Answer:
The value of Cov (X, Y) is 25/6.
Step-by-step explanation:
It is provided that:
[tex]X\sim U(0,10)\\\\Y|X\sim U(0,x)[/tex]
The probability density functions are as follows:
[tex]f_{X}(x)=\left \{ {{\frac{1}{10};\ 0<X<10} \atop {0;\ \text{otherwise}}} \right. \\\\f_{Y|X}(y|x)=\left \{ {{\frac{1}{x};\ 0<Y<x} \atop {0;\ \text{otherwise}}} \right.[/tex]
Then the value of f (x, y) will be:
[tex]f_{X,Y}(x,y)=\left \{ {{\frac{1}{10x};\ 0<X<10,\ 0<Y<x} \atop {0;\ \text{Otherwise}}} \right.[/tex]
Then f (y) is:
[tex]f_{Y}(y)=\int\limits^{10}_{y} {\frac{1}{10x}} \, dx[/tex]
[tex]=\frac{1}{10}\times [\log x]^{10}_{y}\\\\=\frac{1}{10}[\log 10-\log y][/tex]
Compute the value of E (X) as follows:
[tex]E(X)=\frac{b+a}{2}=\frac{10+0}{2}=5[/tex]
Compute the value of E (Y) as follows:
[tex]E(Y|X)=\frac{b+a}{2}=\frac{x+0}{2}=\frac{x}{2}\\\\\text{Then,}\\\\E(E(Y|X))=E(\frac{x}{2})\\\\E(Y)=\frac{1}{2}\times E(X)\\\\E(Y)=\frac{5}{2}[/tex]
Compute the value of E (XY) as follows:
[tex]E(XY)=\int\limits^{10}_{0}\int\limits^{x}_{0} {xy\cdot \frac{1}{10x}} \, dx dy[/tex]
[tex]=\int\limits^{10}_{0}\int\limits^{x}_{0} {\frac{y}{10}} \, dx dy\\\\=\frac{1}{10}\times \int\limits^{10}_{0}{\frac{y^{2}}{2}}|^{x}_{0} \, dx \\\\=\frac{1}{10}\times \int\limits^{10}_{0}{\frac{x^{2}}{2}}\, dx\\\\=\frac{1}{10}\times [\frac{x^{3}}{6}]^{10}_{0}\\\\=\frac{100}{6}\\\\=\frac{50}{3}[/tex]
Compute the value of Cov (X, Y) as follows:
[tex]Cov (X, Y)=E(XY)-E(X)E(Y)[/tex]
[tex]=\frac{50}{3}-[5\times\frac{5}{2}]\\\\=\frac{50}{3}-\frac{25}{2}\\\\=\frac{100-75}{6}\\\\=\frac{25}{6}[/tex]
Thus, the value of Cov (X, Y) is 25/6.
Find the equation of a sphere if one of its diameters has endpoints: (-9, -12, -6) and (11, 8, 14).
= 0
Answer:
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].
Step-by-step explanation:
There are two kew parameters for a sphere: Center ([tex]h[/tex], [tex]k[/tex], [tex]s[/tex]) and Radius ([tex]r[/tex]). The radius is the midpoint of the line segment between endpoints. That is:
[tex]C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)[/tex]
[tex]C(x,y,z) = (1,-2,4)[/tex]
The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:
[tex]r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}[/tex]
[tex]r = 10\sqrt{3}[/tex]
The general formula of a sphere centered at (h, k, s) and with a radius r is:
[tex](x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}[/tex]
Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].
solving these quadratics for x using complete the square 3x^2-4x-1=0
Answer:
in picture
Step-by-step explanation:
Jenna was asked to find a fraction equivalent to 4/6 with a numerator of 14.Her answer is 14/16. What error did jenna make in writing equivalent fractions
Answer: Jenna did not multiply how much 4 goes into 14 which is 3.5 she should have multiplied 4*3.5=14 and 6*3.5=21
Step-by-step explanation:
so the answer should have been 4/6 is equivalent to 14/21
Hopes This HelpsA community sports league is raising money by making custom shirts to sell at league games. They plan to sell the shirts for $13. Each shirt costs $6 to make. They spent $55 for advertising. Use n to represent the number of shirts they sell. Multiply this by the money they make for each shirt, then subtract the advertising cost. Which expression represents the money that the league raises?
O A. 55 – (13 – 6) n
O B. (13-6) n - 55
O C. 13n - 6 - 55
O D. 13 – 6n – 55
Answer:
B. (13-6) n - 55
Step-by-step explanation:
The number of shirts to be sold is n
The cost to purchase one shirt is $13
The cost of making each shirt is $6
Let's assume the shirt is one
Profit for a Shirt = (13-6)
But then there are no number of shirts
Profit= (13-6)n
But then also, an advert was run for the total shirts combined
Profit= (13-6)n -55
Answer:
b. (13-6)n-55
ap3x
Early European explorers who discovered the New World were actually looking for a Northwest Passage in order to- Question 2 options:
find a shorter water-route to Asia.
prove the world was round.
improve trade with Native American Indians.
explore the Great Lakes
Answer:
find a shorter water-route to Asia.
Step-by-step explanation:
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 5 + 54x − 2x3, [0, 4]
Answer:
The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.
Step-by-step explanation:
Let be [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex], the first and second derivatives of the function are, respectively:
[tex]f'=54-6\cdot x^{2}[/tex]
[tex]f''=-12\cdot x[/tex]
Now, let equalize the first derivative to zero and solve the resulting expression:
[tex]54-6\cdot x^{2} = 0[/tex]
[tex]x^{2} = 9[/tex]
[tex]x =\pm 3[/tex]
According to the given interval, only [tex]x=3[/tex] is a valid outcome. Lastly, this is evaluated in the second derivative expression:
[tex]f''=-12\cdot(3)[/tex]
[tex]f'' = -36[/tex]
[tex]x = 3[/tex] leads to an absolute maximum.
[tex]f(3) = 5 + 54\cdot (3) -2\cdot (3)^{3}[/tex]
[tex]f(3) = 113[/tex]
The absolute minimum is determined by evaluating at each extreme of the interval:
[tex]x = 0[/tex]
[tex]f(0) = 5 + 54\cdot (0) -2\cdot (0)^{3}[/tex]
[tex]f(0) = 5[/tex]
[tex]x = 4[/tex]
[tex]f(4) = 5 + 54\cdot (4) -2\cdot (4)^{3}[/tex]
[tex]f(4) = 93[/tex]
The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.
I need some help please.
Answer:
Square Root 34
Step-by-step explanation:
Answer:
[tex]\sqrt{34}[/tex]
Explanation:
sub in the values for x1, x2, y1 and y2
[tex]\sqrt{(-2-3)^2+(2-(-1))^2}[/tex]
subtract and evaluate
= [tex]\sqrt{(-5)^2+3^2}[/tex]
= [tex]\sqrt{25+9}[/tex]
= [tex]\sqrt{34}[/tex]
Given f(x)= 18x + 12, find f(7).
Answer:
138
Step-by-step explanation:
f(x)= 18x + 12
Let x = 7
f(7) = 18*7 +12
= 126+12
= 138
Answer:
f(7) = 138
Step-by-step explanation:
[tex]f(x)= 18x + 12\\f(7) = ?\\\\f(7) = 18(7) +12\\f(7) = 126+12\\f(7)=138[/tex]
Give two other names for WQ
Answer:
Two other names for WQ are QW and line g.
Step-by-step explanation:
A line can have as many points as possible. The two other names for WQ are QW and line g
From the given plane, we can observe the following:
Points W and Q are on the same lineLine g has points Q and W on it.This means that, we can rename WQ as
QW i.e. this is done by writing Q before W.Line g i.e. by giving WQ the name of the line, on which both points are.Hence, the two other names for WQ are QW and line g
Read more about points and lines at:
https://brainly.com/question/2284415
(AM GIVING BRAINLIEST) Find all complex numbers z such that z^4 = -4 Note: All solutions should be expressed in the form a+bi, where a and b are real numbers. plz explain
Answer:
z = {1 +i, 1 -i, -1 +i, -1 -i}
Step-by-step explanation:
Using Euler's formula, you can write this as ...
z^4 = 4e^(i(π+2kπ))
Then the 4th root is ...
z = 4^(1/4)e^(i(π/4 +kπ/2)) = √2(cos(π/4+kπ/2) +i·sin(π/4+kπ/2))
for integers k in the range 0 to 3.
z = √2(±1/√2 ±i·1/√2) . . . signs are independent
z = ±1 ±i . . . . . . signs are independent; hence 4 solutions
z = {1 +i, 1 -i, -1 +i, -1 -i}
_____
Comment on roots of complex numbers
In the complex domain, each number has a number of roots equal to the index of the root. That is, there are four 4th roots. They all have the same magnitude, but their angles are separated by 360°/(root index) = 90°. Here, the principal fourth root of 4∠180° is 4^(1/4)∠(180°/4) = √2∠45° = 1+i.
Adding 90° is equivalent to multiplying by i, so the other 3 roots are √2∠135° = -1+i, √2∠225° = -1 -i, and √2∠315° = 1 -i.
z = {1 +i, 1 -i, -1 +i, -1 -i}
9. The annual interest rate is 21%. The balance after the grace period was $700. No
payments were received. What is the interest for the month?
Answer:
Interest for the month = $12.25
Step-by-step explanation:
Given:
Amount in bank = $700
Rate of interest per month = 21% / 12 = 0.0175
Find:
Interest for the month
Computation:
Interest for the month = Amount in bank × Rate of interest per month
Interest for the month = $700 × 0.0175
Interest for the month = $12.25
If two sets are subsets of each other, what other relationships must they have?
Answer:
Step-by-step explanation:
If A ⊂ B, that is, A is a subset of B
Also, B ⊂ A, that is, B is a subset A
Therefore, A = B in all respect.
A set is a mathematical model for a collection of items. If two sets are subsets of each other, the other relationship they must have is that they both are equal.
What is a set?A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
If there exist two subsets such that A is a subset of B, also, B is the subset of A. Then the two sets are equal or the same.
Hence, If two sets are subsets of each other, the other relationship they must have is that they both are equal.
Learn more about Set:
https://brainly.com/question/8053622
#SPJ2
Why can't you use the product of powers rule to simplify
this expression? Explain.
3^4.2^8
Answer:
Because the base of this expression is not same.
A bicycle has a listed price of $749.95 before tax. If the sales tax rate is 6.5% , find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
749.95+ 44.997 *or 45.00 giving 794.95
Answer the following questions.
Division:
1. 61,982 ÷ 23
2. 803 ÷ 37
3. 816 ÷ 28
4. 219 ÷ 47
5. 2,624 ÷ 82
6. 50,000 ÷ 72
7. 1,333 ÷ 43
8. 6,528 ÷ 16
Multiplication (see image):
Multiplication
2, 56, 0, 56, 18, 0, 3, 0, 20, 12
12, 54, 7, 64, 18, 25, 24, 0, 0, 28
14, 8, 6, 24, 35, 9, 27, 48, 40, 1
0, 3, 18, 16, 8, 7, 0, 0, 36, 48
49, 28, 40, 42, 15, 6, 27, 16, 36, 8
0, 32, 81, 4, 30, 0, 0, 9, 32, 10
30, 2, 45, 16, 5, 0, 0, 14, 35, 18
0, 54, 0, 12, 36, 24, 4, 8, 10, 18
72, 6, 63, 12, 0, 21, 0, 24, 63, 0
21, 20, 9, 15, 45, 0, 6, 72, 5, 4
(3x2 + 3) - (6x + 4) + (3x2 - 5x)
Answer: 16
Step-by-step explanation:
Multiply: (x+3y)(x-2y)? Show steps please
Answer:
x² + xy - 6y²
Step-by-step explanation:
FOIL
(x+3y)(x-2y)
F= x²
O= -2xy
I= 3xy
L= -6y²
Add these together = x² + xy - 6y²
Step-by-step explanation:
Hey, there!
Let me simply clear you.
While multiplying algebraic expression, you must be very careful about sign and brackets.
Here,
[tex](x + 3y)(x - 2y)[/tex]
Let's multiply (x-2y) by (x+3y)
[tex] = x(x - 2y) + 3y(x - 2y)[/tex]
[tex] = ({x}^{2} - 2xy) + (3xy - 6 {y}^{2}) [/tex]
Open brackets.
[tex] = {x}^{2} - 2xy + 3xy - 6 {y}^{2} [/tex]
Simplify the like terms.
[tex] = {x}^{2} + xy - 6 {y}^{2} [/tex]
Therefore, the answer is x^2 + xy- 6y^2.
Hope it helps.....
A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle. The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles. The largest angle is twice the smaller angle plus 20 degrees. The sum of the triangle's interior angles is x + y + z = 180. Which two equations represent the remaining angle relationships? Select each correct answer.
x = 2z + 20
x=2(z+y)−60
x=2z+y−60
x = z + 20
x=60−2(z+y)
The answer can be seen on the attachment that I have given.
The two equations that represent the remaining angle relationships are (x = 60 - 2(y + z)) and (x = 2z + 20) and this can be determined by using the given data.
Given :
A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle.The measure of the largest angle is 60 degrees less than twice the sum of the measure of the other two angles. The largest angle is twice the smaller angle plus 20 degrees. The sum of the triangle's interior angles is x + y + z = 180.The linear equation that represents the situation "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles" is:
x = 60 - 2(y + z) --- (1)
The linear equation that represents the situation "The largest angle is twice the smaller angle plus 20 degrees" is:
x = 2z + 20 --- (2)
Therefore, the correct option is A) and E).
For more information, refer to the link given below:
https://brainly.com/question/2263981
Please help Im stuck in this homework assignment.
Answer:
(0,3)
Step-by-step explanation:
You need to pick a point, P, that will give you a distance from A to P that is twice as long as from P to B, or ration 2:1
Point A is (-2,-7), point B is (1,8), and I picked (0.3) because it looked like it could be, but now we need to test it.
Distance formula is:
[tex]d=\sqrt{(x_{2}-x_{1})^{2} + {(y_{2}-y_{1})^{2} } \\[/tex]
So AP would be
[tex]AP=\sqrt{(0--2)^{2} + {(3--7)^{2} } \\[/tex]
[tex]AP=\sqrt{(2)^{2} + {(10)^{2} } \\[/tex]
Do the same with PB, and you will find it's 5.1, giving an approximate ratio of 2:1.
The perimeter of a square can be expressed by the function f(s) = 4s, where s is the length of the side in inches.
Answer:
answer choice D
Step-by-step explanation:
CORRECT ANSWER IS D
i believe
Hi Folks, please any hand with this equation of a straight line / gradients coordinates excercise please. thanks
don't give up you got it always stay positive
Determine whether the following functions are even, odd, or neither.
f(x) = x2 + 4x - 7:
f(x) = 4.x2 +1:
f(x) = 5x5 – 42:
Simplify the expression to a polynomial in standard form: (4x+5) (x^2-3x-2) PLEASE HLEP
Answer:
[tex]4x^3-7x^2-23x-10[/tex]
Step-by-step explanation:
So we have the expression:
[tex](4x+5)(x^2-3x-2)[/tex]
Distribute. Multiply (4x+5) to each term:
[tex](x^2)(4x+5)+(-3x)(4x+5)+(-2)(4x+5)[/tex]
Distribute:
[tex]=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)[/tex]
Combine like terms:
[tex]=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)[/tex]
Add and simplify:
[tex]=4x^3-7x^2-23x-10[/tex]
And this is in descending order, so it's in standard form.
3. A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation?
A. The speed at which the car travels
B. The age of the car
C. The number of hours the car has traveled
D. The distance the car has traveled
Answer:
The answer is A) the speed at which the car has traveled
Step-by-step explanation:
Help me pls! Anyone?
Step-by-step explanation:
[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]
[tex]\huge{\purple{\underline{\underline{\bf{\pink{Given}}}}}}[/tex]
It is a parrelogram
[tex]\huge\star{\underline{\mathtt{\red{To}\pink{f}\green{i}\blue{n}\purple{d}\orange{-:}}}}⋆[/tex]
X and Y
Solution
angle a = c. (opposite angles of 11gm is equal)
put the values of and c
x+45 = 3x-13
now take the variables to the l.H.S and number to R.H.S
x-3x = -13-45
-2x. = 58
x. = 58÷2
x. = 29
angle d + c = 180° (cointerior angle)
y + 3(29) + 13 =180°
y + 100 = 180°
y. = 80
Hope it helps
Find all solutions of the equation in the interval (0,2π)
cot theta +root 3 = 0
Answer:
θ = 5π/6 rad and 11π/6 rad
Step-by-step explanation:
Given the expression cotθ+√3=0
Subtract √3 from both sides
cotθ+√3-√3=0-√3
cotθ = -√3
Since cotθ = 1/tanθ
1/tanθ = -√3
Reciprocate both sides:
tanθ = -1/√3
θ = tan^-1(-1/√3)
θ = -30°
Since the angle is negative, and tanθ is negative in the second and fourth quadrant.
In the second quadrant;
θ = 180-30
θ = 150°
Since 180° = πrad
150° = 150π/180
150° = 5π/6 rad
In the fourth quadrant;
θ = 360-30
θ = 330°
Since 180° = πrad
330° = 330π/180
330° = 11π/6 rad
Hence the solutions are 5π/6 rad and 11π/6 rad.
4(x - 5) = 4 (4 + x)
Answer:
x=0
Step-by-step explanation:
4(x-5) = 4(4+x)
4x-20 = 16+4x
4x-4x = 16+20
0x=36
x = 36/0
x = 0
hope it might help
Please mark me as brainlist
Ronald and Tim both did their laundry today. Ronald does laundry every 6 66 days and Tim does laundry every 9 99 days.
Answer:
Find a number that can be divided by both 6 and 9, which is 18. That means they will do laundry on the same day every 18 days.
Answer: 18 Days
Step-by-step explanation:
Let's look at their indivigual schedules for hte nex little While
<-0------6------12---->
t=Tim does laundry every 9 days
<-0---------9---------->
They haven't done laundry on the same day again yet, so let's keep going!
When we keep goin, we see thar the multiple first meet at 18
Ronal
<-0----6----18----27---->
Tim
<-0----9----18----27--->
Mathematically, we say that 18 is the least common multiple of 6 and 9. in math notation this looks like:
lcm (6, 9) = 18
Lets See how fast can you Answer an High school Math Problem? 1. What is the degree of 7x + 1? 2. What is the solution to the system x + y = 5 and 3x - y = 3? 3. What is (x^4)/(x^0)? I'll check over your answer! You MUST answer all the question and get all the answers right to get Brainliest! Also I need to see how you got that answer!
Answer:
1) 1
2) (2,3)
3) x⁴
Step-by-step explanation:
1)
We have the expression:
[tex]7x+1[/tex]
The degree of an equation is the largest exponent of the equation.
We can rewrite our expression as:
[tex]=7x^1+1x^0[/tex]
1 is the largest exponent.
Thus, our degree is 1.
2)
We have the system of equations:
[tex]x+y=5\\3x-y=3[/tex]
To solve, we can use substitution.
From the first equation, subtract x from both sides:
[tex]y=5-x[/tex]
Substitute this into the second equation:
[tex]3x-(5-x)=3[/tex]
Simplify:
[tex]3x-5+x=3[/tex]
Add 5 to both sides:
[tex]3x+x=8[/tex]
Combine like terms:
[tex]4x=8[/tex]
Divide both sides by 4:
[tex]x=2[/tex]
So, x is 2.
Substitute this back into the first equation:
[tex]x+y=5[/tex]
Substitute x for 2:
[tex]2+y=5[/tex]
Subtract 2 from both sides:
[tex]y=3[/tex]
Our solution is (2,3)
3)
We have the expression:
[tex]\frac{x^4}{x^0}[/tex]
Anything to the zeroth power (except for 0) is 1. Assuming x is not 0:
[tex]=x^4/1\\=x^4[/tex]
And that's the simplest it can get.
Answer:
[tex]\Huge \boxed{\mathrm{1. \ 1}} \\ \\ \\ \Huge \boxed{\mathrm{2. \ (2,3)}} \\\\\\ \Huge \boxed{{3. \ x^4 }}[/tex]
Step-by-step explanation:
The degree is the largest exponent on the variable.
[tex]7x^1 + 1x^0[/tex]
The largest exponent on the variable is 1.
The degree is 1.
System of equations:
[tex]x+y=5 \\ \\ 3x-y=3[/tex]
Solving y for the first equation.
Subtracting x from both sides.
[tex]y=5-x[/tex]
Substitution method.
[tex]3x-(5-x)=3[/tex]
Distribute negative sign.
[tex]3x-5+x=3[/tex]
Combining like terms.
[tex]4x-5=3[/tex]
Adding 5 to both sides.
[tex]4x=8[/tex]
Dividing both sides by 4.
[tex]x=2[/tex]
Substitution method.
[tex]y=5-2 \\ \\ \\ y=3[/tex]
[tex]\displaystyle \frac{x^4 }{x^0 }[/tex]
Subtract exponents with same bases when dividing.
[tex]x^{4-0}[/tex]
[tex]x^4[/tex]
Which shapes can the composite figure be
decomposed into? Check all that apply.
circle
rectangle
triangle
trapezoid
Square
Answer:
B C D
Step-by-step explanation:
i did the assignment
Answer:
rectangle, triangle,trapezoid
Step-by-step explanation: