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4 years ago

Solve 20x + 12 > 14x + 30

Mathematics

2 answers:

aev [14]4 years ago

8 0

20x + 12 > 14x + 30

Get like terms all on the same side

6x > 18

Divide both sides by the number in front of the x

x > 3

Hope this helps! :)

astraxan [27]4 years ago

3 0

Answer:

B. x>3

Step-by-step explanation:

20x + 12 > 14x + 30 import like terms to the same side of the equation

20x - 14x > 30 - 12

6x > 18 divide both sides by 6

x > 3

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3 years ago

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$\sigma = 12.5$ ---- sample standard deviation

$\sigma^2 = 157.2$ ---- sample variance

Step-by-step explanation:

Solving (a): The sample variance

First, we calculate the midpoint of each class (this is the average of the limits)

So, we have:

$x_1 = \frac{56 + 64}{2} = 60$

$x_2 = \frac{65 + 73}{2} = 69$

And so on

So, the table becomes:

$\begin{array}{cc}{x} & {f} & {60} & {11} & {69} & {15} & {78} & {14} & {87} & {4} & {96} & 11 \ \end{array}$

Calculate the mean

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

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$\bar x = \frac{4191}{55}$

$\bar x = 76.2$

The variance is:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}$

So, we have:

$\sigma^2 = \frac{(60 - 76.2)^2*11+(69 - 76.2)^2*15+(78 - 76.2)^2 *14+(87 - 76.2)^2*4+(96 - 76.2)^2*11}{11+15+14+4+11-1}$

$\sigma^2 = \frac{8488.8}{54}$

$\sigma^2 = 157.2$

The sample standard deviation is:

$\sigma = \sqrt{\sigma^2$

$\sigma = \sqrt{157.2$

$\sigma = 12.5$

Solving (b): The sample variance

In (a), we calculate the sample variance to be:

$\sigma^2 = 157.2$

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Step-by-step explanation:

So to find the average I used a simple but pretty effective method

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3 years ago