An excercise: Let H be a subgroup of index 2 of a group G. Prove that H must be a normal subgroup of G. Conclude that Sn is not simple for n ≥ 3.

Q: n A coin has probability p of showing head when tossed. It tossed n times. Let P, denote the…

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Q: 8. Amelia is running for school president and would like to spread her message as fast as possible.…

A: 1st we will form a differential equation with initial value  to model the situation and then solve…

Q: You may use a software to do calculations but you have to write down the details. The correspondence…

A: We see gcd(11, 27) = 1. Hence 11 has an inverse element mod 27. 11.5 = 5.11 = 55 (mod 27)…

Q: {tr (F")}"_? n=1 What kind the relation of this sequence to the Fibonacci sequence? (10) What is the…

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Q: deal with the eigenvalue/eigenvector problem for n×n real skew-symmetric matrices. Q. Let A be an…

A: It is given that the matrix A is skew symmetric matrix of order n. We know that a matrix S is said…

Q: A lot contains 20 articles. The probability that the lot contains exactly two defective articles is…

A: There are 20 articles in total. Let B1 be the case when the lot contains exactly two defective…

Q: Compute and completely simplify the difference quotient, f(x + h) − f(x) h , for f(x) = 5 − 4x +…

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Q: A population with four age classes has a Leslie matrix L- 0 0.4 0 0 0 0 0.6 0 0.7 0 0 0 If the…

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Q: The graph of an equation is given (a) Find the intercepts. (b) Indicate whether the graph is…

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Q: h y=hx b- a y = (h)(x-b)

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Q: Example Find a solution to the heat flow problem. ou дчи 04 = 70x², 0 0 (1) (2) u(0₁ t) = u(₁T₁ t) =…

A: Given ut=7uxx Let  ux,t=XxTtuxx=x''xTxut=XxT'tut=7uxx⇒XxT't=7X''xTx⇒T't7Tx=X''xXx=λ Case (i): λ=0…

Q: What are the domain and range of the following functions of x? (Assume that all variables take on…

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Q: (Vector spaces) Let M be the vector space of 2 x 2 matrices with real entries, under the usual…

A: Given that M Be the vector space of 2×2 matrices with real entries, under the usual addition and…

Q: Question 28 Graph the equation y = 2 on your paper. Clearly label at least 3 points on the graph.…

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Q: Determine whether the given set, together with the specified operations of addition and scalar…

A: It is given that, ℝ2 be the set of ordered pairs of real numbers with usual addition of vectors and…

Q: Suppose that the function u(x, y) is solution of the problem = 0, 1²+1² < 25, ox² ay² u(x, y) = 5(x…

A: Given ∂2u∂x2+∂2u∂y2=0, x2+y2&lt;25u(x,y)=5(x-y)2-12xy , x2+y2=25 (a) let g(x,y)=x2+y2-25 by lagrange…

Q: Vector space of 2 x 2 matrices with real entries, under the usual tion and scalar multiplication.…

A: Linear transformation

Q: 2. Find the matrix of the linear operator L: P₂ (R)→ P₂ (R) defined by L(c+bx+ar²) = c+(a+b)x² with…

A: To determine the matrix for a linear transformation. Find the value of linear transformation on…

Q: ltiply the rational expression and express the product in simplest form. c² +6c-55 2 16c+55…

A: We use the formulas (a+b)^2= a^2+2ab+b^2 and basic factorization formulas to factor out the…

Q: The height y (in feet) of a punted football is approximated by y = − (16/2025) x2 +(9/5)x+(3/2)…

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Q: Question 3 Ayla needs $10,000 in 5 years' time. How much should Ayla invest now (to the nearest…

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Q: Show that x is a generator of the cyclic group (Z3[x]/&lt;x3 + 2x + 1&gt;)*.

A: In this question, we have to show that x is a generator of the cyclic group  ℤ3xx3+2x+1*. We know…

Q: Show via a sequence of justified logical equivalences that p→ (qr) is logically equivalent to (p^q)…

A: Answer :-  We have to draw the truth table to check the logical equivalence of both statements.

Q: Arguing by Symmetry Use symmetry to show that J JR xy2 dA = 0, where R = [-1, 1] x [-1, l].

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Q: The function f(x) = 0.6 sin(x) represents the velocity of air flow of normal breathing cycles, where…

A: The given function is f(x)=0.6sin2π5x. To Find: (a) The time it takes to complete one cycle. (b)…

Q: CLASSIFICATION OF DIFFERENTIAL EQUATIONS Check the following: x + 3x = 5+1² x + 3t²x = 5 3x + 7x +…

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Q: Use the Alternating Series Test to determine whether the series converges. 8 k Σ 1-1)k+1. 3k³ +1 k=1…

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Q: -pi/8 is wrong. it should be 0

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Q: Let w and a denote the primitive third and sixth roots of unity, respectively. Prove that Q(a) =…

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Q: (E) y-2= (x+4) 2 2x+y=14 (F) y=-2(x-4) +2 1 y=-x+3 3

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Q: 2. Suppose that you are given the following data: X y -1 0 0 1 1 2 39

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Q: A school is installing a flagpole in the central plaza. The plaza is a square with side length 100…

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Q: could be either true or false). Example: EITHER dogs bark OR cows croak. TRUE V FALSE ANSWER: TRUE…

A: Please find the answer in the next step

Q: = cos³ t, y = sin³ t, 0≤ t ≤ 2π Find the arc length of the astroid: x =

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Q: 114. Biology With each breath, a person at rest breathes in about 0.50 L of air, 20.9% of which is…

A: Given volume V=0.50 L Temperature T=20°C pressure, P1=1 atm P2=0.695 atm R=0.08205 Use formula…

Q: Solve the initial value problem y" + 16y = 0, y(0) = 2, y'(0) = −2.

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Q: 6. Consider a spherical tumor of radius R that is covered with capillaries that provide oxygen at…

A: Given: Oxygen concentration=20 nM           Oxygen diffusion coefficient, D=1.8×10-9ms2…

Q: Find the relative minimum and maximum value of the function: ƒ(x) = 8 cos²(x) – 8√3 sin(x) over the…

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Q: Find the APR (rounded to the nearest tenth of a percent) for the loan described below. Purchased a…

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Q: write a polynomial function with rational coefficients so that P(x)=0 has the given roots. A) 2 + i…

A: Solution:-

Q: Describe the definition of function abs.

A: We have to describe the definition of abs function. We usually write the abs function as absx for…

Q: In questions 6 through 10, determine if the alternating series is convergent or divergent. Which…

A: We are given the series  ∑n=1∞(-1)n-1n2n+3 And the series  ∑n=1∞(-1)narctan(n) We have to check if…

Q: O Dr. Manning (Vector spaces) Let F be the vector space of continuous functions f: R → R and let H…

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Q: (6) Find a close formula of ƒ, using the results of the diagonalization above. Must show all work!

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Q: a) Determine if the system is controllable, using the Controllability matrix. b) Find the left…

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Q: This is not a correct representation. I know how to get to this part. What is the representation of…

A: We have to find the power series of f(x)=ln(1+4x3) using integration of f'(x)

Q: 9. Show the Complex Fourier Integral Transform (Fourier transform) of the function defined below (4…

A: To prove that the complex Fourier Transform of the function defined below:…

Q: A periodic function is defined as follows: f(t) = { for 0 ≤t<1 (3 i. ii. iii. where f (t + 2) =…

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