For any two events A and B, we have (i) P(ìB) = P(B) – P(A^B) (ii) P(AB) = P(A) - P(A^B)

Q: Given P(A^c-complement)=0.40, P(B) =0.40, P(AUB)=0.75, P(A)= 0.60, P(B^c)=0.75 Find P((AnB)^c)

A: Additional Law of Probability gives P( A ∪ B ) =P(A) + P(B) - P(A∩B)

Q: Let P(x) be the statement "x spends more than five hours every weekday in class," where the domain…

A: Given that P(x) : x spends more than five hours every weekday in class. (a) ∃xP(x) This can be…

Q: (a³b^5) x (a²b³) =

A: We know that,pq×pr=p(q+r) So,a3×a2=a(3+2)          =a5 b5×b3=b(5+3)          =b8 So, to find (a³b^5)…

Q: verify that3(AB) = (3A)B = A(3B)

A: Given matrix

Q: 9+(_3)=

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Q: (X-4)/(x-7 )-1= 3/(x-7)

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Q: Find the areas of the shaded regions in

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Q: (dvd) ^ (b-vd) :(vb) d

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Q: 3cos3x %3D s² + (v9)

A: We have to solve given problem:

Q: (x*- 7x-x+7) (x - 7) 6) (3v + 4v² – 4v) ÷ (v+ Z

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Q: If x = (1/2)a + (2/3)b + (3/4)c c=(12x-6a-

A: The detailed solution is given below Thank you

Q: If A =  (2   1) and  B = (3 )then BA =            (3   4)                (1)

A: Given A=2134 and B=31

Q: A researcher wanted to estimate the difference between the percentages of users of two tooth- pastes…

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Q: fs=メー4 f(3)3= %3D

A: Substitute the value of x in given equation

Q: f|A| = 9 and |B| = 3, what is |AU B| + |An B|?

A: Given: A=9 and B=3. To find: A∪B+A∩B Formula Used: The relationship between the union and…

Q: Givon flox) =(-2)" and g() Soct2, glee) both (fog) (2) and (gof) (2) %3D

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Q: Suppose that P(A) = 0.12, P(B) = 0.40 and P(B|A) = 0.60. (a) What is P(A and B)? (b) What is P(A…

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Q: Evaluate 3r+(6s)/(7), when r=3 and s=2 (21)/(7)

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Q: Find ify= xln(4x +1)

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Q: 2x-x xp - (r-1)° (x²+1) -0-

A: Given ∫-∞0 2x-x3x-12x2+1 dx                         =-∫-∞0x3-2xx-12x2+1dx…

Q: Differentiate. h(w) (w5+ 8w^) (w-4-w-6)

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Q: Compute the following. (a) P6, 2. (b) C6, 2. (c) P6, 6.

A: P(n,r)=n!n-r!C(n,r)=n!n-r!.r!

Q: 5[3m - (m + 4)] > -2(m - 4)

A: topic:- algebra

Q: 2log_

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Q: f A = (1 2)           (-4 5)   and B (-3   1)            (0  -2) calculate ATB

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Q: P(x) =10x^3-5x^2 +2x+4

A: Value of x is

Q: find

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Q: 1/x-3+1/x+3=10/x2 -9

A: The equation is given by,

Q: (AUB) = ACNBC. Show that P(ACNBC) = 1- P(A) - P(B) + P(ANB)

A: P(Ac∩Bc)=1−P(A)−P(B)+P(A∩B)

Q: S 4x²+1

A: Find the integral by using substitution method

Q: Simplify x-1/2(x/5 – x) + (* ¬/5 – 1) (x^/?), -

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Q: show that A (7b +p) = A (7b) + A (p).

A: Given A = [v1 v2 v3]  ,  b = xyz   and   p = 375

Q: Compute the value of the expression (II",3*+1): (IIH,3').

A:

Q: (3x–1)}

A: Given,          (3x-1)3

Q: 4sqrt(2) was incorrect

A: Given:= f(x,y) = x3y2U = (-3,3) P= (-1,-2)   The directional derivative being negative means that…

Q: 22)x-+183=D9%

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Q: If P(B^c) = 0.8, Find P(B)

A: Given, P(B^c) = 0.8That is, P(Bc) = 0.8Using formula,P(A)+P(Ac) = 1