Theorem 3-12. For n events A1, A2, An, we have 2,.... P(A10A20... nAn) = P(A,) P(A2\A1) P(A3\A¡ nA2) ... xP(A,I A1NA2...nAn 1) ... where P(A; I A¡n Ak n... n Aj) represents the conditional probability of the event A; given that the events Aj, Ak A, have already happened. ....

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: (4) Use standard multiplication to multiply the two sexigesimal numbers 11, 4; 17, 9 and 50, 50: 43,…

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Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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Q: Prove that (1, 2) (1,(1), 2, 3).

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Q: Use proof by contradiction to prove that if x + y > 2, then x > 1or y > 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: Determine all the roots of z +1 = 0

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Q: From Leibnitz theorem °C=

A:

Q: Show that A = has two different factorizations of the form A = L · U where L is lower triangular…

A: Given: A=0001. To show: A has two different factorization of the form A=L·U, where L is lower…

Q: 1- Suppose A=

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Q: verify that (A + B)T = AT + BT

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Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

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Q: (f) 1 x + iy + 1 I-iy

A:

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: re 1 da Ji rVI- (In x)²

A:

Q: its saying that D is wrong and so is fxi

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Q: |z+2i|=|z+1- 3i|

A:

Q: 2. (– 13 + 3i)31

A:

Q: Find the Re and Im parts of exp(z?)

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Q: One version of the Fundamental Theorem of Calculus can be stated as: q [F(a)adua f(a)da = F(q) -…

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Q: Prove Equationally that F A → B → A.

A: Given: ⊢A→B→A

Q: 1 5. What is equivalent to 81

A:

Q: Let 1 2 3 1 A = | 6 -2 3 and I3 =| 0 1 5 4 1 If 2. is a real number, compute 2I3 – A.

A: A = 1236-23524 I3=100010001

Q: (a) Show that if a > 0, then 1/a> 0 and 1/(1/a) = a. (b) Show that if a <b, then a < (a+b) < b.

A:

Q: 3+4i30 -2+i 2-i 5

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Q: beta

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Q: For two real numbers x and y, if 2x + 3y > 7. Prove by contradiction: 18, then either x ≥ 3 or y ≥…

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Q: (x+1)(x-2)². On what interval (2) (x - 5) let g"(x) = is g Concave up? (Note: you are given g" but…

A: g''x=x+1x-22x-5

Q: |u|> c is true for all real numbers if c _ 0.

A: |u|&gt;c is true for all real numbers if c ____ 0.

Q: nd y axsis labelled ?

A: Morphospecies on A Morphospecies on B Morphospecies on C 7 13 3 7 9 4 2 4 4 4 4 2 11 14 10…

Q: MA Let r [-1. 1] and F(x) = f, f(t)dt. where the function f is defined by 1. if x > 0. f(x) = { 0.…

A: f is not continuous at x=0.

Q: Find all values of z such that z5 =1 - i.

A: Given: z5=1-i, To find: All values of z.

Q: Use part one of the fundamental theorem of calculus to y = 3x + 7 t 1 + 1³ dt

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Q: Prove that (R x Q) N (Q × R) = Q x Q

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Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

A: