If (5, 4) and (7,2) are the endpoints of a diameter of a circle, what is the equation of the circle?
2 answers:
Answer:
(x -6)^2 +(y -3)^2 = 2
Step-by-step explanation:
The midpoint (C) is the center of the circle:
C = ((5, 4) +(7, 2))/2 = ((5+7)/2, (4+2)/2) = (6, 3)
A circle with center (h, k) that goes through point (a, b) can be written as ...
(x -h)^2 +(y -k) ^2 = (a -h)^2 +(b -k)^2
Using the values for this problem, we get ...
(x -6)^2 +(y -3)^2 = (5 -6)^2 +(4 -3)^2
(x -6)^2 +(y -3)^2 = 2
You might be interested in
Answer:
a) 60% probability that student took at least one online course
b) 40% probability that student did not take an online course
c) 12.96% probability that all 4 students selected took online courses.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they took at least one online course last fall, or they did not. The probability of a student taking an online course is independent of other students. So we use the binomial probability distribution 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.
3 out of 5 students enrolled in higher education took at least one online course last fall.
This means that
a) If you were to pick at random 1 student enrolled in higher education, what is the probability that student took at least one online course?
This is P(X = 1) when n = 1. So
60% probability that student took at least one online course.
b) If you were to pick at random 1 student enrolled in higher education, what is the probability that student did not take an online course?
This is P(X = 0) when n = 1.
40% probability that student did not take an online course
c) Now, consider the scenario that you are going to select random select 4 students enrolled in higher education. Find the probability that all 4 students selected took online courses
This is P(X = 4) when n = 4.
12.96% probability that all 4 students selected took online courses.