Which organelle lets nutrients into the cell and allows waste products to leave?
Although not an organelle, the cell membrane allows nutrients into the cell and waste products to leave- thus it is referred to being "selectively permeable". The cell membrane is made of a lipid bilayer.
There are three ways to enter and exit the cell membrane: diffusion, facilitated diffusion, and active transport.
Diffusion is the movement of substances down a concentration gradient (from higher to lower concentration). Small particles, such as ions and water, enter the cell via diffusion. These particles can move through the spaces of the lipids that make the cell membrane.
Facilitated diffusion also moves particles down a concentration gradient. However, facilitated diffusion allows for the passage of larger substances into and out of the cell. These substances cannot move between the lipids. Thus, they use a protein carrier to travel in and out of the cell. The shape of the moving object and the protein carrier are complementary. In this way, harmful substances are prevented from entering the cell.
Active transport is like facilitated diffusion in that it also requires a protein carrier. However, active transport is unique in that it pushes objects up the concentration gradient. In order to do so, it requires energy in the form of ATP.