Answer:
The value of a and b are 8 and 1 respectively
Step-by-step explanation:
[tex]f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 , \text{otherwise}\end{matrix}\right.[/tex]
[tex]\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1\\\\c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1\\\\\frac{c}{2}\int_{0}^{1}x\left ( 1-y^2\right )\text{dx}=1\\\\\frac{c}{2}\int_{0}^{1}(x-x^3)\text{dx}=1\\\\\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1\\\\\frac{c}{2}\left [ \frac{1}{2}-\frac{1}{4} \right ]=1\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1\\\\c=8[/tex]
Conditional pdf of [tex]f_{x,y}(x|0.5)[/tex]
[tex]f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}[/tex]
Normalizing pdf of 1
[tex]f_{y}y=\int_{0}^{y} 8yx \text{dx}[/tex]
[tex]f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\\f_{y}y=4y(y^2)\\f_{y}y=4y^3\\f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}=\frac{2x}{0.25}=8x[/tex]
We are given that PDF [tex]f_{x|y}(x|0.5)[/tex] is of the form [tex]ax^b[/tex]
So, on comparing 8x with [tex]ax^b[/tex]
So, a = 8 , b = 1
So, the value of a and b are 8 and 1 respectively
The resulting value of a and b given the conditional PDF of fX|Y(x|0.5) is mathematically given as
a = 8 , b = 1 .
What are the values of a and b?Question Parameters:
a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,
For x∈[0,0.5]
the conditional PDF fX|Y(x|0.5)
Generally, the equation for the function of (x,y) is mathematically given as
[tex]f_{x,y}(x,y)=\left\{\begin{matrix}cxy ,\text{if} 0 \leq x \leq y \leq 1\\ 0 ,\end{matrix}\right.[/tex]
Therefore
[tex]\int_{0}^{1}\int_{x}^{1}cxy \text{dy dx}=1[/tex]
[tex]c\int_{0}^{1}x\left ( \frac{y^2}{2}\right )_{x}^{1} \text{ dx}=1[/tex]
[tex]\frac{c}{2}\left [ \frac{x^2}{2}-\frac{x^5}{4} \right ]_{0}^1=1[/tex]
[tex]\\\\\frac{c}{2}\left ( \frac{1}{4} \right )=1[/tex]
C=8
Where, the conditional PDF fX|Y(x|0.5)
[tex]f_{x,y}(x|0.5)=\frac{f_{xy}(x,y=0.5)}{f_{y}y}[/tex]
We have
[tex]f_{y}y=8y[\frac{x^2}{2}]_{0}^{y}\[/tex]
[tex]f_{y}y=4y^3[/tex]
[tex]f_{x|y}(x|0.5)=\frac{8x(0.5)}{4(0.5)^3}[/tex]
f_{x|y}(x|0.5)=8x
In conclusion. with the pdf in the form of ax^2
8x comparing ax^b
The value of a = 8 , b = 1 .
Read more about Arithmetic
https://brainly.com/question/22568180
Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a height of 12 ft and a radius of 10 ft. How fast does the depth of the water change when the water is 10 ft high if the cone leaks at a rate of 8 cubic feet per minute?
Answer:
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Step-by-step explanation:
Given
Represent radius with r and height with h
[tex]h = 12ft[/tex]
[tex]r = 10ft[/tex]
[tex]Rate = \frac{8ft^3}{min}[/tex] when [tex]h = 10ft[/tex]
Express radius in terms of height
[tex]\frac{r}{h} = \frac{10}{12}[/tex]
[tex]\frac{r}{h} = \frac{5}{6}[/tex]
[tex]r = \frac{5}{6}h[/tex]
First, we need to determine the volume of the cone in terms of height.
[tex]Volume = \frac{1}{3}\pi r^2h[/tex]
Substitute [tex]r = \frac{5}{6}h[/tex]
[tex]V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h[/tex]
[tex]V = \frac{1}{3} * \pi * \frac{25}{36}h^3[/tex]
[tex]V = \frac{25}{108} \pi h^3[/tex]
Differentiate both sides w.r.t time (t)
[tex]\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}[/tex]
Solve for [tex]\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}[/tex]
At this point, [tex]h = 10[/tex] and [tex]\frac{dv}{dt} = \frac{8ft^3}{min}[/tex]
So, we have:
[tex]\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}[/tex]
[tex]\frac{dh}{dt} = \frac{864}{7500\pi}[/tex]
[tex]\frac{dh}{dt} = \frac{216}{1875\pi}[/tex]
Hence:
The rate is [tex]\frac{216}{1875\pi} ft/min[/tex]
Using implicit differentiation, it is found that the depth of water changes at a rate of -0.0764 feet per minute.
The volume of a cone of radius r and height h is given by:
[tex]V = \frac{\pi r^2h}{3}[/tex]
Applying implicit differentiation, we can find it's rate of change, thus:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
In this problem:
Height of 12 ft and radius of 10 ft, thus [tex]h = 12, r = 10[/tex].Radius does not change, thus [tex]\frac{dr}{dt} = 0[/tex].Water leaks at a rate of 8 cubic feet per minute, thus [tex]\frac{dV}{dt} = -8[/tex]Then:
[tex]\frac{dV}{dt} = \frac{2\pi rh}{3}\frac{dr}{dt} + \frac{\pi r^2}{3}\frac{dh}{dt}[/tex]
[tex]-8 = \frac{\pi (10)^2}{3}\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = -\frac{24}{100\pi}[/tex]
[tex]\frac{dh}{dt} = -0.0764[/tex]
The depth of water changes at a rate of -0.0764 feet per minute.
A similar problem is given at https://brainly.com/question/9543179
For how many different positive integers n is each of n, n+2, and n+4 a prime number?
Answer:
3,5,7
Step-by-step explanation:
odd numbers is a multiple of three, at least one of them can't be prime
hope this helps there is 1 of them
-8-x=x-4x < what is the answer Please show work. 37 POINTS
Answer:
-8-x=x-4x
-8-x=-3x
-8=-2x
4=x
Answer:
free robux!?!!?
Step-by-step explanation:
The midpoint M of QR has coordinates (6, 6). Point R has coordinates (5, 7). Find the
coordinates of point Q.
Write the coordinates as decimals or integers.
Answer:
(7,5)
Step-by-step explanation:
Write another ratio that’s is equilevent too.4:6
Answer:
There is 4/6 as a fration or 4.6
Step-by-step explanation:
Answer:
2:3 is equivalent to 4:6
Step-by-step explanation:
I know that these ratios are equivalent because each side of the ratio 4:6, are divided by the same number, 2, 4 divided by 2 is 2 and 6 divided by 2 is 3 which gives us a equivalent ratio of 2:3
Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12-liter batch of iced tea with 90 tea bags.
What will Kermit think of Peggy's iced tea?
Answer:
He will love the Tea
Step-by-step explanation:
12 divided by 2 is 6
We take 6 ( the liter that he likes ) and multiply it by 15. This gives us 90, exactly what Peggy made.
Answer:
It is just right!
Step-by-step explanation:
12 divided by 2 is 6 . We take 6 and multiply it by 15. This gives us 90, which is exactly what Peggy made.
A, B, C, or D???? Please help! Thank you!
Answer:
Step-by-step explanation:
either the c or d
The school store sells 4 pencils for $0.80. What is the unit cost of a pencil?
lines of best fit (regression lines) must touch all dada points on a scatter plot
true or false
Answer:
False
Step-by-step explanation:
A regression line tries to average out all data points, so it may not touch any of them.
Which organelle is marked with an X?
Answer:
cell wall :)
Answer:
Lysosome.
Step-by-step explanation:
If You Saw The Questions Before This One, you can see the Question: Which accurately labels the lysosome? and its X, so the answer is Lysosome
Carly spends $5 for n notebooks. Write an algebraic expression to represent the cost of one notebook.
Answer:
vfgvygfvygybgybgybgybvgybgyvbg
Step-by-step explanation:
cvbnhbvcxzcdfvgbhjkhnfgvcdxsdfggvbgfvygf
Answer:
5÷n
Step-by-step explanation:
5÷n will tell you how much it is for each notebook
Lines m and n are parallel. What is
Answer:
Line m and m is a straight line
Please help I will put brainliest
Answer:
−64x12y12
Good Luck!!!
Answer:
[tex]-64x^{12} y^{12}[/tex]
Step-by-step explanation:
1. remove parentheses by multiplying factors.
2. use exponent rules to remove parentheses in terms with exponents.
3. combine like terms by adding coefficients.
4. combine the constants.
One angle in a triangle measures twice the smallest angle, whereas the largest angle is nine times the smallest angle. Find the measures of all three angles.
° (smallest value)
°
° (largest value)
Step-by-step explanation:
Let the smallest angle be x
2nd angle = 2x
3rd angle = 9x
By angle sum property
x+2x+9x=180°
x=180/12
x=15
Three angles are 15, 30 and 135
Jakes grandmother lives 8 miles away from him.His aunt lives 6 times as far away from him as his grandmother.How far away does his aunt live ?
Answer:
48 miles.
Step-by-step explanation:
If Jake's grandma lives 8 miles away, and his aunt is 6 times as far, then you multiply 6 * 8 and get 48.
Lex be a random variable that represents the pH of arterial plasma (le, acidity of the blood). For healthy adults, the mean of the distribution is - 7.4.1 A new drug for arthritis has
been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.6 with
sample standard deviations - 2.7. Use a 5% level of significance to test the claim that the drug has changed (either way) the mean pH level of the blood.
USE SALT
(a) what is the level of significance?
what is the value of the sample test sisse? (Round your answer to three decimal places)
Answer:
2.304
Step-by-step explanation:
2/3 times 6/7 divided by 2/5
Answer:
so the answer is 1 whole and 3/7 hope this helps :)
explanation:2/3× 6/7 = 4/74/7 ÷ 2/5 = 1 3/7An accounting firm has 900 hours of on-the-clock staff time and 100 hours of reviewing time available to assign each week. The firm charges $300 for a tax return and $2000 for a small business audit. A small business audit requires 100 hours of staff time and 10 hours of review time. A tax return requires 12.5 hours of staff time and 2.5 hours of review time. In order to maximize their revenue for the week, how many small business audits and how many tax returns should the firm schedule? What is their maximum revenue for the week?
Constraints:
Objective Formula:
Answer:
The maximum revenue for the week is $19,000.
Step-by-step explanation:
Denote the variables as follows:
X = small business audit
Y = tax return
The maximizing function is:
Z = 2000·X + 300·Y
The maximizing function is subjected to the constraints:
100·X + 10·Y ≤ 900
10·X + 2·Y ≤ 100
0 ≤ X and 0 ≤ Y
The problem can be solved using the simples method as follows:
Let s and t be slack variables.
Initial:
x y s t b Basic
100 10 1 0 900 s (departing)
12.5 2.5 0 1 100 t
Z -2000 -300 0 0 0
(entering)
Step 1:
x y s t b Basic
1 1/10 1/100 0 9 x
0 1 -1/10 1 10 t (departing)
Z 0 -100 20 0 18000
(entering)
Step 2:
x y s t b Basic
1 0 1/50 -1/10 8 x
0 1 -1/10 1 10 y
Z 0 0 10 100 19000
(entering)
The optimal solution is:
X = 8
Y = 10
The maximum revenue for the week is $19,000.
Solve the inequality.
2(4+2x)25x+5
Answer:
[tex]100x^{2} +200x+5[/tex]
Step-by-step explanation:
Answer:
x ≤ 3
Step-by-step explanation:
hello please help will give brainliest!
Answer:
B
Step-by-step explanation:
The chart says Jana swam 200 miles in 120 s, and Micah swam 200 meters in 104 s.
Answer:
B! It's B!
Step-by-step explanation:
With A, there is a difference of 75 meters.
With C, there is a difference of 25 seconds.
With D, there is a difference of 9 seconds.
But with B, they both show they are correct!
HELP !!!
Find the equation of a line parallel to -3x - 5y = 4 that contains the point (4,3). Write the equation in slope-intercept
form
9514 1404 393
Answer:
y = -3/5x +27/5
Step-by-step explanation:
Since we want a parallel line, we can use the same x- and y-coefficients to find the new constant in the given form:
-3(4) -5(3) = -12 -15 = -27
In the given form, the equation of the desired line is ...
-3x -5y = -27
Solving for y, we have ...
-5y = 3x -27
y = -3/5x +27/5
3. A store manager reports that the mean grocery bill at her store on a Saturday is between
$28.25 and $36.75. To do this, she considered a random sample of customers that Saturday.
What was the sample mean? (Remember that the sample mean is the center of the confidence
interval). What was the margin of error?
Answer:
Hope you understand, and never stop striving to learn!
Step-by-step explanation:
The sample mean is both values added together then divided by 2.
$46.63
The margin of error is the low value divided by the high value * 100% =76.8% (then you have to minus this from 100% so the margin of error is 23.2%)
Please help math lines again my profile is filled with them by now
Answer: Soil loss is caused by a variety of factors, including erosion from wind and water, mechanical tilling, logging, agricultural practices, and poor water management. Erosion and sedimentation, the major effects of soil loss, are widespread and can be devastating.
Erosion
Erosion is a natural process on hill slopes. The rate of erosion is determined by several factors, including soil type, rainfall, and length and percent of slope. Generally, human-induced changes in the landscape lead to higher levels of erosion than would occur naturally. While there are many ways to minimize erosion, vegetative cover is the most effective over the long term. Eroding road.When vegetation is removed, the rate of soil erosion is greatly accelerated, often beyond sustainable levels.
Sedimentation
Eroded soil deposited downslope is referred to as sedimentation. When severe rain or wind events occur or soils are disturbed by human
The Sedimentation Control Act of 1973 requires operators to implement short- and long-term mitigation measures to reduce erosion on- and off-site. Forest landowners who wish to harvest trees are exempt from these regulations if they comply with forestry practice guidelines, which include erosion control measures and mitigation. Best management practices (BMPs) are voluntary practices that reduce sources of se
Step-by-step explanation:
I need help ASAP please
A circle is 360 degrees so 360 = b + 96 + 209
360 = b + 305
b = 55 degrees.
If Jim can read an average of 20 pages in 40 minutes, how many hours would it take him to read a manual containing 90 pages?
Answer:
it takes him 180 kinutes to read 90 pages
what is the y- intercept from the table
-1 because y-intercept is where y meets zero, therefore the y intercept of this graph would be -1<3
Which of the following is not a rational number? (-12/35) (10) (2/0) (2 1/2)
Answer:
(- 12/35) THIS IS THE MAIN ANSWER YOU CAN SEE IN THE GOOGLE
There are 150 people in a school dance. The ratio of adult to students is 2: 3. How
many adults are in the dance ?
Answer:
60 adults
Step-by-step explanation:
There are 60 adults in the dance because as we have 150 people and the ratio of adults to students is 2:3, we need to add 2+3=5. Now we have 5 parts, so 150÷5=30. This means that there are 30 people per part, and as adults hold 2 parts of it, 30 x 2=60. So, there are 60 adults in the dance. Hope it helps!
Can someone please help?
Solve the inequality 4x − 6 > 6x − 20. (5 points)
Answer:
14
[tex] 14 > 2x[/tex]
Step-by-step explanation:
you first have to move 4x to the right side and then add 20 yo the left side to get what i got