A cylindrical bucket and spherical storage container are shown. The bucket has a radius of 6 inches and a height of 15 inches, and the storage container has a diameter of 24 inches. Nicholas says he can fill the entire storage container by filling the bucket 4 times and pouring the contents into the container. Is Nicholas correct? Why or why not.

To know if Nicholas is correct

4(540π) inches³ ≥ 2304π inches³

Unfortunately, 2160π inches³ is less than 2304π inches³. This means Nicholas is absolutely wrong .4 times the volume of the cylindrical bucket is less than the volume of the spherical tank.  

Step-by-step explanation:

The question wants you to look for the volume of the cylindrical bucket and the spherical bucket and know if 4 times the volume of the cylindrical bucket will fill the spherical tank.

volume of a cylinder = πr²h

where

r = 6 inches

h = 15 inches

volume of the cylinder bucket = πr²h

volume of the cylinder bucket= π × 6² × 15

volume of the cylinder bucket = π × 36 × 15

volume of the cylinder bucket = 540π inches³

volume of the spherical storage container

volume = 4/3πr³

r = 24/2 = 12 inches

volume = 4/3 × π × 12³

volume = 4/3 × π × 1728

volume = 6912π/3

volume = 2304π inches³

To know if Nicholas is correct 4(540π) inches³ ≥ 2304π inches³

Unfortunately, 2160π inches³ is less than 2304π inches³. This means Nicholas is absolutely wrong .4 times the volume of the cylindrical bucket is less than the volume of the spherical tank.  

i think is g(1)=-1.

hope that i can

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .