IM: Prove that n(n+1)(2n + 1) %3D 6.

Q: S = {n? : n € N} is denumerable. %3D

A: An Infinite set is denumerable  if it is ,..... equivalent to the set of natural numbers.  Here the…

Q: What is the coefficient of the x^7y^4 in the expansion of (x+y)^11

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Q: 16. 3x So ² (z+y²) dydz 2x pasky

A:

Q: A submarine attempts to sink an aircraft carrier. It will be successful only y two or more torpedoes…

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Q: In Z[V3], the element 2+v3 is:

A: Unit Given element is a unit

Q: Э3: 4ln(2x+3)%3D In 2+1

A: Given equation: 4ln2x+3=ln2+1 We know that the value of ln2=0.693147…

Q: How many non-negative integer solutions (O is allowed) are there to r +y+ z = 24?

A: The given equation is, x+y+z= 24 We know that, For equation,  x1+x2+......xr=n  There are n+r-1Cr-1…

Q: Oa, 1+ 16a, 2+ 225n for n> 2 with initial conditions ag = -23, a1 -19.

A: Given recurrance relation is  an=16an-2+225n     , n≥2 and initial conditions are a0=-23, a1=-19

Q: Differenticte y= (SN( 3))/ (4t 5cos (2x))

A: Given :y=sin(3x)4+5cos(2x)

Q: 4. What is the coefficient of x? a) in (1 + 2x)117 b) in (2 – x)13? c) in (5 – 2x + y)'1, where y is…

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Q: S V64 x da 3 x 2 +c 16 None 3 16 x 2 +c 3 16 x 3 +c 3 2/3

A:

Q: What is the coefficient of the term containing x^7y in the expansion of (3x + y)^8?

A: Topic = Algebra

Q: ΣΕ (2) k%3D1

A: Answer

Q: i. Find the coefficient of x in the expansion of ( 2x –÷) . ii. Hence find the coefficient of x in…

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Q: Find the sixth term of the G.P. 6, 2,..

A: Given first two terms of a geometric progression series,  6,2,... To find the sixth term of the…

Q: 2n n%3D1 712

A: we have to test whether the given series is convergent or divergent

Q: 2n [3] (b) E for n 21 2k k=0

A: Answer

Q: Solve for n. k (3-n) %3D

A: b=k(3-n)pbp=k(3-n)

Q: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

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Q: 8 {4} {{ {}₁ s² + a² s² +6² (1)

A: Given: L-1as2+a2·ss2+b2............(1)12∫sin2t+3u+sin7u-2tdu............(2) We have to find the…

Q: 1. What is KL? %23 3x X +6 K

A: Here we have to find the value of KL from the given triangle.

Q: What is tle sum of P(x) and Q(x) if P(x) = 4x² + 6x – 9 and Q(x) = -7x² - 12x + 8? %3D 1. -3x2 - 18x

A: GIVENP(x) =4x2 +6x-9Q(x)= -7x2-12x+8

Q: ADMATH 8. 2.) cunvergent n. divergent or n=0

A: The given series is

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

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Q: r* – 2 Show, using the definition, that is O(z²). z +1

A: Here, To satisfy the definition of O(x2), we need to find an appropriate choice of c and k.Let’s…

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

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Q: What is the discriminant of the PDE? 2 d2u/dx2= 8 d2u/dt2

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Q: Derive a formula for fx* In x dxwhere a.) n+ -1 b.) n = -1

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Q: What is the coefficient of x5y7 in the expansion of (x+y)12?

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Q: For which situation is n = EX? a. when the values of X have no duplicates b. when the values of X…

A: Solution:- We have given that,      for which situation is  n=Σ X ?

Q: What is the coefficient of x^12.y^13 in expansion (x+yY 25

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: What is the sum of P(x) and Q(x) if P(x) = 4x2 + 6x - 9 and Q(x) = -7x- 12x +8? %3D 1. -3x2 - 18x -…

A: Given P(x) = 4x2 + 6x – 9 d(x) = -7x2 – 12x +8

Q: 2t Mr (t) - %3D 7-ゼ Find the MGF of 2- 3(W-2)

A: # Given: mgf of random variable w is  Mw(t)=9e^2t/(9-t^2)  then to find mgf of Z=3(w-2)??

Q: a2 z a2z If z = In(x² + y²), find + 2 Əx2 ду?

A: The given function is z=ln(x2+y2).

Q: Σ Ea = n². %3D k=1

A: It is given that,  ∑k=1nak=n2

Q: dx Evaluate S o 9x2+4

A: Solution is given below:

Q: In what case of k such that there is only one solution? 2x + ky = 10 kx + 2y = -10

A:

Q: solve for t

A: Given: etln0.2=0.4 we know that nlnm=lnmn                                             ..1 so, by…

Q: 2Fn>Fn+1 for n>3 true or false?

A: Given,       2Fn>Fn+1 for n>3

Q: 3. Show that a2 + b2 + c2 > ab + bc + ca and using this result show that (a) (a + b + c)2 > 3(ab +…

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Q: (エ+1)n n=D1

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Q: Find the coefficient of xy° in the expansion of (x + y)³ 8

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Q: (In 2x)' In V k.

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Q: 3) Let B = Find Least 10 - I- square salution of Bx = 6

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Q: 7. Find k so that dx ke + C.

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Q: What is the coefficient of the term containing x^3y in the expansion of (5x+y)^4?

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Q: What is the coefficient of the term containing x^2y in the expansion of (4x+y)^3?

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!