Using the hypergeometric distribution, it is found that there is a 0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.
In this problem, the bulbs are chosen without replacement, hence the <em>hypergeometric distribution</em> is used to solve this question.
<h3>What is the hypergeometric distribution formula?</h3>
The formula is:
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There are 12 bulbs, hence N = 12.
- 3 are defective, hence k = 3.
The third defective bulb is the fifth bulb if:
- Two of the first 4 bulbs are defective, which is P(X = 2) when n = 4.
- The fifth is defective, with probability of 1/8, as of the eight remaining bulbs, one will be defective.
Hence:
0.2182 x 1/8 = 0.0273.
0.0273 = 2.73% probability that the third defective bulb is the fifth bulb tested.
More can be learned about the hypergeometric distribution at brainly.com/question/24826394
Answer:
<h2>
64 cm²</h2>
Step-by-step explanation:
given:
the scale from a square park to a drawing of the park is 5 m to 1 cm
the actual park has an area of 1,600 m²
find:
what is the area of the drawing of the park
solution:
drawing scale is 5m : 1cm
<u>1,600 m² </u> = <u> 5² m² </u>
x 1² cm²
cross multiply:
5² m² x = 1600 m² (1 cm²)
x =<u> 1600 m² </u>
5² m²
x = 64 cm²
therefore, the area of a square park in the drawing is 64 cm²
The area of a triangle is 1/2 b/h. So what you do is you find base and height, multiply them together and whatever answer you got, you divide by 2.
Example:
A= 1/2 (b x h)
A= 1/2 (4 x 6)
A= 1/2 (24)
A= 12
Hope this helps!
Well, for number 15, this is what I came up with, I hope it is what your teacher is looking for:
So it starts out with 3 butterflies, and it doubles every minute:
3x2 = 6 That is for the first minute
6x2 = 12 That is for the second minute
12x2 = 24 That is for the third minute
24x2 = 48 That is for the fourth minute
So, It asks for using the power of 2 in your answer, that is what I came up with for part A.
For part B I would say something like this:
X represents the number of butterflies left.
The equation, using the information above would be this:
48-7 = X
Then simplify, which would leave you with 41 butterflies.
I hope this helps! :)
Equation 
is converted to 
<u>Step-by-step explanation:</u>
We need to complete the square to transform the expression x^2+4x+2 into the form a(x-h)^2+k . Let's do this :
We have , following equation to convert as :
⇒
⇒ 
⇒ 
⇒
⇒
Comparing this to equation a(x-h)^2+k we get :
Therefore , Equation is converted to .
