Answer:
x^2 -x -2
Step-by-step explanation:
Use polynomial long division.
0 + x^2 -x -2
___________________________________
(2x+3) | 2x^3 +x^2 -7x -6
-2x^3 -3x^2
_________
-2x^2 -7x
+2x^2 +3x
__________
-4x -6
+2x +6
_______
0
This problem can be solved from first principles, case by case. However, it can be solved systematically using the hypergeometric distribution, based on the characteristics of the problem:
- known number of defective and non-defective items.
- no replacement
- known number of items selected.
Let
a=number of defective items selected
A=total number of defective items
b=number of non-defective items selected
B=total number of non-defective items
Then
P(a,b)=C(A,a)C(B,b)/C(A+B,a+b)
where
C(n,r)=combination of r items selected from n,
A+B=total number of items
a+b=number of items selected
Given:
A=2
B=3
a+b=3
PMF:
P(0,3)=C(2,0)C(3,3)/C(5,3)=1*1/10=1/10
P(1,2)=C(2,1)C(3,2)/C(5,3)=2*3/10=6/10
P(2,0)=C(2,2)C(3,1)/C(5,3)=1*3/10=3/10
Check: (1+6+3)/10=1 ok
note: there are only two defectives, so the possible values of x are {0,1,2}
Therefore the
PMF:
{(0, 0.1),(1, 0.6),(2, 0.3)}
Answer:
x = 80
Step-by-step explanation:
Because of the parallel lines and the transversal to the left,
x + 67 = 147
x = 80
She can use 12 jewels for each pair of jeans. In fact, using 12 jewels per jeans implies that she will use 
jewels. The two remaining jewels can't be used on any pair of jeans, otherwise she wouldn't use the same number of jewels for each jeans.
This derives from the fact that, if you divide 50 by 4, you get a result of 12 with a remainder of 2.
