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Sergio [31]
3 years ago
12

A cylinder is inscribed inside of a square prism so that touches each face of the rectangle or prism. The empty space outside of

the cylinder, but inside of the prism is to be filled with a liquid epoxy. If the cylinder has a circumference of 84.78 cm and the writing either prism is 40 cm tall, how many cubic centimeters of epoxy will be required to completely fill the empty spaces?

Mathematics
1 answer:
siniylev [52]3 years ago
6 0
To solve take  (Volume of Prism) - (Volume of Cylinder) = Epoxy

<span>V=(Area of base)(height) 
</span>
Both they Cylinder and prism have a height of 40 inches 
we can find the sides of the base of the prism by finding the diameter of the cylinder.

C=πd    so  84.78 = πd.

Divide both sides by Pi (3.14)
\frac{84.78}{3.14} = 27

Half of the diameter is the radius to find the area of the cylinder base. 27/2=13.5

The volume of Prism is found by
V=l*w*h

 27*27*40 = 29160 sq cm

The volume of cylinder is found by
V= \pi r^{2}h

using  3.14* 13.5^{2}*40 = 22890.6

29160 - 22890.6 = 6269.4 cubic centimeters

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To break even, Liza must answer 2 questions correctly to give her 6 points, because she now has negative 6 points a the result would be a score of 0

Step-by-step explanation

multiply negative 2 by the 3 incorrect questions, and you get negative 6.

divide 6 by 3 to get 2 to find the number of questions she needs to make correct to break even.

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2 years ago
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PLS HELP! WILL GIVE BRAINLIEST!
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I think the answer is 7.06cm

Step-by-step explanation:

cos28°=b(AB)/h(8)

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2 years ago
Tom spent 2.5 hours mowing his neighbors yard. If Tom spent $5 on gas and was paid $25 total. How much
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Answer:

$5 per hour

Step-by-step explanation:

25÷2.5=5

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3 years ago
A consensus forecastis the average of a large number of individual analysts’ forecasts. Suppose the individual forecasts fora pa
Crank

Answer:

a) P(X\geq 3.5)=P(\frac{X-\mu}{\sigma}\geq \frac{3.5-\mu}{\sigma})=P(Z\geq \frac{3.5-5.0}{1.2})=P(Z\geq -1.25)

And we can find this probability using the z table or excel

P(Z \geq

b) P(X\leq 6.0)=P(\frac{X-\mu}{\sigma}\leq \frac{6.0-\mu}{\sigma})=P(Z\leq \frac{6.0-5.0}{1.2})=P(Z\leq 0.833)

And we can find this probability using the z table or excel:

P(Z \leq

c) P(3.5

And we can find this probability on this way:

P(-1.25

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-1.25

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the interest rate of a population, and for this case we know the distribution for X is given by:

X \sim N(5.0,1.2)  

Where \mu=5.0 and \sigma=1.2

We are interested on this probability

P(X\geq 3.5)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X\geq 3.5)=P(\frac{X-\mu}{\sigma}\geq \frac{3.5-\mu}{\sigma})=P(Z\geq \frac{3.5-5.0}{1.2})=P(Z\geq -1.25)

And we can find this probability using the z table or excel

P(Z \geq

Part b

We are interested on this probability

P(X\leq 6.0)

P(X\leq 6.0)=P(\frac{X-\mu}{\sigma}\leq \frac{6.0-\mu}{\sigma})=P(Z\leq \frac{6.0-5.0}{1.2})=P(Z\leq 0.833)

And we can find this probability using the z table or excel:

P(Z \leq

Part c

P(3.5

And we can find this probability on this way:

P(-1.25

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-1.25

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