yes the do have pulleys
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Many people use pulleys in their jobs. The rides like Supreme scream, which go vertically up and down have pulleys in them. Elevators have pulleys in them, and people who ship cargo use pulleys in their cranes.
Archimedes (not a group, a guy) invented pulleys as well as other simple machines.
assuming that your question is what jobs are pulleys used for... then the answer is any job that you need to lift something that is heavy. The pulley give a mechanical advantage when used together with other pulleys to apply more force to move the object
Not necessarily. Some fans use belts on pulleys to transfer the rotary motion of the motor to the fan blade, while others use gears, and some are direct drive.
The Giza Pyramids were constructed using step-walking wooden four-lobe pinion-pulleys with a mechanical advantage of 2.8 (MA=2.8) This ancient pulley was unknown to the modern world until 27 August 2006. The design and operation of this pulley is nothing like any pulley known in the modern world. Google four lobe pinion pulley.