Letters can replace numbers in simple mathematical problems. If M and N represent digits
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The Pythagorean Theorem is used for right triangles only, because it's a mathematical relation between the legs of the triangle and the hypothenuse, where each leg must be less than the length of the hypothenuse.
It's important to correctly identify each element of the triangle, that is, which sides are legs, and which side is the hypothenuse, because the Pythagorean Theorem has a specific order, that means, if we make a mistake identifying each element, then the result will be wrong.
For example, the expression is the theorem, where
is the hypothenuse. This theorem states that the square of the hypothenuse (longest side) is equal to the sum of the square of the legs. So, if we call
a leg instead of the hypothenuse, the theorem won't work.
In order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than 144 seconds.
<u><em>Explanation</em></u>
Given that the time to complete a 200-meter backstroke swim for female competitive swimmers is normally distributed with a mean μ = 141 seconds and a standard deviation σ = 7 seconds
The fastest 6% of female swimmers in the nation are offered college scholarships. So, the probability will be 0.06
According to the normal distribution table, the z-score for probability of 0.06 is 0.5239
Now using z-score formula z= (x- μ)/σ , we will get...
That means, <em>(in whole number)</em>
So, in order to be given a scholarship, a swimmer must complete the 200-meter backstroke in no more than 144 seconds.