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2 years ago

Solve for w, x, and y. Show your work.

Mathematics

1 answer:

sveta [45]2 years ago

5 0

First of all, the left triangle is an equilateral triangle. Which means that all the interior angles are 60 degrees.

4w=60

w=15

Then all 3 sides are equal thus we can set up equation 3x-y=4y then simplify,

3x=5y

Going to the triangle on the right its isosceles we can set up equation 2x+50=180

2x=130

x=75

Substitute this back into equation above 3x=5y

5y=3*75

y=45

Therefore

x=75

y=45

w=15

Done!

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2 years ago

Use a flowchart to prove if the triangles in each pair are congruent. NO LINKS!!!!

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see attached

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2 years ago

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kondor19780726 [428]

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3 years ago

A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data

Rasek [7]

Answer: a. 1.981 < μ < 2.18

b. Yes.

Step-by-step explanation:

A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.

First, we calculate mean of the sample:

$\overline{x}=\frac{\Sigma x}{n}$

$\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}$

$\overline{x}=$ 2.08

Now, we estimate standard deviation:

$s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }$

$s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }$

s = 0.1564

For t-score, we need to determine degree of freedom and $\frac{\alpha}{2}$ :

df = 12 - 1

df = 11

$\alpha$ = 1 - 0.95

α = 0.05

$\frac{\alpha}{2}=$ 0.025

Then, t-score is

$t_{11,0.025}$ = 2.201

The interval will be

$\overline{x}$ ± $t.\frac{s}{\sqrt{n} }$

2.08 ± $2.201\frac{0.1564}{\sqrt{12} }$

2.08 ± 0.099

The 95% two-sided CI on the mean is 1.981 < μ < 2.18.

B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.

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3 years ago

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scZoUnD [109]

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2 years ago