If In x + In(x – 3) = In(7x), then a =

Q: Solve for r: In(x) + In(x + 2) = 3

A: Use the properties of lograthim and simplify.

Q: In the expansion of (x+y)35

A: We use the Binomial Theorem to find the required coefficient in the given question.

Q: pend. Ex 5) m/MPQ = 10x + 5, m/MPN = 2x, m/NPO = 3(x + 7), and m<OPQ = Find x and m/NPO. Ex 6) m/QPO…

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Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: s expansion of 2 , valid in the re of 1/z2 is:

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Q: (c) w = 5ln(7r + 8) %3D O u = r' + 8, w = 5lnu O u = 7r, w = 5 (Inu + In8) O u = In(7r), w = 5 ln(u…

A: w=5 ln(7r+8)

Q: n) the Integral evalu ate car 1- (X² +3) e Xdx

A: Given integral Apply integration by parts formula to integrate

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: In x /1+ (In x)² -dp-

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Q: A factory received a shipment of 11 lightbulbs, and the vendor who sold the items knows there are 3…

A: Given in the question: Total bulbs, N = 11 Defective bulbs, x = 3 Now we will calculate the sample…

Q: Prove that S4 is not isomorphic to D12.

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Q: - Let X1, X2, ...,Xn~N(0,0) and T = Fi (T),Var(T)

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Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

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Q: 2. Evaluate the following dr 2.1.V1-(In)* dr 2.2. VE(1+ z) dr e-e- 2.3.

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: in in Signed-Rank Test a two-sided alternative, we may reject H0 in favor of H1 if either w+ or w-,…

A: Signed rank test for  two tailedHo:M≠Mowe reject Ho, if W+≤Wα and W-≤Wα

Q: Show that F0F1 . . . Fn−1 = Fn − 2 for all n ≥ 1, where Fi is the i-th fermat number

A: To Show -

Q: Prove that E, k2* = (n – 1)2"+1 +2 for all n > 1. =D1

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Q: Find y,(x) if y = In(In(Inx)).

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Q: (-1)" -Σ S. n=1 Vn+1

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Q: X1,, Xn ~ N(-3,2) (random variables) ... Z, = 1(X,X2 + X1X3 + X1X4 + •..+ X1X„), n > 3 %3D (a) Find…

A: From the given information, X1, .....,Xn~N-3,2 And Zn=1nX1X2+X1X3+...+X1Xn, n≥3 Consider,…

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: Suppose we observe X1, X2, ..., X U (0, 1). Show that nX(1) 4 Exp(1). с.

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Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: x² Vx² + 1 .2 Expand In in terms of In x, In(x² + 1) and In(x+ 1). (x+ 1)7

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Q: 42. Show that S 4xys + %3D 1- x2 1- y? 1– 22 (1 – a²) (1 – 3²) (1 – 2²) if xy + xx yz = 1

A: Given that  xy+yz+xx=1 Prove that the expression

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

A: Dot product of perpendicular vectors is 0.

Q: Let D = {2, 4, 8) "For every z D, 2x¹ €

A: Given that set D = { 2, 4, 8}  And statement is  " For every x in D,   2| x". We need to check that…

Q: Prove the following in Z[i]: if a y and 3|y with a and B relatively prime then aß | y. in

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Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: 3sin4t dt 2. 5(1- 3cos21)

A: We have to find integral

Q: It is possible to regress x1 on y. a. True b. Falas

A: From the given dataset we have to check that , is it possible to regress X1 on Y1  or not.

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: Suppose x, n ∈ N and n not equal to  0. Then, show that xn is positive if and only if x is positive

A: Given that x, n∈N and n≠0. According to question, N=0,1,2,3,4,5........ First suppose xn is positive…

Q: 2 In x | Show that 4 x* +1 16

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Q: Compute a (х + 2) dx. O x3 + x² + C O x² (x² + 2x)+C x2 + 2x ) + C 2 - + C 2 + x2 + C 3

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Q: Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

A: Suppose A.B = 0 then we have to show that  Column space of B contained in the null space of A  i.e…

Q: Suppose X~N(113,18), and Z~N(0,1). Then x = 94, is equivalent to z = ______.

A: Given that, Suppose X~N(113,18), and Z~N(0,1). Here, mean μ=113 and standard deviation σ=18

Q: D. Let Find 2,-

A: We will find out the required value.

Q: A manufacturing company employs two devices to inspect output for quality control purposes. The…

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Q: c) Evaluate ſ x*(In x)²dx

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Q: 26. If z = In(x² +y²), find x- ду Əx A) х с) у в) х-у D) 0

A: If z=ln(x2+y2), We need to find x∂z∂y-y∂z∂x.

Q: 2 O Expand Pn = 2x +3x +) in Term of P.f,.

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Q: EVALUATE S(3sin t - 2cos t) dt

A: Topic = Integration

Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

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Q: 7) Show that K± = det [ T 4 J.

A: Sol

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

A: