What is the probability that a randomly chosen student is female, given that the student is Left-handed?! A random sample of 500 students is classified by gender and dominant hand. Left-handed Right-handed Total 5/11 0.2 3/5 O 2/5 Female 100 150 250 Male 120 130 250 Total 220 280 500

Q: Consider the matrix -() 2 0 5 0 0 2 5 A = Find the eigenvalues and eigenvectors of A

A: Ans.   Given matrix      A=520250002 we know that Eigen values are roots of equation     A-λI=0 So,…

Q: Suppose 2 < f'(x) < 6, for –1 < x< 1. Then f(1) – f(-1) is between A) 2 and 10. B) 4 and 12. C) 0…

A: GIVEN : 2 ≤f'(x) ≤6,  for -1 ≤x≤1 TO FIND : f(1) - f(-1) HINT : Mean value theorem

Q: G.. Evaluate the fallowing real integrals by residue. theerem 3 -bm e 응) co3 mx (x4a?) Cx+b?)

A: This is complex analysis problem, we apply the residue theorem to solve the problem.

Q: fx >2 e every wE W.

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Q: 8. Let BC2, C C2 and define if n is odd, В, C, An if n is even. What is lim inf An and lim sup A,?

A: For the solution follow the next step.

Q: ample 6.16 Solve the difference equation 8yes - 6y: + Y = 9 (k> 0) given that y, = 1 and y; =

A: Given the difference equation :

Q: 5. Suppose an > 0, bn > 1 and lim an = 0, lim bn = 1. %3D Define An = {x : an <x < bn}. %3D Find lim…

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Q: Let G be a d regular graph (i.e., all vertices have d neighbors). (a) What are the eigenvalues of…

A: Given:-Gn be a  d regular grapgh(a) If G is d.regular graph then the laplacian is given by…

Q: (a). u(x, y) = e- sin y, (b). v(x, y) : = cos x cosh y, %3D

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Q: 1 Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01)…

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Q: Q4:A. Find the Laplace transform of (1) f(t) = cos?t (2) f(t) = te-3t cos2t

A: If f(t) is a function of t for all positive values of t, then the Laplace transform of f(t) is given…

Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: To illustrate calculations with the unit impulse function, consider evaluation of the following…

A: As per our company guidelines, we can solve first question for you. If you want other questions to…

Q: 4.2. Let a=for n23 (a) Let f be the function given by f(x) = -1/ For x23, fis continuous, xlnx…

A: Please see the attachment  We are supposed to do one problem.

Q: For the following probability distribution 3 4 P(x) 2/5 1/5 2/5 The population variance is . O 0.7 O…

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Q: 21. Suppose A is a field and suppose also that A closed under countable disjoint unions. Show A

A: This is a question of measure theory.

Q: B. Find the autocorrelation function of the periodic function x(t) 1 2 3

A: Introduction -  Definition for periodic signals  If f is a continuous periodic function of period T…

Q: (c) Show that the following linear system is a strictly diagonally dominant: 7x1- X2 - X1 + 7x2 - x3…

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Q: The following data give approximations to the integral 1.5 In x² dx M = N, (h) = 0.13515504, N, (4)…

A: Using Richardson's extrapolation, it can be written that N2(h)=4N1h2-N1h3.

Q: Consider the system shown in Figure 4-50 We wish to design a digital controller such 3. that the…

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Q: Q: By using Euler's equation Solve the following: f\x,リyx) %3D

A: Given:  fx, y, y'=x1+y'2 where y'=yx So, ∂f∂y=0,  ∂f∂y'=xy'1+y'2

Q: 22/Find the Fourier series for the following function? (SM) r)=x for

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Q: Calculate the length L of the hollow hexagon cylinder with closed ends with the thickness of 8 mm,…

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Q: Shanaya graphed the line represented by the equation y =x-6. Write an equation for a is parallel to…

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Q: Suppose f: a,b] → R is continuous and faf=/ for all xie [a,bl Show that f(x)= 0 ft rEla,b).

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Q: Determine the Laplace transforms of the follow- ing functions: 1. (a) 2re2 (b) re (a) (s- 2)2 2. (b)…

A: Laplace transferom

Q: 2. Find the Laplace and Inverse Laplace transforms of the followings: (a) cosh(t)sin(2rt): Hint(cosh…

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Q: a. Show that f has a removable discontinuity at x = 3. f(x) = x²7x+12 x + 2 x = 3

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Q: A carnival ferris wheel with a radius of 14 meters makes one complete revolution every 16 seconds.…

A: Solution:

Q: vationš 50. Consider the 3 observations 3,7,11 for which the mean is 7 and the standard deviation is…

A: Solution: Given information: The  3 observations are  3,7 and 11 The mean is 7  and standard…