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3 years ago

What is 6×9÷18+100-11+4

Mathematics

1 answer:

mojhsa [17]3 years ago

4 0

6 × 9 ÷ 18 + 100 - 11 + 4

Use the order of operations to simplify:

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

6 × 9 ÷ 18 + 100 - 11 + 4

There are no parentheses or exponents, so multiplication comes first. Multiply 6 and 9.

54 ÷ 18 + 100 - 11 + 4

Next is division. Divide 54 by 18.

3 + 100 - 11 + 4

Finally, add and subtract from left to right.

103 - 11 + 4

92 + 4

<h3>Answer:</h3>

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Set A of six numbers has a standard deviation of 3 and set B of four numbers has a standard deviation of 5. Both sets of numbers

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Given:

$\sigma_A=3$

$n_A=6$

$\sigma_B=5$

$n_B=4$

$\overline{x}_A=\overline{x}_B$

To find:

The variance. of combined set.

Solution:

Formula for variance is

$\sigma^2=\dfrac{\sum (x_i-\overline{x})^2}{n}$ ...(i)

Using (i), we get

$\sigma_A^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{n_A}$

$(3)^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$9=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$54=\sum (x_i-\overline{x}_A)^2$

Similarly,

$\sigma_B^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{n_B}$

$(5)^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$25=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$100=\sum (x_i-\overline{x}_B)^2$

Now, after combining both sets, we get

$\sigma^2=\dfrac{\sum (x_i-\overline{x}_A)^2+\sum (x_i-\overline{x}_B)^2}{n_A+n_B}$

$\sigma^2=\dfrac{54+100}{6+4}$

$\sigma^2=\dfrac{154}{10}$

$\sigma^2=15.4$

Therefore, the variance of combined set is 15.4.

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