Measurements are made on the length and width (in cm) of a rectangular component. because of measurement error, the measurements are random variables. let x denote the length measurement and let y denote the width measurement. assume that the probability density function of x is
f(x) = 10 for 9.95 < x < 10.05
f(x) = 0 for otherwise
and that the probability density function of y is
g(y) = 5 for 4.9 < y < 5.1
g(y) = 0 for otherwise

assume that the measurements x and y are independent. find p(x < 9.98)

For the following sequence determine the common difference (if it is an arithmetic sequence) or the common ratio (if it is a geometric sequence).

Consider a graph for the equation y= -3x+4. what is the y intercept? a) 4 b) -4 c) 3 d) -3

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