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Answer:
There is a 99.99998% probability that at least one valve opens.
Step-by-step explanation:
For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem we have that:
Calculate P(at least one valve opens).
This is
Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:
So
Finally
There is a 99.99998% probability that at least one valve opens.
Answer:
Step-by-step explanation:
Let h be the cylinders height and r the radius.
-The volume of a cylinder is calculated as:
-Since the cone is within the cylinder, it has the same radius as the cylinder.
-Let be the height of the cone.
-The area of a cone is calculated as;
The volume of the solid section of the cylinder is calculated by subtracting the cone's volume from the cylinders:
Hence, the approximate area of the solid portion is