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myrzilka [38]
2 years ago
12

Find the general solution to the differential equation modeling how a person learns:

Mathematics
1 answer:
Luda [366]2 years ago
3 0

Here we want to solve differential equations, we will see that the general solution is:

y = A*e^{-t} + 100

We want to solve the differential equation:

\frac{dy}{dt}  = 100 - y

From this is pretty clear that y is an exponential function, with an exponent of -1*t.

We can write it generally as:

y = A*e^{-t} + B\\\\\frac{dy}{dt}  = -A*e^{-t}

Then if we set B = 100 we get:

y = A*e^{-t} + 100\\\\\frac{dy}{dt}  = -A*e^{-t} \\\\\frac{dy}{dt}  = -A*e^{-t} - 100 + 100 = -y + 100

So we just found the general form of the function.

Now we have two cases:

A) y(0) = 35

y(0) = A*e^{-0} + 100  = 35\\=  A + 100 = 35\\\\A = 35 - 100 = -65

In this case, the function is:

y = -65*e^{-t} + 100

B) y(0) = 125

125 = A*e^0 + 100\\\\\125 - 100 = A\\\\25 = A

In this case, the function is:

y = 25*e^{-t} + 100

Now we want to see which one of the two can represent how a person learns. Just look at the graph below:

The green line is the one for y(0) = 35, and the blue one is for y(0) = 125.

Notice that for small values of t, the blue function is really large, thus it can't really model how a person learns (is larger for smaller values of t than for larger values).

So y(0) = 35 represents better how a <em>person can learn</em> (but not exactly, because you can see that it eventually becomes almost constant, which is something that really does not happen) so the correct option is <u>D: none of the above.</u>

If you want to learn more, you can read:

brainly.com/question/353770

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Sergeu [11.5K]
Question: W<span>hat is the correct hypothesis to determine if quality is associated with vendor?

By looking at other resources, I have found the choices given for this question. They are the following:

a. Null</span>: Quality and source of shipment (vendor) are independent; Alternative: Quality and source of shipment (vendor) are dependent.
b. Null: Quality and source of shipment (vendor) are dependent; Alternative: Quality and source of shipment (vendor) are independent.

The test that would be applicable for this type of data would be the Chi-Square Test for Independence. As the name implies, the null hypothesis should be that the two factors are independent since that will be what we will be testing for.

ANSWER: a. Null: Quality and source of shipment (vendor) are independent; Alternative: Quality and source of shipment (vendor) are dependent.

Question: Calculate the value of the test statistic.

Please refer to the attached document for the complete computation for this part. Generally, we need to find the expected value for each cell in the table and perform some calculation explained in the document.

ANSWER: The test statistic is 12.80.

Question: S<span>pecify decision rule at the 1% significance level.

We can get the critical value for Chi-square tests by first looking for the degree of freedom. We can get the df by evaluating the following expression: (rows-1)*(columns-1). In our case, the number of columns is 2 and the number of rows is 3. The df is therefore (2-1)(3-1)=(1)(2)=2.

We then look at a table to determine what the value at the 1% significance level and df of 2 is.

ANSWER: We reject the null hypothesis if the test statistic is greater than the critical value which is 9.2103.

Question: What is your conclusion?
</span>
Since the test statistic (12.80) is greater than the critical value (9.2103), we can therefore tell that it is in the area for rejection.

Thus, we reject the null hypothesis.

ANSWER:
There is enough evidence to conclude that the quality and source of shipment (vendor) are NOT independent.
Download docx
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3 years ago
The American Academy of Periodontology released a survey, revealing that 27% of US adults admit they lie to their dentist about
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Answer:

A: H0: p = 0.27; Ha: p > 0.27

Step-by-step explanation:

The parameter is the population proportion.

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This means the null hypothesis is :

H_0: p=0.27

Periodontist Dr. Garcia believes that the percentage seems low, so his claim is that the percentage should be more than 27%.

This means, the alternate hypothesis is

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Therefore the correct choice is A.

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Answer:

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Answer:

7.25

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