Answer:
Jane: 37 years old
Anne: 17
Step-by-step explanation:
Jane 12 years ago: 5x
Anne 12 years ago: x
In three years into the future:
Jane: 5x+15
Anne: x+15
CURRENT TIME:
Jane: 5x+12
Anne: x+12
Equation (using 3 years into the future ages): 5x+15=2(x+15)
5x+15=2x+30
(subtract 15 from both sides)
5x=2x+15
3x=15
x=5
Therefore, Jane is 37 years old and Anne is 17 years old.
Answer:
C(cone with a radius of 8 units)
Explanation:
When a triangle is spun around its center, it makes a cone (can't make a cylinder because when spun, it doesn't have 2 circular bases). The radius would be 8 because that is what makes the circular base. The 6 is just the height of the triangle and cone once it is spun, it doesn't have anything to do with the base and its radius.
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)}
152.5 is 250% of the number, 61
