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
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true or false. The value -5 is an element of the solution set for the inequality x<-3
Answer: It’s True
The explanation: I did this already and I got an 100% I hope this helps I you have other questions just ask me! Hope you get a good score!
2/3-3/5 = ?/15-?/15
Answer:
10/15-9/15
Step-by-step explanation:
Answer:
2/3-3/5=10/15-9/15
Step-by-step explanation:
You want a common denominator which here is 15. To get to 15 in 2/3 you needed to multiply by 5 and in 3/5 you needed to multiply by 3.
The stem-and-leaf plot shows the test scores of a science class. Use the plot to answer the question.
How many students scored 78?
Answer:
4 students
Step-by-step explanation:
Understanding stem-and-leaf plots
A stem and leaf plot is designed in a way to group the numbers by their values before the ones place;
i.e. 92, 100, 101, 103, 113
Charted as
9 | 2
10 | 0 1 3
11 | 3
So, with that in mind we know 78 is grouped under the 7 | # # #
stem and has the leaf of 8 which is displayed by # | # # # 8
SO,
TO SOLVE:
Count the 8's under the 7 | # # # # group
We can see that there are 4 8's under that section, and assuming that each number is representative of one students score, we can conclude that 4 students scored 78
Hope this helps,
J.M."Jamon"
Pennsylvania State University
Full-Time B.S.CE. Undergrad
Answer:
4 Students
Step-by-step explanation:
If you look at the four and cout how many 8 are across you will get 4!
The circle graph shows how the money will be spent for the party.
Food: 30%
Drinks: 20%
Prizes and favors: 35%
Paper productions: 15%
The class has $300 for a party.
How much will be spent on party favors and prizes?
A: $35.00
B: $105.00
C: $195.00
D: $265.00
Answer:
B. $105.00
Hope this helps!
Which expression is equivalent to fourteen more than the product of three and nine
Answer:
Step-by-step explanation:
The product of 3 and 9 just means to multiply 3 and 9. This is written as:
3 x 9
14 more than this just means to add 14 to the above.
3 x 9 + 14
Graph the line with slope – 7 and y-intercept 6.
Answer:
(✿◠‿◠)
I put the link in the comments!
A graph of the line with a slope of -7 and y-intercept of 6 is shown in the image below.
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 is the slope or rate of change.x and y are the points.b is the y-intercept or initial value.Based on the information provided about this line, the y-intercept is 6 and the slope is -7.
In this context, we can logically deduce that a linear equation that models the line is given by;
y = mx + b
y = -7x + 6
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Find the value(s) of "k" that will cause the equation 4x^2 +kx + 4 to have one real solution.
Answer: k = {8, -8}
Step-by-step explanation:
In order for a quadratic equation to have exactly one solution, the discriminant must equal zero. → b² - 4ac = 0
4x² + kx + 4 = 0
↓ ↓ ↓
a=4 b=k c=4
b² - 4ac = 0
k² - 4(4)(4) = 0
k² = 64
k = √64
k = ± 8
98x34=(100x34)-(1x34)
Answer:
This statement is not true.
Step-by-step explanation:
98*34=3332
and
100*34=3400
1*34=34
3400-34=3366
(100*34)-(1*34)=3366
Please help me with these 2 questions :(
Answer:
1st: y=-2x-3
2nd:y=-2x-13
Step-by-step explanation:
Since the line is parallel to y = -2x-4, its slope is -2. Therefore, we have the equation y=-2x
But when we evaluate that equation at -1, we get -2(-1)=2, but we want to make it equal to -1 when evaluated at -1. Therefore, we can subtract 3, as 2-3=-1.
Therefore, the equation is y=-2x-3.
For the second question, we can use a similar concept. The slope will be -2, but if you directly evaluate it at -4, it's going to be 8, but we want it to be -5, so we subtract 13.
Therefore, the equation is y=-2x-13
Problem 1
Answer: y = -2x-3--------------
Explanation:
Parallel lines have equal slopes but different y intercepts.
Linear equations in the form y = mx+b have slope m and y intercept b.
The slope of y = -2x-4 is m = -2
So any parallel line to this will also have m = -2
Plug (x,y) = (-1,-1) along with the value of m, into y = mx+b and solve for b
y = mx+b
-1 = -2(-1)+b
-1 = 2+b
2+b = -1
b = -1-2
b = -3
The parallel line is y = -2x-3
==============================================
Problem 2
Answer: y = -2x-13--------------
Explanation:
We'll use the same ideas and steps as problem 1.
y = -2x-5 has slope m = -2
The parallel line also has slope m = -2
We want the parallel line to go through (x,y) = (-4,-5)
So,
y = mx+b
-5 = -2(-4)+b
-5 = 8+b
8+b = -5
b = -5-8
b = -13
The parallel line is y = -2x-13
out of 50 students,34 joined the journalism class and 25 joined the robotics club.If 16 students joined both clubs,how many students are in neither club
debate time : crab or lobster best answer gets brainliest
WILL BE MARKED BRAINLYEST
Ray OJ bisects Angle LOK.
Measurement of Angle LOK = 82 degrees.
Solve for x.
Answer:
x = 14
Step-by-step explanation:
<LOJ = 3x
<KOJ = (2x + 12)°
<LOK = 82°
m<LOJ + m<KOJ = m<LOK (angle addition postulate)
3x + 2x + 12 = 82 (substitution)
5x + 12 = 82
5x = 82 - 12 (Subtraction property of equality)
5x = 70
x = 70/5 (division property of equality)
x = 14
11. Given a polynomial P(x) = x³-4x²-5x is one of the zeroes.
a) Factorise P(x) completely
b) Sketch the graph of P(x)
C)Find the domain and range.
Answer:
thats some tuff
Step-by-step explanation:
Answer:
Step-by-step explanation:
P(x)=x³-4x²-5x=x(x²-4x-5)
=x(x²-5x+x-5)
=x[x(x-5)+1(x-5)]
=x(x-5)(x+1)
domain (-∞,∞)
range: (-∞,∞)
blank times blank = 1.5
Answer:
12
Step-by-step explanation:
Answer:
Your answer is:
1) 0.75 * 2
2) 0.3 * 5
Step-by-step explanation:
Hope any of these helped you : )
Can someone please help?
Select all of the nets that can be folded and assembled into a triangular prism like this one.
The correct options for folded and assembled into a triangular prism are;
Option A and Option D.
What is Triangle?
A triangle is a three sided polygon, which has three vertices and three angles.
Given that;
The triangular prism figure after fold is given.
Now, The triangular prism figure is contain two triangles and three squares.
So, In option A;
There are two triangles and three squares.
And, In option D;
There are two triangles and three squares.
Thus, The correct options for folded and assembled into a triangular prism are;
Option A and Option D.
Learn more about the triangle visit:
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Plz help ty very much
Answer:
A fungus breaks down the body of a dead animal or organism.
btw you cant be in college I did this years ago in fourth grade
A fungus breaks down the of a dead animal
who got the answer to this ?
(4x^2+6+7)-(-8x^2-2x+6)
Answer:
12x^2+2x+7
Step-by-step explanation:
Distribute the Negative Sign:
=4x^2+6+7+−1(−8x^2−2x+6)
=4x^2+6+7+−1(−8x^2)+−1(−2x)+(−1)(6)
=4x^2+6+7+8x^2+2x+−6
Combine Like Terms:
=4x^2+6+7+8x^2+2x+−6
=(4x^2+8x^2)+(2x)+(6+7+−6)
=12x^2+2x+7
The linear equation has 5(x + 2) = 5x + 2 A) no solution. B) one solution. C) two solutions. D) infinitely many solutions
it's A it has no solution
Which expression is equal to -12 1/2 + 5 3/4
Answer: A
Step-by-step explanation:
It wants you to make it an in improper fraction
Come One Come All!!!!!
Answer: 1. is A, 2. is C, i dont know 3. 4. is B i think. then 5. is probably option 2
Step-by-step explanation:
Which of the following is NOT true about Nebuchadnezzar?
He created a code of laws that were very strict.
He created the Hanging Gardens for his wife.
He went insane at the end of his life.
He decorated the city with colored bricks and animal statues.
Your answer would be C.
He did not go insane
2/7 divided by 8/9. HURRY
Answer:
9/28 in fraction , 0.3214285714 in decimal
Step-by-step explanation:
0.32142857142 in decimal form
If the length is 4 and the width is 6, what’s the height?
Answer:
The answer to this is: 24
Step-by-step explanation:
The points Q, R, S and T all lie on the same line segment, in that order, such that the
ratio of QR:RS: ST is equal to 1:4:5. If QT = 40, find RS.
Answer:
RS=3
Step-by-step explanation:
Solve for x:
6x+3x+x=10
All parts add up to whole
10x=10
Combine like terms
x=1
Use x to solve for segment lengths:
QR=6x=6(1)=6
RS=3x=3(1)=3
ST=x=1
Therefore RS=3
The length of the line segment RS will be 16 units.
What are collinear points?An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.
Let Q, R, S, and T be the collinear points. Then the condition of the collinear will be
QR + RS + ST = QT
The points Q, R, S, and T all lie on the same line segment, in that order, such that the ratio of QR:RS: ST is equal to 1:4:5. If QT = 40.
Let QR / 1 = RS / 4 = ST / 5 = x
QR = x
RS = 4x
ST = 5x
Then the value of the variable x will be
QR + RS + ST = QT
x + 4x + 5x = 40
10x = 40
x = 4
Then the length of the line segment RS will be
RS = 4x
RS = 4 (4)
RS = 16
Then the length of the line segment RS will be 16 units.
More about the collinear points link is given below.
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Round four hundred seventy-six thousand three hundred twenty-one and fifty thousand eight hundred nine hundred-thousandths to the nearest dollar.
Answer:
476,321.50
476,322
Step-by-step explanation:
Rewrite the following expression: x3 + x5 =
Answer:
x + 8 = x8
Step-by-step explanation:
This is one of the many ways to rewrite this equation. The reason this is a way of rewriting it is because 3x plus 5x equals 8x and if you take away the variable from 3 and 5 and add the numbers together you get 8. So take the variable x add it to 8 and you get x8. Both equations have the same answer so therefor this is another way of writing the equation.
Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne's function?
Complete question is;
Dionne Washington wants to sell natural fruit flavored water at her neighborhood block party. She wrote the amount of money she spent as a function of the number of bottles sold. Which set of numbers would be an appropriate domain for Dionne’s function?
A) 0, 1, 2, 3, 4, …
B) …, −4, −3, −2, −1, 0
C) …, −3, −2, −1, 0, 1, 2, 3, …
D) …, −3.5, −2.5, −1.5, 0, 1.5, 2.5, 3.5, …
Answer:
Option A: {0,1, 2, 3, 4,....}
Step-by-step explanation:
Domain is simply a set of input while the range is a set of output values.
For example, if we have a function named f(x) = x², the domain will be all possible values of x being inputed while the range will be the value of f(x) for all possible values of x inputed.
Now, from the question, we are told that she wrote the amount of money she spent as a function of the number of bottles sold.
If the number of bottles sold is denoted by "x", it means the function is; f(x).
Now, number of bottles has to be a non-negative whole number or simply a non-negative integer. Thus, the possible values of x are all non-negative whole numbers like, 0,1, 2, 3, 4, 5....
Thus,domain is {0,1, 2, 3, 4,....}
Answer:
A. 0,1,2,3,4,.....
Step-by-step explanation:
which figure has 6 lines of symmetry draw is needed
Answer:
C
Step-by-step explanation:
i believe it C.
no matter which point to point of line you go,
it will always be a six line symmetry.
9514 1404 393
Answer:
C
Step-by-step explanation:
Figure C has 6 lines of symmetry as shown in the attachment.
MLN=QPR. What is the measure of <1 and <2?
Answer:
B. <1 = 90, <2 = 40
Step-by-step explanation:
Given that ∆MLN = ∆QPR, it follows that the measure of their corresponding angles would be of the same measure.
<P = right angle = 90°
<1 corresponds to <P, therefore, <1 = 90°
<R = 40°
<2 corresponds to <R, therefore, <2 = 40°.
The answer would be: B. <1 = 90, <2 = 40