All categories

3 years ago

The formula for the volume of a sphere is mc012-1.jpg. What is the formula solved for r?

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

3 0

Answer: The formula to calculate the radius of a sphere if we know the volume is: Cubic root [3V/(4∏)].

Solution:

The formula for the volume (V) of a sphere is:

V=(4∏/3) r^3

Solving for r: Multiplying both sides of the equation by 3/(4∏):

3/(4∏) V = 3/(4∏) [(4∏/3) r^3]

3V/(4∏) = r^3

Cubic root both sides of the equation (raising to the power 1/3):

Cubic root [3V/(4∏)] =Cubic root (r^3)

Cubic root [3V/(4∏)] = r

r = Cubic root [3V/(4∏)]

You might be interested in

A bag contains five white balls and four black balls. Your goal is to draw two black balls. You draw two balls at random. What i

NARA [144]

Answer:

0.1667 = 16.67% probability that they are both black.

Step-by-step explanation:

The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

5 + 4 = 9 balls, which means that $N = 9$

4 are black, which means that $k = 4$

2 are chosen, which means that $n = 2$

What is the probability that they are both black?

This is P(X = 2). So

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,9,2,4) = \frac{C_{4,2}*C_{5,0}}{C_{9,2}} = 0.1667$

0.1667 = 16.67% probability that they are both black.

8 0

3 years ago

A number cube is rolled 450 times. The number 3 comes up 67 times.

adelina 88 [10]

Probability of an event =(Number of favorable outcomes)/(Total number of outcomes) Here, the number of favorable outcomes is the number of times 3 comes up. The number of times 3 comes up = 67 Total number of outcomes is the number of times the cube is rolled. Total number of times the cube is rolled = 450 Therefore, Probability of getting a 3 =67/450 Since 67 is a prime number, 67/450 is the final answer in simplest form.

5 0

3 years ago

Find the break-even point for the firm whose cost function C and revenue function R are given.

katrin2010 [14]

The solution is
to find x, C(x) = R(x)
5x + 10,000 = 15x
 10,000 = 10x, so x = 1,000

5 0

4 years ago

What percent of 8 is 4

HACTEHA [7]

4 = amount

8 = base 

amount / base = percent 

4 / 8 = 0.50 

multiply 100 times the decimal and attact he % symbol 

100 x 0.5 = 50 % 

4 is 50% of 8

5 0

3 years ago

How do I Use the numbers 8, 6, and 2 and one to write an expression that includes an exponent and has a value of 8.

liberstina [14]

Answer:

Step-by-step explanation:

8,6,2, and 1

(2^6 / 8) * 1 = (64/8) * 1 = 8 * 1 = 8

7 0

3 years ago