Pls help me pls I have a test

It can be easily verified that the CDF F(x) derived above satisfies all these properties, and hence it is a valid CDF.

To find the cumulative distribution function (CDF) of the random variable X, we integrate the probability density function (PDF) g(x) over the range (-∞, x].

For x < 0, P(X ≤ x) = 0 because the range of X is 0 ≤ X ≤ 1.

For 0 ≤ x ≤ 1, we have:

P(X ≤ x) = ∫[0,x] g(t) dt

P(X ≤ x) = ∫[0,x] (2 - t) dt

P(X ≤ x) = [2t - (\(t^2\))/2] evaluated from 0 to x

P(X ≤ x) = 2x - \(x^2\)/2

For x > 1, P(X ≤ x) = 1 because the range of X is 0 ≤ X ≤ 1.

Therefore, the CDF of the random variable X is:

F(x) = 0 for x < 0

F(x) = 2x - \(x^2\)/2 for 0 ≤ x ≤ 1

F(x) = 1 for x > 1

To check that this is a valid CDF, we need to verify that it satisfies the following properties:

F(x) is non-negative for all x.

F(x) is non-decreasing for all x.

F(x) approaches 0 as x approaches negative infinity.

F(x) approaches 1 as x approaches positive infinity.

It can be easily verified that the CDF F(x) derived above satisfies all these properties, and hence it is a valid CDF.

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Full Question ;

If the probability density of a random variable is given by x g(x)= {2-X 0 0 < x <1 1<x<2 elsewhere Compute u and o

To maximize its profit, a monopolist would choose option d: q = 30 and p = 60.

To maximize profit, a monopolist would choose the outcome that corresponds to the highest profit level.

Profit is calculated as total revenue minus total cost.

Let's analyze each option:

a. q = 45 and p = 45:

In this case, the monopolist produces a quantity of 45 units and sets the price at $45.

To determine if this is the optimal choice, we need to compare the revenue and cost associated with this outcome with the other options.

b. q = 60 and p = 30:

Here, the monopolist produces a higher quantity of 60 units but sets a lower price of $30.

c. q = 30 and p = 30:

This option represents a lower quantity of 30 units and a price of $30.

d. q = 30 and p = 60:

In this scenario, the monopolist produces a lower quantity of 30 units but sets a higher price of $60.

To determine the optimal outcome, we need to consider the monopolist's cost structure.

Without information about costs, we cannot definitively identify the optimal choice.

The monopolist would consider both revenue and cost implications to maximize profit.

However, we can make some general observations:

Option a (q = 45 and p = 45) and option c (q = 30 and p = 30) result in the same price and may have similar revenue implications.

The choice between these options would depend on the cost structure and profit margins.

Option b (q = 60 and p = 30) could result in higher revenue due to the higher quantity sold, but the lower price may affect profit margins.

Option d (q = 30 and p = 60) may result in higher prices and potentially higher profit margins, but the lower quantity sold may affect revenue.

Ultimately, the monopolist would need to assess the revenue, cost, and profit implications of each option to determine the optimal outcome for maximizing profit.

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The slope of the tangent line to the graph of f(x) = −x² + 4x at x = 4 is 0, and the equation of the tangent line is y = 0.

The slope of a tangent line to a graph of a function is a measure of how steeply the function is increasing or decreasing at a certain point. A tangent line is a line that just touches the graph at a single point and has the same slope as the graph at that point.

Here we need to find the slope of the tangent line to the graph of

=> f(x) = −x² + 4x at x = 4,

we first need to determine the derivative of the function. The derivative of the function gives us the rate of change of the function, which is the slope of the tangent line.

Here The derivative of f(x) = −x² + 4x is given by

=> f'(x) = −2x + 4.

Now we have to find the slope of the tangent line at x = 4, we evaluate the derivative at x = 4:

=> f'(4) = −2 * 4 + 4 = 0.

So, the slope of the tangent line at x = 4 is 0.

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Answer:

616.788

   OR

616.79 (rounded answer)

Step-by-step explanation:

Answer:

616.78891

Step-by-step explanation:

1 liter is 1.05669 quarts

Good luck!

The value of the fractions is 10.

We know,

A fraction is described as the part of a whole.

The different types of fractions are;

Here, we have,

Given the fractions;

3 1/4 + 2 1/8 +2 7/8+1 3/4

convert to improper fractions, we have;

13/4 + 17/8 + 23/8 + 7/4

Find the LCM

26 + 17 + 23 + 14 /8

Find the values

80/8

divide the values

10

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complete  question:

What is the answer 3 1/4 + 2 1/8 +2 7/8+1 3/4+1 3/4 +? Show the work

Answer: B. Additive Inverse

Answer:

1) C

Step-by-step explanation:

Step 1)

First we have to plot ↓

2x ≥ y + 2

And that looks like Image 1

Step 2)

Second we have to plot ↓

2x - 5y ≤ 10

and that looks like Image 2

a. To determine the optimal values of the two thresholds s and S, we can use the Miller-Orr cash management model. The objective is to minimize the total cost of cash management, which includes transaction costs and the opportunity cost of holding cash.

Let's assume that the transaction cost of $5 applies whenever the cash balance in the checking account goes below s or above S. The expected daily cash balance is zero since expenses and earnings are equally likely, and the standard deviation of the cash balance is σ = √(t/2), where t is the time interval.

The optimal value of s is given by:

s* = √(3rT/4C) - σ/2,

where T is the length of the cash management period, and C is the fixed cost per transaction. The optimal value of S is given by:

S* = 3s*,

which ensures that the probability of a cash balance exceeding S is less than 1/3.

Using r = 0.1, T = 1 day, and C = $5, we obtain:

s* = √(30.11/4*5) - √(1/2)/2 = $16.82

S* = 3*$16.82 = $50.47

Therefore, the optimal values of the two thresholds are s* = $16.82 and S* = $50.47.

b. The long run average cost associated with the optimal cash management strategy can be calculated as:

Total cost = (s*/2 + S*) * σ * √(2r/C) + C * E(N),

where E(N) is the expected number of transactions per day. Since expenses and earnings are equally likely, E(N) = (S* - s*)/2 = $16.83. Therefore, the total cost is:

Total cost = ($16.82/2 + $50.47) * √(1/2) * √(2*0.1/$5) + $5 * $16.83 = $1.38 per day.

Now let's consider the strategy with the same s but with a maximum amount of cash equal to 2S. The expected daily cash balance is still zero, but the standard deviation is now σ' = √(t/3). The optimal value of S' is given by:

S' = √(3rT/2C) - σ'/2 = $35.35.

The long run average cost associated with this strategy is:

Total cost' = (s/2 + S') * σ' * √(2r/C) + C * E(N'),

where E(N') is the expected number of transactions per day. Since the maximum amount of cash is now 2S, we have E(N') = (2S - s)/2 = $34.59. Therefore, the total cost is:

Total cost' = ($16.82/2 + $35.35) * √(1/3) * √(2*0.1/$5) + $5 * $34.59 = $1.30 per day.

Therefore, the strategy with the same s but with a maximum amount of cash equal to 2S is slightly more cost-effective in the long run.

c. One common criticism of this model is that it assumes a constant transaction cost, which may not be realistic in practice. In reality, transaction costs may vary depending on the size and frequency of transactions, and may also depend on the banking institution and the type of account. Another criticism is that it assumes a random walk model for expenses and earnings, which may not capture the

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Answer:

seek the attachment

Step-by-step explanation:

comment if you have questions

Answer:

Explanation:

Let the speed of the first person be x mph and the speed of the second person be y mph

Since one person's speed is faster than the other, we can have:

Mathematically, distance equals the product of speed and time

The time traveled by each person is 1.5 hours

The distance traveled by each of them is:

The sum of the two equals 18 miles

Thus:

Recall;

This means that the first person was walking 5 mph while the second was walking 7 mph

Answer: The variable x represents the independent variable.

Step-by-step explanation:

Answer:

The variable x represents the independent variable.

Step-by-step explanation:

Just answered in on Edge it's correct.

The length of the kite's line can be determined using the concept of similar triangles. By setting up a proportion between the length of the kite's line and its shadow, we can solve for the unknown length.

Let's denote the length of the kite's line as "x." We can form a proportion between the lengths of the kite's line and its shadow:

(line length)/(shadow length) = (height)/(shadow height)

Plugging in the given values, we have:

x/6 = 9/9

Simplifying the equation, we find:

x = 6

Therefore, the length of the kite's line is 6 feet.

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Answer:

The weight in kilograms of a 150 pound person is 68.039 kg

Step-by-step explanation:

Weight = 150 pounds.

We need to convert this to kg,

Now, 1 pound = 0.453592 kg.

Then, 150 pounds will be,

150 pounds = 150(0.453592) kg

So, 150 pounds = 68.039 kg

The weight of a 150 pound person is approximately 68.04 kilograms.

To convert the weight of a person from pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms.

Given that the person weighs 150 pounds, we can multiply this value by the conversion factor to find the weight in kilograms:

Weight in kilograms = 150 pounds * 0.4536 kilograms/pound

Weight in kilograms = 68.04 kilograms

Therefore, the weight of a 150 pound person is approximately 68.04 kilograms.

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The heights of the bars of a histogram corresponding to frequency values.

This is further explained below.

Generally, The number of instances of a recurring event that takes place in a certain amount of time is referred to as its frequency.

When compared to spatial frequency, it is sometimes referred to as temporal frequency, and when compared to angular frequency, it is sometimes referred to as ordinary frequency.

Both of these names stress the difference between the two types of frequency.

In conclusion, The heights of the individual bars in a histogram correspond to the frequency values being shown.

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Main Answer: Let X=a/b and y=c/d. Then, X*y = (a/b)*(c/d) = (ac)/(bd)

Explanation: Given X = a/b and y = c/d, we are to find the product of two rational numbers, X and Y. Using the definition of multiplication, we have: X * y = a/b * c/d. We can simplify this expression by multiplying the numerators together and the denominators together, as follows: X * y = ac/bd. Hence, the product of two rational numbers X and Y is given by (ac)/(bd).

In mathematics, any number that can be written as p/q where q 0 is considered a rational number. Additionally, every fraction that has an integer denominator and numerator and a denominator that is not zero falls into the category of rational numbers. The outcome of dividing a rational number, or fraction, will be a decimal number, either a terminating decimal or a repeating decimal.

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Answer:

The ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

Step-by-step explanation:

How to determine ordered pair?

To determine if an ordered pair is a solution to two systems of equations, substitute the values ​​of the variables into each equation. If an ordered pair makes both equations true, it is the solution of the system.

To find the ordered pair solutions for the system of equations, we need to solve the two equations simultaneously.

f(x) = x² + 1 ...(1)

f(x) = -x + 3 ...(2)

Setting the two equations equal to each other, we get:

x² + 1 = -x + 3

Rearranging this equation, we get:

x² + x - 2 = 0

Factoring this quadratic equation, we get:

(x + 2)(x - 1) = 0

Therefore, the solutions for x are x = -2 and x = 1.

Substituting these values of x into either equation (1) or (2), we get:

For x = -2: f(-2) = (-2)² + 1 = 5, and f(-2) = -(-2) + 3 = 5.

For x = 1: f(1) = 1² + 1 = 2, and f(1) = -1 + 3 = 2.

Therefore, the ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

In step 2, she didn’t use an x and y from the same coordinate pair

We can easily understand by the attachment of the question:

From the figure,

We have to find the slope

We know that, The formula of slope is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

The formula to calculate the slope between two points and substitute the values:

\(m=\frac{5-1}{3-5}\)

m = 4/-2

m = -2

The equation of the line in point slope form is:

\(y_2-y_1=m(x_2-x_1)\)

Take the point (3,5)

m = -2

y - 5 = -2(x - 3)

y - 5 = -2x + 6

y = -2x + 6 + 5

y = -2x + 11

Therefore,  In step 2, she didn’t use an x and y from the same coordinate pair.

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The complete question is:

Helena wrote the equation using point-slope form for the line that passes through the points (5, 1) and (3, 5). Analyze the steps of her work using the point-slope form to write the equation. equation In which step did Helena make an error? In step 1, she substituted the x values for y and the y values for x. In step 2, she didn’t use an x and y from the same coordinate pair. In step 3, she solved for the wrong variable. Helena did not make an error.

The two solutions for A that satisfy the given equation are A = 60 degrees and A = 300 degrees.

To solve for A, we can start by rearranging the equation to isolate sin^4A:

sin^4A = sin^3A - sin^2A - cosA

Next, we can use the identity sin^2A + cos^2A = 1 to substitute cosA:

sin^4A = sin^3A - sin^2A - (1 - sin^2A)

Simplifying, we get:

sin^4A = sin^3A - 2sin^2A + 1

Now we can use the fact that sin^2A = 1 - cos^2A to substitute sin^2A:

sin^4A = sin^3A - 2(1 - cos^2A) + 1

Expanding and simplifying, we get:

sin^4A = sin^3A - 2 + 2cos^2A

Next, we can use the identity sin^2A + cos^2A = 1 to substitute 1 - sin^2A for cos^2A:

sin^4A = sin^3A - 2 + 2(1 - sin^2A)

Simplifying, we get:

sin^4A = -sin^4A + sin^3A + 2

Adding sin^4A to both sides, we get:

2sin^4A = sin^3A + 2

Dividing both sides by 2sin^3A, we get:

sinA/2 = 1/2 or sinA/2 = -1

Solving for A, we get:

A = 60 degrees or A = 300 degrees

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Answer:

the answer for just eliminate the variables and to the solving tho get the answer as they get the answer to the number above

Answer:

x=3, y=1

x=3, y=2

Hope this helps!

The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.

Statistical analysis is the method of using statistical techniques to collect and analyze data, evaluate its reliability and determine its statistical significance. The following are the primary purposes of statistical analysis:Provide summaries and descriptions of data: One of the most important applications of statistical analysis is to present data in a clear and concise manner. Summarizing the data can assist people in making sense of the data and drawing inferences from it.

For example, data can be summarized using graphs, charts, or tables. Identify patterns and relationships: The goal of statistical analysis is to identify any patterns or relationships that exist within the data. For example, statistical analysis can be used to determine if a product's sales are correlated with a specific time of year.

Test hypotheses and draw conclusions: Statistical analysis is used to test hypotheses and draw conclusions about a population or phenomenon. This is accomplished by using statistical techniques to determine whether or not the data supports a particular hypothesis. Statistical analysis can also be used to determine the probability of an event occurring in the future.

The primary purpose of statistical analysis is to transform information into data. Therefore, the correct option is a)transform information into data.

The complete question is as follows:

The primary purpose of statistical analysis is to:

a)transform information into data.
b)select samples and make inferences about populations
c)convert data into useful desicion-making information
d)perform statistical computations

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Answer:

11

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the point on the line y = 2x + 3 that is closest to the origin (0,0), we can use the concept of the shortest distance between a point and a line.

The line y = 2x + 3 can be rewritten as 2x - y + 3 = 0 in standard form. The distance between a point (x, y) and the line can be calculated using the formula:

distance = |Ax + By + C| / √(A² + B²)

In this case, A = 2, B = -1**, and **C = 3. Plugging these values into the formula, we can calculate the distance between the origin and the line.

The point on the line that is closest to the origin is the one where the distance is minimized. By finding the point that satisfies the minimum distance condition, we can determine the coordinates of the point.

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we can conclude that yes, the function is periodic with period T =  π/2

A function is periodic if for any input X, there exists a value T (where T is the period) such that:

f(x) = f(x + T).

In this particular case, we are told that the period should be π/2, so let's check that.

We can see that:

f(π/4) = 1.2

If we add the period to the argument, we get:

π/4 + π/2 = π/4 + 2π/4 = 3π/4

Now, on the table we can see that:

f(π/4 +π/2 ) = f(3π/4) = 1.2

So at the moment, it seems to be periodic.

Let's try another point.

f(3π/2) = 0.6

If we add the period:

3π/2 + π/2 = 2π

And in the table we can see that:

f( 2π) = 0.6

So we can conclude that yes, the function is periodic with period T =  π/2

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Answer:

it's 9

Step-by-step explanation:

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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Answer:

a

Step-by-step explanation:

since x = 4, then the graph would be an vertical line at x = 4. Hence at intercept on x axis, y is 0 and x = 4.

Answer:

x = 13

Step-by-step explanation:

7x/7 = 91/7

cancel the common factor of 7

cancel the common factor

7x/7 = 91/7

divide x by 1

x = 91/7

simplify the right side

divide 91 by 7

x = 13