The amount of caffeine in the body of a healthy adult after drinking espresso decreases exponentially, with a half-life of approximately 6 hours. that is, every 6 hours, the amount of caffeine in the body decreases by 50%. charlotte wants to go to sleep at 11 pm and does not want more than 20 milligrams (mg) of caffeine in her system at that time. what is the latest time charlotte can drink a 2-ounce shot of espresso that contains 80 mg of caffeine? a. 5 am b. 11 am c. 11: 30 am d. 12 pm

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24