Is the set {(x1, x2) ∈ R2; 2x1+x2 ≥ 1} convex? Justify your objection.

Q: Let S = {(r.y) R²: (x-1)² + y² ≤4 and y> √3}. Question a. Find the interior, exterior and boundary…

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Q: 2. Solve: 3 -X-2 x²- 11 1 X x=²=₂+x²= 1² and state any NPV's. X-2 X+1

A: This is question of calculus.Here one equation is given We have to solve it.And state the…

Q: x>4 UX32 - Graph & Set notation

A: Inequalities are defined as the relationship between two values that are not equal or compared to…

Q: = For what values of k does the graph of f(x) a) k > 64 b) * 4 d) k < 64 x² + 16x + k x² + 7x have…

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Q: What Is the equation, in factored form, of the quadratic function shown In the graph? 5.

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Q: Consider a small shop with only one checkout counter. The arrivals of customers are distributed…

A: Solution Dear student as per guidelines we answer the first question only when multiple questions…

Q: Prove that for any sets A, B, X - X − (An B) = (X − A) U (X – B). -

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Q: Find the value of a for which 4 1 is in the set 2 H = span -3 4 -2 a =

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Q: Is L = {x+ix : x ∈ R} an open subset of C? A closed subset of C? Both? Neither? Justify your answer.…

A: To analyze : The subset L=x+ix : x∈ℝ ⊂ ℂ

Q: Question 1: For this question, use: f(x) = ax² + bx² + cx + d a) Choose integer values for a, b, c…

A: The end behaviors of a function are the values that the function will attain when the variable of…

Q: What is the constraint for: “Store 1 can only be opened if store 6 is opened.”? X1 + ( _ _ _ ) X6…

A: It's a binary programming problem constraint. Where variable Xi only take two values 0 and 1 X1-X6=0…

Q: 2. Maximize z = 2x₁ + x₂ subject to: x1 + x₂ ≤7 2x₁ ≤ 11 2002 ≤7 X1, X20 ₁ and 2 integers

A: The given problem is to solve the given linear programming problem for the given constraints. Given…

Q: 14. A computer software company models the profit on its latest video A game using the relation P=…

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Q: Which of the following statements is/are not correct? It is possible to have more than one comer…

A: Here  When objective function is parallel to any of the Constarints then there is mutiple solution…

Q: Does A − (B − C) = (A − B) ∪ C hold for all sets A, B, and C? Prove or give a counterexample for…

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Q: der the problem maxx + 2y subject to x² + y² ≤ 1 and x + y 20

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Q: estion x² +1 if x-1 If f(x)= what is f(-2)? A) 4 B) -5 C) -7 D) 5

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Q: Evaluate [ V21+12x-9x²dx

A: The given integral ∫21+12x-9x2dx can be evaluated as, ∫21+12x-9x2dx=∫21+-9x2-43xdx…

Q: 3. Let U= {x: xEZ, 0≤x< 15} A = { x: x E N and (x − (m + 3)(x − (m + 2) = 0}, B = {8,6,7,9} and a.…

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Q: e the restriction(s): 2x2-32 4x-8 2) Зx-6 x+4

A: The given function is 2x2-323x-6∙4x-8x+4

Q: 3. Let V be the set of all ordered triple in R³, and F, the set of real numbers, where the…

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Q: Consider the following LP: Minimize z = 2x1 + 3x2 + x3 Subject to: x1 + 2x2 + x3 ≥ 2 x1x2x3 = 1 ₁…

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Q: Which of the following defines the domain of |4x-8<12? A) -8<x<-4 B)-4 <x < 8 C) -1<x< 5 D) 1<x<5

A: We can solve the inequality in order to get the solution.

Q: Find the value of a for which v= 8 a -4 -12 is in the set 4 0 -4 -1 0 {6E9 2 -3 5 -3 -4 2 H = Span

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Q: xdx 3x2 + 5 ® ;(3=° + 5) +C I + C (A) B (3x2 + 5) 7 + C + (3x? + 5) + C 12 D) (32² + 5) + C E) (3x?…

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Q: 3. Let U= {x: xEZ, 0<x< 15} A = { x: x E N and (x − (m + 3)(x − (m + 2) = 0}, B = {8,6,7,9} and - a.…

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Q: Given: Min C = 3X1 + 7X2 + 5X3 Subject to: X1 + X2 + X3 ≥ 50 2X1 + 3X2 + X3 > 100 X1, X2, X3 ≥ 0 9.…

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Q: Let l1 and l2 be as above. Describe precisely the intersection l1 lz and justify your answer.

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Q: Let a,b be two different points in R^n one. We notice that d=(a,b)>0 (why is that so ?). Prove that…

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Q: Suppose X - U(2, 7). Determine P(X > 6 | X > 5). Note: This is a very challenging problem.

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Q: Which of the following sets are convex and which are not? 2 a. {(x₁, x₂) x² + x²₂² ≥ 3}. b. {(x₁,…

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