The length of the radius will be 22 units.
<h3>What is the radius?</h3>The radius of a circle is defined as the distance of the center of the circle to its outer layer. It is a locus of a point present at some distance from the center point.
Now from the question, we have an expression:
By solving the above equation we get
Hence the length of the radius will be 22 units.
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Let = amount of salt (in pounds) in the tank at time
(in minutes). Then
.
Salt flows in at a rate
and flows out at a rate
where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.
Then the net rate of salt flow is given by the differential equation
which I'll solve with the integrating factor method.
Integrate both sides. By the fundamental theorem of calculus,
After 1 hour = 60 minutes, the tank will contain
pounds of salt.
Answer:
See the proof below.
Step-by-step explanation:
Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."
Solution to the problem
For this case we can assume that we have N independent variables with the following distribution:
bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:
From the info given we know that
We need to proof that by the definition of binomial random variable then we need to show that:
The deduction is based on the definition of independent random variables, we can do this:
And for the variance of Z we can do this:
And if we take common factor we got:
And as we can see then we can conclude that