An arc subtends a central angle measuring \dfrac{3\pi}{5}
1 answer:
Answer:
3/10
Step-by-step explanation:
The central angle of the arc is .
The circumference of an arc of a circle is given as:
where C= circumference of the circle
θ = central angle of the arc
Therefore, the circumference of the arc is:
The circumference of the arc will be 3/10 of the circumference of the circle.
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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.