Samantha wants to buy a dress that costs $20. The sales tax is 6%. How much is the sales tax?
1 answer:
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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
<h3>The lateral area for the pyramid with the equilateral base is 144 square units</h3>
<em><u>Solution:</u></em>
The given pyramid has 3 lateral triangular side
The figure is attached below
Base of triangle = 12 unit
<em><u>Find the perpendicular</u></em>
By Pythagoras theorem
Therefore,
<em><u>Find the lateral surface area of 1 triangle</u></em>
<em><u>Thus, lateral surface area of 3 triangle is:</u></em>
3 x 48 = 144
Thus lateral area for the pyramid with the equilateral base is 144 square units