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beks73 [17]
2 years ago
15

Find the missing side lengths. Leave your answers as radicals in simplest form. Show your work to support your answer ​

Mathematics
1 answer:
kotegsom [21]2 years ago
3 0

Answer

x=2 and y=2√2

Step-by-step explanation:

\sin( \alpha )  =  \frac{2 \sqrt{2} }{x }  \\ x =  \frac{2 \sqrt{2} }{ \sin(45) }  \\ x = 4 \\  {x}^{2}  =  {y}^{2}  + 2 \sqrt{2}  \\  {4}^{2}  =  {y}^{2}  + (2 \sqrt{2 \: )}^{2}  \\ 16 =  {y}^{2}  + 8 \\ 16 - 8 =  {y}^{2}  \\ y =  \sqrt{8}  \\ y = 2 \sqrt{2}

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We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.

Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).

Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

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The formula for constructing a <u>confidence interval for means</u> is as follows:

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Plug these values into the formula for the confidence interval:

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<h3>Finding the Critical Value (t*)</h3>

In order to find t*, we can use this formula:

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So, let's plug in the confidence interval 95% (.95) into the formula:

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<h3>Constructing Confidence Interval</h3>

Now, let's finish the confidence interval we created:

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We can calculate the confidence interval, using this formula, to be:

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We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.

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