We have been given an equation of circle . We are asked to find the center and radius of the circle.
First of all, we will write equation of circle is standard form , where center of circle is at point (h,k) and radius is r.
Let us complete the square for both x and y.
Adding half the square of coefficient of x and y term, we will get:
Therefore, the center of the circle is and radius is 4 units.
Answer:
(a) The probability distribution is valid.
(b) The probability that x = 30 is 0.30.
Step-by-step explanation:
The probability distribution of the random variable <em>X</em> is:
<em> x</em>: 20 | 25 | 30 | 35
f (<em>x</em>): 0.20 | 0.15 | 0.30 | 0.35
(a)
The properties of a probability distribution are:
All the probability value are more than 0 and less than 1.
Compute the sum of all the probabilities as follows:
The sum of all probabilities is 1.
Thus, the probability distribution is valid.
(b)
Consider the probability distribution table.
The probability of <em>X</em> = 30 is,
P (X = 30) = 0.30.
Thus, the probability that x = 30 is 0.30.