ms 1 gold marbles, & ver marbles, and 24 black marbles. Someone offers to pl You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win black, you lose $1. What is your expected value if you play this game?

Q: 1. Let T: R³ R³ be the linear transformation given by T(x, y, z)= (x + y, x + 2y -z, 2x + y +z). Let…

A: Let us solve above problem

Q: b) 2

A: We have to simplify the given expression.

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Q: Q.No.4.a. When problem become unrestricted after changing primal to dual simplex Method justify your…

A: Given information:Minz=x1−3x2+3x3Subjectto:3x1−x2+2x3≤72x1+4x2≥−12−4x1+3x2+8x3≤10x1,x2,x3≥0To find:…

Q: Is Q x Z a closed subset of R2? An open subset of R²?

A: Since  is dense in , it is possible to find a sequence in which converges to . But,  not belongs to…

Q: Consider the sequence defined by a_n= (4n + (-1)^n2 - 2)/8 for every integer n > 0. Find an…

A:

Q: Problem 2: f(x)=x+sin(x). (a) Show that is a fixed-point of f. This question approximates the…

A: Problem 2 :A point x0 is said to be a fixed point of a function f  if  f(x0) = x0

Q: 4 State whether the following functions are injective and/or surjective. Let R* denote the…

A:

Q: Show that Q(√2) = {r + s√2 | r, s € Q} is a field. Note that for any r, s E Q, r + s√2 € R (i.e. Q…

A:

Q: Find the general solution of the system x'(t) = Ax(t) for the given matrix A. A = -1 1 0 1 4 1 0 131…

A:

Q: The set of Gaussian integers modulo p for prime p∈P, i.e. Zp[i]={[k+li]∣ [k],[l]∈Zp} together with…

A:

Q: 27. Using the Levi-Civita symbol expand the following vector products: (i) (ii) Vx(Ã×B) X X(XB)…

A:

Q: Find the Laplace transform, F(s) of the function f(t) = 9t² – 3t – 10 F(s) = s> 0

A: Given that the function is                          To find the Laplace transform of the given…

Q: Show that ℚ(√2) = {r + s√2 | r, s ∈ ℚ } is a field. Note that for any r, s ∈ ℚ, r + s√2 ∈ ℝ (i.e. ℚ…

A: We prove that Q(√2) is a field by showing the following properties.Commutative ring with unity.No…

Q: 26.2 Analysis of multiple variable functions (#differentiation) Let f(x, y) = (a) Find the first and…

A: As per our company guidelines, we are supposed to answer only the first three subparts of the…

Q: Show that if a, b, c ER then: (i) − ( ² ) = (-)--)) b (j) 1-¹ = 1. (k) -0 =0. (1) Prove that 0 is…

A: Given that

Q: Let x, y € Z. Prove that if 2 | (x² - y2) then 4 | (x² - y²)

A: We know that the sum of two odd numbers is an even number.Also, the difference between two odd…

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A:

Q: Let A and B be rings. Define addition and multiplication on the Cartesian product A x B by (x,y) +…

A:

Q: The vectors ~={]-=[B]-=[C]~-[&] -=[] V3 and v5 -2 8 V₁ 2 1 V₂ V4 -17 generate R³. Find a subset of…

A:

Q: Give an example of a topological sort, a maximal chain, and a maximal anti-chain.

A: Topological Sort: In a directed acyclic graph (DAG), a topological sort is a linear ordering of its…

Q: Prove or disprove: If A, B, and C are sets, then A × (B − C) = (A × B) – (A × C).

A:

Q: A Consider the following DAG: L B G D C LL F E Give an example of a topological sort, a maximal…

A: Let us define the definitions one by one......................Topological Sort:The topological sort…

Q: side is the the (a) 1 (b) 3 Assume that (2,3, =) " where the left-hand product of two matrices. If…

A:

Q: Question 3 Consider the matrix Given that 0 -2 A = 7 [20 0 6 It is given that matrix A has 2 unique…

A: has two unique eigen values.One of the eigen value is  with multiplicity

Q: Use Lagrange multipliers to find the extreme values of  the functon subject to the given constraint.…

A:

Q: Show that the set Sa n { x = S² + [Ë ¹0g (A, (X)) ≥ a}. = ++ log i=1 where a € R and λ; (X) is the…

A:

Q: Pictured are the contours (z=0 to z=4.5 contour interval 0.5) of f(x, y) = x² + 2xy + y² together…

A:

Q: A perpetuity-Immediate has yearly payments of $R and a nominal rate of interest is 12% per year…

A: It is given that the interest rate is 12% per year convertible monthly. Thus, the interest per year…

Q: Show that if a, b, c ER then: (e) If a 0, then a-¹ #0 and (-a)-¹ = (a-¹). (f) a¹ =1⇒a= 1. (g)…

A: Given that

Q: (a) Let a and b be integers. Show that (3a + 2b)2 + (2a − 3b)2 = (3a − 2b)2 + (2a + 3b)2= 13(a2 +…

A:

Q: $5000 is invested into two accounts. One pays 5% interest and the other pays 7%. The total…

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Q: You are told that f(x) is everywhere continuous, passes through the point (6, 3) and f(x) +3 lim x-4…

A:

Q: your initial discussion post, reflect on the activity by answering the following questions: How can…

A: An absolute value expression that is greater than a value is considered an OR statement because it…

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A:

Q: Find the Laplace transform, F(s) of the function f(t) = 3, t > 0. F(s) = = 1 v? ds dt dx

A:

Q: Let the temperature of a point in R³ be given by T (x, y, z) = 7x² + 7z². Compute the heat flux…

A:

Q: 1. Compute the Jacobian determinant of the transformation 4+5u cos v 2 + 3u sin vi T(u, v): =

A: Let us solve above problem

Q: Use the graphs below to evaluate the derivative. (((x)) | x = 5 dx = 80 0 f(x) 80 x 80 0 80 g(x)

A:

Q: number of cars shipped on day n. Specify a flow di- agram and a difference equation (in standard…

A: let's describe the processes using difference equations:Inventory Update:The inventory q[n] at the…

Q: Which of the following is less than 2 ? O 19/11+3/4 O 1 1/4+2/5 O 19/15 +7/11 O 13/6+1/2

A: We will apply basic mathematical operations to find numbers less than 2.

Q: Show that if a, b, c ER then: (a) a−b=-(b-a). (b) (a + b)(ab) - a(a - b) + b(b-a) = 0. (c) a b=0⇒a=0…

A: To prove Hence proved.

Q: You are given the following vectors in terms of their components in the {x, ŷ, 2} basis: A = x +…

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Q: degree 2 or more in R.

A:

Q: Let A = {X € R³ : X and (1, 2, 3), (1, 0, 1) are linearly depedent} Show that A is closed in R³.

A: A={X∈R3:X,(1,2,3),(1,0,−1)are linearly dependent} are same as  A=span{(1,2,3),(1,0,−1)}To show that…

Q: Suppose B is a 5 x 5 matrix and Nul B is NOT the zero subspace. Do you have enough information to…

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Q: B = Solve for X the matrix equation 2XTA= B, where A = 11 1 and -1₁ [8 -6]

A:

Q: Give examples of two sets A and B such that An P(A) = B and P(A) ≤ AUB.

A:

Q: Use the simplex method to solve the linear programming problem. Maximize subject to: with z = 3x₁ +…

A: