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3 years ago

Find the radius of a circle with a circumference of 96 feeer

Mathematics

2 answers:

alexira [117]3 years ago

5 0

2 pi r = 96

r = 96 / 2 pi = 15.28 feet

Gnesinka [82]3 years ago

3 0

The formula for circumference is C = 2πr.

The question gives you the circumference (C in the formula), and you need to find the radius (r in the formula). Begin by isolating r in the circumference formula.

C = 2πr
C/2π = r
r = C/2π

Now you can plug 96 for C and solve to find r.

r = C/2π
r = 96/2π
r ≈ 96/6.28
r ≈ 15.29

Answer:
The radius of a circle with a circumference of 96 feet is approximately 15.29 feet.

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80 is 15% of what number

ryzh [129]

So 15%=15/100=3/20 so
80=3/20 of a number
multiply both sides by 20/3 to clear fraction
1600/3=a number
533.33
te number is 533.3333333

7 0

3 years ago

“the difference between five times a number and twice that number” ?

Gekata [30.6K]

Answer:Let

x-----------> the number

we know that

The expression "the difference between five times a number and twice that number" is equal to

5x-2x

therefore

the answer is

5x-2x

6 0

3 years ago

Solve for x 2/3 (x - 2) = 4x

cluponka [151]

Answer:

$-\frac{2}{5} =x$

Step-by-step explanation:

$\frac{2}{3} (x-2)=4x$

First, solve the brackets.

$\frac{2x}{3}-\frac{4}{3} =4x$

$\frac{2x-4}{3} =4x$

Now you can use cross multiplication.

$\frac{2x-4}{3} =\frac{4x}{1}$

$2x-4=3*4x$

$2x-4=12x$

Now take 2x to the other side.

$-4=12x-2x$

$-4=10x$

$\frac{-4}{10} =\frac{10x}{10}$

$\frac{-4}{10} =x$

Now let us make the fraction in it's simplest form.

For that divide both sides by 2.

$-\frac{2}{5} =x$

Hope this helps :-)

Let me know if you hav any other questions :-)

6 0

2 years ago

Can someone help me with this question

katovenus [111]

A because you add the inside then multiple

7 0

2 years ago

A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 second and

Lina20 [59]

Answer:

a) $0.81-2.62\frac{0.34}{\sqrt{110}}=0.725$

$0.81+2.62\frac{0.34}{\sqrt{110}}=0.895$

So on this case the 99% confidence interval would be given by (0.725;0.895)

b) $n=(\frac{2.58(0.34)}{0.1})^2 =76.95 \approx 77$

So the answer for this case would be n=77 rounded up to the nearest integer

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".

$\bar X=0.81$ represent the sample mean

$\mu$ population mean (variable of interest)

s=0.34 represent the sample standard deviation

n=110 represent the sample size

Part a

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:

$df=n-1=110-1=109$

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(0.005,119)".And we see that $t_{\alpha/2}=2.62$

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

$0.81-2.62\frac{0.34}{\sqrt{110}}=0.725$

$0.81+2.62\frac{0.34}{\sqrt{110}}=0.895$

So on this case the 99% confidence interval would be given by (0.725;0.895)

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigmas}{\sqrt{n}}$ (a)

And on this case we have that ME =0.1 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

We can assume the following estimator for the population deviation $\hat \sigma =s =0.34$

The critical value for 99% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.005;0;1)", and we got $z_{\alpha/2}=2.58/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(0.34)}{0.1})^2 =76.95 \approx 77$

So the answer for this case would be n=77 rounded up to the nearest integer

4 0

3 years ago