HELP 20 POINTS I NEED AN ANSWER ASAP!!

A sphere is just enclosed inside a right circular cylinder. If the volume of the sphere is 140 cm3, find the volume of the gap b

alexgriva [62]

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Find Radius :
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$\text {Volume of a sphere =} \dfrac{4}{3} \pi r^3$

$\dfrac{4}{3} \pi r^3 = 140$

$\pi r^3 = 140 \times \dfrac{3}{4}$

$\pi r^3 = 105$

$r^3 = \dfrac{105}{ \pi}$

$r = 3.22 \ cm$

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Find volume of the cylinder :
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$\text {Volume of the cylinder = } \pi r^2h$

$\text {Volume of the cylinder = } \pi ((3.22)^2(3.22 \times 2)$

$\text {Volume of the cylinder = } 209.77 \ cm^3$

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Find volume of the gap :
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$\text {Volume of gap = } 209.77 - 140$

$\text {Volume of gap = } 69.77 \ cm^3$

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$\bf \text {Answer : } 69.77 \cm^3$
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6 0

3 years ago

Using traditional methods, it takes 10.1 hours to receive a basic driving license. A new license training method using Computer

Law Incorporation [45]

Answer:

We need to conduct a hypothesis in order to check if the technique performs differently than the traditional method, the system of hypothesis would be:

Null hypothesis: $\mu =10.1$

Alternative hypothesis: $\mu \neq 10.1$

$t=\frac{10.5-10.1}{\frac{1.4}{\sqrt{12}}}=0.990$

$p_v =2*P(t_{(11)}>0.990)=0.343$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the technique performs differently than the traditional method at 10% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=10.5$ represent the sample mean

$s=1.4$ represent the sample standard deviation

$n=12$ sample size

$\mu_o =10.1$ represent the value that we want to test

$\alpha=0.1$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the technique performs differently than the traditional method, the system of hypothesis would be:

Null hypothesis: $\mu =10.1$

Alternative hypothesis: $\mu \neq 10.1$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{10.5-10.1}{\frac{1.4}{\sqrt{12}}}=0.990$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=12-1=11$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(11)}>0.990)=0.343$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL reject the null hypothesis, so we can't conclude that the technique performs differently than the traditional method at 10% of signficance.

7 0

3 years ago

If an angle is three times of its supplement, find the angle

zavuch27 [327]

Answer:

<h2>135° angle</h2>

Let the angle be x it's supplement = (180-x)

x = 3 (180-x)

⇒x=540−3x

⇒4x=540⇒x=135°

Step-by-step explanation:

Hope it is helpful....

5 0

3 years ago

Integer Basics

Furkat [3]

Can you retype whatever you’re asking in this please?

7 0

3 years ago

Find the distance between the points: (1,2) and (-3,0)

faltersainse [42]

You can create a right angled triangle.
Find the hypotenuse.
The third point of the triangle is (1,0)
using pythagoras, the value of a is 2, b is 3. 2^2 +3^2 = 13.
Therefore the distance between the two points is $\sqrt{13}$

7 0

3 years ago