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prisoha [69]
3 years ago
14

A sphere of radius 2x m has an area of ​​152.4 m2 and a volume of 360.9 m3. How much will the area and volume of another sphere

of radius r = 3x measure?
I will do anything if you tell me this
Mathematics
1 answer:
VladimirAG [237]3 years ago
4 0

Answer:

V = 1218.0375m^{3}

A = 342.9m^{2}

Step-by-step explanation:

Area:

A = π r^{2}

152.4 = π (2x)^{2}       *Square 2x*

152.4 = π 4x^{2}          *Divide by π*

48.510 = 4x^{2}           *Divide by 4*

12.128 = x^{2}             *Square root*

\sqrt{12.128} = x           *Solve*

x ≈ 3.482

Now take the same equation but replace 2x with 3x

A = π r^{2}\\

Now replace x with 3.482 and solve for area.

A = 342.9m^{2\\}

Volume:

V = \frac{4}{3} π r^{3}               *Insert variables*

360.9 = \frac{4}{3} π (2x)^{3}     *Cube 2x*

360.9 = \frac{4}{3} π (8x^{3})     *Multiply \frac{3}{4} on both sides*

270.675 = π (8x^{3})    *Divide by π*

86.159 = 8x^{3}           *Divide by 8*

10.770 = x^{3}             *Cube root*

\sqrt[3]{10.770} = x            *Solve*

x ≈ 2.208

Now take the same equation but replace 2x with 3x

V = \frac{4}{3} π (3x)^{3}    

Now replace x with 2.208 and solve for volume.

V = 1218.0375m^{3}

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in a random sample of 28 people, the mean commute time to work was 31.2 minutes and the standard deviation was 7.3 minutes. assu
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Answer:

The margin of error of u is of 3.8.

The 99% confidence interval for the population mean u is between 27.4 minutes and 35 minutes.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

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Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.995. So we have T = 2.7707

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 2.7707\frac{7.3}{\sqrt{28}} = 3.8

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error of u is of 3.8.

The lower end of the interval is the sample mean subtracted by M. So it is 31.2 - 3.8 = 27.4 minutes

The upper end of the interval is the sample mean added to M. So it is 31.2 + 3.8 = 35 minutes

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A system equivalent to this one is

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