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2 years ago

A company surveyed all of the employees in their Columbus, Ohio office,

Mathematics

1 answer:

satela [25.4K]2 years ago

7 0

Answer:

B. They did not survey employees in other offices around the country

Step-by-step explanation:

1. A random sample is when you randomly choose options from the whole list. In this case, they make it clear that there are other offices. They didn't give a chance to the rest of the offices to take a survey.

2. Surveying "all" the employees is not what a random sample is. A random sample is supposed to help make it more distributed among the people you survey. Making all of them take it in a cluster is not random.

3. The other choices don't make sense because they don't mention anything about them: nothing about the employees working 5 years, nothing about it being conducted electronically, and nothing about a time limit.

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How do you do this question?

ElenaW [278]

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is $u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x$

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.