Show that if one event a is contained in another event b (i. e., a is a subset of b), then p(a) ≤ p(b). [hint: for such a and b, a and b ∩ a' are disjoint and b = a ∪ (b ∩ a'), as can be seen from a venn diagram.] since a is contained in b, we may write b as , the union of two mutually exclusive events. then p(b) = and p(b) = . then, since it follows that p(b) ≥ . this proves the statement. for general a and b, what does this imply about the relationship among p(a ∩ b), p(a) and p(a ∪ b)? p(a) ≤ p(a ∩ b) ≤ p(a ∪ b) p(a ∪ b) ≤ p(a ∩ b) ≤ p(a) p(a) ≤ p(a ∪ b) ≤ p(a ∩ b) p(a ∩ b) ≤ p(a) ≤ p(a ∪ b) p(a ∩ b) ≤ p(a ∪ b) ≤ p(a)

If f(x)=-x^2+6x-1 and g(x)=3x^2-4x-1,find(f+g)(x)

The constitution gives congress the power to create federal courts lower than the supreme court higher than the supreme court equal to the supreme court, unaffected by the supreme court.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.