A mixer is provided for mixing a substance in a container. The mixer includes a motor; a frame configured to be controlled by the motor to rotate on an axis; a carrier disposed at a first end of the frame and configured to hold the container; a counterweight disposed at a second end of the frame opposite to the carrier, wherein the counterweight position relative to the axis is adjustable. The mixer may be a stand-alone unit, or it may be disposed in an apparatus for dispensing a cosmetic composition.