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krok68 [10]
2 years ago
6

Solve the proportion for x. 4/(5x) = 8/9

Mathematics
1 answer:
Verdich [7]2 years ago
5 0
4     8
---   -----
5x    9

5x*2=9
5x=4.5
x=4.5/5 or 0.9
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Answer:

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Step-by-step explanation:

There's two good ways to do this problem.

Option 1:

Translate "x varies directly as y" into the equation y=kx

Then you have to find k. After you "reset" your y=kx equation, fill in k and then solve for x. See image.

Option 2:

Translate "varies directly" into a proportion, which is two fractions equal to each other:

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a) P(5

And we can find this probability with this difference:

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And using the norma standard distribution or excel we got:

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And using the complement rule we got:

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(7.37,1.25)  

Where \mu=7.37 and \sigma=1.25

We are interested on this probability

P(5

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(5

And we can find this probability with this difference:

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And using the norma standard distribution or excel we got:

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Part b

For this case we want this probability:

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And we can use the z score and we got:

P(X>6) =P(Z> \frac{6-7.37}{1.25}) = P(Z>-1.096)

And using the complement rule we got:

P(Z>-1.096) =1-P(Z

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