If P(A)=0.2, P(B)=0.3, and P(A∪B)=0.5, then P(A∩B)=?

Q: Let a = - 2ỉ - 4j – k and b = 4j + 2k. Find — ả + b. V

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Q: The coefficient of gªy³in (5x + y)® is 54 . (C).

A: Here the given expression

Q: ii Sketch y = f(x), y= f¯'(x), and y = x _on the same set of axes.

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Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: Find the convolution of (a) 2tu(t) and t³u(t) (b) eu(t) and tu(t) (c) e2tu(t) and etu(t). Answers 1.…

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Q: Find the product D (xD – 3) A) xD²– 2D B xD²+4D (c) xD² – 3D D xD²+3D

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Q: Show that 2 (-r × B)² = (r² B² – (r. B)²) And, further that r² B² (r. B)² = B² (x² + y²) - If B = B₂

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Q: Suppose y = (x² + 3æ)(x – 2)(x² + 1).

A: Given y=x2+3xx-2x2+1  We solve this by using product rule  ddxuv=udvdx+vdudx

Q: (d + g) Q² + (e + s) PQ = a (d + g) PQ+a(e+s) P² + (b+ f) Q+(c+ r) P. (15) By subtracting (14) from…

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Q: Which of the following is equivalent to (1-x)(1+x) -3x(2-x)  A. -4x2 - 6x + 1  B. 2x2 - 7x + 1 C.…

A: Given expression is (1-x)(1+x) - 3x(2-x)

Q: Minimization: Z = 5X, + 6X, + 10X, + 7X, + 19X5 Subject to: %3D 5X, + X2 + 3X3 – 4X, + 3X5 2 2 -2X,…

A: In this problem we can observe that all Xj ≥0 and so, Z can be minimum 0 as all coefficients of Xj…

Q: 9=a(0)2+b(+c 17-a(82+ b(8)+C 18=a(18)2 +b(18)+C

A: Solve the equation to find a,b,c

Q: What’s (E∩F)×(F∪G)

A: We are given that E = {1, 2}, F = {2, 3} and G = {3, 4}.Now, E∩F = {2} and F∪G = {2, 3, 4}.

Q: If S(8f(x)+ 5) dr = 8 , then

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Q: Find a pair of integers x and y such that 66x + 48y = gcd(66, 48)

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Q: Provide counterexamples for If (A −B) ∩ (A −C) = ∅, then B ∩ C = ∅.

A: The solution is given as

Q: 4. Find mRS. (5x + 6)" R (11x-72)

A: The chord of a circle is a line segment joining the two points on the circumference of a circle. If…

Q: Suppose P(A) = .17, P(B) = .18, and P(C) = .65. Assume that P(D | A) = 3 P(D | B) = 8 P(D | C). Find…

A: Given,P(A) = 0.17P(B) = 0.18P(C) = 0.65P(D | A) = 3P(D | B) = 8P(D | C)

Q: 5 Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (27, 0)…

A: To find the standard equation of the ellipse

Q: Find (a) c23 and (b) c32, where C = 5A + 2B,

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Q: Subtract (x − 5) − (x2 + 2).  A x2 + x − 3  B −x2 + x − 3 C −x2 + x − 7 would it be A B or C

A: Given that  Subtract (x − 5) − (x2 + 2)

Q: what does P(A∩B) = if P(A)=0.63, P(B)=0.47, P(B∩A¯¯¯¯)=0.27

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Q: 1 xp= V2x + 1

A: To find: The value of integral ∫0412x+1dx. Given that: The integral is ∫0412x+1dx. Formula used: The…

Q: Which of the following polynomials is the correct simplified form of 10y3-2y3-16y2+8y2?

A: From the given problem:   10y3-2y3-16y2+8y2   Now simplifying the given polynomials:…

Q: (d) Show that x² – 4 is a factor of x* – 5x³ + 2x? + 20x – 24.

A: