Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.
What is Random Variable?
A continuous random variable is a random variable where the data or value can assume infinitely many values ( meaning it’s a continuous set of data. )
For example a random variable measuring the time taken for someone to cook rice is continuous since there are an infinite number of possible times that can be done.
a) If the random variable Y has a uniform distribution on the interval (0, 1), then the probability density function (PDF) of Y is given by:
[tex]f_Y(y) = 1 for 0 < y < 1[/tex]
= 0
If we let W = Y, then the PDF of W is simply the same as the PDF of Y, since W and Y are equal. Therefore, the PDF of W is given by:
[tex]f_W(w) = 1 for 0 < w < 1[/tex]
= 0
b) If we let W = VY, where V is a constant, then the PDF of W is given by:
[tex]f_W(w) = f_Y(w/V) / |V|[/tex]
Substituting in the expression for the PDF of Y, we get:
[tex]f_W(w) = 1/|V| for 0 < w/V < 1[/tex]
= 0
If V > 0, then this reduces to:
[tex]f_W(w) = 1/V for 0 < w < V[/tex]
= 0
If V < 0, then the range of w is reversed and the PDF becomes:
[tex]f_W(w) = -1/V for V < w < 0[/tex]
= 0
The normalization factor [tex]|V|[/tex] is necessary because the transformation
W = VY stretches or compresses the original uniform distribution on the interval (0, 1) by a factor of [tex]|V|[/tex].
Hence, Distribution of the random variable W = Y. b distribution of the random variable W = VY is derived.
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What is the greatest common factor of 33 and 49
Answer:
1
Step-by-step explanation:
All factors of 33 : 1, 3, 11, 33
All factors of 49 : 1, 7, 49
So the Greatest Common Factor for 33 and 49 is 1
there are 75 animals at the animal shelter. if 27 are hamsters, what percent are hamsters
36% of the animals in the shelter are hamsters.
Step-by-step explanation:1. Find the quotient between the amount of hamsters and the total of animals.[tex]\frac{27}{75}= 0.36[/tex]
2. Convert the decimal into a percentage.0.36 = 36%.
3. Conclude.36% of the animals in the shelter are hamsters.
a,b)Find the phasor form of the following E-field, the polarization type, and plot the vector on the X-y axis (z-0) for one period a) E(z,t) = xZcos(wt kz) y4cos(wt kz) b) E(z,t) = R2cos(wt + kz) - 94sin(wt + kz)
a) The phasor form of E-field = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz) is 2√5 L(-63.43).
Polarization type is linearly polarised.
b) The phasor form of E-field = ?
E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz) is E(z,t) =2√5 L(-143.43). polarization type is elliptical.
We have given that
E⃗(z,t) =2xˆcos(wt - kz) - 4 yˆcos(wt - kz)
|r⃗ | = √((2cos(wt - kz))² + (- 4cos(wt - kz))²)
= √(4cos²(wt - kz) + 16cos²(wt - kz))
= √(20cos²(wt - kz))
= 2√5 cos(wt - kz)
φ = 4cos(wt - kz)/(2cos(wt - kz))
= tan⁻¹ 1(-2) = -63.43°
So, E(z,t) = 2√5 L(-63.43)
b) E(z,t) = xˆ 2cos(wt + kz) - yˆ 4sin(wt + kz)
= xˆ 2cos(wt + kz) - yˆ 4cos(wt + kz -π/2)
|r| = √((2cos(wt + kz))² + (- 4sin(wt -+kz))²)
= √20
phi = tan⁻¹(- 4cos(wt - kz)/(2cos(wt - kz)) - π/2
= tan⁻¹( -2) + π/2 = - 143.43
so, E(z,t) =2√5 L(-143.43)
E(z,t) = xˆ 2cos(wt - kz) - yˆ 4cos(wt - kz)
if wt = 0°
E(z,t) = xˆ 2cos(0 - kz) - yˆ 4cos(0- kz)
= 2xˆ - 4yˆ
wt = 30° , E(z,t) = xˆ 2cos( - kz) - yˆ 4cos(0- kz)
E(z,t) = √3/2(2) xˆ - √3/2(4) yˆ
= √3xˆ - 2√3yˆ
for wt = 45°
E(z,t) = √2 xˆ - 2√2 yˆ
for wt = 90° =>E(z,t) = 0
for wt = 60° , E(z,t) = xˆ - 2 yˆ as seen in above graph that is linear polarised
For part (b) ,
E(z,t) = 2 xˆcos(wt - kz) - 4yˆ sin(wt + kz)
From graph elliptical polarised,
for wt = 0 , E(0,t) = 2 xˆ
for wt = 90° , E(0,t) = -4yˆ
for wt =180° , E(0,t) = -2 xˆ
for wt = 270° , E(0,t) = -4yˆ
Hence, we get the answer of both parts.
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Select all of the equations that are equivalent to 8k = 20. 8k – 4 = 20 + 4 8k ÷ 4 = 20 ÷ 4 8k × 3 = 20 × 3 8k + 10 = 20 + 10 8k × 5 = 20 ÷ 5
Answers : ACD
The equations that are equivalent are (b) 8k ÷ 4 = 20 ÷ 4, (c) 8k × 3 = 20 × 3 and (d) 8k + 10 = 20 + 10
How to determine the equations that are equivalent?From the question, we have the following parameters that can be used in our computation:
8k = 20.
Divide both sides of the equation by 4
So, we have the following representation
8k ÷ 4 = 20 ÷ 4
Multiply both sides of the equation by 3
So, we have the following representation
8k × 3 = 20 × 3
Add 10 to both sides of the equation
So, we have the following representation
8k + 10 = 20 + 10
Hence, the equivalent equation is 8k + 10 = 20 + 10
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Tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues placing pins so that each pin is 1 unit east and 3 units north in relation to the previous pin. Which of the following points will have pins? Select all that apply.
A coordinate plane has an x-axis labeled East from 0 to 10 in increments of 1 and a y-axis labeled North from 0 to 10 in increments of 1.
A.
(5, 6)
B.
(6, 8)
C.
(7, 10)
D.
(8, 17)
E.
(9, 18)
F.
(10, 21)
Answer:
A, B, C.
Step-by-step explanation:
A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 20%.
The volume expression for the box is 1.728lwh and it means that the volume increases by 72.8%
How to determine the volume expression for the box?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Length = l
Width = w
Height = h
The volume of a box can be calculated using
Volume = lwh
Rewrite the volume equation as
v = lwh
When the dimensions of the box are increased by 20%, we have the following expressions
Length = 1.2l
Width = 1.2w
Height = 1.2h
So, the new volume is
V = 1.2l * 1.2w * 1.2h
Evaluate
V = 1.728lwh
Hence, the expression is 1.728lwh
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A food company sells its corn flakes in boxes of two different sizes: the regular box and the family value box. For the family value box, the length, width, and height of the box have all been increased by 20%.
Determine the expression for the new volume
Multiply 3.7x and 6x.
A: 9.7x
B: 9.7x2
C: 22.2x
D: 22.2x2
Answer:
22.2x²
Step-by-step explanation:
3.7x = 3.7 × x
6x = 6 × x
Multiplication of 3.7x and 6x
= 3.7 × 6 × x × x
= 22.2 × x²
= 22.2x²
Answer:
C. 22.2x^2
Step-by-step explanation:
David invests $800 into an account with a 2.3% interest rate that is compounded semiannually.
How much money will he have in this account if he keeps it for 5 years?
Round your answer to the nearest dollar.
To calculate how much money David will have in this account after 5 years, we first need to find out how much interest the account earns each year. To do this, we need to multiply the interest rate by the amount of money in the account. In this case, the interest earned each year would be $800 * 0.023 = $18.40.
Next, we need to calculate how much interest the account earns over the 5-year period. Since the interest is compounded semiannually, this means that the interest is earned twice per year. Therefore, the total amount of interest earned over 5 years would be $18.40 * 2 * 5 = $184.
Finally, we need to add the interest to the original amount of money in the account to find out how much money David will have after 5 years. In this case, the total amount of money David will have after 5 years is $800 + $184 = $984.
Therefore, if David keeps the money in this account for 5 years, he will have $984.
Answer:
$897
Step-by-step explanation:
We know:
P = 800
n = 2
r = 2.3
t = 5
Write Equation:
[tex]F = 800(1+\frac{\frac{2.3}{100} }{2} )^{2(5)}[/tex]
Evaluate:
896.9
Thus the answer is $897
a coin is flipped 10 times how many outcomes will have exactly 4 tails and start and end with different faces
There are a total of 2^10 = 1024 possible outcomes for a coin flipped 10 times. Out of these, there are only 10 outcomes that have exactly 4 tails and start and end with different faces.
To count the number of outcomes with 4 tails, we can use the binomial coefficient formula: n choose k = n!/(k! * (n-k)!), where n is the total number of flips (10 in this case) and k is the number of tails (4 in this case). This gives us 10 choose 4 = 10!/ (4! * 6!) = 210 outcomes with 4 tails.
To count the number of outcomes that start and end with different faces, we can consider the first and last flips separately. The first flip can be either heads or tails and the last flip can also be either heads or tails, for a total of 2 * 2 = 4 possibilities.
Thus, there are a total of 210 * 4 = 840 outcomes that have exactly 4 tails and start and end with different faces. However, there are two outcomes (THTHTHTHTHT and TTHTHTHTHTH) that are counted twice in this total, so we need to subtract these from the total to get the correct number of outcomes. This gives us 840 - 2 = 838 outcomes.
Finally, we need to subtract the two outcomes that start and end with the same face (HHHHHHHHTH and THHHHHHHHH). This gives us a total of 838 - 2 = 836 outcomes.
Therefore, there are a total of 836 outcomes that have exactly 4 tails and start and end with different faces out of a total of 1024 possible outcomes.
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Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 6, 0 ≤ v ≤ 1.
Answer:
684.
Step-by-step explanation:
Find the value of 3 - 12 by 5
Answer: 3/5
Step-by-step explanation:
Let x be the required solution:
so, x= 3- (12/5)
⇒ 5x = 15-12 (Multiplying both sides 5 so that the denominator is the same)
⇒ 5x = 3
∴ x = 3/5
Please I need help and please show work rational function lots of points
If cos 0= 3/5 what is the measure of the angle
Credit recovery
By using trigonometry, it can be calculated that The measure of the angle is 53.13° First option is correct.
What is Trigonometry?
Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles. It is used to calculate lengths, angles, and other geometric figures. Trigonometry has applications in many fields, including engineering, astronomy, and navigation. The most common trigonometric functions are sine, cosine, and tangent. These functions are used to solve problems related to triangles, circles, and other geometric figures. Trigonometric identities are also used to solve algebraic equations. Trigonometry is an important tool for studying the physical world, as it allows us to calculate the position and motion of objects in space.
There are six trigonometrical functions. They are
[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\cos\theta = \frac{baser}{hypotenuse}\\tan\theta = \frac{perpendicular}{base}\\cot\theta = \frac{base}{perpendicular}\\sec\theta = \frac{hypotenuse}{base}\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]
Trigonometry is a very important tool in mathematics.
Here, the trigonometric function given is
[tex]cos\theta = \frac{3}{5}[/tex]
[tex]\theta = cos^{-1}(\frac{3}{5})[/tex]
[tex]\theta = 53.13^{\circ}[/tex]
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Find the value of x
Area of rectangle = 50
Answer:
x = 3.66
Step-by-step explanation:
Area of a rectangle = length * width
In this case:
(x+10)x = 50
x*x + x*10 = 50
x² + 10x - 50 = 0
x = {-10±√((10²) -(4*1*-50))} / (2*1)
x = {-10±√(10² + 200)} / 2
x = {-10±√(100+200)} / 2
x = {-10±√300} / 2
x = {-10±17.321} /2 aprox,
It is a geometric figure so only the positive value is taken.
x = {-10+17.321} / 2
x = 7.321/2
x = 3.66
Check:
3.66(3.66+10) = 50
3.66*13.66 = 50
Let’s find 3/4-1/6
First write the subtraction with a common denominator then subtract
Answer:
7/12
Step-by-step explanation:
I set up the equation, but I first had to find the common denominator which is 12 so I multiplied 3/4 by 3 (top and bottom) and I multiplied 1/6 by 2 (also top and bottom) So I got 9/12-2/12 and when I subtracted I got 7/12
(hope you understood how I got my answer..)
On the coast of Oregon, mussels cover most of the rocky shoreline. Two mussel predators include Pisaster (ochre stars) and Nucella (whelks). A sixty-day removal study was conducted, and the results are presented in the graph. Which of the following conclusions is best supported by the data in the graph?
Because Pisaster is a keystone species, the proportion of living mussels was comparable to the control after Nucella removal.
Is the ochraceous Pisaster a keystone species?Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.
Pisaster ochraceous: prey or predator?Sea otters and sea gulls hunt for and eat Pisaster ochraceous. Its function as a keystone species has been well researched. When it was gone from Washington's intertidal regions, the area's species diversity declined.
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Please help please and thank you
Answer:
Z
Step-by-step explanation:
Angle V is congruent to angle z because they have the same placement in the letter order.
How much would you need to deposit in an account now in order to have $2,000.00 in the account in 13
months?
Assume the account earns 4.01% simple interest.
in your account now.
You would need to deposit _____ in your account now.
Answer:
$1916.73
Step-by-step explanation:
[tex]I=Prt=P(0.0401)(13/12) \\ \\ \implies P+P(0.0401)(13/12)=2000 \\ \\ P=\frac{2000}{1+(0.0401)(13/12)} \approx \$1916.73[/tex]
Miguel is mailing packages.Each small package cost him $2.20 to send.Each large package cost him $3.90.How much will it cost him to send 6 small packages and 1 large package?
Answer: $13.50
Step-by-step explanation:
It will cost Miguel $13.50 to send 6 small packages and 1 large package. To find the total cost, we can first calculate the cost of sending the small packages by multiplying the cost per small package by the number of small packages: 2.20 * 6 = $<<2.20*6=13.20>>13.20
We can then add the cost of the large package to find the total cost: 13.20 + 3.90 = $<<13.20+3.90=17.10>>17.10.
Therefore, it will cost Miguel $17.10 to send 6 small packages and 1 large package.
teh velocity of a partilce in ft/s, moving along the x axis is given the function v(t) e^t te^t when 0
The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.
What is Acceleration ?
Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.
Given,
Velocity v= x² − 5x + 4
now, the acceleration
a = dv/dt
a = 2x (dx/dt) - 5x(dx/dt)
given that, v= dx/dt =0
so, a = 2x*0−5*0
a=0 m/sec²
so, the acceleration is zero ,when the velocity is zero.
Hence ,The magnitude of the acceleration of the particle is zero when the velocity of the particle is zero.
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Given question is incomplete , the complete question is given below:The velocity of a moving particle along the x-axis is given as v= x² − 5x + 4, where x denotes the x−coordinate of the particle in meters. Find the magnitude of the acceleration of the particle when the velocity of the particle is zero?Find the slope of the line graphed below
Answer: -5/3
Down -5
right 3
Step-by-step explanation: count the distance between the 2 dots looking from the y axis (up and down)and from the x axis (left to right)
Find the product of (x − 2i)2.
what number do you get by adding 59 hundred to 31 thousandths?
im not sure if you made a mistake and meant hundredths or not but if you are adding hundreds it would be 59.031 but if you adding hundredths is would be 0.621.
Practice 21: Combine the like terms to make a simpler expression
A. -3n-7+6n + 1
B 7x+5-3x
D. 12x² -5+7x² - 11x
a)
C. 6x + 4 + 15-7x
E 6g + 11 + 8g² - 15w
1 point
The like terms to make a simpler expression is 19 x^2-6 x+9 n-6
Group like terms
What is simpler expression?
Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplication, dividing, adding, or subtracting to be done.
[tex]=12 x^2+7 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements[tex]: $12 x^2+7 x^2=19 x^2$[/tex]
[tex]=19 x^2+7 x-3 x-11 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements: [tex]$7 x-3 x-11 x=-7 x$[/tex]
[tex]=19 x^2-7 x+3 n+6 n-7+1+5-5[/tex]
Add similar elements: [tex]$3 n+6 n=9 n$[/tex]
[tex]=19 x^2-7 x+9 n-7+1+5-5[/tex]
Add the numbers: [tex]$-7+1+5-5=-6$[/tex]
[tex]=19 x^2-7 x+9 n-6[/tex]
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Emilie buys new packages of seeds. The cost C of the new seeds equals one half the weight W of the package. Write an equation to represent this relationship
Answer:
C = W/2
CHECKING
let W = 10
C = W/2
C = 10/2
C = 5
C = 5 W = 10
Therefore we proved that C = W/2 is correct equation.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-You want to see how average political views (10 point continuous scale from extreme liberal to extreme conservative) is predicted by social class (3 categorical levels) and religious affiliation (yes/no). You suspect that the effect of religious affiliation changes between social classes.
The average of the provided numbers is calculated by dividing the total number of values by the sum of all the values that different socioeconomic classes are affected differently by religion membership.
What is an average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a collection of data, we add up all the values and divide this sum by the total number of values. a single number (such as a mean, mode, or median) that encapsulates or depicts the overall importance of a collection of disparate data. unkind sense 1b.: a calculation that approximates the arithmetic mean. an intellectual level that is characteristic of a group, class, or series. superior than average.
[tex]65, 85, 70, 90, 105.[/tex]
Average =
[tex](65+85+70+90+105)/5\\= 415/5\\= 83\\[/tex]
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find the values of x in the following, giving brief reasons for your answers.
please help me, thank you.
Answer:
For the first one x= 60 degrees
Second one x= 125 degrees
Step-by-step explanation:
a) To figure out this we can see that the total of angles in a 5- angled shape is 540 degrees.
So (2x X 4) + x = 540 degrees
= 9x= 540
= x = 60
b) To figure out this we can see that the total of angles in a 7- angled shape is 900 degrees.
So 60+2x+x+x+x+x+90= 900
= 150 +6x= 900
= 6x= 750
= x= 125
A chef preheats an oven. It starts at room temperature, 68°F, and heats up 23°F per minute.
How long does it take for the oven temperature to reach 275°F?
Write and solve an equation to find the answer.
minutes hi
Answer:
93 minutes
Step-by-step explanation
23/68 x/275= 93 min
The midpoint of PR is (-6,9). P=(-15,4)
What are the coordinates of point R?
R=(_,_)
Answer:
R = (3, 14 )
Step-by-step explanation:
given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula
calculate the midpoint of PR using this formula and equate x and y coordinates to the coordinates of the given midpoint
let coordinates of R be (x, y ) and P = (- 15, 4 ) , then
[tex]\frac{x-15}{2}[/tex] = - 6 ( multiply both sides by 2 )
x - 15 = - 12 ( add 15 to both sides )
x = 3
and
[tex]\frac{y+4}{2}[/tex] = 9 ( multiply both sides by 2 )
y + 4 = 18 ( subtract 4 from both sides )
y = 14
the coordinates R = (3, 14 )
in the U
f(x) =
f'(x) =
xsinx COSX
oxsinx - cosx + (xsinx) - D[cosx)
+
D[x sinx] =
J₁
11
=
o[f(x). g(x)] = f'(x) g(x) + f(x
$6
D[sinx]
D[x]. sinx + x.
. Sinx
Sinx + x CUSX
1
sinx +X COSX
x COSY
£²
(x) = (sinx +xcosx) COSX + (xsinx)(-sinx)
f'(x) =
2
X Sin x