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3 years ago

What is the surface area of the sphere?

Mathematics

1 answer:

Fantom [35]3 years ago

7 0

Answer:

<em>The surface area of the sphere is 314 mi².</em>

Step-by-step explanation:

According to the given diagram, the diameter of the sphere is 10 mi.

If the radius is $r$ , then diameter $=2r$

So....

$2r=10\\ \\ r=\frac{10}{2}= 5$

<u>Formula for the surface area of a sphere</u>: $A_{S}= 4\pi r^2$

Plugging the value of $r$ into this formula, we will get...

$A_{S}=4\pi(5)^2\\ \\ A_{S}=4\pi(25)\\ \\ A_{S}=4(3.14)(25)\ \ [Using\ \pi=3.14]\\ \\ A_{S}=314$

So, the surface area of the sphere is 314 mi².

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According to a study by the American Pet Food Dealers association, 63 percent of U.S. households own pets. A report is being pre

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Answer

$z=\frac{0.7 -0.63}{\sqrt{\frac{0.63(1-0.63)}{300}}}=2.511$

$p_v =2*P(z>2.511)=0.012$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of households with pets is different from 0.63. This data disagree deom the Pet food association

Step-by-step explanation:

Data given and notation

n=300 represent the random sample taken

X=210 represent the households with pets

$\hat p=\frac{210}{300}=0.7$ estimated proportion of households with pets

$p_o=0.63$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that true proportion is 0.63:

Null hypothesis: $p=0.63$

Alternative hypothesis: $p \neq 0.63$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.7 -0.63}{\sqrt{\frac{0.63(1-0.63)}{300}}}=2.511$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>2.511)=0.012$

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Answer:

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