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3 years ago

-12x + 12 = 4 - 15x + 9

Mathematics

1 answer:

emmainna [20.7K]3 years ago

8 0

Answer:

x = 1/3

Step-by-step explanation:

-12x + 12 = 4 - 15x + 9

Combine like terms

-12x +12 = -15x+13

Add 15x to each side

-12x+12 +15x = -15x+15x+13

3x+12 = 13

Subtract 12 from each side

3x+12-12 = 13-12

3x = 1

Divide by 3

3x/3 = 1/3

x = 1/3

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Nataly [62]

Answer:

1. $\bar X=5.10$

2. $\sigma=0.47$

3. $\sigma^2=0.22$

Step-by-step explanation:

QUESTION 1

The given data set for the expenditure is

$4.85,5.10,5.50,4.75,4.50,5.00,6.00$

The formula for calculating the mean is given by,

$\bar X=\frac{\sum x}{n}$

We need to add all the expenditure and divide by the total number of days.

$\bar X=\frac{4.85+5.10+5.50+4.75+4.50+5.00+6.00}{7}$

This gives us,

$\bar X=\frac{35.7}{7}$

$\Rightarrow \bar X=5.10$ to the nearest hundredth.

QUESTION 2

The standard deviation of the data set is given by the formula;

$\sigma =\sqrt{\frac{\sum(x-\bar X)^2}{n} }$

This implies that,

$\sigma =\sqrt{\frac{(4.85-5.10)^2+(5.10-5.10)^2+(5.50-5.10)^2+(4.75-5.10)^2+(4.50-5.10)^2+(5.00-5.10)^2+(6.00-5.10)^2}{7} }$

This will give us,

$\sigma =\sqrt{\frac{(-0.25)^2+(0.00)^2+(0.40)^2+(-0.35)^2+(-0.60)^2+(-0.10)^2+(0.90)^2}{7} }$

$\sigma =\sqrt{\frac{0.0625+0+0.16+0.1225+0.36+0.01+0.81}{7} }$

$\sigma =\sqrt{\frac{61}{280} }$

$\sigma =0.466775$

to the nearest hundredth,

$\sigma =0.47$ .

QUESTION 3

The variance is the square of the standard deviation.

$\sigma^2 =(0.46675)^2$

$\sigma^2 =0.217857$

To the nearest hundred gives,

$\sigma^2 =0.22$

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