The variance Var[X] is -3/x + C.
To find the variance of a random variable X with a given density function, we need to evaluate the integral of [tex]x^{2}[/tex] multiplied by the density function f(x) over the entire support of X.
Given the density function f(x) = 3/[tex]x^{4}[/tex] for x > 1, we can calculate the variance as follows:
Var[X] = ∫([tex]x^{2}[/tex] * f(x)) dx
Using the given density function, we substitute it into the integral:
Var[X] = ∫([tex]x^{2}[/tex] * (3/[tex]x^{4}[/tex])) dx
= ∫(3/[tex]x^{2}[/tex] ) dx
Now, we can integrate the expression:
Var[X] = 3 * ∫(1/[tex]x^{2}[/tex] ) dx
The integral of 1/[tex]x^{2}[/tex] is given by:
∫(1/[tex]x^{2}[/tex] ) dx = -1/x
So, substituting the integral back into the variance equation:
Var[X] = 3 * (-1/x) + C
Since we don't have specific limits of integration provided, we will leave the result in general form with the constant of integration (C).
Therefore, the variance of the random variable X is given by:
Var[X] = -3/x + C
Note that the variance may be expressed differently depending on the context and specific requirements of the problem.
Correct Question :
Suppose a random variable X has the following density function: f(x) = 3/[tex]x^{4}[/tex] where x > 1. Find Var[X].
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after preparing a horizontal analysis of Blanchet
corporations balance sheet for 2019, what are some observations you
can make?
Overall, the horizontal analysis of Blanchet Corporation's balance sheet for 2019 suggests positive growth and financial stability.
There has been a significant increase in total assets from the previous year. This indicates potential growth and expansion in the company's operations.
The liabilities have also increased, but not at the same rate as the assets. This suggests that the company may have taken on additional debt or financing to support its growth.
The retained earnings have shown a positive trend, indicating that the company has been profitable and able to retain a portion of its earnings for reinvestment or future use.
The equity section has also grown, which can be attributed to the increase in retained earnings and potentially additional capital investments.
The increase in assets and retained earnings indicates the company's ability to generate profits and reinvest in its operations. However, the increase in liabilities should be carefully monitored to ensure it is manageable and sustainable in the long term.
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The following code is intended to solve the system of equations but contains errors. What are the errors and so determine the intended output? 3x, +2x2 - *= 10 >> A - 1 3 2 -1; 1 3.2; 1 -1]; --*+ 3x2 + 2xy = 5 >> b = [ 10; 5; -1]: *1-*3 = -1 >> X = A//b Errors Intended MATLAB Output Question 7. The word 'SMILE' can be coded as a column vector by using the relevant numbers for its place in the alphabet (E = 5). The word can then be encrypted using matrix multiplication on the left by A. 3 3 0 30 -30 --2 0 0 0 1 0 0 -3 0 0 0 33 lo-1 2 0 1 (1) What is the column vector of the encrypted word 'SMILE'? 120 -21 (1) What word was encrypted as -63 ? (Don't do it by hand, life's too short.)
The given code contains multiple errors, including syntax errors and incorrect variable assignments. Consequently, it would not produce the intended output.
The intended code is meant to solve a system of equations. However, it contains errors that hinder its functionality. These errors include syntax mistakes and incorrect variable assignments. Let's break down the code to understand the issues and determine the intended output.
In the first part of the code, the matrix A is incorrectly defined. The commas are placed before the plus sign, resulting in a syntax error. Additionally, the second element in the matrix should be 2x^2, but it is not written correctly. The code also uses the *= operator, which is not a valid mathematical operation.
Moving on to the second equation, the matrix b is defined correctly. However, the code uses colons instead of semicolons to separate the elements.
Next, the line "*1-*3 = -1" suggests some arithmetic operation, but it is not written correctly and lacks clarity.
Finally, the code attempts to solve the system of equations by assigning X to the result of A divided by b using the "//" operator, which is not a valid operation for matrix division in MATLAB.
Due to these errors, the code would generate error messages and fail to produce the intended output.
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Let f and g be functions from the positive integers to the positive integers defined by the equation
f(n)= 2n+1 g(n)=3n-1
f∘f
g∘g
f∘g
g∘f
the compositions are:
f∘f: 4n + 3
g∘g: 9n - 4
f∘g: 6n - 1
g∘f: 6n + 2
To find the compositions f∘f, g∘g, f∘g, and g∘f, we substitute the function expressions into the compositions:
1. f∘f:
(f∘f)(n) = f(f(n))
= f(2n+1)
= 2(2n+1) + 1
= 4n + 2 + 1
= 4n + 3
So, (f∘f)(n) = 4n + 3.
2. g∘g:
(g∘g)(n) = g(g(n))
= g(3n-1)
= 3(3n-1) - 1
= 9n - 3 - 1
= 9n - 4
So, (g∘g)(n) = 9n - 4.
3. f∘g:
(f∘g)(n) = f(g(n))
= f(3n-1)
= 2(3n-1) + 1
= 6n - 2 + 1
= 6n - 1
So, (f∘g)(n) = 6n - 1.
4. g∘f:
(g∘f)(n) = g(f(n))
= g(2n+1)
= 3(2n+1) - 1
= 6n + 3 - 1
= 6n + 2
So, (g∘f)(n) = 6n + 2.
Therefore, the compositions are:
- f∘f: 4n + 3
- g∘g: 9n - 4
- f∘g: 6n - 1
- g∘f: 6n + 2
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A fcompany has a constant 306200 shares during the fiscal year. At the beginning of the year it has an equity of $4699902 in their balance sheet, and during the year, as indicated by the income statement, it has a net income $399786 and pays out $297789 in dividends. What will be its book value per share at the end of the fiscal year? Answer to two places.
The book value per share at the end of the fiscal year will be approximately $15.35.
To calculate the book value per share, we need to divide the equity at the end of the fiscal year by the number of shares outstanding. Let's break down the calculation:
The number of shares outstanding: The company has a constant 306,200 shares during the fiscal year.
Equity at the beginning of the year: The balance sheet shows an equity of $4,699,902 at the beginning of the year.
Net income: The income statement indicates a net income of $399,786.
Dividends paid: The company pays out $297,789 in dividends.
To find the equity at the end of the fiscal year, we need to add the net income and subtract the dividends paid from the equity at the beginning of the year:
Equity at the end of the fiscal year = Equity at the beginning of the year + Net income - Dividends paid
= $4,699,902 + $399,786 - $297,789
= $4,801,899
Finally, to calculate the book value per share, we divide the equity at the end of the fiscal year by the number of shares outstanding:
Book value per share = Equity at the end of the fiscal year / Number of shares outstanding
= $4,801,899 / 306,200
≈ $15.65 (rounded to two decimal places)
Therefore, the book value per share at the end of the fiscal year will be approximately $15.35.
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A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle. The python is
2.6
π
2.6π2, point, 6, pi meters long.
What is the radius
r
rr of the circle that the python forms?
Answer: 1.3
Step-by-step explanation:
The radius of the circle that python forms is 1.3 meters.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Given that,
Length of python = 2.6π meters
The length of the python forms the circumference of the circle after curling.
Circumference of a circle = 2π r, where r is the radius.
2π r = 2.6π
2r = 2.6
r = 2.6 / 2
r = 1.3
Hence 1.3 meters is the radius of the circle.
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help me out? :)
don't guess, if u dont know just dont answer. NO LINKS.
Answer:
A cube
Step-by-step explanation:
If you fold it, you'll see
The sales budget for Modesto Corp. shows that 20,000 units of Product A and 22,000 units of Product B are going to be sold for prices of $10 and $12, respectively. The desired ending inventory of Product A is 20% higher than its beginning inventory of 2,000 units. The beginning inventory of Product B is 2,500 units. The desired ending inventory of Product B is 3,000 units. Budgeted purchases of Product B for the year would be:
Multiple Choice
24,500 units.
22,500 units.
16,500 units.
26,500 units.
20,500 units.
Answer:
22500 units
Step-by-step explanation:
Ending inventory =. 3000
Beginning inventory = 2500
Good sold = 22000
Beginning inventory + budgeted purchases - goods sold = ending inventory
2500 + x - 22000 = 3000
2500 + x = 3000 + 22000
2500 + x = 25000
x =25000 - 2500
x = 22500 units
Budgeted purchases of product for the year.
List the factor pairs of ac for the trinomial 12x^2-5x-2.
Answer:
(3x - 2) (4x + 1)
Step-by-step explanation:
12x² - 5x - 2
Since the first term has a coefficient, you need to multiply -2 with 12 to get -24.
Two factors that add up to -5 and have a product of -24 are -8 and 3.
12x² - 8x + 3x - 2
Rearrange the expression to find the GCF.
12x² + 3x - 8x - 2
3x (4x + 1) + (-1)2(-4x -1)
3x (4x + 1) - 2 (4x + 1)
(3x - 2) (4x + 1)
Michelle ordered 200 T-shirts to sell at the school carnival. She paid $2.80 per shirt, plus 5% of the total
order for shipping. When she sells each T-shirt at the carnival, she adds a 150% markup to the total price
she paid for the shirt (including the cost of shipping).
For what price does she sell each T-shirt?
Answer:
$7.35
Step-by-step explanation:
We have 200 shirts
Cost $2.80 each
plus a 5% charge for shipping.
Selling price
150% markup
Recall when we use percentages, we need to express them as decimals.
Michelle's cost for each shirt was
2.80 (1.05) = 2.94
The markup is
2.94 (1.50) = 4.41
The markup is added to the cost to get the final selling price.
2.94 + 4.41 = $7.35
Michelle will sell each shirt for $7.35
78.75 is what percent of 225?
Answer:
35%
Step-by-step explanation:
1. Multiply 78.75 by 100
78.75* 100 = 7875
2. Divide this by 225
7875/225 = 35
3. Make this number a precent 35%
Find the optimum solution and draw the graph
Maximise Z= x + y, subject to x - y S-1, -x + y = 0, x,
The optimum solution for the maximization problem is Z = 0 at the point (0, 0). The graph of the feasible region consists of the line y = x and the shaded region above the line y = x - 1.
To compute the optimum solution and draw the graph for the maximization problem:
Maximize Z = x + y
Subject to the constraints:
x - y ≤ 1
-x + y = 0
x, y ≥ 0
First, let's plot the feasible region by graphing the constraints on a coordinate plane.
For the constraint x - y ≤ 1, we can rewrite it as y ≥ x - 1. This represents a boundary line with a slope of 1 and a y-intercept of -1. Shade the region above this line to satisfy the constraint.
For the constraint -x + y = 0, rewrite it as y = x. This represents a line passing through the origin with a slope of 1. Plot this line.
Next, plot the x and y axes and shade the feasible region that satisfies both constraints.
To compute the optimum solution, we need to evaluate the objective function Z = x + y at the corner points (vertices) of the feasible region.
The corner points can be identified by the intersection of the lines and the feasible region boundaries. In this case, there is only one corner point, which is the intersection of the lines y = x and y = x - 1. Solving these equations simultaneously gives x = 0 and y = 0.
Thus, the optimum solution occurs at the corner point (0, 0), where Z = 0 + 0 = 0.
Therefore, the optimum solution is Z = 0 at the point (0, 0).
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PLEASE HELP AND SHOW AN EXPLANATION ITS DUE IN 30 MINUTES!! Donna wants to create a stained glass window composed of one quarter circle, two semicircles, and one parallelogram. Which measurement is closest to the amount of stained glass in square inches Donna will
need to create the window?
What is the area of a circle whose diameter is 102
Answer:
area = 8167.14 units ²
Step-by-step explanation:
area = πr²
r = 102/2 = 51
area = (3.14)(51²) = 8167.14 units ²
A population grows according to an exponential growth model, with an initial population of 3,120 and a population of 3,790 after 6 years. Complete the formula, where P is the population and n is the number of years: P=3,120*(_)
Answer : The value of the missing term is (1+0.2147)^6≈ 150.
Explanation :
A population grows according to an exponential growth model, with an initial population of 3,120 and a population of 3,790 after 6 years.
The formula where P is the population and n is the number of years is given by the expression:
P = 3120*(1+r)^n where r is the growth rate and n is the number of years. For the given problem, the initial population, P₀ is given as 3,120 and the population after 6 years is given as 3,790. So, the population increased by 3,790 - 3,120 = 670 people in 6 years. Using this data, we can calculate the growth rate, r using the following formula: r = (P - P₀)/P₀n=6P = P₀*(1+r)^n Where P₀ = 3,120 and P = 3,790,r = (P - P₀)/P₀ = (3,790 - 3,120)/3,120 = 670/3,120 ≈ 0.2147 P = 3,120*(1+0.2147)^6 ≈ 150 * 3,120
Therefore, the value of the missing term is (1+0.2147)^6 ≈ 150.
Answer: (1+0.2147)^6.
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in the xy-plane, which of the following is an equation of a vertical asymptote to the graph Of y=sec(6x-pi)? (A) x=pi/6 (B) x=pi/4 (C) x=pi/3 (D)=x=pi/2 (E) x=pi
The equation of a vertical asymptote to the graph of y = sec(6x - π) is x = π/6. Hence, option a is correct.
The function y = sec(6x - π) has vertical asymptotes at the values of x where the denominator of sec(6x - π) becomes zero. The reciprocal of sec(θ) is cos(θ). Because the cosine function has the values π/2, 3π/2, 5π/2, we will insert such an input that we get 0 in denominator.
6x - π = π/2
Solving for x,
6x = π/2 + π
6x = 3π/2
x = (3π/2) / 6
x = π/6
Therefore, the equation of a vertical asymptote to the graph of y = sec(6x - π) is x = π/6.
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Project (Matlab ): Spline interpolation In this project, you must write a code that performs a cubic spline interpolation on any given set of data points (2o, yo), (21, 31), (Xn, Yn).
The following Python code demonstrates how to perform cubic spline interpolation using the scipy library
How to depict the codeimport numpy as np
from scipy.interpolate import CubicSpline
# Define the data points
x = np.array([20, 21, ...]) # X coordinates of the data points
y = np.array([y0, 31, ...]) # Y coordinates of the data points
# Create the cubic spline interpolation
cs = CubicSpline(x, y)
# Generate interpolated values
x_interpolated = np.linspace(x[0], x[-1], num=100) # Adjust 'num' for desired number of interpolated points
y_interpolated = cs(x_interpolated)
# Print interpolated values
for i in range(len(x_interpolated)):
print(f"({x_interpolated[i]:.2f}, {y_interpolated[i]:.2f})")
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A line segment drawn between points B and C on a circle forms its diameter. Point A is taken arbitrarily on the circumference of the circle, and line segments are drawn from A to B and A to C. Classify ∠BAC.(1 point)
acute angle
obtuse angle
straight angle
right angle
Answer:
Option D
A right angle
Step-by-step explanation:
in circle geometry, we have several theorems that govern angles formed by chords drawn in circles.
One of the theorems states that the angle subtended on the circumference of a circle by a chord which is drawn across the center of the circle (which is the diameter) equals 90 degrees. This means that it is a right-angle.
Analytically, we can also sketch out the problem and see that we can divide the shape formed by points BAC into an isosceles triangle. (The two radii forming the sides while the diameter forms the base). We can also run a bisector of the isosceles triangle through point A to meet the diameter. We can see that it forms two 45 by 45 degree right-angled triangles. Thus proving that angle BAC is indeed a right angle.
PLEASE HELP
A company makes two different size ice cream cones The small accounts are 3.5 inches tall and have a diameter of 3 inches The large cones are5.1 inches tall and have a diameter of 4.5 inches about how much greater to the nearest 10th of Cubic inch is the volume The larger cone than the smaller cone 
Answer:
19.545
Step-by-step explanation:
please do it in 30 minutes please urgently... I'll
give you up thumb definitely
please do B part only
(b) Show that cov(ra, rt) = 10²e-(s+t) (e²s 1). Deduce that var(r) = 10²(1-e-2¹).
9. The Vasicek term structure model for the short interest rate, r₁, follows the stochastic differential equation dre (ar)dt+odB, where a and are constants and B, is a standard Brownian motion.
In the Vasicek term structure model, the covariance between ra and rt is given by cov(ra, rt) = 10²e-(s+t) (e²s 1). From this, we can deduce that the variance of r is var(r) = 10²(1-e-2¹).
In the Vasicek term structure model, the short interest rate, r₁, follows the stochastic differential equation:
dr₁ = a(b - r₁)dt + σdW
where a and b are constants, σ is the volatility parameter, and dW is a standard Brownian motion.
To find the covariance between rₐ and rₜ, we use the covariance formula for the stochastic differentials equation:
cov(dr₁, drₜ) = cov(a(b - r₁)dt + σdW, a(b - rₜ)dt + σdW)
Since the covariance between the Brownian motion terms is zero, we only need to consider the covariance between the drift terms:
cov(a(b - r₁)dt, a(b - rₜ)dt) = a²(b - r₁)(b - rₜ)dt²
Integrating this expression over the time interval [0, s+t], we obtain:
cov(ra, rt) = a²(b - ra)(b - rt)∫[0,s+t] dt = a²(b - ra)(b - rt)(s + t)
Given cov(ra, rt) = 10²e-(s+t) (e²s - 1), we can equate the expressions and solve for a²(b - ra)(b - rt):
10²e-(s+t) (e²s - 1) = a²(b - ra)(b - rt)(s + t)
Simplifying the equation, we have:
(b - ra)(b - rt) = 10²e-(s+t) (e²s - 1)/(a²(s + t))
From this equation, we can see that the covariance depends on the values of b, ra, rt, s, t, and a.
To deduce the variance of r, we set t = s in the above equation:
(b - ra)(b - ra) = 10²e-2s (e²s - 1)/(a²(2s))
Simplifying further, we obtain:
var(r) = (b - ra)² = 10²(1 - e-2s)/a²
Hence, the variance of r is given by var(r) = 10²(1 - e-2s)/a².
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30^2 + 15^2 = c^2
Use pythagorean theorem
Answer:
c = 33.5
Step-by-step explanation:
[tex]30^{2} + 15^{2} = c^{2}[/tex]
[tex]900 + 225 = c^{2}[/tex]
[tex]1125 = c^{2}[/tex]
(find square root of both sides to get c alone)
[tex]c = 33.541[/tex]
5x + 1 = 6x - 8 x= como puedo resolverla
Answer:
X = 9
Step-by-step explanation:
What is the area?
____ Square millimeters
Answer: 210 mm²
Step-by-step explanation:
A = 1/2(long base + short base) x height
A = 1/2(18 + 10)(15)
A = 1/2(28)(15)
A = 210 mm²
nicole wants to conduct a survey of the opinions of students at her middle school. which survey sample would give her the most accurate results?
Answer:
Step-by-step explanation:
Solution
The sample must be selected at random.
Solve the following quadratic equation for all values of xx in simplest form. 3(x+1)²-15=-12
Answer:
x = 0, -2
Step-by-step explanation:
An investor who earns $65,000 from employment and saves 4.5 percent from his total income would have increased her net worth in one year by O a. $2925. O b. $0. O C. $3000. O d. $2900.
To calculate the increase in net worth from the savings, we need to find 4.5% of the total income earned.
Total income earned = $65,000
To determine the increase in net worth from savings, we calculate 4.5% of the total income. Multiplying $65,000 by 4.5% gives us $2,925.
Savings = 4.5% of $65,000
[tex]=0.045*$65,000\\=$2,925[/tex]
This represents the amount saved by the investor over the course of one year. Therefore, the investor's net worth would have increased by $2,925. This amount reflects the portion of income saved and not spent, contributing to the overall growth of the investor's financial position.
Therefore, the investor would have increased her net worth by $2,925 in one year.
The correct answer is A. $2,925.
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1. In which number does the 6 have a value that is one-tenth the value of the 6 In 34,7612
A 16,305
B. 28,695
C. 51,364
D. 78,426
Answer:
ok
Step-by-step explanation:
GIVING BRAINIEST!!
Which equation represents: "72% of what number is 64"
64 = 0.72 (x)
x = 7.2 (64)
64 = 7.2 (x)
x = .72 (64)
Answer:
64 = 0.72 (x)
Step-by-step explanation:
Answer: 64 = 0.72 (x)
Step-by-step explanation:
In ΔSTU, the measure of ∠U=90°, UT = 12, SU = 35, and TS = 37. What ratio represents the secant of ∠T?
Answer: hi
Step-by-step explanation:
look at hers
Answer:
secT=
adjacent
hypotenuse
=
12
37
Step-by-step explanation:
use multiples to determine the LCM of 45and 60
Answer:
LCM of 45 and 60: 180
Step-by-step explanation:
plzzz helllp i need it done in 20 mins
Answer: C
Step-by-step explanation: calculate the decimal and put it into the calculator to get the fraction
Step-by-step explanation:
[tex] {10}^{ - 3} \\ = \frac{1}{10 \times 10 \times 10} \\ = \frac{1}{1000} \: or \: 0.001[/tex]
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