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2 years ago

sphere a has radius 4 and a hemisphere b has a radius 8. fin the ratio of the volume of A to the volume of b

Mathematics

1 answer:

salantis [7]2 years ago

4 0

Answer:

A/B = 0.125

Step-by-step explanation:

Givens

r for Sphere A = 4

r for Sphere B = 8

Solution

Volume A = 4/3 pi r^3

r = 4

Volume A = 4/3 pi 4^3

Volume A = 4/3 pi 64

Note: there is no point in expanding the result. 4/3 and pi are going to cancel out when you set up the volume formula

Volume B = 4/3 pi * r^3

r = 8

Volume B = 4/3 pi * 8^3

Volume B = 4/3 pi * 512

Ratio A to B = 4/3 pi * 64 / 4/3 * pi * 512 Cancel 4/3 pi

Ratio A to B = 64/512

Ratio A to B = 1/8

Ratio A to B = 0.125

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Find point G on AB such that the ratio of AG to GB is 3:2.

lora16 [44]

Using proportions, the coordinates of point G are given as follows:

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<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The points A and B are given as follows:

A(-3, 4) and B(5,0).

For this problem, we have that the ratio of AG to GB is 3:2, hence:

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x = 1.8.

The y-coordinate of G is found as follows:

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Hence the coordinates of point G are given as follows:

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More can be learned about proportions at brainly.com/question/24372153

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1 year ago

The weights of the fish in a certain lake are normally distributed with a mean of 11 lb and a standard deviation of 6. if 4 fish

Alexus [3.1K]

Since the sample standard deviation is now known, we use the z-score test. The formula is given as:

z= (X – μ) / (s / sqrt(n))

Where,

X = sample mean = 8.6 lb to 14.6 lb

μ = population mean = 11 lb

s = population standard deviation = 6

n = sample size = 4

1st: Calculating for z when x = 8.6 lb

z = (8.6 – 11) / (6 / sqrt4)

z = - 0.8

Using the standard distribution table for z:

Probability (x = 8.6 lb) = 0.2119

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z = (14.6 – 11) / (6 / sqrt4)

z = 1.2

Using the standard distribution table for z:

Probability (x = 14.6 lb) = 0.8849

Therefore the probability that the mean weight will be between 8.6 and 14.6 lb:

Probability (8.6 ≤ x ≤ 14.6 ) = 0.8849 - 0.2119

Probability (8.6 ≤ x <span>≤ 14.6 ) = 0.673 (ANSWER)</span>

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