Psopostion:-Let G be a diset psoduct of H and k. Then 2(G) Is f Z(H) and Z(k) . disect product

Q: Prove Corollary 2.48: Let A ∈ Mn×n(F ). Then A is invertible if and only if LA is invertible

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Q: ssignment Active Using the Fundamental Theorem of Algebra Find the root(s) of f (x) = (x- 6)²(x +…

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Q: exp(x) exp(— г) - tanh(x) x ɛ [-2,2] in 4 sub–intervals exp(x) + exp(— х) The nodes are x,= – 2, x,=…

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Q: Finding the kernel and range of L. X1 X1+ X2 Where the L X2 L: R3-R2 X2+ X3 x3

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Q: (i) Find all the conjugacy classes of D4. Give the details of your work.

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Q: ACTIVITY 2: Let's Explore! 1. For each of the following, divide the polynomial P(x) by the divisor…

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Q: 1. (10 points) Consider the set V of polynomials of the form ac® + bx4+ca² +d, where a, b, c, d e R.…

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Q: a) Sketch a diagram to illustrate how to create a bijective function f:E→N−{100,200}, where E is the…

A: Bijective mapping: one-one & onto Bijective mapping means all elements of set E map to…

Q: Using pencil, paper and calculator, form the Lagrange interpolating polynomial corresponding to the…

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Q: { 1 + x + x², x + x², x²}. %3D for P2. Let p(x) = -1 +x + 2x2. Then [p(x)]B = %3D %3D

A: The given basis is B=1+x+x2,x+x2,x2 for p2. let p(x)=-1+x+2x2 We have to find,  p(x)B=?

Q: The sum of divisors function o is the arithmetic function defined by the rule σ(n)Σd. d|n (a) Show…

A: According to the given information, The sum of divisors function is the arithmetic function defined…

Q: (b) Consider f(x) = 2x³ + 3x² + 4 in Z[], and the evaluation homomorphism 2 [2] : Z₁ [2] → Zg. (i)…

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Q: Solving for x if x=5(mod)7 is similar to finding [5] with respect to the relation R on Z defined by…

A: We know x≡y(mod)n  means  x-y=nk for k∈Z

Q: (c) For the partial order you identified above, is every pair of elements of Z comparable? (You…

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Q: z = -11 – 6i; determine the following: 1. z-5

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Let f(x)= x* +2.x-ax2 +bx (i) Find the values of a and b so that the multiplici ty of the root 1 of…

A: Polynomial Factorization: A polynomial can be written as a product of two or more polynomials of…

Q: p(5)* Define T: P2 → R² by T(p) Find a non-trivial element of the kernel. .P(6). p(t)

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Q: (3) Conjugate the map f(x) = 2x² +x – 3 to a map of the form Q(x) = x² + c. Find the conjugacy map h…

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Q: Let f(x) = x'/3. [1, 3] 4 rectangles Find Ax. a) b) List the subintervals. 2.

A: (2) Given function is fx=x13 and interval is 1,3 and n=4. (a) first we will find the Δx…

Q: VxVx2((f(x1) = f(x2)) → (x1 = x2)) O composite O injective O surjective O bijective

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Q: Which one of the following statements concerning polynomials is true? Select one: a. Every…

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Q: 1 Let f(x): and g(x) = x2 – 6x. x + 8 Find the domain of the composition (fog)(x)using set notation.…

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Q: a++x2 5x +1 < x2-4x +3 Şolve this modules imequality → sohve for e

A: Given: The given inequality is x+1+x2-5x+1&lt;x2-4x+3

Q: 5'- If f and g are R-I then the product fg is R-I (H.W)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let S = {1 + x, 1 − x, 1 + x^2, 1 − x^2}. Prove that span(S) = P_2(R), the set of all polynomials of…

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Q: decide if the given statement is true or false,and give a brief justification for your answer.If…

A: The given statement Wx1, x2(t) and Wx2, x1(t) are the same is false.

Q: Corollary 5.31. If p(x) is irreducible in F[x] and p[x] divides the product r¡(x)· · · rn(x) for…

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Q: n congruence classes mz reduce the eqiation am' = b, to the form x = c, either by finding convenient…

A: (A) Let y=x2 then the given congruence relation becomes, ay≡b mod m that is 2y≡13 mod 19 This…

Q: direct and direct let be a k. then pooduct of is z'G) product ZCH) and zck).

A: To show that Z(G) is a direct product of Z(H) and Z(K) when given that G is a direct product of H…

Q: x + + x -x %3D B.s (9 C-スり(E-メ) E-トE-*ェX S. Let /(x)=x +x+1 and g(x) x-3. Find the following new…

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Q: (-1)"+1 1- 2n Given the set A = The infimum of A is

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Q: Finding the kernel and range of L. X1 X1+ X2 Where the L X2 , L: R³¬R? X2+ X3 x3

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Q: Suppose that factor AB is significant and that both A and B are significant. This is called…

A: We have Strong heredity: If the interaction AB is significant and that both A and B are significant…

Q: IExamplé.19-371. By consjdering the limit of three points, Lagrange's interpolation formula for…

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Q: Math 48A/248A Group Work #13 - Piecewise Defined Functions (2.1/2.2) Names: Make a clear,…

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Q: 2 3 4 5 6. f = 1 (i 43 5 2 6) (a) Write the permutation f' as a product of disjoint cycles,…

A: We can calculate the permutation of f7 from right to left then take the LCM of disjoint cycle

Q: the degree of homogeneity, if there is one, for eac 1 X1,X2, X3) = - xf +x +x X2 X3 O gro finotion:…

A: Introduction: For a function f(x,y), the degree of homogeneity is an integer n such that,…

Q: y" (a) = a(z-3) where a is and bis-. VWrite a comma-separated list.

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Q: (2) Conjugate the map f(x) = 3x(1 – x) to a map of the form Q(x) = x² + c. Find the conjugacy map h…

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Q: 3 Exawple: let アミ1 3-r - 2 such that lAl=0• 2-V Find

A: Given that  Matrix A  If deta=0  Then to find the value of r

Q: AB,9: BC and h: CD functions. Let/: 1. Show that ho (gof) = (hog) of 2. If f and g are bijective, is…

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Q: Finding the kernel and range of L. X1 X1+ X2 Where the L X2 L: R3-R? X2+ X3 x3

A: Find the range and kernel of L L(x1,x2,x3)=(x1+x2,x2+x3)

Q: Describe all the homomorphisms from K4 to C4.

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Q: counterexample.) Prove If ACAndamscaoha OEA →-(@EB).") and AnC=Ø and AnD=Ø, then C=D. then for any =…

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Q: Horner's rules is means for evaluating a polynomial at a point xo using minimum number of…

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Q: Find the decomposition a = a||b + alb with respect to b if a = (x, y, z), b = (1, 1, 1). (Give your…

A: In this question, we have to write a given vector a = &lt;x, y, z&gt; in form of addition of two…

Q: Question By Gauss-Jordan Elimination, evaluate A and verify A'A=I for: A = 3

A: Gauss - Jordan Elimination method is also known as row - reduction technique.

Q: (a) find fanction f anel so that fog =H. H(x) =(5-2x3)2 (b) find the domain of the composite…

A: See the attachment

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.