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No friction at all.

There are two forces: the Downward force called WEIGHT and the Upward force called the NORMAL FORCE.

Since these two are in opposite directions and are, by definition, equal, they cancel out and there is no net force. Because there is no force, there is no acceleration, and in this case where there is no initial movement, the object stays at rest.

if there were a frictional force between the object and the surface, it would be in a direction with at least some horizontal component, but since there would be no other force to cancel this out, the object would be accelerating in some direction.

It is defined as "at rest", so there is no frictional force. If you were to push the furniture across the surface, then there WOULD be friction to resist the force you were applying.

EDIT: This answer is only partly correct.

The force of friction is zero if the furniture is at rest. However, if there is a force acting on the furniture that is less than the maximum static friction force (so the furniture still doesn't go anywhere), the force of friction equals the other force.

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Q: How much friction acts on the furniture when it is at rest on a horizontal surface?
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