Answer:
The probability of the number of starfish dropping below 3 is 0.0463.
Step-by-step explanation:
Let X represent the number of starfish in the tide pool.
X follows a Poisson distribution with mean 6.4.
The formula for Poisson distribution is as follows.
![P(X=x) = e^{-6.4} * [6.4^{x} / x!] when x = 0, 1, ...](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%3D%20e%5E%7B-6.4%7D%20%2A%20%5B6.4%5E%7Bx%7D%20%2F%20x%21%5D%20when%20x%20%3D%200%2C%201%2C%20...)
otherwise
We need to find the probability that the number of starfish in the tide pool drops below 3.
Therefore, the required probability is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X=2)
P(X < 3) = 0.00166 + 0.01063 + 0.03403
P (X < 3) = 0.0463
Answer:
381 different types of pizza (assuming you can choose from 1 to 7 ingredients)
Step-by-step explanation:
We are going to assume that you can order your pizza with 1 to 7 ingredients.
- If you want to choose 1 ingredient out of 7 you have 7 ways to do so.
- If you want to choose 2 ingredients out of 7 you have C₇,₂= 21 ways to do so
- If you want to choose 3 ingredients out of 7 you have C₇,₃= 35 ways to do so
- If you want to choose 4 ingredients out of 7 you have C₇,₄= 35 ways to do so
- If you want to choose 5 ingredients out of 7 you have C₇,₅= 21 ways to do so
- If you want to choose 6 ingredients out of 7 you have C₇,₆= 7 ways to do so
- If you want to choose 7 ingredients out of 7 you have C₇,₇= 1 ways to do so
So, in total you have 7 + 21 + 35 + 35 + 21 +7 + 1 = 127 ways of selecting ingredients.
But then you have 3 different options to order cheese, so you can combine each one of these 127 ways of selecting ingredients with a single, double or triple cheese in the crust.
Therefore you have 127 x 3 = 381 ways of combining your ingredients with the cheese crust.
Therefore, there are 381 different types of pizza.
Answer:
The fraction of the total distance to her uncle's house that was traveled on Sunday is 1/7
Step-by-step explanation:
Let the total distance from Madison house to her uncle is 1 unit
She travels 5/7th of the total distance on Saturday
Remaining distance = 
She travels 1/2 of the remaining distance on Sunday.
Hence, the fraction of the total distance to her uncle's house that was traveled on Sunday is 1/2 * 2/7 = 1/7
Answer: 17 cm
Step-by-step explanation:
For a regular figure where the area of the base is B, and the height is H, the volume is calculated as:
V = B*H
Here we know that the base of the prism is B = 3 cm^2, and the volume of the prism is 51 cm^3
Then:
B = 3cm^2
V = 51cm^3
If we replace those in the equation above, we get:
51 cm^3 = (3cm^2)*H
Solving this for H gives:
(51 cm^3)/(3 cm^2) = H = 17 cm
The height of the tubing is 17 cm
