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Tema [17]
3 years ago
6

What is the simplest form of root 3.025

Mathematics
1 answer:
Andreyy893 years ago
3 0
Answer: √3025

Explanation:

1) By convention if you do not mention the index of the root it is square root.

2) By definition the square root of a number x is the numberwhose square is the original number, i.e.

√3025 = 55 because 55^2 = 3025.

3) 3025 is a perfect square because it is the square of a whole numbe.

4) It is easy to find the square root of a perfect square, but if the number is not easily reknownm as a perfect square you will have to probe with several numbers until finding the square root.

For example, you might easily realize that 50^2 is 2500, and that 60^2 is 3600, so you start testing numbers greater thatn 50 and less than 60 until you get 55^2 = 3025.

5) How can you simplify a radical? If you know the properties of radicals you can simplify a radical easily.

You start by decomposing 3025 into its prime factors.

That will result into:

3025 =5^2{11}^2

Then, by radical properties:

\sqrt{5^2{11}^2} = \sqrt{5^2}  \sqrt{{11}^2} =(5)(11)=(55)

So, the simplest form of √3025 is 55.
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Using a discrete probability distribution, it is found that:

a) There is a 0.3 = 30% probability that he will mow exactly 2 lawns on a randomly selected day.

b) There is a 0.8 = 80% probability that he will mow at least 1 lawn on a randomly selected day.

c) The expected value is of 1.3 lawns mowed on a randomly selected day.

<h3>What is the discrete probability distribution?</h3>

Researching the problem on the internet, it is found that the distribution for the number of lawns mowed on a randomly selected dayis given by:

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P(X = 2) = 0.3, hence, there is a 0.3 = 30% probability that he will mow exactly 2 lawns on a randomly selected day.

Item b:

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.2 = 0.8

There is a 0.8 = 80% probability that he will mow at least 1 lawn on a randomly selected day.

Item c:

The expected value of a discrete distribution is given by the <u>sum of each value multiplied by it's respective probability</u>, hence:

E(X) = 0(0.2) + 1(0.4) + 2(0.3) + 3(0.1) = 1.3.

The expected value is of 1.3 lawns mowed on a randomly selected day.

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