“Ring! Ring!” your phone alarm goes off. “Ring! Ring!” The constant ringing seems extra loud this time. “RING! RING!” You turn off the alarm and place your phone in your backpack. It’s 7:30 am, still dark out, and worst of all Thursday morning, the day before Friday. If you don’t leave as soon as possible you will be late for school. You begin getting dressed and you choose not to turn on any lights so that you won’t shock your eyes. As you are about to put on your socks you realize there is one problem. You do not match your socks up so they are all loose in the drawer. You know you have 8 black socks and 8 white socks but because they were not folded together you wonder this question. “How many socks do I need to pull out so that I will guarantee I have a pair of black socks OR a pair of white socks?” *remember you can’t see in the dark*

3

Step-by-step explanation:

because if you pull out three socks 2 of them at least, will be the same color .

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