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Q: {-) Evaluate the domain of f(x)=Ven(Sx-XE)

A: The given function is f(x)=ln5x-x24

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: 31. Let f(x) = [x²/3]. Find f(S) if a) S= (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: The given function is, fx=⌊x2/3⌋. To Find: f(S) for the following set S, (a) S=-2,-1,0,1,2,3 (b)…

Q: Show that if gcd (a, y) = 1 and a \ xy Then a\ x

A: Definition : Greatest common divisor ( gcd): Let  a and b be are two  integers, not both 0.  A…

Q: Suppose X ∼ Binom(n, p). Show that E[X] = np.

A: Suppose Its probability mass function is defined as,Where,

Q: Let X~N(10,9).

A: The mean of the distribution is 10. The standard deviation of the distribution is 9.

Q: . Prove that an→L = Jan] → |L]. (Make cas

A: Given that an is a sequence which converges to L that is, an→L. Then we have to prove that |an|…

Q: Let Z∼N(0,1). Find P(-2<Z<1).

A: From the provided information,Z~N (0, 1)The probability P (-2&lt;Z&lt;1) need to be calculated.

Q: Let X~N(10,9). Find P(Z > -2)

A: It is given that, X~N(10,9)

Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

A:

Q: let fai) = -x+7| -1-342| whare XER GIue Explietly expression for z y the full Bmupliyind

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Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find a. D' b. D-A c. P(A)

A: Note:-Since you asked multiple subparts,according to our policy we can solve only first three sub…

Q: When is S \ T = T \ S for sets S, T? Give an example

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Q: Let X~ N (24, 49), Find P( 10<X< 38)

A: Given sample are: 24, 49 Mean of these samples are: μ=24+492=36.5 Standard deviation:…

Q: Show dz 4 In= 는I미페 - for a<0. x <

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Q: 2h 1+h )-2 = 1 – if h<<r Prove that ( %3D r

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Q: Evaluate iy ( + + " ). Nin t

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Q: et x + y+ z=5 where x, y, z E R. Prove that x² + y² + z² >

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Q: Soluti 03 16. A 11 22 1 Let Ax- b be a linear svstem of n eauations in n unknowns, and assume that A

A: Given: A = 03-2114225, b = 75-2  and Ax = b To find: The value of matrix x.

Q: If xly, then show that ||x+ y|| = ||x- y|!.

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Q: Let z=x+iy  Let w=a+ib

A: To prove the equality of the two given angles

Q: Show that if x is in both W and W-, then x = 0.

A: Dot product of perpendicular vectors is 0.

Q: Suppose u, v belong to V. Prove that = 0 if and only if ||u|| ≤ ||u+av|| for all a belong to F

A: We have to prove  if and only if

Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Let S={(0,-1,1),(0,-2,-1),(1,1,2)}.

A: S?

Q: -3 < x To nenen Is fox is odd ? even or

A: Use definition of odd and even .

Q: prove with a table if x → y then xor y xor y = y

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: how that ℝ3 = span( 1 1 2 1 2 1 0 3 -1

A: We want to show that  any vector can be written as linear combination of the three  given vectors…

Q: 3.) if f(x)= akw f(x) = x-1 and (X) X-1 What is the valule of

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Q: PiU Let ZoCQ ( -iS Z has Lest uPper bound Proferty? 2-is Z has grest lower bound Profer to?

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Q: Let x, y € Z. Prove that if 2 | (x² - y2) then 4 | (x² - y²)

A: We know that the sum of two odd numbers is an even number.Also, the difference between two odd…