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4 years ago

Explicit and Recursive Functions:

Mathematics

1 answer:

aleksandr82 [10.1K]4 years ago

7 0

In this problem we need to find the value of a and b. So given that t<span>he function should be in the form f(n) = an + b and we know each value of n, then out goal is to find a and b.

For getting this purpose, we need to find a system of two equations (given that we have two unknown variables)

Therefore:

(1) f(0) = a(1) + b = 18
</span>∴ a + b = 18
<span>
(2) f(1) = a(2) + b = 24
</span>∴ 2a + b = 24<span>

Solving for a and b we have:

a = 6
b = 12

Finally:

f(n) = 6n + 12</span>

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The dot plot shows the number of books lent by a school library during a 10-day period.

Katyanochek1 [597]

The mean absolute deviation of the number of books is 1.84

<h3>How to determine the mean absolute deviation?</h3>

The dot plot of the number of books is in the attached figure.

From the figure, we have:

x f

1 1

2 2

3 2

4 3

5 1

6 2

7 3

8 1

Start by calculating the mean using:

$\bar x= \frac{\sum fx}{\sum f}$

So, we have:

$\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}$

Evaluate the sum and products

$\bar x= \frac{69}{15}$

Divide

$\bar x= 4.6$

The mean absolute deviation is then calculated as:

$|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}$

So, we have:

$|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}$

Evaluate the absolute difference

$|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}$

Evaluate the sum of products

$|\bar x|= \frac{27.6}{15}$

Divide

$|\bar x|= 1.84$

Hence, the mean absolute deviation of the number of books is 1.84

Read more about mean absolute deviation at:

brainly.com/question/3250070

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