion of a group of values. Z-score is measured in terms of standard deviations from the suggested. If a Z-score is 0, it suggests that the statistics point's rating is identical to the mean rating.

According to the question;

Mean (μ) = 13 years

Standard deviation (σ) = 1.5 years

The z score can be used to find the probability of a random variable occurring over a normally distributed parameter if its mean and standard deviation is given. z = x- μ /  σ

The z score can then be used to find the probability of a randomly selected hot water heater lifespan being below that value: P ( Z < z)

First, find the z score for 12 and 15

z = 12 - 13 / 1.5 = - 0.6667

z = 15 - 13 / 1.5 = 1.333

Therefore,

P ( X < 12) = P ( Z < - 0.6667 ) ≈ 0.2525

P ( X < 15) = P ( Z < 1.333 ) ≈ 0.9087

To find the probability of a randomly selected hot water heater having a lifespan between 12 and 15 over this distribution, subtract the P for the lower value from the P for the higher value.

P ( - 0.6667 < X < 1.333 )  = P ( Z < 1.333 ) - P ( Z < - 0.6667 ) = 0.9087 - 0.2525 = 0.6562

P ( 12 < X < 15 ) ≈ 65.62%

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To find the t-statistic for the given percentiles, we need to know the sample mean, sample standard deviation, and degrees of freedom (df). Assuming that we are dealing with a sample of size 55, we can use the t-distribution to calculate the t-statistics.

(a) To find the t-statistic for the 45th percentile, we first need to find the corresponding t-score. Using a t-distribution table or a calculator, we can find that the t-score for the 45th percentile with 54 degrees of freedom is approximately -0.1812.

Next, we can use the formula for calculating the t-statistic:

t = (x - μ) / (s / √n)

where x is the sample percentile, μ is the population mean (which is unknown), s is the sample standard deviation, and n is the sample size.

Since we don't know the population mean, we can use the sample mean as an estimate. Let's assume that the sample mean is 10 and the sample standard deviation is 2. Then, the t-statistic for the 45th percentile can be calculated as:

t = (x - μ) / (s / √n) = (0.45 - 10) / (2 / √55) ≈ -10.03

Therefore, the t-statistic for the 45th percentile is approximately -10.03.

(b) To find the t-statistic for the 95th percentile, we first need to find the corresponding t-score. Using a t-distribution table or a calculator, we can find that the t-score for the 95th percentile with 54 degrees of freedom is approximately 1.6759.

Next, we can use the same formula for calculating the t-statistic:

t = (x - μ) / (s / √n)

Assuming that the sample mean is still 10 and the sample standard deviation is 2, the t-statistic for the 95th percentile can be calculated as:

t = (x - μ) / (s / √n) = (0.95 - 10) / (2 / √55) ≈ -26.97

Therefore, the t-statistic for the 95th percentile is approximately -26.97.

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Answer: c

Step-by-step explanation:

In order to be parallel, the slope must be the same. This means slope is 2

Now one of the point is 5,-1, so do 2x5 + x = -1, so x = -11

meaning b is -11

so the equation should be y=2x-11

Answer:

L is 132

3168 people voted for J

Step-by-step explanation:

The distance from the sun to the other focus is 5.01 × 10⁹ m.

(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;

2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.

(b) To express this in terms of solar radii, we set up a ratio;

(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2

Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.

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Complete question is;

The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.

Answer:

C. $26 is the closest estimate

Step-by-step explanation:

127.59 rounded is 128

128 x 0.2 = 25.6
25.6 is closest to 26 so C is the answer

so that is the closest estimate
this should be correct! :)

Answer:

4x+13

Step-by-step explanation:

bc 12-8=4

6+7÷13

Step-by-step explanation:

f(x) = (x + 2)(x - 3)(x + 12) = 0

(x + 2)(x - 3)(x + 12) = 0

so, the zeros of the function :

=> x1 = -2

=> x2= 3

=> x3 = -12

The solution to differential equation (9) is y = \(2e^{(x-1)\). The solution to differential equation (11) is y = (x + 1)² / 2 which is not a solution.

Given differential equations arey = x - y; y' = y²(1 - x)

N 9. y = \(2e^{(x-1)\) solves y = x - y

Here the given differential equation is y = x - y.

We need to find whether y = \(2e^{(x-1)\) is a solution to the given differential equation or not.

Substituting y = 2e^(x-1) in y = x - y, we get

y = x - \(2e^{(x-1)\)

Now we need to verify if y = x - 2e^(x-1) is a solution to the given differential equation or not.

Differentiating y w.r.t. x, we gety' = 1 -  \(2e^{(x-1)\)

On substituting these values in the given differential equation we get

y = y'1 - x - y² ⇒ y' = y²1 - x - y

Thus, we can conclude that y = 2e^(x-1) is indeed a solution to the given differential equation.

N 11. y = (x + 1)² / 2 solves y' = y²(1 - x)

Here the given differential equation is y' = y²(1 - x).

We need to find whether y = (x + 1)² / 2 is a solution to the given differential equation or not.

Differentiating y w.r.t. x, we gety' = x + 1

Substituting y = (x + 1)² / 2 and y' = x + 1 in y' = y²(1 - x), we get

x + 1 = (x + 1)² / 2 × (1 - x) ⇒ (x + 1)(2 - x) = (x + 1)² ⇒ (x + 1)(x + 3) = 0

Thus, the possible values of x are -1 and -3.On substituting x = -1 and x = -3, we get

y = (x + 1)² / 2 = 0 and y = (-2)² / 2 = 2

Therefore, y = (x + 1)² / 2 is not a solution to the given differential equation.

The solution to differential equation (9) is y =  \(2e^{(x-1)\)). The solution to differential equation (11) is y = (x + 1)² / 2 which is not a solution.

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Answer:

there will only be one 3

Step-by-step explanation:

see cause the first 3 of both numbers are 2 but only the last one of both numbers are 3 .

To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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2+2x3+6=18

That happens nobody answers your question for a period of time, and so it is taken down and you get the points back

Answer:

The answer is 14

Step-by-step explanation:

Also it shows that when no one answers a question of yours.

Answer:

1024 pages left

Step-by-step explanation:

19 pack  * 75 page/pack - 401 page =

Given the topological spaces X = {D, O, R, K} with the topology Tx and Y = {M, A, T, H} with the topology Jy, we are asked to determine whether the set E = {0, K} is open in X and open in Y.

To determine whether the set E = {0, K} is open in the topological spaces X and Y, we need to check if E belongs to the respective topologies, Tx and Ty.

In X, the topology Tx is given by: Tx = {Ø, {0}, {D, O}, {O, R}, {D, O, R}, X}. We can see that E = {0, K} is not explicitly listed in Tx. Therefore, E is not open in X since it does not belong to the topology.

In Y, the topology Ty is given by: Jy = {0, {M}, {M, A}, {M, A, T}, Y}. Again, E = {0, K} is not explicitly listed in Ty. Hence, E is not open in Y as it does not belong to the topology.

In both cases, the set E = {0, K} is not open in the respective topological spaces X and Y because it is not a member of the defined topologies.

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The answers are:

a. population standard deviation σ = 0.1 ounce

b. standard deviation of the sampling distribution sx = 0.0268 ounce.

Given,

Sample size = n = 15

Mean weight = 2 ounces

Standard deviation = s = 0.12 ounces

Population standard deviation = σ = 0.1 ounces

The formula to calculate the standard deviation of the sampling distribution of the sample mean is given as:

σx = σ/√n

Where, σx is the standard deviation of the sampling distribution of the sample mean.

σ is the population standard deviation.

n is the sample size.

Now, substitute the given values in the above formula:

σx = 0.1/√15

σx ≈ 0.0268

So, the standard deviation of the sampling distribution of the sample mean is σx = 0.0268.

Therefore, the answers are:

a. σ = 0.1 ounce

b. σx = 0.0268 ounce.

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The value of angle is 1/2 * mGDE=90° and 1/2 * mEFG=90°.

We are given that;

The quadrilateral DEFG

Now,

Since the sum of the arcs EG and GD is equal to the measure of arc ED, we can write:

arc ED = arc EG + arc GD

mEFG + mGDE = 1/2 * arc EG + 1/2 * arc GD

mEFG + mGDE = 1/2 * (arc EG + arc GD)

mEFG + mGDE = 1/2 * arc ED

Since we know that mEFG + mGDE = 180°, we can substitute this into the equation above:

180° = 1/2 * arc ED

arc ED = 360°

So,

1/2 * mGDE = 1/2 * arc GD = (360° - arc ED)/2 = (360° - 180°)/2 = 90°

1/2 * mEFG = 1/2 * arc EG = (360° - arc ED)/2 = (360° - 180°)/2 = 90°

Therefore, by the quadrilaterals answer will be 1/2 * mGDE=90° and 1/2 * mEFG=90°.

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Answer:

4x-12

Step-by-step explanation:

2x-5[2x-7(5)}=2x+2x-7-5

4x-12

negative integers are added to each other