Prove that the operation * defined on M2x2(R) by taking A * B = A. B V A,B E M2x2(R). %3D is an associative operation on Z

Q: 2 Gire ample the which the derintin exist for right hand devivtive to kept haud detivalin?

A: A function f(x) is said to be differentiable at a point 'c' if both the left hand derivative(L.H.D.)…

Q: Prove or disprove: if A and B are denumerable, then ANB is denumerable.

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Q: Q) prove that aset A is non denumerable iland only if AxAXA is nondenumerable

A: In this question, we have to show that a set A is non denumerable if and only if A×A×A is non…

Q: By using caushy Rieman prove that C. Prove thatd az az ae

A: According to the given information, it is required to use Cauchy Riemann to prove that:

Q: find Rang, coefficiend of Rangs, Quartile devialion and cocfficient, of of the following OD classes…

A: Range= Largest term-shortest term R=L-S Here S= 1-0.5= 0.5 L= 60+0.5= 60.5 R= 60.5-0.5= 60…

Q: Use Newlon's Me thod with the runclion $r(x)=x^{2}-2$ and inilial value $x_{0}=3: to calculate…

A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

Q: prove if P>-l then Citp = I+np %3D n€ IN

A: The given statement is not TRUE. Counter example is taking n = 2.

Q: a Which of he pocess e satoay? that in some cases you may not be able to get an eact exresin.In…

A: a) Note that Therefore Yk has a pmf of a Poisson random variable, which implies that it is a…

Q: © Let Y Le the bunduy of the dise Dle) for ocrcl Suppise fisc on the open disc ole,n Such that Must…

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Q: Prove that S3 = Inn(S3) = Aut(S3).

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Q: Prove that S4 is not isomorphic to D12.

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Q: Find the dircetiond Darevitive ef He Fouctien in the divéchen oF olOs O20)

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Q: For wich of the following Lunchions is Roll's theovem applicabre in [o,2] O 2/3 f13) = (x-1) f(1) =…

A: By Rolles Theorem, for a function f:[a,b]→R, if  (a) f is continuous on [a,b](b) f is differentiable…

Q: 1 Evaluate using Convolution theorem : L

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Q: - check the exi's tence of limol of the Lunetiom 41n at X= 1 %3D 2X+/ こ Xラ-3

A: To check: The existence of the limit of the function. Given: The function is fx=2x+1     -1≤x≤1x22-3…

Q: Prove by induetion onn that for all irdegers nz2, Nz2,Gilit)

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Q: 1] Let X,YER. Prove that VxVy(4x+9y>9⇒(x>5/4 Vy> 4/9)) using method of indirect proof.

A: Prove that ∀x∀y4x+9y>9⇒x>54∨y>49, where x, y∈ℝ. Prove the statement using method of…

Q: let R be for of King and acR.UThen a3-a Prove all that R is commutative

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Q: Prove: If f1, f2 € R(a) on [a, b] with fi < f2, then ' fi da < s' fz da

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Q: 94) Show that F= ;². ?' is Consenvatwe and gind potintial - the sealar

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Q: if JERLA.b] and it hex)- J(x). except for finite mumber of Paint in Cab] then that he Rlab] prove.…

A: if g ∈R[a,b] and if h(x) = g(x) except for a finite number of points in [a,b] then prove that h…

Q: Prove that d24 and s4 are not isomorphic. List elements and there order.

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Q: Let D={(txy.2) : x²ny2sz²s 324, z2 Evaluate z dv.

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Q: Prove in duc tion: the fillowing usny the frimcifle of kiathemotical 1 +1 + + t 3. n+3 2n

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Q: Show that 2"=nCk and 0 = [(-1)^nck k=0 HINT: Consider(1-1)" and (1+1)" k=0

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Q: find z trans foyms of folleing -an simwn ĭ

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Q: Prove that, IXI<a Rf and If -aL X Z a

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Q: Is provethat V3 is lrrational hunber

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 3. Prove that Re(2-+z')<4 when z<1.

A: a.          x+y ≤x + y                                             (triangle inequality)b. Re(z1+z2)…

Q: Let a, be such that asb. Prove that tx Eqt ax cbx

A: Concept: We have a,b∈Q means that a, and b belongs to the rational numbers and a&lt;b means that a…

Q: Let D be the red region in the below figure. y Then ff, -3dzdxdy is Onegative )equal to zero…

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Q: Let an= こn らnf1 a) de ter mine whetber I an] is conver g ent or diver gent b) determine whether

A: Since part a and part b both are same, I am doing part a.

Q: s] Assume that is an operation on S with identity element e, and that x * (y * 2) = (x * z2) * y for…

A: A operation  " o " on S is said to be commutative if x o y = y o x  for all x and y in S  And…

Q: Use Lemma 5.4.3 to find RT if RS 6 and VR = 4.

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Q: Check the lineor delende nee or IndePondence fature for seto below: in M UR 2x2 1 o in PsUR) B)…

A: The solution is given as

Q: Determine all the number(s) c which satisfy the conclusion of Rolles Theorem for

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Q: find the desivalive d the functian ha)= ainfse and compute h'(2) Th o

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Q: Let X= Ucy) out of standard er dere d unierm and Y= Uc5) out of

A: From the given information, X=U(4) out of 8 standard ordered uniform and Y=U(5) out of 8 standard…

Q: Compute/o . Show your work.

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Q: (ii) A = 82 + &V1+ 4

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Q: Check Al That Apply nent an imege of exactly one element

A: This is a problem of function.

Q: Let a * b = 2ab be defined on Z*. 1. Is * Commutative? 2. Is * Associative? 3. What is the identity…

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Q: Evaluate the integral. (Hint: rewrite cot, do u-sub) 7π/3 4 cot dt 7n/6 O 28 In 3 -14 In 3 -28 In 3…

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Q: Prove that √2+√5 is irritational

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Q: Apply any method to prove that alb (or a nand b), which is defined to be ¬(a ^ b) is complete. Write…

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Q: Suppose that r, s are integers (possibly different from x, y res that ar + bs = c. Show that there…

A: Introduction: Let us suppose that two integers are a and b, greatest common divisor of these two…

Q: * lnn is © Divergent O Commegent a Conditional © None ☺ Conergent O d O b a

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Q: Evaluate the integral. O sV3+4 + C V3+4 + C V3+4 O 5V3+2 V3+2 + C + C In x

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.