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 Any probability result that is true for unconditional probability remains true if everything is conditioned on some event P ( A ∣ ( B ∩ C)) = P ( A ∩ B ∩ C) P ( B ∩ C) which is what you think the result should be But observe that if you multiply and divide the right side of ( 3) by P ( C)), you can get which is just ( 2)I j h n _ k k b h g Z e v g u c i Z d _ l,Binomial Probability, b (x;

P(AB) = P(A) P(B) P(A\B) P(AjB) = P(A\B) P(B) P(ABC) = P(A) P(B) P PMisc formulas nP k= n!To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW If `a,b,c` are in AP and `x,y,z` in GP, prove that `x^(bc)y^(ca)z^(ab)=1`

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 Calcular (a b c) Si P(x) º Q(x) Siendo P(x) = 4x2 3x 2 Q(x) = (a b 1)x2 (b – c 2)x (c – Recibe ahora mismo las respuestas que necesitas! p" p" p" w helen ave santiago ct oak leaf whippoorwill nblvd gunn caye ln tarpon cove blvd bal harbor ct waxwing ct como ct carolyn ln san carlo ln danial lake dr8 S R 8 s 4 F = @ 6 3 = 8 r F k 4 k 3 E f J J O I O H N G x z J b J H N w J N X x z J I H G 4 = a 8 = 8 7 = E p V 7 J s O 6 C z 8 L S H d P N 8 Z = \ 4 J < I J H O G Y J H y X \ Z X \ c L N x

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Proof Let P(x) be a polynomial of degree n with integer coefficients Assume there exist three distinct integers a, b, c such that P(a) = b, P(b) = c, P(c) = a Since the integers are distinct, there is a least among them Without loss of generality, write a < b and a < c Note that, for any two real numbers x, y , P(x) − P(y) = an(xn − ynN = 1 (a) Calculate and plot the base current and collector current waveforms and calculate the pulse width, (b) If due to temperature variation h FE increases to 30, then calculate the pulse width Solution (a) We have i B = 3 115 30 mA 05 10 nV CC R t L V R n V i CC CC C 2 = t 3 3 2 3 10 15 05 10 (1) 15 = 30 10 3 5 103t p RY l { S e I z C C l I Ή ς݁I ~ N V B E A o E o Q A Ă S D ǃA N Z X W } V y N G X g p b N Sin P/ QUEST PACK 4in1 z ̔ ̂ق ɁA y l { S e I z C C l I Ή ς݁I ~ N V B E A o E o Q A Ă S D ǃA N Z X W } V y N G X g p b N Sin P/ QUEST PACK 4in1 z ̐V i ̃N ` R ~ m ߂ l ́A ̏Љ T C g ցB

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3 Exponents Let a,b,m, and n be numbers (a) Exponents distribute over products, but not over sums (ab) n= a b but (ab) n6= an b (b) A negative exponent can always be viewed as a denominator, and vice versa a−n = 1 an (c) Two terms with exponents can only be multiplied if they share the same base;To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW if `a,b,c` are in `GP` and `a^x=b^y=c^z` prove that`1/x1/z=2/y`If `B={xx=(2n1)/(n2), n in W and n lt 4} ` then B can be wirtten as

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