a pool is leaking water at a constant rate. The amount of water in the pool changes by -1 1/4 every hour. what is the total chan
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Answer:
0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they have a birthday in May, or they do not. The probability of a person having a birthday in May is independent of any other person. This means that the binomial probability distribution is used to solve this question.
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 combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Probability of a person being in May:
May has 31 days in a year of 365. So
Group of 20 friends:
This means that
What is the probability that at the May celebration, exactly two members of the group have May birthdays?
This is P(X = 2).
0.2773 = 27.73% probability that at the May celebration, exactly two members of the group have May birthdays
Differentiate both sides of the equation of the circle with respect to , treating
as a function of
:
This gives the slope of any line tangent to the circle at the point .
Rewriting the given line in slope-intercept form tells us its slope is
In order for this line to be tangent to the circle, it must intersect the circle at the point such that
In the equation of the circle, we have
If , then
, so we omit this case.
If , then
, as expected. Therefore
is a tangent line to the circle
at the point (1, -2).