Aaron bought a set of plastic ice cubes with a mixture of water and air inside.

what volume of water and air is inside each of the plastic ice cubes?

The volume of water and air inside the plastic ice cube is 3000 mm³

Step-by-step explanation:

* Lets described the figure

- It consists of two identical rectangular pyramids stuck together

 in their bases

- The dimensions of the base are 15 mm and 20 mm

- The height of ice cube is 30 mm

∴ The height of each pyramid = 30 ÷ 2 = 15 mm

* Lets talk about the volume of the rectangular pyramid

- The pyramid has a rectangular base and 4 triangular faces

- We have formulas to calculate the volume of the pyramid.

- To find the volume, we use the formula V = (1/3)AH, where

 A = area of the pyramid's base and H = height of the pyramid

∵ The dimensions of the base are 20 mm and 15 mm

∴ A = 20 × 15 = 300 mm²

- The height of the pyramid is 15 mm

∵ H = 15 mm

∵ V = 1/3(AH)

∴ V = 1/3(300 × 15) = 1500 mm³

- The ice cube made from two identical rectangular pyramids

∴ The volume of the ice cube = 2 × 1500 = 3000 mm³

- The volume of the water and the air inside the ice cube equal

 the volume of the ice cube

* The volume of water and air inside the plastic ice cube is 3000 mm³

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752