The solution of the expression (- 4b² + 8b) + (4b³ + 5b² - 8b) would be
(4b³ + b² ).
Used the concept of the equation that states that,
An equation is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
Given that,
The equation is,
(- 4b² + 8b) + (4b³ + 5b² - 8b)
Now, combine like terms of the equation and simplify as,
(- 4b² + 8b) + (4b³ + 5b² - 8b)
4b³ - 4b² + 5b² + 8b - 8b
4b³ + b²
Therefore, the solution is (4b³ + b² ).
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The random variables X and Y are jointly continuous, with a joint PDF of the form fX,Y(x,y)={cxy,0,if 0≤x≤y≤1,otherwise, where c is a normalizing constant. For x∈[0,0.5] , the conditional PDF fX|Y(x|0.5) is of the form axb . Find a and b .
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 .
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Helpppppppppppppppppppppppppppppppppppp
Which statement about -8 and
-12 is true?
Answer:they are both neagtive numbers.
Step-by-step explanation:
they say it right in front of you.
Joe buys lunch at a local cafe for 8.60 if she leaves a 15% tip how much does she spend at the cafe
Answer:
dhvbhdvhdhddjbd
Step-by-step explanation:
Molly has three pairs of shoes. 1 cost $40, 2 cost $20, and 3 cost $25, if she got 50% off for all shoes, what price was each shoe?
Answer:
20, 10, 12.50
Step-by-step explanation:
the abbreviation for the constant change in a graph or table?
Answer:
ROC
Step-by-step explanation:
ROC. rate of change
On a table or graph, the constant change is same as the unit rate, rate of change or slope, which can be denoted as m.
Constant change on a graph or table simply refers to the rate of change of the output (y) over the change in input (x).
Constant change in a graph or table is the same as the unit rate or the slope value which is dented by the letter m.
Constant rate of change, unite rate, and slope can be denoted as m of a graph or table.
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Write an equation of a line in slope-intercept form that passes through the point (-2, 4) and has a slope of -3. (no spaces in your answer)
Answer:
y = - 3x - 2
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
y = - 3x + b Input Slope
Step 3:
4 = - 3 ( - 2 ) + b Input x and y
Step 4:
4 = 6 + b Multiply
Step 5:
- 2 = b Subtract 6 on both sides
Answer:
y = - 3x - 2
Hope This Helps :)
89.95 DVD player; 5% discount
Answer:
The answer is $85.45 after the 5% discount
johanna prepares a mixture of salad mixed with mayonnaise carrots cucumber lettuce and cheese. what type of mixture divine salad is? why do you think so?
Answer:
johanna prepares a mixture of salad mixed with mayonnaise carrots cucumber lettuce and cheese. what type of mixture divine salad is? why do you think so
Help out
It is due at 7:00
Answer:
I want the free points. Sorry :)
Find all values of k the value of the fraction 11k−15/3 is greater than the value of the fraction 5−2k/4 .
Answer:
k>3/2
Step-by-step explanation:
To solve this, you need to do fraction cross-multiplying.
So, If a/b=c/d, then a*d=c*b
After you cross-multiply, you get this: (11k-15)*4>3(5-2k)
If you simplify 3(5-2k), you get 15-6k
Then, simplify the next side as well
The full simplified expression should be: 44k-60>15-6k
If you add 60 to both sides, you get 44k>-6k+75
Then add 6k to both sides 50k>75
Then all you have to do is divide both sides by 50 and you get:
K>3/2 OR k>1.5
Graph the line of the slope of 1/4 and includes the point (0,2)
Answer:
I'm on Edulastic.com taking a 100 Q test and this question is on it!
Step-by-step explanation:
Imao im fgging confused
The graph of the required line [tex]\bold{y=\frac{x}{4}+2}[/tex] is given below.
Slope point form of equation of line: -An equation of line with slope m and passing through point (p, q) is:
(y - q) = m × (x - p)
We have been given the slope of the line m = 1/4,
and a point (p, q) = (0, 2)
Using the slope-point form equation of line would be,
⇒ (y - 2) = 1/4 × (x - 0)
⇒ (y - 2) = 1/4(x)
⇒ y = x/4 + 2 ...............................(1)
So, the equation of the line is [tex]y=\frac{x}{4} +2[/tex].
To plot the line we need at least two coordinate points.
We have been given a point (0, 2).
We need to find another point.
Substitute x = -4 in equation (1),
⇒ y = (-4)/4 + 2
⇒ y = -1 + 2
⇒ y = 1
So, another point on the line would be (-4, 1).
Now, we plot points (0, 2) and (-4, 1) on coordinates plane.
Then the graph of the line [tex]\bold{y=\frac{x}{4}+2 }[/tex] is as shown in figure.
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Please help me i dont understand
Answer:
5
4
6
.........................
Don’t understand this question
You roll two dice. The first dice shows a ONE and the other dice rolls under the table and you cannot see it. Now, what is the probability that both dice show one?
how many faces does the dice have? I'm gonna assume it had six faces.
Answer:
1/6
Step-by-step explanation:
since the dice has one 1 on it and it cannot be seen
Solve two-step equations
2 = 4s + –10 i need it ASAP
Answer:
s=3
Step-by-step explanation:
Answer:
s=3
Step-by-step explanation:
simplify the equation to the form, which is simple to understand
and then move all terms containing s to the left and all other terms to the right!
pls look at the picture attached! i need help
it is 9 aahh it says to short well 3 times 9 is 27 then minus 17 is less than 13
Answer:
v <= 10
(-infinity, 10]
Step-by-step explanation:
3v - 17 <= 13
+17 +17
3v <= 30
3v/3 30/3
v <= 10
(-infinity, 10]
Question 1
Manipulate the base area and the height of the pyramid, setting different values for each. Record the base dimensions, height, and the exact
volume for two kinds of pyramids: one with a square base and one with a rectangular base. Also calculate the decimal value of each volume, and
verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
Step-by-step explanation:
The length of a rectangle is 3.7 inches when rounded to the nearest tenth of an inch.
Answer:
what is the answerrrrrrrStep-by-step explanation:
(x + 8)(x-8)
answer choices
A x2 + 8x + 64
B x²-64
C x² + 64
x2 + 16X - 64
Step-by-step explanation:
we know the formula(x^2-y^2)=(x+y)(x-y)
so (x+8)(x-8)=x^2-8^2=x^2-64
so the right answer is B
Mary has a bag with 80 pieces of candy. She gives ¼ of her candy to John and 10% to Lisa. How much more candy did she give to John then Lisa?
Answer:
12 pieces
Step-by-step explanation:
80 pieces of candy
1/4 is 25% or 20 pieces of candy
10% would be 8 pieces of candy
subtract the two. Your answer is 12
Answer:
He had 14 more pieces
Step-by-step explanation:
So 80/4 is 20 pieces. So we know John has 20. Now she has 60 left since 80-20 is 60. Now 10 percent of 60 would be 6 pieces. We can subtract 6 from 20 to find out how many more pieces John had. 20-6 is 14. So John had 14 more than Lisa
Which lines are perpendicular to the line y - 1 = {(x+2)? Check all that apply.
Oy + 2 = -3(x - 4)
Oy- 5 = 3(x + 11)
Oy=-3x -
5
y y = 1x-2
=
3x + y = 7
Answer: A C E
Step-by-step explanation:
y = -1x-2 is the perpendicular line of the given line y - 1 = {(x+2).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The product of slope of perpendicular lines will be equal to minus one.
y-1=x+2 the line has a slope of +1.
The slope of the perpendicular line will be -1.
y = -1x-2 is the perpendicular line of the given line y - 1 = {(x+2).
Hence, y = -1x-2 is the perpendicular line of the given line y - 1 = {(x+2).
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5. (01.07A MC)
Which number line best shows the position of ? (5 points)
J7
HHHH +
-4 -3
-1 0 1 2
+
4
-2
3
3
7
HHH H
-4 -3 -2 -1 0 1 2 3
+
4
7
HH
-4
-3 -2
-1 0 1 2
3
4
-
OL
7
t. +
3 4 5
-5 -4
-3 -2
-1 0 1 2
Answer:
if u could include a photo it may help more ..thanks
Math
What is the number of solutions in this system?
No solution
Infinitely many solutions
One solution
Answer:
should be Infinitely many solutions
Step-by-step explanation:
Damien left his house at time Zero and drove to the store, which is 12 blocks away, at a speed of 6 blocks per minute. then he stopped and went into the store for 5 minutes. from there, he drove in the same direction at speed of 2 blocks per minute until he got to the bank, which is 12 blocks away from the store. he stopped at the bank for 2 minutes. then he drove home at a speed of 6 blocks every minute. make a graph of showing the number of blocks away from home that Damien is x minutes after he leaves his house, until he gets back home.
Answer:It take her 20 minutes, but I dont know how to graph yet, so I can only tell you that xx=20
7th grade math help me plzzzz
Answer:
B.
Step-by-step explanation:
Answer:
0.05 per ounce
Step-by-step explanation:
5.20 per 40 is 0.13 per ounce
whereas
2.70 per 15 is 0.18 per ounce
Is 8(3x+2) and 4(6x÷4) equivalent?
Answer:
x= - 8/9
Step-by-step explanation:
Cameron has 75% as many shirts as her brother. How many shirts does her brother have if Cameron has 9 shirts?
Answer:
12 t-shirts
Step-by-step explanation:
12 x 75% = 9 = 9 t-shirts
Please help what Is 4/5 divided by 2
Answer:
2/5
Step-by-step explanation:
Answer:
2.25 is your answer
Step-by-step explanation:
what is the 12
th term rule of the linear sequence 13 7 1 -5 -11
Answer:
-53, f(n) = -6(n-1) + 13
Step-by-step explanation:
given the equation to this linear/arithmetic sequence for the nth term: f(n) = -6(n-1) + 13
f(12) = -6(12-1) + 13
f(12) = -6(11) + 13
f(12) = -66 + 13
f(12) = -53
*substitute and simplify*
______________
f(n) = f(1) + d(n-1)
given f(1) = 13, f(2) = 7, and f(3) = 1
7-13 = 1-7 = -6 = d
= f(1) + d(n-1)
f(1) = 13 so
the equation must be f(n) = 13 - 6(n-1) or -6(n-1) + 13