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Licemer1 [7]
3 years ago
6

Find x and y, given that line WS and line VT are parallel. Show all work!

Mathematics
1 answer:
bulgar [2K]3 years ago
7 0

In the given diagram, the traingles USW and UTV are similar triangles and thus the following ratio equality applies to them.

\frac{VT}{WS} =\frac{VU}{WU}=\frac{TU}{SU}..........(Equation 1)

Checking the diagram given, we see that:

VT=y, WS=22, VU=8, ST=x-2

WU=WV+VU=12+8=20

TU=5

SU=ST+TU=(x-2)+5=x+3

Thus, substituting the required values in (Equation 1) we get:

\frac{y}{22}=\frac{8}{20}=\frac{5}{x+3}

Now, as can be clearly seen, to find y we will use the first two ratios as:

\frac{y}{22}=\frac{8}{20}

y=\frac{8\times 22}{20}=8.8

In a similar manner, to find the value of x we can use the last two ratios:

\frac{8}{20}=\frac{5}{x+3}

After cross multiplication we get:

5\times 20=8(x+3)

Which can be simplified as:

x+3=\frac{100}{8} =12.5

Thus, x=12.5-3=9.5

Therefore, the required answer is:

x=9.5 and y=8.8



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You are planning on applying to the Knirhsdaeh institute as a psychology counselor. They hire millions of psychologists around t
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The 98% of the confidence interval for the true average salary of Knirhsdaeh employees as a psychology counselor

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Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given that the mean of the sample = $81 k</em>

<em>Given that the size of the sample 'n' = 23</em>

<em>Given that the standard deviation for the salaries is $13 k</em>

<u><em>Step(ii):-</em></u>

<u><em>98% of the confidence interval for the true average salary of Knirhsdaeh employees is determined by</em></u>

<u><em /></u>(x^{-} - t_{0.02} \frac{S.D}{\sqrt{n} } , x^{-} + t_{0.02} \frac{S.D}{\sqrt{n} })<u><em /></u>

<u><em>Degrees of freedom = n-1 = 23-1 =22</em></u>

<u><em /></u>t_{0.02} = 2.5083<u><em /></u>

(81 - 2.0583 \frac{13}{\sqrt{23} } , 81 + 2.0583 \frac{13}{\sqrt{23} } )

( 81 - 5.57940 , 81 + 5.57940)

(75.4206, 86.5794)

<u><em>Final answer:-</em></u>

The 98% of the confidence interval for the true average salary of Knirhsdaeh employees as a psychology counselor

(75.4206, 86.5794)

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3 years ago
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