The graph below represents the linear equation y = one-half x minus 3. On a coordinate plane, a line goes through (0, negative 3) and (6, 0). A second linear equation is represented by the data in the table. x y –1 1 0 0 2 –2 3 –3 What is the solution to the system of equations? (–2, –4) (1, –1) (2, –2) (4, –4)

Consider the function f(x)=−2/3x+5 . what is f(1/2) ? enter your answer, as a simplified fraction, in the box. f(1/2)=

Saline iv fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. a new supplier sells 500 ml bags for $2 each. the hospital uses about 10,000, 1000 ml bags each month. nurses report that about half of the bags are more than half full when they are discarded. if you are going to use only one supplier, which size bag provides the best deal, and how much will you save each month? compare the cost of the new supplier to the current one.

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).