Mathematics, 03.08.2019 22:30, alextoro

In a box of 12 pens, a total of 3 are defective. if a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?

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Answer in fraction form: 6/11
Answer in decimal form: 0.54545
(note: the answer in decimal form is approximate)

There are 12 pens total. Assuming we select without replacement, there are 12 ways to pick the first selection and then 11 to make the second selection. So there are 12*11 = 132 ways to pick two pens from a pool of twelve. This is if order mattered. Since order doesn't matter we divide by 2 to get 132/2 = 66

There are 66 ways to pick two pens out of a pool of twelve. This is where order does NOT matter.
We'll use this value later. Call it N = 66

We have 12 pens, of which 3 are defective. So 12-3 = 9 non-defective pens.
There are 9 ways to pick the first non-defective pen. Then 8 ways to pick the second non-defective pen
Making 9*8 = 72 ways to pick the two non-defective pens if order mattered
Again order doesn't matter so 72/2 = 36 is the total number of ways to pick the two non-defective pens.
Call this value M = 36

Now divide M over N
M/N = 36/66 = (6*6)/(6*11) = 6/11

The probability in fraction form is 6/11
Using a calculator, we get 6/11 = 0.54545 which is approximate

answered: Guest

$y> \frac{1}{3}x$ and y≤ -x +4 .

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 = $\frac{1-0}{3-0} = \frac{1}{3}$ .

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

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

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

$y> \frac{1}{3}x$ .

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

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

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

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

answered: Guest

the correct answer would be:

220 centimeters

to get this you can use the pythagorean theorem

hope this

step-by-step explanation:

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In a box of 12 pens, a total of 3 are defective. if a customer buys 2 pens selected at random from t...