Shane is thinking about apprenticing as a plumber and notes that master plumbers in his region of the country make about $55,000 a year starting out. However, salaries are expected to increase by about 10 percent over the next four years. How much can Shane expect to make when his apprenticeship is over in four years?

Which of these numbers of simulations of an event would be most likely to produce results that are closest to those predicted by probability theory? 15, 20, 5, 10

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

The angle of elevation from point a to the top of the cliff is 38 degrees. if point a is 80 feet from the base of the cliff , how high is the cliff ?