Let C = {0,2, –1, 100, 12} and let D = {-1,2, 14}. %3D a) |C u D| = b) |C n D| = c) |C – D| = d) |D – C| =

Q: Find P(A U B), given that P(A) = 0.5. P(B) = 0.4, and A and B are mutually exclusive. 0.8 0.7 0.9…

A: We have given that P(A) = 0.5 P(B) = 0.4 Also, given that A and B are mutually exclusive

Q: If P(A|B) = P(A), then O P(BNA) = P(B)+P(A) %3D %3D N(BŪA) = N(B)+N(A) O P(B|A) = P(B) O P(A) = P(B)

A:

Q: HW Le A 88° 16.1 21 C. 26 In the diagram above of AABC, determine the mZB

A: In a given triangle, we have∠A=88°a=26b=16.1c=21we have to find ∠B and ∠C

Q: Show that for n, m e Z+, gcd(2" – 1,2 – 1) = 28cd(n,m) – 1.

A: To prove : gcd(2n-1, 2m-1)=2gcd(n,m)-1where n,m ∈ℤ+

Q: If S is a subset of T , then u (T) sp" (S)

A: It is Always True

Q: Given that n(S) = 44, n(A) = 15, n(ANB) = 7, and n(A u B) = 24, then n(B) = %3D %3D %3D

A: Probability is defined as a number between 0 and 1 representing the likelihood of an event…

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: 4. What are the values of A, B, C, and D so that 1 a. A = b. A = C. A = d. A = HALA00 B= C= B B 1 8'…

A:

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (4, 0, −3, 5), v = (0, 2,…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Find E, 28 + 12(k – 2). uk%3D1 7,392 2,800 2,342 3,696 1,848 а. b. C. d. е.

A: Consider ∑k=12428+12(k-2) = ∑k=12428+∑k=12412(k-2)= 28∑k=1241+12∑k=124(k-2)=…

Q: If E, F are independent, E and D are disjoint. P(D)=0.2, P(E)= 0.5, P(F)=0.5. What is P(E ⋂ F' ⋂…

A: We have to find P(E ⋂ F' ⋂ D').

Q: Let Z = min[X, Y]. P[Z <= 5] ? E[Z] ? P[X < Y]?

A:

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (3, 4), v = (2, −3)

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: sed, three bag cantains 9 balle fwo 6f which are F bue and four Glack. wi e bulls are drawn fran the…

A: There are total 9 balls, among which 2 are red balls, 3 blue balls and 4 black balls.

Q: Let w = z. In(xy?z³), then which of the following is :? O a. O b. c. O d. 0 Oe.

A:

Q: 20. Let (). ()- u = v = If æu + yv = w. (æ, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2 (D) –1/2…

A: To find the value of x-y from the given vectors.

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (2, −2, 1), v = (2, −1,…

A: Given

Q: Let C = {x ∈ P(A) : ∃y ∈ x, y ∈ A and y /∈ B}. Prove that P(A) − P(B) = C.

A:

Q: 1. Prove: Va, b, c E Z: alb and blc = alc 2. Give an example with a = 7 and b, c + 7.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Given that P(4) = 0.2, P(B)= 0.7, and P(A|B) = 0.12. Then P(A B)= 0.233 0.184 O None of other…

A: Given P(A)=0.2P(B)=0.7P(A|B)=0.12

Q: o Evaluate , S, Só (x – 2y + 2z)dz dydx.

A:

Q: 43 If uzzt+y+z , u?v =y+z,u³w=z, Show that a (x,4,z)

A: Q3. Here, u=x+y+zand,u2v=y+z⇒v=y+zu2=y+z(x+y+z)2and,u3w=z⇒w=zu3=z(x+y+z)3

Q: Let z-2 z-2 n st pC& >0.5)20.9 and y:bin (n,o.38), find or

A: Y~Binomialn, 0.38 Compute the mean and the standard deviation of Y using the formulae: Y=np…

Q: Let D={(x,y,2) : x2+y2+z?s 1600, z2 o}. Evaluate - z dv.

A:

Q: Given u = (5,0, 0) and v = (5, 5, 0), which of the following represents u x v?

A:

Q: Compute the dimension of V,(Tỷ – Tỷ, TẬT, – T†T,) C P³.

A: Given that X=ϕ is a topological space. We have to compute the dimensions of the following.…

Q: Let v = (a, b, c). Calculate v × i, v × j, and v × k.

A: given: v=a,b,c we have to calculate v×i, v×j and v×k

Q: Show that for n, m e Z+, gcd(2" – 1,2m – 1) = 2gcd(n,m) – 1.

A:

Q: (7) Given A, P € M„(R), show that if A is skew-symmetric, then B = PT AP is also skew- symmetric.

A: Here we have to Prove B is skew symmetric.

Q: Given: f (x, y, 2) = z0 + 5x*y%z® _ #°yA 2x°y" + 5æ*y®z° – z°y4 ,3,,7.5 .48 3.4 Required: fzay, fzzy

A: Given f(x,y,z) = 2x3y7z5+5x4y8z6-x3y4 . We need to calculate the value of fzxy and fzzy .…

Q: Find P(C/A) and P(C) if p(A1) = 0.6 B1 0.8 0.7 C1 A1 C2 A2 0.7 B2 0.8 %3D [Hint: P(C/A) =…

A: Probability mass function P(X=xi) Simple facts about pmf  ∑(X=xi) =1iP(X=xi ∩ X=xj)=0 if i≠jP(X=xi ∪…

Q: In (R, Tµ), if A = (1,3) n (Q – Z) then A = - %3D O a. [1,3] n (Q- Z) O b. R O c. [1,3] – {2} O d.…

A: Given that, In ℝ,ζυ, if A=1,3∩ℚ-ℤthen calculate the value of A.

Q: Find (a) u ∙ v, (b) v ∙ v, (c) ||u||2, (d) (u ∙ v)v, and (e) u ∙ (5v).u = (−1, 2), v = (2, −2)

A: u→=-1,2v→=2,-2a u→.v→=?     u→.v→=-12+2-2           =-2+-4          =-6u→.v→=-6

Q: p(x, y) 3/24 2/24 1/24 1 2/24 5/24 2/24 2 6/24 1/24 2/24 Е(X), Е(Y), H(X), н(Y, НХ Ү), аnd HIX, Y)

A: It is an important part of statistics. It is widely used. Since the question has multiple sub parts…

Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: Consider the following scenario: Let P(C) = 0.4 Let P(D) = 0.5 If C and D are independent, find…

A: (1) It is clear that events C and D are independent. The value of PC∩D is, PC∩D=PCPD=0.4×0.5=0.2…

Q: Let X1,., X, N(u, o?). iid N(H, o?). Find E(), if ju = X1 + (X2 + + X(n %3D 2(n-3) 17 16 4 O 17(n-2)…

A: Given that, E(X1)= E(X2)= ......E(Xn)= mu

Q: Let z = a?y – ry?, x = e 4, y = e2t, then which of the following is 2e2t + 2e 2t a. O b. -2e2t – 2e…

A:

Q: If W= R Cx, y,Z),g (x,y)=a,hcx,Z)= C, then Find dlw

A: Use chain rule of differentiation to solve this problem.

Q: If A (x, y, z) = (5y – az) i + (3z + bx) j + (cy – 4x) k is conservative, what are the values of a,…

A:

Q: Let m e N and a, b e Z be such that (a, m) = 1 and (b, m) %3D = 1. Let h = 0m(a), k = 0m (b), and…

A: Let m∈ℕ and a, b∈ℤ be such that a, m=1 and b, m=1. Let h=oma, k=omb,  and  n=omab. We need to show…

Q: Let z, w e C. Show that |2 + w? + |z – w? = 2(|2|2 + |w?). %3D

A: We will show the given result.

Q: Given R = Z₁₂, M = {0, 4,8], then R/M is

A: We know the definition of quotient ring ,  R/M = a + M / a ∈ R We have given that , R = ℤ12  and  M…

Q: B) Prove that (A + B) +(C + D) = (A+B) (C+D) %3D

A:

Q: Ue he dhe g A IBhdependant APAR ndd) dapandert And Independent. Aand

A:

Q: T is self adjoint if (Tx, y>= (x, Ty> o > |(Kr.x>|| o

A:

Q: Exercise 4.6.9. If a < a', show that D CD7.

A: Given that, α'&gt;α The aim is to show that, Dfα'⊂Dfα. It is enough to show that if c∈Dfα' then…

Q: If z, w E C, then |zw| = |2||w|.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Compute d(ū, ū), d(ū, w) and d(ū, w) where ū, ū and w are

A: Given: u¯=12-48, v¯=8-241 and w¯=2-418 To find: du¯, v¯, du¯, w¯ and dv¯, w¯ where d is distance…

Q: 11. In crdle O, m BÁC = 296o. Find m 2 AOB. =2960. Find m z AOB. %3D A A. 110 B. 116 C. 55 D. 58"

A: