Final answer:
Mary Eagle used inductive reasoning to conclude that the sharpener was out of order based on her repeated observations of pencil points breaking.
Step-by-step explanation:
Mary Eagle utilized inductive reasoning when concluding that the sharpener was out of order after her experience with trying to sharpen three pencils and having the points break each time. Inductive reasoning involves using related observations to arrive at a general conclusion. It is unlike deductive reasoning, which starts with a theory or premise and reaches a specific conclusion based on that initial premise. Inductive reasoning is widely used in scientific and everyday contexts and is particularly valuable in forming hypotheses that can be later tested with deductive reasoning.