Answer the following questions. a. in the general education course requirement at a college, a student needs to choose one each from social sciences, humanities, natural sciences, and foreign languages. there are 5 social science courses, 4 humanity courses, 4 natural science courses, and 3 foreign language courses available for general education.

a. how many different ways can a student choose general education courses from these 4 areas?
b. four people are chosen from a 25-member club for president, vice president, secretary, and treasurer. in how many different ways can this be done?
c. in how many different ways can 5 tosses of a coin yield 2 heads and 3 tails?

Solve the system of equations y= 3/2 - 1, -x+ y =-3

Astore ordered 750 candles a total wholesale cost of $7910.20. the soy candles cosy $12.17 each and thespecialty candles cost $9.58each. how many of each were bought?

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