Let A(z) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t = 0 and t = x for the graph below. Evaluate A(z) for x = 1, 2, 3, and 4. 5 4 3 2- 1 A(1) = 3 A(2) = 3 A(3) A(4) = 4.5 = 5 2 3 4 X X X 8

Q: . If n(A) = 15, n(B2)= 20, and n(A ∩ B) = 10,find n(A ∪ B)

A: Given: nA=15, nB=20, nA∩B=10

Q: 2. K-5InX+3 find dw dr dw

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Q: aluate. 11! 4!(11- 4)!

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Q: If P(A) = 0.29 , P(B) = 0.32,  P(A | B) = 0.38 then P(A ∩  B) =

A: Bayes' theorem can be used to compute conditional probabilities and isexpressed as P(A|B)…

Q: [2 3 2. Given A = 30 2 B = C= -2]. Verify that (AB)C = A(BC) %3D

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Q: 4 3 Find A given that (21) = 2 1

A:

Q: 1.4.7. .(3η- 2) E(-1)" 7.9.11.......(2n+5)

A: Given : ∑n=1∞(-1)n 1.4.7.....(3n-2)7.9.11.......(2n+5)   To Find: Whether it is convergence or not…

Q: -3 show that B = B". 7. Given that B= 4 -9 -2 5 - 4 2.

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Q: . Write (12)(13)(14) in the form æ(12), where a E A¸. Write (1234) (12)(23), in the form a(1234),…

A: Given, (12)(13)(14) and we have to write this in the form alpha(12), where a in A4. Similarly, write…

Q: Convert ff Incxag) dA.aver. the.regian.cx.<e. segian.e.x+y.c.e. -.to.polar.form. and.…

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Q: Which of the following is equivalent to (D-3)(e³xy)? 3e-³x Dy e³xDy a. b. c. e-3xDy d. 3e³xDy

A: D-3e3xy

Q: In S, if T-{(G { G {), them r ) is In S, if T-1(G )G 2 3 \1 2 3 2 3 }, then 3 1 2 3 2 3

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Q: If (R – {0}, .) = (Q,.) then 1=0 1=-1 -1=0

A: For the given statement

Q: If P( A U B) = 0.5 , P (B) = 0.2, P (A)=0.4 then || P(B|A) Is?

A: GivenP(A∪B)=0.5P(B)=0.2P(A)=0.4

Q: 10 8 8. 6. 4. 4. 12 12 4. 4. C 8. 3 10 10 Which is similar to X? 5. 3.

A:

Q: /(r² – 8)5

A: Use substitution method to find the integral

Q: 10. Let a = (1,-1,2), b = (2,0,−1), and = (3,-2,0). Evaluate or explain why the expression is…

A: The vectors:

Q: and y= If a = 3, then x =

A: Solve using the properties of trigonometric rations

Q: 18

A:

Q: If P(n-1,3):P(n,4) = 1:9,Findn.

A:

Q: 1. Find P (AN B).

A: Here use basic probability rule

Q: 6. If -2 determine all values of x and y for which A= A.

A:

Q: . If n(A) = 30, n(B) = 40, and n(A ∪ B) = 45,find n(A ∩ B).

A:

Q: 3. The diagram at the right shows two different kinds of birdfeeders that are used to attract birds.…

A:

Q: What is m 24?

A:

Q: Let 1 -2 1 -1 -3 1 3 A = -2 -1 1 -1 3 0 1 3 0 -4 Then nullity(A) = 2 4 3 O None

A:

Q: 10. (x² – 2x + 1)e2 dr

A: Integrate function using integration by parts

Q: 14. (a) Is 2 C {2, 4, 6}? (b) Is {3} E {1, 3, 5}?

A: Introduction: Subsets are a subset of the mathematical concept of Sets. A set is a collection of…

Q: 5. A B Suppose that P(A)=0.4, P(B)=0.5 and P(AUB) = 0.42. Are A and B independen Yes, A and B are…

A: Given that  P(A) = 0.4 , P(B) = 0.5

Q: 9. Given u =(2,-2), v = (5,8), and w = (-4, 3), find each of the following. (a) u v (b) (u - v)w (c)…

A: