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Harlamova29_29 [7]
3 years ago
8

The length of a rectangle represented by 4a plus 3B and it's width is represented by 3a minus 2b. Write a polynomial for the per

imeter of the rectangle. What is the minimum perimeter of the rectangle if a equals 12 and b equals a non zero number?
Mathematics
1 answer:
Svetach [21]3 years ago
7 0
The polynomial for the perimeter starts from the formula for the perimeter of a rectangle as written below:

Perimeter = 2L + 2W = 2( L + W)
Perimeter = 2(4A + 3B + 3A - 2B)
Perimeter = 2(7A - B)
Let perimeter be P,
P = 14A - 2B  --> this would be the polynomial

Let's substitute A=12 to the polynomial:
P = 14(12) - 2B = 168 - 2B
To determine the minimum P, set it to 0.0001.
0.0001 = 168 - 2B
B = 83.999 or 84

Thus, the minimum perimeter is achieved if the value of B approached to 84.

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Answer:

t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864

p_v = 2*P(\chi^2_{14}>16.786)=0.5355

And the 2 is because we are conducting a bilateral test.

\alpha=0.05 since the the p_v >0.05 we fail to reject the null hypothesis.

\alpha=0.01 since the the p_v >0.01 we fail to reject the null hypothesis.

Step-by-step explanation:

Data given

\mu=7 population mean (variable of interest)

\sigma=0.2 represent the population standard deviation

s=0.219 represent the sample deviation

n=15 represent the sample size

\alpha=0.05,0.01 represent the values for the significance level  

Hypothesis test

On this case we want to check if the population standard deviation is equal or not to 0.2, so the system of hypothesis are:

H0: \sigma = 0.2

H1: \sigma \neq 0.2

In order to check the hypothesis we need to calculate the statistic given by the following formula:

t=(n-1) [\frac{s}{\sigma_o}]^2

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

t=(15-1) [\frac{0.219}{0.2}]^2 =16.7864

P value

We know the degrees of freedom of the distribution 14 on this case and we can find the p value like this:

p_v = 2*P(\chi^2_{14}>16.786)=0.5355

And the 2 is because we are conducting a bilateral test.

\alpha=0.05 since the the p_v >0.05 we fail to reject the null hypothesis.

\alpha=0.01 since the the p_v >0.01 we fail to reject the null hypothesis.

3 0
3 years ago
Jose needs to memorize words on a vocabulary list for French class. He has memorized 20 of the words, which is four-fifths of th
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Answer:

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In order to solve this the easiest way you can use equivalent fractions.

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Since 4 times 5 equals 20 we can multiply 5 times 5 to get our answer.

\frac{4}{5} * \frac{5}{5} = \frac{20}{25}

25 is the answer. But, if we couldn't have gotten to 20 through the multiplication we could use a proportion. That would look like the initial problem but instead of a "?" we would use a variable. I will use <em>t</em> for total.

\frac{4}{5} = \frac{20}{t}\\

So now we have our problem set up. The next step is to cross multiply. 4 by <em>t</em> and 5 by 20.

4t = 5 * 20\\4t = 100\\

And now we can solve it like a normal algebra problem.

\frac{4}{4}t = \frac{100}{4}\\t = 25

Either way, we get 25.

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