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2 years ago

Solve C = 2πr (solve for "r") C = 15

Mathematics

2 answers:

Jobisdone [24]2 years ago

6 0

C = 2 pi r

but c = 15

15 = 2 pi r
15 = 2 * (22/7) * r
r = (15*7) / 2 / 22
r = 2.386

Lady_Fox [76]2 years ago

6 0

For this case we have the following equation:

$C = 2\pir$

From here, we clear the value of r:

$r = \frac{C}{2\pi}$

Substituting the values in the obtained equation we have:

$r = \frac{15}{2\pi}$

Doing the calculations we have:

$r = 2.4$

Answer:

The value of r is given by:

$r = 2.4$

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Information provided

$\bar X_{1}=28.5$ represent the mean for Miami

$\bar X_{2}=35.2$ represent the mean for Baltimore

$\sigma_{1}=7.2$ represent the population standard deviation for Miami

$\sigma_{2}=9.1$ represent the population standard deviation for Baltimore

$n_{1}=40$ sample size selected for Miami

$n_{2}=10$ sample size selected for Baltimore

$\alpha=0.05$ represent the significance level

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$p_v$ represent the p value for the test

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We want to check if the commiting times are different in the winter for the two cities, so then the system of hypothesis are:

Null hypothesis: $\mu_{1} = \mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

Since we know the population deviations the statistic for this case is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

Replacing the info provided we got:

$z=\frac{28.5-35.2}{\sqrt{\frac{7.2^2}{40}+\frac{9.1^2}{40}}}}=-3.652$

Now we can calculate the p value since we are conducting a bilateral test the p value would be:

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Since the p value is very low we have enough evidence to reject the null hypothesis that the true means are equal at 5% of significance.

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