How to find the other endpoint with the given endpoint and midpoint?

1 answer:

6 0

To find the other endpoint with a given endpoint and midpoint, you subtract the midpoint values from the endpoint, then with whatever the answer is, you subtract that from the midpoint.

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A box has five items, three good and two defective. three items are selected at random without replacement. let x be the number

user100 [1]

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)}

7 0

3 years ago

The nose of the origami dog is a right angle with sides that are 2 cm, 3 cm, and 3.6 cm long. What is the area of this triangle?

Maslowich

Given:

The sides of a right triangle are 2 cm, 3 cm, and 3.6 cm.

To find:

The area of the right triangle.

Solution:

Area of a triangle is:

$Area=\dfrac{1}{2}\times base\times height$

In the given triangle 3.6 cm is the largest side, it means 3.6 cm is the length of the hypotenuse. So, 2 cm and 3 cm and the base and height of the triangle.

Now, the area of the given triangle is:

$Area=\dfrac{1}{2}\times 2\times 3$