Answer:
13
Step-by-step explanation:
Draw a picture!
You have a right triangle with legs of 5 and 12.
By the Pythagorean Theorem, the hypotenuse is √(5²+12²) = 13
Using the definitions of the mean and of the standard deviation of a data-set, we have that:
- The standard deviation would remain constant.
<h3>What are the mean and the standard deviation of a data-set?</h3>
- The mean of a data-set is given by the <u>sum of all values in the data-set, divided by the number of values</u>.
- The standard deviation of a data-set is given by the <u>square root of the sum of the differences squared between each observation and the mean, divided by the number of values</u>.
When the measure of 84 is added to the data-set, we have that:
- A measure greater than the mean is added, hence the mean would increase.
- The difference squared between 84 and the mean of 81 is of 9, which is the same as the standard deviation, which would remain constant.
More can be learned about the mean and the standard deviation of a data-set at brainly.com/question/26941429
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Using the definition,
The numerator in the difference quotient is
Multiply the numerator and denominator by the conjugate of this expression,
The modified numerator reduces to a difference of squares,
Simplify this to get
Since x is approaching 4, it never actually takes on the value of 4, so (x - 4)/(x - 4) reduces to 1. Then the limit is equivalent to
and the remaining limand is continuous at x = 4, so that
