The radius of the earth is approximately 3960 miles find the approximate surface area to volume ratio of the earth

1 answer:

8 0

$\bf \begin{array}{llll}
\textit{surface area of a sphere}\\\\
s=4\pi r^2
\\\\\\
\textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}
\end{array}\quad 
\begin{cases}
r=radius\\
-----\\
r=3960
\end{cases}
\\\\\\\\
\cfrac{s}{V}\qquad \cfrac{4\pi 3960^2}{\frac{4\pi 3960^3}{3}}\implies \cfrac{\frac{4\pi 3960^2}{1}}{\frac{4\pi 3960^3}{3}}\implies \cfrac{4\pi 3960^2}{1}\cdot \cfrac{3}{4\pi 3960^3}
\\\\\\
\cfrac{3}{3960}\implies \cfrac{1}{1320}$

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Answer:

Step-by-step explanation:

From the given information:

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No of polio cases X₁ = 57

Now, in the vaccine group:

the proportion of polio cases is:

$\hat p_1 = \dfrac{57}{200000}$

= 0.000285

The number of children that were randomly allocated to the placebo group, n₂ = 200,000

No of polio cases X₂ = 142

In the placebo group

the proportion of polio cases is:

$\hat p_2 = \dfrac{142}{200000}$

Null and alternative hypothesis is computed as follows:

H₀: There is no difference in the proportions of polio cases between both groups.

H₁: There is a difference in the proportions of polio cases between both groups.

Let assume that the level of significance ∝ = 0.05

The test statistic can be computed as:

$Z = \dfrac{\hat p_1-\hat p_2}{\sqrt{\dfrac{\hat p_1 \hat q_1}{n_1}+ \dfrac{\hat p_2 \hat q_2}{n_2}}}$

$Z = \dfrac{0.000285-0.000710}{\sqrt{\dfrac{0.000285(1-0.000285)}{200000}+ \dfrac{0.000710(1-0.000710)}{200000}}}$

$Z = \dfrac{-4.25\times 10^{-4}}{\sqrt{\dfrac{0.000285(0.999715)}{200000}+ \dfrac{0.000710(0.99929)}{200000}}}$

Z = - 6.03

P-value = 2P(Z < -6.03)

From the Z - tables

P-value = 2 × 0.0000

= 0.000

We reject the H₀ provided that P-value is very less.

Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.

7 0

3 years ago

Ok but the fact that the d'amelios had to cheat in trivia when they already had an advantage of 4x brain power proves that tikto

jok3333 [9.3K]

You are right don’t worry

7 0

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