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: (b) (-1)" (b)(-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: (b): Evaluate: (8t³ – 9t² + 10)dt

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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: For x2 + Bx + C = (x + a) (x + b), which of the followingmust be true?(a) ab = B and a + b = C(b) a…

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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: 8² 8²v 8² = (x² + y² +2²) −¹, then + + is 822 მ2 If v=

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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: Find A.

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Q: Let A=(¹). 3¹). Find 3A³2A² + 5A - 12.

A: Given: A=1-123 We are required to find: 3A3-2A2+5A-I2

Q: 3 Perform the operation: (2x* + 5x+8x +24) - (x+2) 12 A. 2+x+6+ x+2 B. 2+ 112 + 9x + 18x + 44 + x+2…

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Q: 2a +4aX+2b-ax=bx-C=D2x-8X-4 a:? vb=?, C:?

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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: Add (4x² + xy² – 7y³), (-7x² + 3x²y² + 9y³), and (5x² + 12xy? – 8x?y? - 4y³)

A: Here we have to add the givne expressions,  4x2+xy2-7y3, -7x2+3x2y2+9y3, and 5x2+12xy2-8x2y2-4y3

Q: Q1: Determine if a +b+c+d=10 where a, b, c, d ER are such that: 6x³+3x²-5 -1 2a x-l + 3b x+1 + cz…

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Q: Consider the following quantities in IR", (a) What will the solution set become (ie, what type of…

A: Solving systems of linear equations is a fundamental topic in linear algebra, with many real-world…

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.

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Q: Determine the value of 7A+6B if 19x2 + 41x + 16 A (x+ 1)² Cx +B (x – 1)(x +1)2 Answer:

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