A spot light illuminates a circular spot on a stage and can be represented by the equation (x – 13)² + (y – 4)2 = 16. Joel is standing at (11,4) and
Amerra is at (8,5). Are they both in the spotlight?
Joel is the only one in the spotlight
Amerra is the only one in the spotlight
Both are in the spotlight
Neither are in the spotlight
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An oil exploration company currently has two active projects, one in asia and the other in europe. let a be the event that the asian project is successful and b be the event that the european project is successful. suppose that a and b are independent events with p(a) = 0.2 and p(b) = 0.8. (a) if the asian project is not successful, what is the probability that the european project is also not successful? (b) what is the probability that at least one of the two projects will be successful? (c) given that at least one of the two projects is successful, what is the probability that only the asian project is successful? (round your answer to three decimal places.)

Harold moves no more than 43 of his sheep and goats into another field fewer then 22 of his animals are goats

Amodified roulette wheel has 36 slots. one slot is 0, another is 00, and the others are numbered 1 through 34, respectively. you are placing a bet that the outcome is an odd number. (in roulette, 0 and 00 are neither odd nor even.) a. what is your probability of winning? the probability of winning is startfraction 17 over 36 endfraction . (type an integer or a simplified fraction.) b. what are the actual odds against winning? the actual odds against winning are nothing: nothing. c. when you bet that the outcome is an odd number, the payoff odds are 1: 1. how much profit do you make if you bet $10 and win? if you win, the payoff is $ nothing. d. how much profit should you make on the $10 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? $ nothing (round to the nearest cent as needed.)