Using the hypergeometric distribution, it is found that there is a 0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.
The people are chosen without replacement from the sample, hence the <em>hypergeometric distribution </em>is used to solve this question.
<h3>What is the
hypergeometric distribution formula?</h3>
The formula is:
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7DC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
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 is a total of 18 people, hence
.
- 2 people will be chosen, hence
.
- David and Valerie corresponds to 2 people, hence
.
The probability that both get picked is P(X = 2), hence:
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7DC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
![P(X = 2) = h(2,18,2,2) = \frac{C_{2,2}C_{16,0}}{C_{18,2}} = 0.0065](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20h%282%2C18%2C2%2C2%29%20%3D%20%5Cfrac%7BC_%7B2%2C2%7DC_%7B16%2C0%7D%7D%7BC_%7B18%2C2%7D%7D%20%3D%200.0065)
0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.
You can learn more about the hypergeometric distribution at brainly.com/question/25783392
Answer:
N(p) = 22 + 10p
In graphing the function, N(p) = 22 + 10p
would be the slope and 10;
and 22 would be the y-intercept.
Step-by-step explanation:
Let p represents the number of transactions.
Each transaction is worth 10 points, then p transactions are worth 10p points.
Customers automatically earn 22 points when they sign up.
The total amount of points is
N(p) = 22 + 10p
In graphing the function, N(p) = 22 + 10p
would be the slope and 10;
and 22 would be the y-intercept.
For this parabola we have:
f ( 0 ) = 8
and : f ( 1 ) = 24
In the first equation ( A) :
f ( 0 ) = - 16 * ( 0 - 1 )² + 24 = - 16 * 1 + 24 = 8 ( correct )
f ( 1 ) = - 16 * ( 1 - 1 )² + 24 = 24 ( correct )
For B:
f ( 0 ) = - 16 * ( 0 + 1 )² + 24 = - 16 + 24 = 8 ( correct )
f ( 1 ) = - 16 * ( 1 + 1 )² + 24 = - 16 * 4 + 24 = - 64 + 24 = 40 ( false )
For C:
f ( 0 ) = - 16 * ( 0 - 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24 ( false )
For D:
f ( 0 ) = - 16 * ( 0 + 1 )² - 24 = - 16 - 24 = - 40 ( false )
f ( 1 ) = - 16 * ( 1 - 1 )² - 24 = - 24 ( false )
Answer:
A ) f ( t ) = - 16 * ( t - 1 )² + 24
The volume of a pyramid can be calculated as:
![V=\frac{1}{3}\cdot B\cdot H](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%20B%5Ccdot%20H)
Where B is the area of the base and H is the height. We are given V = 60 cubic inches and H = 5 inches. Solving for B:
![B=\frac{3V}{H}](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B3V%7D%7BH%7D)
Substituting:
![B=\frac{3\cdot60in^3}{5in}=36in^2](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B3%5Ccdot60in%5E3%7D%7B5in%7D%3D36in%5E2)
The area of the base is 36 square inches.
We must choose the option whose area is 36 sq in.
A square of a side length of 6 inches has an area of:
![A=(6in)^2=36in^2](https://tex.z-dn.net/?f=A%3D%286in%29%5E2%3D36in%5E2)
Thus, the correct choice is D.
Answer:
= 4n
Step-by-step explanation:
Note that the values on the second row are 4 times the corresponding values on the first row , that is
1 × 4 = 4
5 × 4 = 20
10 × 4 = 40
12 × 4 = 48
15 × 4 = 60
25 × 4 = 100
Then
n × 4 = 4n ← nth term rule