Question

question 1
6 pts
find the mean of the following numbers:
11, 18, 16, 19, 13, 13, 16, 13
round to the nearest tenth if necessary.

question 2
6 pts
solve for ( x ).
( \frac{1}{7}=-\frac{4}{9}x )
convert the answer to a decimal and round to the nearest tenth if necessary.

Explanation:

Step1: Calculate the sum of the numbers

$$11 + 18+16 + 19+13+13+16+13$$
$$=(11 + 18)+(16 + 19)+(13 + 13)+(16 + 13)$$
$$=29+35 + 26+29$$
$$=119$$

Step2: Calculate the number of elements

There are \(n = 8\) numbers.

Step3: Calculate the mean

The mean formula is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Substitute \(\sum_{i=1}^{n}x_{i}=119\) and \(n = 8\) into the formula: \(\bar{x}=\frac{119}{8}=14.875\)

Step1: Solve for \(x\)

Given \(\frac{1}{7}=-\frac{4}{9}x\). Multiply both sides by \(-\frac{9}{4}\) (the reciprocal of \(-\frac{4}{9}\)) to isolate \(x\).
\(x=\frac{1}{7}\times(-\frac{9}{4})\)
\(x=-\frac{9}{28}\)

Step2: Convert to a decimal

\(x=-\frac{9}{28}\approx - 0.3214\)

Answer:

\(14.9\)

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