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neonofarm [45]
3 years ago
9

Show work please~

Mathematics
1 answer:
love history [14]3 years ago
5 0

For every 1 cup of blue paint, \frac{10}{4} cups of red paint are needed

For every 1 cup of red paint, \frac{4}{10} cup of blue paint is needed

For every 4 cups of red paint, \frac{16}{10} cups of blue paint are needed

<em><u>Solution:</u></em>

Given that, there are 3 1/3 red cups of paint for every 1 1/3 cups of blue paint

Therefore, ratio is

Red : blue = 3\frac{1}{3} : 1\frac{1}{3}\\\\Red : blue = \frac{10}{3} : \frac{4}{3}

<h3><u>For every 1 cup of blue paint, ___ cups of red paint are needed</u></h3>

Let "x" be the cups of red paint needed

Then we get,

\frac{10}{3} : \frac{4}{3}\\\\x : 1

This forms a proportion

1 \times \frac{10}{3} = \frac{4}{3} \times x\\\\x = \frac{10}{4}

Therefore, 10/4 cups of red are needed for 1 cup of blue

<h3><u>For every 1 cup of red paint, ___ cup of blue paint is needed</u></h3>

Let "x" be the cups of blue paint needed

Then, we get

\frac{10}{3} : \frac{4}{3}\\\\1 : x

This forms a proportion

\frac{10}{3} \times x = \frac{4}{3} \times 1\\\\x = \frac{4}{10}

Thus, 4/10 cups of blue are needed for 1 cup of red paint

<h3><u>For every 4 cups of red paint,___ cups of blue paint are needed</u></h3>

Let "x" be the cups of blue paint needed

Then, we get

\frac{10}{3} : \frac{4}{3}\\\\4 : x

This forms a proportion

\frac{10}{3} \times x = \frac{4}{3} \times 4\\\\x = \frac{16}{10}

Thus 16/10 cups of blue paint are needed for every 4 cups of red paint

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\sigma=7 represent the population standard deviation  

n=10 represent the sample size  

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Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96  

Now we have everything in order to replace into formula (1):  

29.4-1.96\frac{7}{\sqrt{10}}=25.06  

29.4+1.96\frac{7}{\sqrt{10}}=33.74  

So on this case the 95% confidence interval would be given by (25.06;33.74)  

Part b

What are H0 and Ha for this study?  

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Alternative hypothesis :\mu>25  

Compute the test statistic

The statistic for this case is given by:  

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z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

We can replace in formula (1) the info given like this:  

z=\frac{29,4-25}{\frac{7}{\sqrt{10}}}=1.988  

Give the appropriate conclusion for the test

Since is a one side right tailed test the p value would be:  

p_v =P(z>1.988)=0.0234  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis.    

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