Randomization in an experiment is important because it ensures that
a.) the treatments have an effect on the response.
b.) the groups of subjects are similar, on average, in all respects before applying the different treatments to the different groups.
c.) each treatment is thought of as a value of the explanatory variable

C.) each treatment is thought of as a value of the explanatory variable

Step-by-step explanation:

The main purpose for using randomization in an experiment is to control the lurking variable and establish a cause and effect relationship.

If we do not control lurking, or confounding, variables, we cannot accurately establish a cause and effect relationship; this means we cannot ensure that each treatment is a value of the explanatory variable.

answer: the first graph

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be