There are 8 students on the minibus. Five of the students or boys. What fraction of the students are boys

The data given below contain the state cigarette taxâ€‹ (in $) for all 20 regions of a country.

g100num [7]

Answer:

(a) $\bar x= 1.583$ -- Population Mean

(b) $s = 1.032$ --- Population standard deviation

(c) See Explanation

Step-by-step explanation:

Given:

Cigarette tax for 20 regions

Solving (a): The population mean

This is calculated as:

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

$\sum x = 1.36 + 1.70 + 2.50 + 0.45 + 1.18 + 0.64 + 3.46 + 0.57 + 2.00 + 0.80 + 1.60 +0.98 + 0.36 + 2.24 + 4.35 + 0.62 + 2.70 + 1.78 + 1.53 + 0.84$

$\sum x = 31.66$

$n = 20$

So, we have:

$\bar x= \frac{31.66}{20}$

$\bar x= 1.583$

Solving (b): The population standard deviation

This is calculated as:

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

$\sum (x -\bar x)^2 = (1.36 - 1.583)^2 + (1.70 - 1.583)^2+ (2.50 - 1.583)^2+ (0.45 - 1.583)^2+ (1.18 - 1.583)^2+ (0.64 - 1.583)^2+ (3.46 - 1.583)^2+ (0.57 - 1.583)^2+ (2.00 - 1.583)^2+ (0.80 - 1.583)^2+ (1.60 - 1.583)^2+(0.98 - 1.583)^2+ (0.36 - 1.583)^2+ (2.24 - 1.583)^2+ (4.35 - 1.583)^2+ (0.62 - 1.583)^2+ (2.70 - 1.583)^2+ (1.78 - 1.583)^2+ (1.53 - 1.583)^2+ (0.84- 1.583)^2$

$\sum (x -\bar x)^2 = 21.29222$

So:

$s = \sqrt{\frac{21.2922}{20}$

$s = \sqrt{1.06461}$

$s = 1.032$

Solving (c):

Population mean tells the average amount while the standard deviation represents the spread from the calculated mean

Option (4) is correct

6 0

3 years ago

Which pairs of angles in the figure below are vertical angles?

ch4aika [34]

Answer: Option A and Option C.

Step-by-step explanation:

For this exercise it is important to know the definition of "Vertical Angles".

When two lines intersect or cross, there are a pair of angles that share the same vertex and they are opposite each other. This pair of angles are known as "Vertical angles".

By definition, Vertical angles are congruent, which means that the have the equal measure.

In this case, you can observe in the picture provided in the exercise that the line TI and the line WN intersect each other at the point S.

You can identify that the pair of angles that are opposite to each other and share the same vertex are the shown below:

$\angle ISN$ and $\angle TSW$