A building across the street casts a shadow that is 2424 feet long. your friend is 66 feet tall and casts a shadow that is 44 fe
2 answers:
Answer:
The height of the building is 3636 feet long
Step-by-step explanation:
The rule of three is a way of solving problems of proportionality between three known values and one unknown, establishing a relationship of proportionality between all of them. In the case of direct proportionality, when one magnitude increases, the other increases (or when one magnitude decreases the other magnitude will also decrease)
This is an example of direct proportionality where the rule of three can be applied as follows:
44 feet (Long of the shadow of your friend) ⇒ 66 feet (Height of your friend)
2424 feet (Long of the shadow of the building) ⇒ x (Height of the building)
So, to solve this direct proportionality you do the following calculation:
x=
x=
<em>x=3636</em>
<em>This means that the height of the building is 3636 feet long</em>
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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