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3 years ago

What is the volume of a sphere with a radius of 4 cm? Use 3.14 for pi. Round to the nearest hundredth.

2 answers:

5 0

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\quad 
\begin{cases}
r=radius\\
-----\\
r=4
\end{cases}\implies V=\cfrac{4\pi 4^3}{3}\implies V=\cfrac{256\pi }{3}$

erik [133]3 years ago

3 0

Answer:

V = 50.24cm^3

Step-by-step explanation:

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3 years ago

An article presents measures of penetration resistance for a certain fine-grained soil. Fifteen measurements, expressed as a mul

balu736 [363]

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$2.64-2.14\frac{1.32}{\sqrt{15}}=1.911$

$2.64+2.14\frac{1.32}{\sqrt{15}}=3.369$

So on this case the 95% confidence interval would be given by (1.911;3.37)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=2.64$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=1.32 represent the sample standard deviation

n=15 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=15-1=14$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,14)".And we see that $t_{\alpha/2}=2.14$

Now we have everything in order to replace into formula (1):

$2.64-2.14\frac{1.32}{\sqrt{15}}=1.911$

$2.64+2.14\frac{1.32}{\sqrt{15}}=3.369$

So on this case the 95% confidence interval would be given by (1.911;3.37)

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