61. Let Y be a subspace of X. A separation of Y is a pair of disjoint nonempty sets A and B whose union is Y, neither of which contains a limit point of the other. Then Space Y is connected if there is no Separation of Y

Q: Problem 1 Let Z denote the integers. Let S = {0 a,b e z} (a) Prove that S is a subring of M2 (Z) (b)…

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A: Given: 5) a∈A 6) a,b∈A To find: Table

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Q: (B) Define the triangle group. Then 1. Find all subgroups of it. 2. Is it abelian? Why?

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Q: ABC is a triangle in which the vertical angle C is 60°. If the bisectors of the base angles A, B…

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Q: 2x V 1 + 2e dx a = 0 b= 1 use 9 nodes, n=9 use composite simpson 1/3 rule

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Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

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Q: Q8: What is the difference between homomorphism and isomorphism?

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Q: nsert 4 arithmetic means between 24 and 56. nsert 5 arithmetic means between 2 and 38.

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Q5:(A) Let R=(Z12 ,+12, -12 ). Find a) Maximal ideals of R b) Is (Z12, +12) a simple group? c) Is…

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Q: The quotient of 33288

A: Given: 33288

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A: We have to solve the given differential equation using undermined coefficients.

Q: |4x dA R.

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Q: Let Fib (n) be the nth term of the Fibonacci Sequence, with Fib (1) = 1, Fib (2) = 1 and Fib (3) =…

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Q: Consider the following sets: U= {set of integers) A = {3, 6, 9, 12, 15, 18} C= {3, 6, 9, 12} E=(3,…

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Q: -1 0 12 0 1 0. -3 -1 12 1 -3 -3 Ans. -1, ;-5, ; 3, -1 -4 1 1 -4 -1 1 3. ..

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Q: Let W be a subspace of an inner product space V. The orthogonal complement of W is the set w+ = {v €…

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Q: 1. To the right, you are given a contour plot for the function : = f(z.y). (a) Estimate the values…

A: We will use definition of partial derivative and contour diagram to  to find sign of fx and fy

Q: The degree of precision of a quadrature formula whose error term is "(E) is: 5 2

A: The degree of precision of a quadrature formula is the largest positive integer n such that the…

Q: 2. Show that p q is congruent to (p - 4)A .

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Q: Q3: (A) Prove that 1. There is no simple group of ord er 200. 2. Every group of index 2 is normal.

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Q: 1. Solve the following system of linear equations xi + 2x2 + 3x3 + 4x4 + 5xs = 5 2x1 - 3x2 + 4.x3 -…

A: GIven equations in matrix form: AX=D 123452-34-5111-1-115-4-32134-3-46x1x2x3x4x5=510897

Q: g) ² sin h) 1+z i)

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Q: (D3 – D2 + 4D – 4)y = 2e* sin(2x) – 3e*

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Q: If three dice are thrown, how many possible outcomes would show A sum of 6? A sum of ≥ 5? A sum less…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: You generate a scatter plot using Excel. You then have Excel plot the trend line and report the…

A: Let us find the correlation coefficient.

Q: Find the saddle point and solve the game Player B B, B2 B3 A, 15 3 Player A A, 6. 5 A3 -7 4 3 70 2.

A: We need to find the saddle point and solve the game              Player B Player A B1 B2 B\3…

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Q: A. For each of the following arithmetic sequences, find a) the common difference; b) the equation of…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 1. How many terms are there in an arithmetic sequence where a̟ = 12,an = 60 and d = 8? %3D

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

Q: 8. Let n > 2. Consider the n x n symmetric tridiagonal matrix over R c10 0 1 0 0 1 ... 1 ... с 1 An…

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Q: roblem 2. Let V be the set of all real numbers; define by u v = uv and o by aov = a+v. V a vector…

A: In this question, the concept of vector space is applied. Vector Space When W is a vector subspace…

Q: = kx, where x(t) > 0 and k is a constant. Hint: Separable. d. x = Dekt 1. What is the solution to…

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Q: Q5. Solve the following classification problem with the perceptron rule. Apply each input vector in…

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Q: Consider a power series f(z) = Ean(z – zo)". 1. If f converges at a point z1 # z0, then it is…

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Q: Q4i prove that 1. Let R be a commutative ring with identity and I be a maximal ideal of R. Then the…

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Q: Use a quadratic regression to predict the company's profits in the year 2016. a. 469000 b. 705000 C.…

A: We are only allowed to solve one question at a time and up to three sub-parts. Please post the…

Q: Prove that There is no simple group of order 200.

A: Given: Group of order 200. We have to prove that the group of order 200 is not simple. As per policy…

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

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Q: Let G be a group and a E G be such that o(r) 20. Find the orders of r, xt, a0, al4 and r30. %3D

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Q: A box contains balls: 3 red, 4 blue, and 5 yellow. A ball is hen randomly picked. What is the…

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Q: Question 3 Assume that g(r) be a function on (0, 100) and has a derivative g(z) and a primitive…

A: Fundamental  theorem of calculus part2   If f is a  real-valued function on a closed interval [a,b]…

Q: Use Shell Method to find the volume of the solids of revolution described in each item. Find the…

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Q: Consider a confidence interval, with confidence coefficient 1- a, for the mean of a normal…

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Q: Use the main theor 't take powers)

A: We have to show that 12 must be the primitive root of 25 by using the main theorem on the primitive…