Heart failure is due to either natural occurrences (86%) or outside factors (14%). outside factors are related to induced substances or foreign objects. natural occurrences are caused by arterial blockage, disease, and infection. suppose that 18 patients will visit an emergency room with heart failure. assume that causes of heart failure between individuals are independent.

round your answers to three decimal places (e. g. 98.765).

(a) what is the probability that 3 individuals have conditions caused by outside factors?

probability =

(b) what is the probability that 3 or more individuals have conditions caused by outside factors?

probability =

(c) what is the mean and standard deviation of the number of individuals with conditions caused by outside factors?

mean =

standard deviation =

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

Y= 4x + 3 y = - 1 4 x - 5 what is the best description for the lines represented by the equations?

Kristen is wrapping presents for the holidays. she has a box that measures 4 ft. x 2 ft. x 2 ft. how many square feet of wrapping paper does she need to cover the box without overlapping?