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3 years ago

What is the volume of a hemisphere with a radius of 29.8 cm, rounded to the nearest tenth of a cubic centimeter?

Mathematics

1 answer:

Sveta_85 [38]3 years ago

6 0

Answer: 55,425.2 cm3

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Volume of a hemisphere = 2/3 π radius^3

Replacing with values given and solving for V (volume)

V = 2/3 π (29.8) ^3 = 55,425.2 cm3

In conclusion, the volume of the hemisphere is 55,425.2 cubic centimeters.

Feel free to ask for more if needed or if you did not understand something.

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Read 2 more answers

A simple random sample from a population with a normal distribution of 98 body temperatures has x =98.90 °F and s =0.68°F. Const

Ludmilka [50]

Answer:

$0.609 \leq \sigma \leq 0.772$

And the best conclusion would be:

D. This conclusion is safe because 1.40 °F is outside the confidence interval.

Step-by-step explanation:

1) Data given and notation

s=0.68 represent the sample standard deviation

$\bar x =98.90$ represent the sample mean

n=98 the sample size

Confidence=90% or 0.90

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=98-1=97$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.