The rockwell hardness of a metal is determined by

impressing a hardened point into the surface of the

metal and then measuring the depth of penetration of the

point. suppose the rockwell hardness of a particular

alloy is normally distributed with mean 70 and standard

deviation 3. (rockwell hardness is measured on a continuous

scale.)

a. if a specimen is acceptable only if its hardness is

between 67 and 75, what is the probability that a randomly

chosen specimen has an acceptable hardness?

b. if the acceptable range of hardness is (70-c, 70+c) ,

for what value of c would 95% of all specimens have

acceptable hardness?

Find the roots of the equation below. x^2 - 6 + 9 = 0

Quadrilateral abcd in the figure below represents a scaled-down model of a walkway around a historic site. quadrilateral efgh represents the actual walkway. abcd is similar to efgh. what is the total length, in feet of the actual walkway?

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