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timofeeve [1]
3 years ago
7

A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the

high-quality version is 4.4
MB. Yesterday, there were 1070 downloads of the song, for a total download size of 4393 MB. How many downloads of the standard version were there?
Mathematics
1 answer:
GrogVix [38]3 years ago
3 0

s +h = 1070 ( total number of downloads)

Rewrite as s =1070 - h

2.9s + 4.4h = 4393 ( total download size)

Substitute:

2.9(1070-h) + 4.4h = 4393

Simplify:

3103 - 2.9h + 4.4h = 4393

Combine like terms:

3103 + 1.5h = 4393

Subtract 3103 from each side:

1.5h = 1290

Divide both sides by 1.5:

h = 1290 / 1.5

h = 860

Replace h with 860 in first equation to solve for s:

s + 860 = 1070

s = 1070 - 860

s = 210

There were 210 standard downloads and 860 high quality downloads

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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:

  • P(X = 0) = 0.2.
  • P(X = 1) = 0.4.
  • P(X = 2) = 0.3.
  • P(X = 3) = 0.1.

Item a:

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.

More can be learned about discrete probability distributions at brainly.com/question/24855677

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