If сx 3D су (тod n) and c >0 then а) х%3D у (тоd cn) b) х%3D у (тod n) c) x = y (mod“) d) None of thes

Q: 4-IN THE ADJACENT FIGURE, IF AB = AC AND DB = EC, PROVE THAT ABEC = ACBD

A: Consider the side AB as x. Since AB is equal to AC, so, AC is also equal to x. Consider the side BD…

Q: vdor (2,1,3) be the {1,)1), (1, 2, >).(O, 1, 0)1 be the {ll,),l), (1, 2,3).CO,1, 0)) linear…

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Q: 2. Using OLS or any other suitable method, Prove that E(ß1) = B1 E(ßo) = Bo

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Q: If x, y,z are integer's numbers and if x \ y then x\ z then: 1) Show that x\ ym - zn for m,ne z 2)…

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Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: 15, If neZ, then nº +3n +4 is even. (Try cases.) ho bn 6. If two integono

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Q: a) Show that fi (x) = cos x, f2(x) = cos 2x are orthogonal on [-7, n].

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Prove: Vn, meZ,if n and m are odd, then n-m is even

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Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x\ ym – zn for m,n e Z 2)…

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Q: prove that div A マ - Kr

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Q: 8. Chords AC and DE intersect at Point R in OQ. If AR = 6, RC = 7, and DR = 3, what is RE? %3D %3D

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Q: 1> =a,-4,57is to U=2,-4,5 812.Detemmine -> onthogonal

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Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: 1/3 If (x+iy) =a+ ib, Prove that

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Q: 2) of Ec, 4" is convngend can we conclude that coch of these are comvergent: (4)

A: Given The sires is convergent then,

Q: (6) If u, =*-!P«(x)Pn -1(x) dx, show that nu, + (n – 1)n-1 = 2, %3D and hence evaluate u„.

A: Given un=∫-11x-1PnxPn-1xdx

Q: 2. If 0 is in QIII then 180° < 0 < 270° and must be in since

A: 180°&lt;θ&lt;270°

Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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Q: az Find if yz – In z = x + y ax

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Q: 6. Prove: 4 |x – y| 0, then x = y Vx, yER

A: To solve Q.6 Prove: If x-y&lt;ε, ∀ε&gt;0, then x=y ∀x,y∈ℝ If (Given) Then (To prove) ∀ε&gt;0,…

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

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Q: 6. Show that (1) Cou(B1, g) = 0 (2) Cov(3o, B1) %3D

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Q: *10. Suppose AB = CD, AB 1 BC, and CD I BC. (a) Why must AC BD? (What congruence criterion…

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Q: Prove that CP PS AM BN 9. MQ NR

A: Consider the equation

Q: Suppose X has n elements and Y has m elements. How many bijections X → Y are there?

A: To find: The number of bijections X → Y are there. Given information: X has n elements and Y has m…

Q: 9. Write a 2-column proof: Given: p // q , Zg = (59 + 5x)° , %3D Za = (11x – 7)° Prove: Za = 114°…

A: Explanation of the answer is as follows

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

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Q: two positive iontages and bare by 2, them prove that. (2° +1) is most divisible by (2²-1) let a with

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Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

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Q: If x<y, prove that x<(x+y)/2<y?

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Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: В 3 0. -2 12 15 10 -7 2 -3 0 15 0. 12 0 10 anglusis (on ugur own pgper), and determine the

A: This is a problem of linear transformation, linear algebra, matrix algebra.

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: 3. Prove that: na” u[n] = az (a-z)2

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Q: 2 FIND PROJECてION マ=<2,8,97 THE OF く,2,37 ONTO %3D ( Use proper notation wer) in ans u your

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Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: prove for n=l,2,3. e that +2+3+..+h = ncn+l) 2. %3D %3D

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Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

Q: Prove: 4 x,,x2x, ER, then |x, +x, +.. + x,| s |x,|+|x,|+... + |x,|

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Q: true or false without justify The sel { 1,2,t, 3,,4,+, csx, coss is mot Ti Bomded in (CToi], Ul6)…

A: True.

Q: Theorem 5 there is auniqe Reul for X=2 Sit X ER

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Q: 5|8" – 3", Vn EN

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Q: Given: mZB = 42° and mZACD = 78° %3D Prove: mza = 36° %3D a 42 78°

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Q: Compute Simits If they the eist 8+iz z²+4 hit Zマ-2 Re 2

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Q: (2, Prove that Ž (Pn+ Pn+1) hr 9=U (y+1) 27-²8 (14+ 2x=-1) y

A: What is Legendre Polynomial: Legendre polynomials are a set of complete and orthogonal polynomials…

Q: what expressi on is equivaient to this. (n-a)!

A: n!(n-2)!+n=n×(n-1)×(n-2)!(n-2)!+n  [we use the idea of factorial]=n(n-1)+n=n2-n+n  [distribute n]=n2

Q: . Prove that, e²i = e²1=22. ez2

A: Let,z1=x1+iy1z2=x2+iy2z1-z2=x1+iy1-x2+iy2=x1+iy1-x2-iy2z1-z2=x1-x2+iy1-y2…

Q: If x,y,z are integer's numbers and if x \y then x \ z then: 1) Show that x\ ym – zn for m, ne z 2)…

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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.