Let (pos S) be the set of all positive combinations of the points of S. Which of the following statements are true? 1: (pos S)n(aff S) = conv S II: If a unique linear combination of points %3D both positive and affine, then it must be convex. А. I B. Neither I or II C. I D. Both I and II

Q: 1- sketch the set of points determined by the given condition: (a) z-4+1=3 (b) 17-11 2+4 |

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

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A: Let y=fx be  a function which takes the value x1, y1, x2, y2 So, there are two pairs of values of x…

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Q: Lt A 28 be anbitrary closed subsets 9 (X,d) 3f A°=4 e B'= ¢ the give Such That AUB)"=X. erample an

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Q: Show that S {x€R* |2,• 24. • O} is/isn't %3D convex

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Q: Let P = v?R/(R +r)² as in Example 8. Calculate dP/dr, assuming that r is variable and R is constant.

A: Given:

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: The dimension of the set W = {(2t – s, s, t) : s, t e R} of R is equal to: %3D

A: The dimension of the set W={(2t-s,s,t) : s,t ∈ R} of R3 x=2t-s y=s z=t (t,s) ∈ R   This can be…

Q: If ||u|| = 2, ||v|| =√3 , and u x v = 1, find ||u + v||.

A: Given that u=2,   v=3   and  u*v=1. This implies that,

Q: 1: One of the hayfields on Rob's farm has shape and size modeled by a quadrilateral QC R? with…

A: Given:- Corners of the quadrilateral hayfields farm  is (3, 1), (6, 2),(3, 6) and (2, 4) We first…

Q: Which of the following points is at a distance of 5V2 from the origin. * O (0,0) O (5,0) O (5,5) O…

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Q: Let P and Q be two points in R’. If P = (1, 2, 3) and PQ then Q = (O0:C) 2

A: if P = ( P1, P2, P3 ) and Q = ( Q1, Q2, Q3 ) are two points in ℝ3 then

Q: M and N are the midpoints of sides RS and RT of ARST, respectively. M. R MN = x2 + 7 x(2x + 7)…

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Q: It gER[a,b] and if h(x)=q(x) except for a finite number of points in [ab],then prove that he R[ab]…

A: The continuous set of [a,b] should be divided into finite sets first.

Q: For what value of k,the points (k,k),(2,3) and(4,-1) are collinear.

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Q: Let B be a subset of R4. Which of the following statements are correct? If |B| = 5, then B is not…

A: The objective of the question is choose the correct option.

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Q: For what values of c is the set {t +3, 2t +c2 +2} linearly independent?

A: The given set: t+3,2t+c2+2

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A: Answer Option (1) We know that, dimension of R4 is 4. But here given B is a subset of R4  and |B| =…

Q: Prove that P(A) - P(3)| 4 P(AAB). where A is the symmetric difference.

A: The following identity can be proved after breaking the LHS and RHS into mutually exclusive events,

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Q: If given points A at (6, 3) and B at (-1, 4), determine AB. A 5/2 В 2/5 C V26 D V74

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Q: Find f, and f, and evaluate each at the given point. f(x, y) = eXy2, (In 5, 2) fo(x, y) f,(x, v) =…

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Q: If w=f(p, q, r), where p-z2-y², q=y²-22, and r = 22-2², show that 1 Ow x 8x + 1 8w у ду + 18w z Əz…

A: Given w=f(p,q,r)and p=x2-y2,   q=y2-z2 and r=z2-x2

Q: Given M = {(r, y), 1 < ² + y² < 4} C R². (a) Determine dM and aM. b) Is M connected? Pathwise…

A: See the attachment

Q: If R is symmetric, then R 1 is symmetric. True False

A: We have determined that if R is symmetric then R-1 is symmetric or not. If R is symmetric, then R-1…

Q: has solutions of the form R(p) etmzting whe

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Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: If X and Y are independent RVs following N(8, 2) and N(12, 4/3 ) respectively, find the value of 2…

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Q: V and for all r € R. Show that (V, 1

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Q: Determine if the following three points are collinear: (-8, 12) (3, 5) (25,-9) O They are collincar.…

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Q: Show thet the fens- 14 ベ+ ナ (A+1)(2p+1) (P+1) (241)(38+) (uluse convedges if 8a and divesgus if Bsd…

A: We will use the following results to solve the given problem : Result 1 : ( Ratio Test )  Suppose…

Q: Let linear tiansformation I(4)=(2,32and Tls0) =(3B,2) Cheek whether T? exists or noti2 Find T. E=R…

A: The objective is to check whether inverse of T exists or not and find it.

Q: Let A = (m, n) and В 3 (х, у) . If A and В lie in one horizontal line and is to the right of A which…

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Q: Given that: P(AN B) = 0.15, P(B) = 0.3 and P(A)=D0.2 %3D %3D Then :P(A U B) is

A: Ans - Given P(A∩B) = 0.15, P(B) = 0.3  and P(A) = 0.2  Then Find P(A' U B) = ?

Q: 4.4. Suppose that u = (1,3) and v = (3, 1). (a) Sketch the points tu + žv, žu +v, and žu + jv. (b)…

A: Solution: Given u=1,3 and v=3,1

Q: Is i,,3 a linearly independent set?d O Given ū;| and Ĵs 2 2. 2. -3 3

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Q: The values of C, and C, so that y(x) = C, e3x + C, e-3x satisfies the %3D following conditions: y(0)…

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Q: Given4ABC, let P,Q, andR be points on sides BC,AC, andAB, respectively, with RQ∦BC, and so that…

A: Consider the equation

Q: Find (t), given 7(t) = (- 2 In(5t), - 5/5t, – et). %3D F'(t) =

A: Explanation of the solution is given below...

Q: 4.4. Suppose that u = (1,3) and v = (3, 1). %3D (a) Sketch the points ļu + žv, ļu + ļv, and u + tv.…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: If p(2.3. – 6),Q(3, – 4,5) ate two points find DCs of OP,QO and PQ where O is the origin

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Q: If g € ([a,b] and g(x) € [a,b] for all x € [at] then g has only one fixed point in[a, b] true O O…

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Q: 6. If UV bisects XY at point W, which statements must be true? Select all the true statements. (A UW…

A:

Q: Find the pointP such that v = PQ has the components (-9.75, 5.75, – 16.5). Q = (-7.75, 6.75, –9.5)…

A:

Q: c=12 31 1) 1 show that Symmetric OR Neither simmetric. either 'c' is Skew symmetric

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Q: Let B be a subset of R4. Which of the following statements are correct? □ If |B| = 5, then B is not…

A: Introduction: Spanning set and linear independence are very significant in basis of a vector space.…

Q: The set {t, –3t?} of P2 is linearly independent. O True O False

A: x=t  --------------equation 1y=-3t2  -------------equation 2now from equation 1 and 2y=-3x2means y…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.