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3 years ago

If XY=18, YZ=14, and XZ=20, find the radius of each circle.

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

8 0

Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P + Y M = 18 X P - M Z = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6 /* ( - 1 )X P - M Z = 4 X P + Y M = - 6 X P - M Z = 4 Y M - M Z = - 2 Y M + M Z = 14 2 Y M = 12 => Y M = 6M Z - 6 = 2 => M Z = 8X P + 6 = 18
X P = 12
Radii of the circles are: 12, 8 and 6.

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kati45 [8]

Answer:

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Alternative hypothesis: $\rho \neq 0$

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And the statistic to check the significance of a coeffcient in a regression is given by:

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For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

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Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

$t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}$

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

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3 years ago

Chris made $136 for 8 hours of work.

jasenka [17]

Answer:

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Answer:

D. 1/4 and 9/36

Step-by-step explanation:

If two ratios make a proportion then it can be shown as:

a/b = c/d ⇒ ad = bc

Let's verify the answer choices with this method

A. 1/4 and 5/25

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1*36 = 4*9
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