Three adults and five children are seated randomly in a row. In how many ways can this be done if the three adults are seated together?

Q: Find the order of the element (2, 3) in the direct product group Z4 × 28. Compute the exponent and…

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Q: 2. A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)

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Q: 2. Sketch the graph of f(x). Function. sin(x) using the Problem-Solving Strategy for Drawing the…

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Q: Let CR denote the circle z = Rei (0 ≤ 0≤ 2π). Show that lim R→∞ CR 2-4 (2² + 1) (2³ — 5) dz = 0

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Q: i) ii) (P V Q) ^ -(P AQ) (P Λ Ο ^ R) V (P ^ →Q ^ R) V (Ρ ^ ¬Q ^ ¬R)

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Q: Given that A = -2 y 0 -5- 14 and B = [2 -3 -3 x _6] find the entry in row 2, column 1 of the matrix…

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Q: Write TRUE if the truth value of the statement is incorrect, otherwise write FALSE. It is not true…

A: We have two statements  (1) It is not true that 64 is a perfect square and a nonagon has seven…

Q: 5 1 i) (x + ।४ ii) (a-4b)7

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Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium- 100 has been reduced…

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Q: Test the series for convergence or divergence. 97² n! n = 1 O convergent divergent

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Q: By integrating surface element of a sphere, find area of a strip on the surface of a sphere from 8=…

A: To Find: Area of a strip on the surface of a sphere from θ=45° to θ=135°, where Radius of the sphere…

Q: The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the…

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Q: x= x² + 3y - 3x + xy and y = xy + x.

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Q: Given P(A) = 0.3 and P(B/A) = 0.2. Then P(An B) =

A: Option(1) is true.

Q: Given P(A) = 0.3 and P(B/A) = 0.2. Then P(An B) = O O 0.6 O 0.63 O 0.56 0.48

A: Given P(A) = 0.3P(B/A) = 0.2

Q: JA ITI system is described by the D.E. y +6 Y+8y=2X(+) find h(t), then find y(t) if X(t) = te²t tro-

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Q: Prove that at a party where there are at least two people, there are two people who know the same…

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Q: r2 ex dx Jo ex+1

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Q: Let f(x, y) = g(x) + h(y) where g(x) and h(y) are positive. If g(x₁) ≥ g(x)and h(yo) ≥ h(y) then…

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Q: Suppose the life span of a laboratory animal is defined by a Rayleigh density function with a=0 and…

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Q: Pool construction. Refer to the rectangular swimming pool shown below. a. Find the perimeter of the…

A: The pool is rectangular in shape. a. The perimeter of the rectangle is =2(length+width) =2(150+75) =…

Q: Given the following set S of polynomials, find a polynomial p(x) in P₂ so that SU {p(x)} spans P2…

A: Here given set S=-5x2+4x-9, -8x2-6x+8 First, check whether S is Linearly independent or not.…

Q: 5. Solve (t³ +7t³x²)dt + xe* dx=0 with x(0) = 0. Leave in implicit form

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Q: Topology let X be an t be all a infinite Show let topology on X in which subsets of X that Tis…

A: Given :  X be an infinite set and τ be a topology on X such that all the infinite subsets of X are…

Q: A triangle has four sides or a straight line has 90o angle if and only if a bicycle has two wheels…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: (a) Test the convergence of the series given by (r+1)! Σ r!(er) r=1 . G C M . 2

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: ped Given f(x, y) = m (x,y) (the quadratic Taylor expansion used in trust region methods, x^2y^2 +…

A: Given that: fx,y=x2y2+x2+y2, at 0.1,0.2 The objective is to determine the value of mx,y and rho. Now…

Q: A = ¬{¬[(¬P → Q) ^ R] v ¬Q} ↔ (Q ^ R)

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Q: Graph the break even points: Cost Function = C(x)=1800+500x Revenue function = R(x)= 500-0.04x

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Q: By integrating all three surface elements of a cylinder, find the surface area of a cylindrical pie:…

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Q: Find the solution of the given initial value problem: y"" + y' = sec(t), y(0) = 11, y′(0) = 5, y'(0)…

A: To Solve: The differential equation given with initial conditionsy'''+y'=sec(t) , y(0)=11, y'(0)=5,…

Q: 5. Krypton-85 is an inert radioactive noble gas with a half-life of approximately 10.76 years. a.…

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Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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Q: Let S be a subspace of R" and let S be its orthogonal complement. Prove that S is also a subspace of…

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Q: 8 A LTI system is described by the D.E. ÿ + 6 ý +8y -2t find h(t), then find y(t) if X(t) = te²t…

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Q: Consider the vector-field (a) Show that F = (x + yeª + sin y)i + (eª + x cos y)j. is conservative.…

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Q: Problem 2. Put n balls randomly into m boxes, and let § be the number of empty boxes. Calculate…

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Q: A tailor has the following materials available: 16 square yards of cotton, 11 square yards of silk,…

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Q: A child psychologist is interested in the number of times, x, a newborn baby's crying wakes its…

A: We are given that PX≤1 or X=5=1450 So, P0+P1+P5=1450250+a+b=1450a+b=1250

Q: EXER 3.2 - LINEAR ALGEBRA Write v =(4,4,5) as a linear combination of x=(1,2,3), y =(-2,0,1) and z =…

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Q: (b) Find the critical points. (c) For each critical point, find the corresponding linear system.…

A: Given system is dxdt=x(-1+2.5x-0.3y-x2)dydt=y(-1.5+x) Let f(x,y)=x(-1+2.5x-0.3y-x2)g(x,y)=y(-1.5+x)…

Q: 2. consider the differential equation = (y-2) (4 Q. Determine all stationary solutions and sketch…

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

Q: 1. When the function x is of a single variable e.g x= x(t) then the differential is termed (a) First…

A: The answer is ordinary differential equation. Option C is correct.

Q: 5 -4 -3 Given that D = [3₁] B =[²36₁], and c = 7 2 x true? -6 Z -4 9 (1) DD¯¹ = D¯¹D = I₂ where 1₂…

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Q: Obtain the term of the power series of sin(x + 1) where n = 3 for a value of x = 3.20.

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Q: 6 Find the Taylon Series representation function centered fon the at following function a = π f(x) =…

A: According to our company guidelines we were supposed to solve only 1st question. Kindly post the…

Q: Solve the given differential equation by undetermined coefficients. y" + 6y = -294x²e6x ||

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Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

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Q: 22. Let d = gcd(a, b). Prove that ged(a/d, b/d) = 1. Fl of th om of congruences

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Q: i) ii) ¬(P V Q) ^ ¬(РЛQ) ¬(P^ Q ^R) V (P^ ¬Q ^R) V (Р^ ¬Q^ ¬R)

A: Given: Let us consider the given Boolean expressions, i) ~P∨Q∧~P∧Q ii) ~P∧Q∧R∨P∧~Q∧R∨P∧~Q∧~R