Aand b are involved in a duel. the rules of the duel are that they are to pick up their guns and shoot at each other simultaneously. if one or both are hit, then the duel is over. if both shots miss, then they repeat the process. suppose that the results of the shots are independent and that each shot of a will hit b with probability pa, and each shot of b will hit a with probability pb. what is (a) the probability that a is not hit? (b) the probability that both duelists are hit? (c) the probability that the duel ends after the nth round of shots? (d) the conditional probability that the duel ends after the nth round of shots given that a is not hit? (e) the conditional probability that the duel ends after the nth round of shots given that both duelists are hit?

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.