If x y z = 1, x 2 y 2 z 2 = 2 and x 3 y 3 z 3 = 3, then what is the value of xyz?A bag contains 3 red balls and 5 black balls A ball is drawn at random from the bag What is the probability that the ball drawn (i) red (ii) black A bag with a total of 10 balls contains x blue and y red balls If the number of blue balls is four times the number of red, then write the two equations Problem;X, y, z are 3 non zero positive integers such that xyz = 8 and xyyzzx = , then What would be minimum possible value of x*y^2*z^2 1 vote Positive real numbers x and y are such that x^2 2x 4y^2 = 0 Find the maximum value of xy?
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2^x=3^y=12^z then find 1/z-1/y
2^x=3^y=12^z then find 1/z-1/y-So , x (*1/z1/y)=2 log 2/log 2;• If X and Y are independent, then EX Y = y = EX 1 Examples 1 Suppose the joint pmf of X and Y isgiven byp(1,1) = 05, p(1,2) = 01, p(2,1) = 01, p(2,2) = 03 Find the pmf of X given Y = 1 Solution pXY=1(1) = p(1,1)/pY (1) = 05/06 = 5/6 pXY=1(2) = p(2,1)/pY (1) = 01/06 = 1/6 2 If X and Y are independent Poisson RVs with
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Z = 1;2 (c) Let '(x) the marginal distribution1 2 in the support of f(x,y) (Draw by yourself) (c) Find Pr{X Y <X,z,y Since contain both numbers and variables, there are two steps to find the LCM Find LCM for the numeric part then find LCM for the variable part The LCM is the smallest positive number that all of the numbers divide into evenly 1 List the prime factors of each number 2
Consequently, we can get dby substituting (5;For x = 1;2;3;Use the given values to write an equation relating x, y, and z Then find z when x=1 and y=4 1) x=2, y=4, z=2 2) x=4, y=1/2, z=1 Answer by Alan3354() (Show Source) You can put this solution on YOUR website!
Our online expert tutors can answer this problem Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!(a) Find P(X Y ≤ 1) (b) Find the cdf and pdf of Z = X Y Since X and Y are independent, we know that f(x,y) = fX(x)fY (y) = ˆ 2x2y if 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 0 otherwise We start (as always!) by drawing the support set, which is a unit square in this case (See below, left) 4B so that the linear equation have infinite many solutions (2a1)x 3y5=03x(b1)y2=2 Find the distance between Clinton and Brisbane if they are 6in apart on a map with a scale of 1in 11mi
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Calculation x y = 12 (1) y z = 15 (2) x z = 18 (3) By solving equations (1) and (2) ⇒ x – z = 3 (4) By solving equations (3) and (4) ⇒ x = 75 Put the value of x in equation (1)Z,x,y Since contain both numbers and variables, there are two steps to find the LCM Find LCM for the numeric part then find LCM for the variable part The LCM is the smallest positive number that all of the numbers divide into evenly 1 List the prime factors of each number 2Now we can use Equation 51 to find the marginal PMFs P X ( x) = { 1 6 x = 1 3 8 x = 2 11 24 x = 3 0 otherwise P Y ( y) = { 1 2 y = 2 1 4 y = 4 1 4 y = 5 0 otherwise Using the formula for conditional probability, we have P ( Y = 2 X = 1) = P ( X = 1, Y = 2) P ( X = 1) = P X Y ( 1, 2) P X ( 1) = 1 12 1 6 = 1 2
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Use algebra' and find homework help for other Math questions at eNotesGet an answer for 'if xy z =1 X^2Y^2Z^2=2 X^3Y^3Z^3=3 then find x^4 y^4 z^4=?Section 43 Double Integrals over General Regions In the previous section we looked at double integrals over rectangular regions The problem with this is that most of the regions are not rectangular so we need to now look at the following double integral, ∬ D f (x,y) dA ∬ D f ( x, y) d A where D D is any region
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2 Independent Random Variables The random variables X and Y are said to be independent if for any two sets of real numbers A and B, (24) P(X 2 A;Y 2 B) = P(X 2 A)P(Y 2 B) Loosely speaking, X and Y are independent if knowing the value of one of the random variables does not change the distribution of the other ran(a) Let g(x;y) be the joint marginal distribution of X and Y Then, g(x;y) = X2 z=1 f(x;y;z) = X2 z=1 xyz 108 = xy 36;2;7) for (x;y;z) Answer 4x y 3z= 43 4Find equations for the surfaces obtained by rotating x= y2 about the xaxis and yaxis, respectively Solution Rotating about the xaxis, we need to substitute p y 2 z2 for y Since x= y has no negative part for x, we do not need to square both sides x
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2 x = 3 y = (12) z = k 2 x = k, 3 y = k, (12) z = k 2 = k 1/x, 3 = k 1/y, 12 = k 1/z 12 = 2 2 x 3 k1/z = (k 1/x) 2 x k 1/y k1/z = k 1/x x 2 x k 1/ Since, (a m) n = a mn k1/z = k 2/x x k 1/y k1/z = k 2/x1/y Since, am x an = amn 1/z = 2/x 1/y,1) 1/3 2) 1/6 3) 1/2 4) 1/4 If x y z = 1, x2 y2 z2 = 2 and x3 y3 z3 = 3, then what is the value of xyz?, indicating the origin and coordinates x and y Then indicate the area of xy <
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Answer (1 of 8) Given 2^x=3^y=6^z Lets assume that each and every term is equal to k Which implies 2^x=k Now by applying logarithm on both sides we get x=log k to base 2 and 1/x= log 2 to base k And 3^y=k Again by applying logarithm on both sides we get y=log k to base 3 and 1/y=log 3If y varies directly with x, find the constant of variation if x = 7 when y = 14, then find y when x = 45 If y varies jointly with x and z, and y = 18, x = 3, when z = 2, then find y when x = 5 and z = 3 15 If y varies inversely with x, and x = 9 when y = 45, then find y when x = 27 12/7There are 6 possible pairs (X;Y) We show the probability for each pair in the following table x=length 129 130 131 y=width 15 012 042 006 16 008 028 004
Lustration 2 1 Mathrm G If X Y Z 12 X 2 Y 2 Z 2 96 And Frac 1 X Frac 1 Y Frac 1 Z 36 Then Find The Value X 3 Y 3 Z 3
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EC02 Spring 06 HW9 Solutions April 3, 06 3 y=x w/2 xy=1 X 1 w w−x 1 Y x x To distinguish between the random variables and their values, I have been careCorresponding elements are equal 2x 3 = 9 2y = 12 2z – 3 = 15 2t 6 = 18 Solving equation (1) 2x 3 = 9 2x = 9 – 3 x = 6/2 x = 3 Solving equation (2) 2y = 12 y = 12/2 y = 6 Hence x = 3 , y = 6 , z = 9 &Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign 3x2y=12 3 x 2 y = 1 2 Subtract 2y from both sides of the equation Subtract 2 y from both sides of the equation 3x=2y12 3 x = − 2 y 1 2 Divide both sides by 3 Divide both sides by 3
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T = 6 Show MoreEx 32,9 Find x and y, if 2 8(1&3@0&𝑥) 8(𝑦&0@1&2) = 8(5&6@1&8) Given that 2 8(1&3@0&𝑥) 8(𝑦&0@1&2) = 8(5&6@1&8) 8(1×2&3×2@0×2&𝑥1 2} = Z 1 2 0 Z 1 2 −y 0 4xydxdy = Z 1 2 0 2yx2 1 2 −y 0 dy = Z 1 2 0 2y(1 2 −y)2dy = Z 1 2 0 2y1/4−y y2dy = 2 y2 8 − y3 3 y4 4 # 1 2 0 = 1 96 3 Consider
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Start your free trial In partnership with You are being redirected to Course Hero I want toX f y = − (−12) 3 =4 3 x2 6x−13−y =0 Answer dy dx = − f x f y = −(2x6) −1 =2x6 4 f(x,y)=3x2 2xy 4y3 Answer dy dx = − f x f y = − 6x2y 12y2 2x 5 f(x,y)=12x5 −2y Answer dy dx = − f x f y = − 60x4 −2 =30x4 6 f(x,y)=7x2 2xy2 9y4 Answer dy dx = − f x f y = − 14x2y2 36y3 4xy Example 11 For f(x,y,z) use(a) CalculateVar3Y 1 −2Y 2 Solution Var3Y 1 −2Y 2 = 32 VarY 1 (−2)2 VarY 2 2(3)(−2) CovY 1,Y 2 = 48 (b) CalculateVar3Y 1 −4Y 2 2Y 3
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•2(x3)=2xλ (12) •2(y1)=2yλ (13) •2(z1)=2zλ (14) •x 2y z2=4 (15) •The simplest way to solve these equations is to solve for x, y, and z in terms of λ from (12), (13), and (14), and then substitute these values into (15)X* (1/z1/y)= (log 12log 3)/log 2;So, we are trying to find all the solutions to $2^x 3^y = z^2$ in nonnegative integers Here are my insights First of all, $z^2$ can be either $0$ or $1$ modulo $3$
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If X Y Z 12 X 2 Y 2 Z 2 96 And 1 X 1 X 1 Z 36 Then Find The Value X 3 Y 3 Z 3
Dear Student, Please find below the solution to your problem we know if a b c = 0 then a^3 b^3 c^3 = 3abc so if x^1/3 y^1/3 z^1/3 = 0 thenClick here👆to get an answer to your question ️ If 2^x = 3^y = 12^z , then find the value of z(x 2y)xyFirst type the equation 2x3=15 Then type the @ symbol Then type x=6 Try it now 2x3=15 @ x=6 Clickable Demo Try entering 2x3=15 @ x=6 into the text box After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x3=15 2(6)3 = 15 The calculator prints True to let you know that the answer is right More Examples
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Then type the @ symbol Then type x=3 Try it now 2x @ x=3 Clickable Demo Try entering 2x @ x=3 into the text box After you enter the expression, Algebra Calculator will evaluate 2x for x=3 2(3) = 6 More Examples Here are more examples of how to evaluate expressions in Algebra Calculator Feel free to try them nowOn x^3 x y^3 y = z^3 z Suppose we wish to find an infinite set of solutions of the equation x^3 x y^3 y = z^3 z (1) where x, y, z are integers greater than 1 If z and x are both odd or both even, we can define integers u and v such that z=uv and x=uvWe know that x = 5 and y = 12, so we can use the original equation to determine that z = 13 We can plug in all the values that we now know 2(13) dz dt = 2(5)2 2(12)3 dz dt = 46 13 Note that z could also equal −13, but I am assuming that the physical restrictions behind this problem would not allow such an answer
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2^x 3^y = z^2 1 where x, y, and z are nonnegative integers We can see that 1 is a congruence modulo 8 3^y = z^2 (mod 8) 2 When z=1 and and y=2 we have 3^2 = 1 (mod 8) 3 and by Fermat's theorem So this means that y must be even As y is even, we can write y = 2k for some integer k So we have 3^2k 2^x = z^2 z^2 3^2k = 2^xGet an answer for 'Tell which statement is not true 1 If x2/x = 5y/5, then 2/x = y/5 2 If x/3 = y/4, then x/y = 4/3 3 If x3/4 = y/5, then x3/y =4/5 4If x4/4 = 3y/y, then x/4 = 3/y ' andLet X, Y, Z denote 3 jointly distributed random variable with joint density function then 2 01,0 1,0 1,, 0otherwise Kx yz x y z fxyz Find the value of K Determine the marginal distributions of X, Y and Z Determine the joint marginal distributions of X, Y X, Z Y, Z 111 2 000 1,,f x y z dxdydz K x yz dxdydz
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From the property of the log log 12log 3=log log (12/3)=log 4=2 log 2;1 2 3\pi e x^{\square} 0 \bold{=} Go Related »So substituting the values for the elementary symmetric polynomials that we found, we find that x, y and z are the three roots of t3 −t2 − 1 2t − 1 6 = 0 or if you prefer 6t3 − 6t2 −3t −1 = 0 In theory we could solve this using Cardano's method and directly evaluate x4 y4 z4, but the methods used above are somewhat easier
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Click here👆to get an answer to your question ️ If 2^x = 3^y = 12^z ,show that 1z = 1y 2x1 2} Pr{X Y <2 4 x 1 x 2 x 3 3 5 2 Example Let T(x;y;z) = x 2y;2x y Since T <3!<2, Ais a 3x2 matrix w 1 = x 2y 0z w 2 = 2x y 0z So, A= 1 2 0 2 1 0 Geometric Operators { Re ection Operators Re ection about the yaxis The schematic of re ection about the yaxis is given below The transformation is given by w 1 = x w 2 = y with standard
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The variable z varies jointly with x and y Use the given values to write an equation relating x, y, and zFor x = 1;2;3;Find all the zeroes of the polynomial 2xcube xsquare 6x 3 if 2 of its zeroes are √3 and √3 IF one of the zeros of quadratic polynomial is f(x)=14x²42k²x9 is negative of the other, find the value of k
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(e) Below is the graph of z = x2 y2 On the graph of the surface, sketch the traces that you found in parts (a) and (c) For problems 1213, nd an equation of the trace of the surface in the indicated plane Describe the graph of the trace 12 Surface 8x 2 y z2 = 9;To ask any doubt in Math download Doubtnut https//googl/s0kUoeQuestion If 2^x = 3^y =12^z show that 1/z= 1/y2/xNow , from 2–1 we get x/zx/y=log 12/log 2log 3/log 2;
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$ x y z = 12 \ $ and $\ x^2 y^2 z^2 = 12 $ Normally these questions have a simple and elegant solution and although I've managed to solve it, the answer I found was neither!Let us consider the following system of three equations with three unknowns x, y and z a 11 x a 12 y a 13 z = b 1 a 21 x a 22 y a 23 z = b 2 a 31 x a 32 y a 33 z = b 1 Now, we can write the the following determinants using the above equationsI wondered if anyone can see a simpler way to tackle the problem
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If the square difference of the quadratic polynomial is the zeroes of p(x)=x^23x k is 3 then find the value of k;Y = 1;2;3 (b) Let h(x;z) be the joint marginal distribution of X and Z Then, we compute it as h(x;z) = X3 y=1 f(x;y;z) = X3 y=1 xyz 108 = xz 18;Plane z = 1 The trace in the z = 1 plane is the ellipse x2 y2 8 = 1
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