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Solution set of a quadratic inequality. Let C CR" be the solution set of a quadratic...
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set. - 2(4x-5)<2 Choose the correct and per below that is the solution set to the inequality O A. {x[x> 1} or (1,00) OB. {x\x < 1) or (-0,1) O C. {x}x< - 1} or [-00,- 1] OD. {x[x> 1} or [1.00]
Solve the inequality. Express your answer using set notation or interval notation. Graph the solution set. - 5(3x-6) < - 30 Choose the correct answer below that is the solution set to the inequality. O A. {X/X> 4) or (4,00) OB. {X/X <4) or (-0,4) O C. {XIX > 4) or (4.00) OD. {X/X <-4} or (-0,-4) Choose the correct graph below that is the solution set to the inequality. OA OB -6 6 9 -9 -6 -3 0 3...
plz use the definition solve the question Definition 1. Given a set A CR, an elementu ER is an interior point of A if there exists an e > 0 such that (x - 5,3 +E) CA. The interior of A is the set Aº consisting of all interior points of A. A set A is called open if A= A'. Definition 2. Given a set A CR, an element X ER is a limit point of A if for...
For this chapter the Cauchy-Schwarz inequality can be used (without a proof). (C – S) |u7v|2 < (uTu)(v7v) = ||_||- ||0||?, for all u, v ER", with equality only if u and v are parallel (u= lv, for some scalar 1). For the next three problems, let B be a symmetric and positive definite nxn matrix, and let geRn be a nonzero column vector. Define pu = - gʻg -9, and pB = -B-19. g? Bg P1) Prove that ||...
8.1. Consider the problenm min f(x) (P) t. g(x)s0 where f and g are convex functions over R" and X CR" is a convex set. Suppose that x is an optimal solution of (P) that satisfies g(x")<0. Show that x is also an optimal solution of the problem min f(x) s.t. xX. 8.1. Consider the problenm min f(x) (P) t. g(x)s0 where f and g are convex functions over R" and X CR" is a convex set. Suppose that x...
Let B C R" be any set. Define C = {x € R" | d(x,y) < 1 for some y E B) Show that C is open.
Looking for full solutions of question (a)(b)and(c) Problem 4. Let A CR. Given any a, b € R, with a <b, define (a,b) A = {2 € A:a < x <b}. We call (a, b) A an open interval in A (or an open interval relative to A). a) Show that (a, b) A = (a,b) n A. b) Prove that a set V C A is relatively open in A if and only if for every 3 EV, there...
5) Let X be a random variable with mean E(X) = μ < oo and variance Var(X) = σ2メ0. For any c> 0, This is a famous result known as Chebyshev's inequality. Suppose that Y,%, x, ar: i.id, iandool wousblsxs writia expliiniacy" iacai 's(%) fh o() airl íinic vaikuitx: Var(X) = σ2メ0. With Υ = n Ση1 Y. show that for any c > 0 Tsisis the celebraed Weak Law of Large Numben
Let the universal set be R, the set of all real numbers, and let A {xE R I -3 sxs 0, B {xER -1< x 2}, and C xE R | 5<xs 7}. Find each of the following: (a) AUB {xR-3 < x2} s -3orx > 과 xs. (b) AnB xR-12 {*E찌-1 <xs마 frER< -1 orx {*ER|x s -1 or*> 아 (c) A {*ER-3 <x< 아} {*ER|-3 < 아} s-3 orx> 아 frER< 3 orx x s 0 (d) AUC...
Could someone help me solve this question and show all work 7. Let X = (x1,.. . , x.) be a data set. Let sz-SD(X). Let Y = aX-b. (a) Show that Sy-SD(Y) = lal&z. (b) Show that Median(Y) = a . Median(X) + b. (c) Can you write the relation between Q1(y) and Q1 (X). What happens if a < 0.