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navik [9.2K]
2 years ago
15

Write an equation describing the relationship of the given variables. y varies inversely as the cube root of x and when x=125, y

=8.
Mathematics
1 answer:
notka56 [123]2 years ago
4 0

Answer:

y = 40 / x^1/3

Step-by-step explanation:

Given that :

y α x^1/3

y = k * 1 / x^1/3

y = k / x^1/3

When x = 125 ; y = 8

8 = k / 125^1/3

Cube root of 125 = 5

8 = k / 5

8 * 5 = k ; k = 40

Hence, expression becomes :

y = 40 / x^1/3

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The weight of a product is normally distributed with a mean of four ounces and a variance of .25 squared ounces. What is the pro
ololo11 [35]

Answer:

P(X>3.75)=P(\frac{X-\mu}{\sigma}>\frac{3.75-\mu}{\sigma})=P(Z>\frac{3.75-4}{0.5})=P(z>-0.5)

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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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

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

X \sim N(4,\sqrt{0.25}=0.5)  

Where \mu=4 and \sigma=0.5

We are interested on this probability

P(X>3.75)

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(X>3.75)=P(\frac{X-\mu}{\sigma}>\frac{3.75-\mu}{\sigma})=P(Z>\frac{3.75-4}{0.5})=P(z>-0.5)

And we can find this probability using the complement rule and we got:

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3 years ago
Calculate the volume of the figure.
dimaraw [331]

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Step-by-step explanation:

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Volume of the a cube uses the formula s^3 where s is the side length.

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Add 6 and 27 to find the total volume.

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What is the expanded form of this number?<br><br> 509.307
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