Consider three random variables, U, V, and W. Suppose we know that U = 3V+2 and U = 5W – 23. If E(V) = -5, evaluate E(W). OA-13 13 OB- OC.-3 36 OD 5 O E 2
Answers
Consider three random variables, U, V, and W. The answer is E(W) = 2.
To solve for E(W), we need to use the fact that U is equal to both 3V+2 and 5W-23. We can set these two expressions equal to each other:
3V + 2 = 5W - 23
Solving for V in terms of W, we get:
V = (5W - 25) / 3
Now we can use the formula for the expected value of a linear function of a random variable:
E(aX + b) = aE(X) + b
In this case, we have:
V = (5W - 25) / 3
So:
E(V) = E((5W - 25) / 3) = (5/3)E(W) - 25/3
We know that E(V) = -5, so we can substitute that in:
-5 = (5/3)E(W) - 25/3
Solving for E(W), we get:
E(W) = (-5 + 25/3) / (5/3) = 2
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Related Questions
Let f be the function defined by f(x)=xlnx for x>0. On what open interval is f decreasing?
Answers
The function f(x) = xlnx is decreasing on the open interval (0, e^-1).
To find the interval on which the function f(x) = xlnx is decreasing, we need to find the intervals where the first derivative f'(x) is negative.
Using the product rule of differentiation, we can find the first derivative of f(x) as
f'(x) = x × (1/x) + ln(x) × 1 = 1 + ln(x)
Now, we need to find the values of x where f'(x) < 0
1 + ln(x) < 0
ln(x) < -1
x < e^-1
Therefore, f(x) is decreasing on the interval (0, e^-1).
Note that we exclude x = 0 from the interval because the function is not defined for x ≤ 0.
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25 points !! Please help me! What’s the volume to this question? Urgent !
Answers
Answer:
381 in^3
Step-by-step explanation:
The volume of the green block is V1 = length(width)(height), or
V1 = (16 in)(7 in)(3 in) = 336 in^3, and
the volume of the red triangular prism is V2 = (1/2)(3 in)(5 in)(6 in) =
V2 = 45 in^3
So the total volume is the sum of these two results: 381 in^3
Find the values of x (there are two) when the ratio of the area of the shaded portion of the figure to the total area of the figure is 15.75/48.
Hint: First, set up a ratio between the areas of the two triangles. Remember that the area of a triangle is calculated by: A=1/2bh
Answers
Step-by-step explanation:
the hint they give you is right, if you follow that you'll get
shaded area= (x+0.5)(x+1.5)/2
shaded area= (x²+2x+0.75)/2
shaded area= ½x² + x + 0.375
total area= (2x)(x+5)/2
total area= x² + 5x
since the ratio
\( \frac{shaded \: area}{total \: area} = \frac{15.75}{48} = \frac{0.5 {x}^{2} + x + 0.375}{ {x}^{2} + 5x} \)
rearranging the terms you'll get
(15.75)(x²+5x)=(0.5x²+x+0.375)(48)
15.75x²+78.75x = 24x²+48x+18
-8.25x²+30.75x-18=0
using the quadratic formula you'll get the values
x1=3
x2=0.727
Evaluate |2 5/6 +y| for y= 7/4
Answers
Answer:
Step-by-step explanation:
Quadrilateral ABCD has coordinated A(-4,3)B(-3,6)C(0,8)D(-2,5). Prove that quadrilateral ABCD is a parallelogram.
Answers
Answer:
The plotted dots connect to create a parallelogram with two sets of parallel lines in the second quadrant
Step-by-step explanation:
This might be a little tricky to explain but I will try my best.
A parallelogram is a four-sided plane rectilinear figure with opposite sides parallel.
The first pair of numbers is in the second quadrant the second set is also in the second quadrant a little bit up and to the right. The third set in the line a little up, the last set is again in the second quadrant and a little further down and near the middle.
Sorry if the answer isn't what you had hoped for, feel free to ask questions about it and I'll explain the best I can.
Choose the congruency statement that indicates that both quadrilaterals are congruent
Answers
Answer:
Step-by-step explanation:
The second one
6,10,14,...
Find the 30th term.
Answers
Answer:
6,10,14,...
Find the 30th term.
18,22,26,30
Explanation:
+4 each time?
1. Suppose that the equilibrium income, Y₁, in an economy is 800,000,000 pesos, and that the slope of the planned expenditure (PE) function given below is 2/8. PE=C(Y-T) +I+G Suppose further that the government of the said economy increases its purchases by 2,000 pesos. Using the Keynesian cross model, a. [5 points] determine the value of the new equilibrium income, Y₂, given the increase in government purchases b. [10 points] using a graph, clearly show and explain the difference/s between the change in government purchases, AG, and the change in equilibrium income AY Y₂ - Y₁. =
Answers
a. The new equilibrium income, Y₂, given the increase in government purchases, can be determined by calculating the change in autonomous expenditure (AG) and multiplying it by the multiplier.
b. The graph will show the initial aggregate expenditure (AE₁) and the new aggregate expenditure (AE₂) after the increase in government purchases. The difference between the change in government purchases (AG) and the change in equilibrium income (AY) can be visually represented by the vertical distance between the two equilibrium levels on the graph.
a. To determine the new equilibrium income, Y₂, we need to calculate the change in autonomous expenditure (AG) and multiply it by the multiplier. In this case, the change in government purchases is 2,000 pesos. Since the slope of the planned expenditure function is 2/8, the multiplier is the reciprocal of the slope, which is 8/2 = 4.
Therefore, the change in equilibrium income (AY) is equal to AG multiplied by the multiplier:
AY = AG * multiplier = 2,000 * 4 = 8,000 pesos.
The new equilibrium income, Y₂, is equal to the initial equilibrium income, Y₁, plus the change in equilibrium income (AY):
Y₂ = Y₁ + AY = 800,000,000 + 8,000 = 800,008,000 pesos.
b. On the graph, the horizontal axis represents the level of income (Y), and the vertical axis represents aggregate expenditure (AE). The initial equilibrium level of income, Y₁, is where AE₁ intersects the 45-degree line, which represents the level of income equal to aggregate expenditure. After the increase in government purchases, the new equilibrium level of income, Y₂, is where the new AE₂ curve intersects the 45-degree line.
The vertical distance between the two equilibrium levels, Y₂ and Y₁, represents the change in equilibrium income (AY). The change in government purchases (AG) is represented by a shift of the AE curve. The graph visually demonstrates the difference between the change in government purchases (AG) and the resulting change in equilibrium income (AY).
Using the Keynesian cross model, we have determined the new equilibrium income, Y₂, by calculating the change in autonomous expenditure (AG) and multiplying it by the multiplier. The difference between the change in government purchases (AG) and the change in equilibrium income (AY) can be shown and explained through a graph, illustrating the shift in aggregate expenditure and the vertical distance between the initial and new equilibrium levels.
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develop a class shapes 2d to represent all 2d geometric shapes excluding line. class should represent the name of the object (a string) the color of the objects (color) and methods that all subclasses should implement (abstract methods) including:
Answers
This is the UML diagram for the development of the program, in which Shapes 2D is the superclass and Circle, Square, Triangle, Rectangle, Rhombus, and Parallelogram are subclasses.
This is the program in C++ demonstrating the above classes.
#include<iostream>
using namespace std;
class shapes
{
public:
string name;
string color;
virtual void getAttributes()=0;
};
class Circle: public shapes
{
public:
float radius;
Circle(string n,string c, float r)
{
name=n;
color=c;
radius=r;
}
float getPerimeter()
{
return(2*(3.142)*radius);
}
float getArea()
{
return((3.142)*(radius*radius));
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Square:public shapes
{
public:
float side;
Square(string n,string c, float s)
{
name=n;
color=c;
side=s;
}
float getPerimeter()
{
return(4*side);
}
float getArea()
{
return(side*side);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Triangle:public shapes
{
public:
float base;
float height;
float side1;
float side2;
float side3;
Triangle(string n,string c)
{
name=n;
color=c;
}
float getPerimeter()
{
cout<<"Enter side1\n";
cin>>side1;
cout<<"Enter side2\n";
cin>>side2;
cout<<"Enter side3\n";
cin>>side3;
return(side1+side2+side3);
}
float getArea()
{
cout<<"Enter base\n";
cin>>base;
cout<<"Enter height\n";
cin>>height;
return((0.5)*base*height);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Rectangle:public shapes
{
public:
float length;
float breadth;
Rectangle(string n,string c, float l,float b)
{
name=n;
color=c;
length=l;
breadth=b;
}
float getPerimeter()
{
return(2*(length+breadth));
}
float getArea()
{
return(length*breadth);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Rhombus:public shapes
{
public:
float diagonal1;
float diagonal2;
float side;
Rhombus(string n,string c)
{
name=n;
color=c;
}
float getPerimeter()
{
cout<<"Enter Side\n";
cin>>side;
return(4*side);
}
float getArea()
{
cout<<"Enter diagonal 1\n";
cin>>diagonal1;
cout<<"Enter diagonal 2\n";
cin>>diagonal2;
return((0.5)*diagonal1*diagonal2);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
class Parallelogram:public shapes
{
public:
float base;
float height;
Parallelogram(string n,string c, float b,float h)
{
name=n;
color=c;
base=b;
height=h;
}
float getPerimeter()
{
return(2*(base+height));
}
float getArea()
{
return(base*height);
}
void getAttributes()
{
cout<<"Name :"<<name<<endl;
cout<<"Color :"<<color<<endl;
}
};
int main()
{
int choice;
while(1)
{
cout<<"\n\nEnter your choice :";
cout<<"\n1 for Circle\n";
cout<<"2 for Square\n";
cout<<"3 for Triangle\n";
cout<<"4 for Rectangle\n";
cout<<"5 for Rhombus\n";
cout<<"6 for Parallelogram\n";
cin>>choice;
system("cls");
switch(choice)
{
case 1:
{
float r;
cout<<"Enter radius\n";
cin>>r;
Circle c("Circle","Yellow",r);
c.getAttributes();
cout<<"Perimeter : "<<c.getPerimeter()<<endl;
cout<<"Area : "<<c.getArea()<<endl;
}break;
case 2:
{
float side;
cout<<"Enter side\n";
cin>>side;
Square s("Square","Red",side);
s.getAttributes();
cout<<"Perimeter : "<<s.getPerimeter()<<endl;
cout<<"Area : "<<s.getArea()<<endl;
}break;
case 3:
{
Triangle t("Triangle","Green");
t.getAttributes();
cout<<"Perimeter : "<<t.getPerimeter()<<endl;
cout<<"Area : "<<t.getArea()<<endl;
}break;
case 4:
{
float l,b;
cout<<"Enter Length and breadth\n";
cin>>l>>b;
Rectangle r("Rectangle","Blue",l,b);
r.getAttributes();
cout<<"Perimeter : "<<r.getPerimeter()<<endl;
cout<<"Area : "<<r.getArea()<<endl;
}break;
case 5:
{
Rhombus r("Rhombus","Purple");
r.getAttributes();
cout<<"Perimeter : "<<r.getPerimeter()<<endl;
cout<<"Area : "<<r.getArea()<<endl;
}break;
case 6:
{
float b,h;
cout<<"Enter base\n";
cin>>b;
cout<<"Enter height\n";
cin>>h;
Parallelogram p("Parallelogram","Pink",b,h);
p.getAttributes();
cout<<"Perimeter : "<<p.getPerimeter()<<endl;
cout<<"Area : "<<p.getArea()<<endl;
}break;
}
}
}
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Select all of the angles that have the same measure as angle 1. Assume the lines are parallel.
Answers
Answer:
gimme the brainliest
A protractor is used to measure an angle. Which of the following could be the measure of the angle if we know it is an acute angle?
125°
75°
0°
it can't be determined
Answers
Answer:
75
Step-by-step explanation:
An acute angle has a measure of less than 90 degrees.
Answer:
75°
Step-by-step explanation:
acute angle is an angle less than 90°
The answer appears in the image, this is for practice and please tell me an explanation on how you got the answer.
Answers
After their concert, the cat quartet invites
their friends to a party. Of the total number
of cats shown, 5 of the cats have striped tails.
How many cats have striped tails?
Draw a visual model to show how you can
find the number of cats that have striped tails.
Answers
Answer:
5 Cats have striped tails. It gave you extra info, to distract you.
Identify the key features of the parabola that is formed by the equation. f(x)=-4.9x^2+19.8x+58
Round your answers to the nearest whole number.
x-intercept, y-intercept, and the vertex.
Answers
Parabolas are used to represent quadratic functions. The x-intercepts of the parabola are -1.969 and 6.01. Vertex of the parabola are 2.02 and 78.002.
A quadratic function is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.
The function is given as:
f(x) = \(4.9x^{2} + 19.8x+58\)
Next, we plot the graph of the function f(x)
From the graph (see attachment), we have the following features
Vertex = (2.02, 78.002)
Line of symmetry, x = 2.02
x-intercepts = -1.969 and 6.01
Hence, the x-intercepts of the parabola are -1.969 and 6.01 and Vertex of the parabola are 2.02 and 78.002.
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Let Y1 < Y2 < Y3 be the order statistics of X1, X2, and X3, where Xi are uniformly distributed between 0 and 1. Find the density of Z = Y3 – Y1.
Hint:
Theorem 5.4.6 Let X.i),..., X(n) denote the order statistics of a random sample, X1,..., Xn, from a continuous population with cdf Fx(r) and pdf fx(x). Then the joint pdf of X) and X(j),1 < i
You may first find the joint pdf of Y1 and Y3 from above theorem, and define Z= Y3 – Y1 and W= Y3. Then, you may use the bi-variate transformation method to find the pdf of Z and define its support.
Answers
The density of Z = Y3 - Y1 is: f(z) = 2(1-3z+3\(z^2\)) for 0 < z < 1
To find the density of Z = Y3 - Y1, we first need to find the joint density of Y1 and Y3. Using Theorem 5.4.6, we know that the joint density of the order statistics Y1, Y2, and Y3 is:
f(y1, y2, y3) = n!/[(i-1)!(j-i-1)!(n-j)!] * [Fx(y1)\(]^(i-1)\) * [Fx(y2) - Fx(y1)\(]^(j-i-1)\) * [1 - Fx(y2)\(]^(n-j)\)* fx(y1) * fx(y2) * fx(y3)
where i = 1, j = 3, and n = 3.
Since Xi are uniformly distributed between 0 and 1, fx(x) = 1 for 0 < x < 1, and Fx(x) = x for 0 < x < 1.
Plugging in the values, we get:
f(y1, y2, y3) = 3!/[0!2!1!] * y1^0 * (y2-y\(1)^1\) * (1-y2\()^2\) * 1 * 1 * 1
= 6(1-y2\()^2\)(y2-y1)
To find the density of Z, we define W = Y3 and note that Z = W - Y1. Using the bivariate transformation method, we can express the joint density of Z and W as:
g(z,w) = f(y1 = w-z, y2, y3 = w) * |J|
where |J| is the Jacobian determinant of the transformation:
z = w - y1
w = y3
Taking the partial derivatives of the transformation with respect to y1 and y3, we get:
∂z/∂y1 = -1, ∂z/∂y3 = 0
∂w/∂y1 = 1, ∂w/∂y3 = 1
Therefore, |J| = |-11 - 01| = 1.
Plugging in the joint density and Jacobian, we get:
g(z,w) = 6(w-z)(1-w\()^2\)
To find the density of Z, we integrate out W from 0 to 1, since that is the range of the uniform distribution of Xi:
f(z) = integral of g(z,w) dw from w=0 to w=1
= integral of 6(w-z)(1-w\()^2\) dw from w=0 to w=1
= 2(1-3z+3z^2) for 0 < z < 1
Therefore, the density of Z = Y3 - Y1 is:
f(z) = 2(1-3z+3\(z^2\)) for 0 < z < 1
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PLEASE HELP!!! 50 PTS
Answers
Answer:
200,176.32016703
correct me if im wrong
Step-by-step explanation:
sorry kung mali
Answer:
UH FOOT
Step-by-step explanation:
HEY CAN ANYONE PLS ANSWER DIS!!!!!!
Answers
PLSSSSS HELP 20 POINTS!!!!! NEEDE BY NOV 19 2022The length of the side of a rhombus is 14 in. The measure of each obtuse angle is 160°. Find the length of the longer diagonal of the rhombus.
Answers
Answer:
27.57 in
Step-by-step explanation:
You want the length of the longer diagonal of a rhombus with side lengths 14 inches and obtuse angle 160°.
Law of CosinesThe law of cosines can be used to find the diagonal length. The length of the third side (c) is given by ...
c² = a² +b² -2ab·cos(C)
where a and b are the other two sides, enclosing angle C.
Applicationc² = 14² +14² -2·14·14·cos(160°)
c² = 392 -392·cos(160°) ≈ 760.35951
c ≈ 27.5746
The longer diagonal is about 27.57 inches long.
Answer:
Step-by-step explanation:
fars
Which number is a common factor of 28 and 98
Answers
Answer:
common factors of 28 and 98, that are 1, 2, 14, and 7.
Step-by-step explanation:
hope it helps
Answer:
14
Step-by-step explanation:
28 = 2 x 2 x 7
98 = 2 x 7 x 7
Common factor of 28 and 98
= 2 x 7
= 14
EMERGENCY HELP NEEDED!!!!! 20 POINTS!!! WILL MARK BRAINLIEST!!!
A regular polygon has the same number of lines of symmetry as the number of sides. For example, a pentagon has 5 sides and 5 lines of symmetry. The number of degrees apart each line of symmetry is equals 360 degrees divided by the number of sides. The pentagon's lines of symmetry are 360/5 degrees apart, or 72 degrees apart. How many degrees apart are the triangle's lines of symmetry?
60 degrees
180 degrees
90 degrees
120 degrees
Answers
Work Shown:
360/n = 360/3 = 120
Answer:
120 degrees
Step-by-step explanation:
A triangle has Three sides, so according to the given information, it should also have three lines of symmetry. To calculate the degrees apart each line of symmetry is in a triangle, we can use the same formula
Degrees apart = 360 degrees / number of sides
For a triangle:
Degrees apart= 360 degrees / 3 sides
Therefore, the lines of symmetry in a triangle are 120 degrees apart
question some of the students enrolled at college t are part-time students and the rest are full-time students. by what percent did the number of full-time students enrolled at college t increase from the fall of 1999 to the fall of 2000 ? (1) there were 50 more full-time students enrolled at college t in the fall of 2000 than in the fall of 1999. (2) the total number of students enrolled at college t increased by 5 percent from the fall of 1999 to the fall of 2000.
Answers
As percent did the number of full-time students enrolled at college t increase from the fall of 1999 to the fall of 2000 is 25%.
A percentage is a fraction of a whole number expressed as a fraction of 100. It is often used to describe the change in a quantity over time or between different groups.
There were 50 more full-time students enrolled in the fall of 2000 than in the fall of 1999, we can calculate the change in the number of full-time students as follows:
Change in full-time students = 50
To calculate the percentage change, we need to know the initial number of full-time students in the fall of 1999. This information is not provided, so we will use the information that the total number of students enrolled at College T increased by 5 percent from the fall of 1999 to the fall of 2000.
Let's call the total number of students enrolled at College T in the fall of 1999 "x". Then, the total number of students enrolled at College T in the fall of 2000 would be x + 5% of x.
x + 5% of x = x + 0.05x = 1.05x
To find the number of full-time students in the fall of 2000, we can subtract the change in full-time students from the total number of students enrolled at College T in the fall of 2000:
Number of full-time students in fall of 2000 = 1.05x - 50
To calculate the percentage change, we divide the change in full-time students by the initial number of full-time students and multiply by 100:
Percentage change = (50 / x) * 100
Where the value of x as 2000, then the percentage is
=> (50/2000) * 100 = 25%.
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GEOMETRY Express the volume of each solid as a monomial. a. 9h6b. 9h8c. 27h6d. 27h8
Answers
The volume of a rectangular prism of width W, length L, and Height H is calculated as:
\(V=W\cdot L\cdot H\)The solid in the figure is a cube (W = L = H) with a side length of
\(W=L=H=3h^2\)Calculating the volume:
\(\begin{gathered} V=3h^2\cdot3h^2\cdot3h^2 \\ V=27h^6 \end{gathered}\)Choice c.
PLEASE HELP!!!! Jul is using the graph of an exponential function to represent the value of an investment where x is the number of years Jul has owned the investment. Which statement correctly describes a key feature of the function?
Answers
Answer: the answer is D
Step-by-step explanation:
Trust me
the domain of the function is x greater than equal to 0.
Answer: The domain of the function is x>0. So D just took the test, got it right!
Step-by-step explanation:
Fill in the blanks please
Answers
11. The slope and y-intercept for each linear equation include:
y = 2x + 3 slope = 2 y-intercept = 3
y = -1/2(x) + 1 slope = -1/2 y-intercept = 1
The lines are perpendicular.
12. 4y = 8x - 2 slope = 2 y-intercept = -2
-4x + 2y = -1 slope = 2 y-intercept = -1/2
The lines are parallel.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Question 11.
Based on the information provided above, we have the following linear equation;
y = mx + b
y = 2x + 3 ⇒ slope = 2 y-intercept = 3
y = -1/2(x) + 1 ⇒ slope = -1/2 y-intercept = 1
For perpendicular lines, we have:
m₁ × m₂ = -1
2 × m₂ = -1
m₂ = -1/2
Question 12.
Based on the information provided above, we have the following linear equation;
y = mx + b
4y = 8x - 2 ≡ y = 2x - 1/2 slope = 2 y-intercept = -1/2
-4x + 2y = -1 ≡ y = 2x - 1/2 slope = 2 y-intercept = -1/2
m₁ = m₂ = 2.
Therefore, the lines are parallel.
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2.) A microscope is set so it makes an object appear 5 x 10² times larger than its actual size. A virus has a diameter 1.8 x 10^-6 meter. How large will the diameter of the virus appear when viewed under the mīcroscope?
Answers
Answer:
\(9\times10^{-4}\text{ meters}\)Explanation:
The diameter of the virus is given below:
\(1.8\times10^{-6}\)The microscope is set so that the object appears 5 x 10² times larger than its actual size.
Therefore, the diameter of the virus when viewed under the mīcroscope is:
\(\begin{gathered} =5\times10^2\times\text{Actual Size} \\ =5\times10^2\times1.8\times10^{-6} \end{gathered}\)We then simplify our result by collecting like terms.
\(\begin{gathered} =5\times1.8\times10^2\times10^{-6} \\ =9\times10^{2+(-6)} \\ =9\times10^{2-6} \\ =9\times10^{-4}\text{ meters} \end{gathered}\)Simplify a5 divided by a3
Answers
Answer:
a^2
Step-by-step explanation:
a^5 / a^3
We know that x^y / x^z = x^ ( y-x)
a^ ( 5-3) = a^ 2
Answer:
a squared OR a2 OR a^2
Step-by-step explanation:
So we need to remember that numbers and exponents are different. When we divide a5 by a3, we subtract 3 from 5. That gives us 2. So the exponent is 2 and the answer is a2. I hope this helped! :)
Integrate f(x,y) = In (x² + y²) / √(x² + y²) over the region 1 ≤ x² + y² ≤ e^6. The answer is ______
(Type an exact answer, using as needed. Do not factor.)
Answers
For Integration f(x,y) = In (x² + y²) / √(x² + y²) over the region 1 ≤ x² + y² ≤ e^6. The exact answer to the given integral is 6π(e^6 - 1).
The answer is given by ∫∫(r * ln(r²) / r) dr dθ, where the limits of integration for r are 1 and e^3, and for θ are 0 to 2π. In polar coordinates, x = r * cos(θ) and y = r * sin(θ), where r represents the distance from the origin and θ represents the angle. The Jacobian determinant of the coordinate transformation is r.The integral becomes ∫∫(r * ln(r²) / r) dr dθ. To determine the limits of integration, we note that 1 ≤ x² + y² ≤ e^6 corresponds to 1 ≤ r² ≤ e^6. Taking the square root, we have 1 ≤ r ≤ e^3.The integral then becomes ∫ from 0 to 2π ∫ from 1 to e^3 (r * ln(r²) / r) dr dθ. Simplifying, we have ∫ from 0 to 2π ∫ from 1 to e^3 ln(r²) dr dθ.
Integrating with respect to r, we get [1/2 * r² * ln(r²)] evaluated from 1 to e^3, which simplifies to [1/2 * (e^6 - 1) * ln(e^6)].Finally, integrating with respect to θ, we have [1/2 * (e^6 - 1) * ln(e^6)] * θ evaluated from 0 to 2π. Since ln(e^6) = 6, the expression simplifies to [1/2 * (e^6 - 1) * 6 * θ] evaluated from 0 to 2π.Plugging in the limits, we get the final answer: [1/2 * (e^6 - 1) * 6 * 2π] = 6π(e^6 - 1).
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a political action committee launches a new advertisement aimed at building support for a policy that would expand health insurance to low-income americans through increased government funding. according to zaller’s receive-accept-sample (ras) model, who would be most susceptible to this message?
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According to Zaller's Receive-Accept-Sample (RAS) model, individuals who are most susceptible to the message of a political action committee launching a new advertisement aimed at expanding health insurance to low-income Americans through increased government funding would be those who both receive and accept the message.
The RAS model suggests that individuals have varying levels of political knowledge and are exposed to different sources of information. Those who are more likely to receive the message are individuals who are politically interested and engaged, while those who are more likely to accept the message are individuals who have limited political knowledge and are less critical of the information presented to them.
Therefore, in the context of the advertisement aiming to expand health insurance to low-income Americans, the most susceptible individuals would be those who are politically interested but have limited political knowledge. These individuals may be more likely to accept the message without critically evaluating its content.
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Kayla buys a video game for $19 plus a 6% tax. Michael buys a volleyball for $18 plus a 6% tax. Enter the difference in the amount Kayla and Michael paid, including tax. Round your answer to the nearest cent. HELP ME OUT PLEASE
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Answer:
Kayla = $20.14
Michael = $19.08
The Difference = 1.06
Step-by-step explanation:
How to solve.
First, you need to add up how much Kayla is paying for the video game, plus the 6% tax.
19.00 + 6% = 20.14
Then, you need to do the same with Michael's.
18.00 + 6% = 19.00
To find the difference between how much Kayla and Michael paid for their items, you need to subtract their total.
20.14 - 19.00 = 1.06
and the nearest cent would be 1.10.
I hope this helped.!
What are the roots of this quadratic equation? 3x^2+10=4x
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Step-by-step explanation:
The root of an equation is when x=0.
We need to rewrite this as 3x²-4x+10=0.
The quadratic formula is
(-b+or-sqrt(b²-4ac))/2a
so 4+or-sqrt(16-120)/2a
since the sqrt can no be negative this answer will have imaginary numbers.
(4+2i sqrt(26))6 and (4-2i sqrt(26))6
simplified is
x=(2+i sqrt(26))/3 and x=(2-i sqrt(26))/3