Verify that the vector X is a solution of the given system. X' = 1 0 1 1 1 0 −2 0 −1 X; X = sin(t) − 1 2 sin(t) − 1 2 cos(t) −sin(t) + cos(t) For X = sin(t) − 1 2 sin(t) − 1 2 cos(t) −sin(t) + cos(t) , one has X' = 1 0 1 1 1 0 −2 0 −1 X = .

Peter applied to an accounting firm and a consulting firm. he knows that 30% of similarly qualified applicants receive job offers from the accounting firm, while only 20% of similarly qualified applicants receive job offers from the consulting firm. assume that receiving an offer from one firm is independent of receiving an offer from the other. what is the probability that both firms offer peter a job?

*let m∠cob = 50°30’, m∠aob = 70° and m∠aoc = 20°30’. could point c be in the interior of ∠aob? why? a. point c could be the interior of aob but it is not the only case b. point c is the interior of aob c. point c is not the interior of aob d. the given is not possible for the plane geometry answer

Aculture started with 4,000 bacteria. after 5 hours, it grew to 5,200 bacteria. predict how many bacteria will be present after 19 hours. round your answer to the nearest whole number.