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3 years ago

What is the extracts volume of the largest cone that can fit into a cube with edges of 10 inches

1 answer:

4 0

Volume of a cone = π r² h/3

I envisioned a cone inside a cube. I only identified the necessary value to compute for the exact volume of the largest cone.

Edges of the cube is 10 inches. When the circle part of the cone is placed in the circle, the diameter would be 10 inches also. I divided it by 2 to get the value of the radius, resulting to 5 inches.

The height of the cone is also the height of the cube. Thus, it is 10 inches.

Volume of the cone = 3.14 * (5in)² * 10in/3
V = 3.14 * 25in² * 3.33 in
V = 261.405 in³ or 261.41 in³ VOLUME OF THE LARGEST CONE THAT CAN FIT IN A 10 INCH CUBE

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aliya0001 [1]

Answer:

$t=\pm 2.95$

Step-by-step explanation:

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 t distribution or Student’s t-distribution is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".

The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.

Data given

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$\alpha=1-0.99=0.01$ represent the significance level

n =16 represent the sample size

We don't know the population deviation $\sigma$

Solution for the problem

For this case since we don't know the population deviation and our sample size is <30 we can't use the normal distribution. We neeed to use on this case the t distribution, first we need to calculate the degrees of freedom given by:

$df=n-1=16-1=15$

We know that $\alpha=0.01$ so then $\alpha/2=0.005$ and we can find on the t distribution with 15 degrees of freedom a value that accumulates 0.005 of the area on the left tail. We can use the following excel code to find it:

"=T.INV(0.005;15)" and we got $t_{\alpha/2}=-2.95$ on this case since the distribution is symmetric we know that the other critical value is $t_{\alpha/2}=2.95$

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3 years ago

The landscaper pours 200 gallons of herbicide in a pond. The herbicide degrades 10% each week. The landscaper will put another d

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The answer is one third or 1/3 multiply diagonal both ways and then multiply denominators

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2 years ago

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matrenka [14]

Answer:

Step-by-step explanation:

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2 years ago

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