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3 years ago

A cone has radius of 5 cm and a slant height of 10cm what is the surface area of the cone

1 answer:

7 0

Let's remember that the formula for the surface area of a cone is $\pi{r^2} + \pi{r}{l}$ , where r is the radius and l is the slant height.

All we need to do to complete this problem is plug in the values that were given to us since we have all the necessary parts of the equation.

${5^2}\cdot\pi + \pi\cdot{5}\cdot{10} = 25\pi + 50\pi = \boxed{75\pi} = \boxed{235.62}$

Our answer is 75pi cm^2, or 235.62 cm^2.

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A data set includes 103103 body temperatures of healthy adult humans having a mean of 98.998.9degrees°f and a standard deviation

dangina [55]

Answer:

$98.9-2.62\frac{0.65}{\sqrt{103}}=98.73$

$98.9+2.62\frac{0.65}{\sqrt{103}}=99.07$

So on this case the 99% confidence interval would be given by (98.73;99.07)

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".

$\bar X=98.9$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=0.65 represent the sample standard deviation

n=103 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:

$df=n-1=103-1=102$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,102)".And we see that $t_{\alpha/2}=2.62$

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

$98.9-2.62\frac{0.65}{\sqrt{103}}=98.73$

$98.9+2.62\frac{0.65}{\sqrt{103}}=99.07$

So on this case the 99% confidence interval would be given by (98.73;99.07)

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Answer:

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5, 25, 109, 2725 divided by 5, 5, 109, gives no remainder. They are integers and prime numbers of 2725, they are also called composite number.

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