The mean square value of x is approximately 7111.11.
The given probability density function (PDF) is:
px(x) = kx(20-x), for 0 ≤ x ≤ 20
px(x) = 0, elsewhere
where k is a constant that ensures that the PDF integrates to 1 over its domain.
To find the value of k, we use the fact that the integral of the PDF over its domain equals 1:
[tex]\int_0^{20}[/tex] kx(20-x) dx = 1
Expanding and solving for k, we get:
k[tex]\int_0^{20}[/tex] (20x - x²) dx = 1
k [10x² - (1/3)x³] | from 0 to 20 = 1
k [4000 - (1/3)8000] = 1
k = 3/(8000)
Therefore, the PDF is:
px(x) = (3/(8000))x(20-x), for 0 ≤ x ≤ 20
px(x) = 0, elsewhere
To find the mean of x, we use the formula:
E[x] = [tex]\int_0^{20}[/tex] x px(x) dx
Substituting the PDF, we get:
E[x] =[tex]\int_0^{20}[/tex] (3/(8000))x²(20-x) dx
This integral can be evaluated using integration by parts.
Let u = x²(20-x) and dv = dx, then du/dx = 40x - 2x² and v = x.
Using the integration by parts formula, we get:
∫ u dv = uv - ∫ v du
= x³(20/3) - [tex]x^4/4[/tex] - [tex]\int_0^{20} (40x^3 - 2x^4) / 8000\: dx[/tex]
= (20/3) [tex]\int_0^{20} x^3 dx - (1/4) \int_0^{20} x^4 dx[/tex]
= (20/3)[tex](20^4/4)[/tex] - [tex](1/4)(20^5/5)[/tex]
= 2666.67
Therefore, the mean of x is approximately 2666.67.
To find the mean square value of x, we use the formula:
[tex]E[x^2][/tex] = [tex]\int_0^{20} x^2[/tex] px(x) dx
Substituting the PDF, we get:
[tex]E[x^2][/tex] = [tex]\int_0^{20}[/tex] (3/(8000))x³(20-x) dx
This integral can also be evaluated using integration by parts.
Let u = x³(20-x) and dv = dx, then du/dx = [tex]60x^2 - 3x^3[/tex] and v = x.
Using the integration by parts formula, we get:
∫ u dv = uv - ∫ v du
= [tex]x^4(20/4) - x^5/5 -[/tex] [tex]\int_0^{20} (60x^4 - 3x^5) / 8000\: dx[/tex]
= (20/4) [tex]\int_0^{20}x^4 dx - (1/5) \int_0^{20} x^5 dx[/tex]
= [tex](20/4)(20^5/5) - (1/5)(20^6/6)[/tex]
= 7111.11
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The mean of x is approximately 2666.67 and the mean square value of x is approximately 7111.11.
To find the mean square value of x, we use the formula:
= px(x) dx
Substituting the given PDF, we get:
= (3/(8000))x³(20-x) dx
We can use integration by parts to evaluate this integral. Let u = x³(20-x) and dv = dx, then du/dx = 60x² - 3x³ and v = x. Using the integration by parts formula, we get:
∫ u dv = uv - ∫ v du
= x⁴(20/4) - ∫ x²(60x² - 3x³) dx
= (5/2)x⁴ - 20x⁴ + x⁵/5 + C
where C is the constant of integration. Evaluating the integral between 0 and 20, we get:
= [(5/2)(20⁴) - 20(20⁴) + (20⁵/5)]/8000 - [(5/2)(0⁴) - 20(0⁴) + (0⁵/5)]/8000
= 7111.11
Therefore, the mean square value of x is approximately 7111.11.
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can someone help me on this and plz explain
40 POINTS!
3. Suppose a point at (2,3) is translated to (7,-1). What rule describes this translation?
O A. (x, y) + (x + 5, y - 4)
O B.(z,y) → (2 – 5,y + 4)
O c.(x, y) = (x + 9,y - 2)
O D. (x, y) → (2 – 9,y + 2)
Which expression is equivalent 10x+10
A.2x+5x+4x+5+5
B.2x+8x+1+3+6
C.5x+5x+2+4+4+1
D.2x+9x+5+5
(7th grade) Combing like terms.
Answer:
the answer to that question is letter A.2x+5x+4x+5+5
Lucy spent a total of $6.60 on 5 apples and a package of grapes. If the package of grapes cost $2.35, how much did each apple cost? Do not put a $ in your answer.
Each apple costs $
3 plus tax
Step-by-step explanation:
I don't understand this? help me! Linear functions 9th-grade math
Answer:B i think
Step-by-step explanation:
Solve the equation y – 5x = –7 for y.
A. y = 5x – 7
B. y = –5x – 7
C. y = 5x + 7
D. y = –5x + 7
Answer:
the answer is B
Step-by-step explanation:
Answer: A. y = 5x -7
Step-by-step explanation:
Y - 5x = -7
+ 5x + 5x
Y = 5x - 7
**you can’t subtract -5x to -5x because it’s already a negative. It should be a positive 5x so you can move it to the other side.
Which phrase describes the algebraic expression 5+w
A: the product of 5 and w
B: the quotſent of 5 and w
C: w more than 5
D: 5 less than w
Answer:
The answer probably is A
Select all ordered pairs that satisfy the function y =
= 8x + 3
A.
(0,3)
B.
(-1, 43)
C.
(0, -45)
D.
(5, 43)
Answer:
A. (0,3)
Step-by-step explanation:
2x3(5-4)/6.2
Algebra
6/6.2 OR 0.627
Step-by-step explanation:
[tex] \frac{2 \times 3(5 - 4)}{6.2} [/tex]
6(1)/6.2 = 6/6.2 OR 0.627
como simplificar 9/3
k + 11 = -3k- 25 + 2k
Answer:
k = -18
Step-by-step explanation:
1. The Clock
[tex] \sqrt{81} [/tex]
∆ has the coordinates (3, 1), (5, 2), (4, 3). ∆´´´ has coordinates (-1, 2), (1, 3) and (0, 4). Which choice describes the translation of ∆ to ∆´´? A +4 units in the direction of x and -1 units in the direction of y B -4 units in the direction of x and +1 units in the direction of y C +4 units in the direction of x and +1 units in the direction of y D -4 units in the direction of x and -1 units in the direction of y
Answer:
B -4 units in the direction of x and +1 units in the direction of y
Step-by-step explanation:
Given
[tex]A = (3, 1), (5, 2), (4, 3)[/tex]
[tex]A^{-1}= (-1, 2), (1, 3) (0, 4)[/tex]
Required
Determine the translation from A to A-1
Take (3,1) from A and (-1,2) fro A-1 as points of reference,
For translation to occur, we make use of:
[tex](3 + x,1+y) = (-1,2)[/tex]
By comparison:
[tex]3 + x = -1[/tex] and [tex]1 + y = 2[/tex]
Solve for x and y
[tex]3 + x = -1[/tex]
[tex]x = -1-3[/tex]
[tex]x = -4[/tex]
[tex]1 + y = 2[/tex]
[tex]y = 2 - 1[/tex]
[tex]y=1[/tex]
(B) is correct.
The radius of circle is 9. Using pie, which equation expresses the ratio of the circumference of the circle to the circle's
diameter?
Answer:
B) C/18 = PI
Step-by-step explanation:
C = PI * Diameter
C = PI * 2R
C = PI * 18
C/18 = (PI * 18)/18
C/18 = PI
Which set of ordered pairs (x, y) could represent a linear function?
A = {(3,5), (5,1), (7, -2), (9,-6)}
B = {(2,-5), (5,1), (6,3), (7,6)}
C = {(-4,3), (-2,0), (0, -4), (2, –7)}
D = {(-3,7), (-1,5), (1,3), (3, 1)}
Answer = C
because all are not in set pairs only no. C is pair of set
At Jefferson Middle School, eighty-two students were asked which sports they plan to participate in for the coming year. Twenty students plan to participate in track and cross country; six students in cross country and basketball; and eight students in track and basketball. Twelve students plan to participate in all three sports. A total of thirty students plan to participate in basketball, and a total of forty students plan to participate in cross country. Ten students don't plan to participate in any of the three sports.
How many students plan to just participate in track?
Answer:
20
Step-by-step explanation:
HELP QUICK. By combining three equations, it can be shown that a2+b2=c2. One of the equations is c=e+f. Which of the following could be the other two equations?
Answer:
bc=eb and ca=fa
please tell me if this is actually the right answer
Step-by-step explanation:
bc=eb and ac=fa is wrong
bc=eb and ca=fa is right
cb=eb and ac=fa is wrong
ba=eb and ab=fa is wrong
If the sum of the interior angles of a polygon is 29160, how many sides does it have?
Answer:
fhuguyguy
Step-by-step explanation:
3. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
Write a rule for the linear function shown in the graph.
A. y = 5/3x + 1
B. y = 3x - 1
C. y = 2/5x + 1
D. y = -5/2x - 1
Answer:
D. y= -5/2x - 1
Step-by-step explanation:
Hope this helps. Sorry if it doesn't
maths homework please help me
Answer:
sorry i dont know that im grade 6
Answer:
Which I marked they are wrong I think because they all came out of that lines
What expression is equivalent to 1/3 x -1/5
repost, algebra help needed please
Answer:
y- intercept = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
f(x) = [tex]\frac{1}{2}[/tex] [tex](6)^{x}[/tex]
To find the y- intercept let x = 0 , then
f(0) = [tex]\frac{1}{2}[/tex] [tex](6)^{0}[/tex] [ [tex]6^{0}[/tex] = 1 ]
= [tex]\frac{1}{2}[/tex] × 1 = [tex]\frac{1}{2}[/tex] ← y- intercept
fractionsss
15/7 = 2 1/7 right?
Answer:
Yepp!!
Step-by-step explanation:
[tex]\frac{15}{7}[/tex] = 2[tex]\frac{1}{7}[/tex]
Find x and y. please help
Answer:
[tex] x = 4 \sqrt{2} [/tex]
[tex] y = 4 \sqrt{6} [/tex]
Step-by-step explanation:
[tex] \sin 45 \degree = \frac{x}{8} \\ \\ x = 8 \sin 45 \degree \\ \\ x = 8 \times \frac{1}{ \sqrt{2} } \\ \\ x = \frac{8 \sqrt{2} }{2} \\ \\ x = 4 \sqrt{2} \\ \\ \\ \tan 30 \degree = \frac{x}{y} \\ \\ \frac{1}{ \sqrt{3} } = \frac{4 \sqrt{2} }{y} \\ \\ y = 4 \sqrt{6} [/tex]
whats 8/7 as a decimal?
NEED HELP AND RIGHT ANSWER DONT RUSH! REWARD BRAINLIEST
Answer:
1.) x = 49 or x = -49
2.) x = -1/2 or x = -5
1. Points A and B are to be mapped onto a number line according to two equations. The solution to the equation 2 24 3 A is the coordinate of point A. The solution to the equation 20 0.2 B is the coordinate of point B.
(a) Solve the first equation to find the coordinate of point A. Show your work. (
b) Solve the second equation to find the coordinate of point B. Show your work.
(c) Determine the distance between points A and B. Explain.
PLZ HELP!! ASAP
Answer:
A. 2.11.5 B. 31
Step-by-step explanation:
2.11.5 B.31
Answer: A) 2/3 * 24/1 = 2/1 * 8/1 = 16/1 = 16
B) 20 = -B/0.2
20 * 0.2 = 4
C) The distance between the two points is 20, if the point for a is 16, and the distance for b is 4, you would have to add those two together and get 20.
Step-by-step explanation:
What’s 20 times 69?????
Answer:
1,380
Step-by-step explanation:
Answer:
20x69 = 1,380
What is on the twentieth floor .it goes Down 11 floors and then up 5 floors what floor is the elevator now
Answer:
6th floor
Step-by-step explanation:
‼️ PLEASEEE HELPP ‼️
Answer:
x=18
Step-by-step explanation:
When a triangle has a midline the midline (in this case "3x-43") is 1/2 of the base of the triangle (in this case "4+x") so you can then say
4+x = 2(3x-43)
Solve that out to find that x = 18