Groundhog's Day is on February 2nd each year. On this day, in Punxsatawney, Pennsylvania, thousands of onlookers watch to see if Phil, the groundhog, will cast a shadow. If he does, then six more weeks of winter are predicted. If he doesn't, then an early spring is predicted. Historically, Phil's prediction has only been correct about 40% of the time.

Using complete sentences, design a simulation to determine the probability that Phil's prediction will be correct at least two out of the next three years. Make sure to explain how you would use the simulation to determine the probability.

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