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# M3.3.14

Solves real-world problems involving percents.

### Lower Calories, Lower Fat: Making a Healthier Cake Without Loss of Taste

This example calculates the reduction in total calories and calories from fat when applesauce is substituted for oil in a cake recipe.

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### Why is Summer Hot?

It is quite common for people to believe that summer is warmer than winter,
basing the explanation on the belief that Earth is closer to the Sun during the
summer than in the winter. Even a sizable fraction of Harvard graduates carry
this belief (Schneps, 1987, mentioned in Green, 2003). In reality, this is exactly
opposite the situation in the northern hemisphere. The separation of Earth and
Sun is greatest at the beginning of July and least at the beginning of January.
More direct sunlight and the greater duration of daytime in summer months

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### Water Bottles, Root Beer, and Air

The common plastic water bottle makes a useful container for demonstrating properties of gases and liquids. As typical examples, we know that "air" is a gas (made up of nitrogen, oxygen, water vapor, ozone, carbon dioxide, and several "trace" gases) and water is a liquid. We should also note that gases and liquids are both "fluids". That is, they can flow or change shape, rather than having a fixed shape like a solid.

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### Square Root of 2: Irrational, Yes! Impractical, No!

For the mathematically inclined person, irrational numbers such as a2 are fascinating, both from a historical perspective, and as a classic example of using the reductio ad absurdum proof, to prove the irrationality of a2. However, the majority of students, when introduced to the irrational number a2, might be excused for not being fascinated by it, and might believe that a2 has not much practical use.

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### Dr. Smith vs. The Lawyer

A lawyer's use of some very simple science and math. The facts are true, although simplified; the company names have been changed.

Acme Enameling Company operated a cast-iron foundry and enameling plant, where it made bathtubs and sinks for twenty-seven years. It dumped factory wastes on vacant property behind the plant. Zenith Construction Company then bought the property and used it as a construction waste landfill.

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