Farah predicts that the average text messages sent by her family will be 2042 messages each of the last 6 months in 2019. The number of text messages used during 5 of those months were 2800, 2481, 2105, 1975, 2732. How many text messages must be sent during the sixth month for her prediction to be true?

159 text messages

Step-by-step explanation:

Given that:

Predicted average = 2042

Number of months = 6

Number of texts for each of last 5 months :

Let number of text that must be sent in the sixth month = x

Predicted Average = (sum of texts / Number of months)

2042 = (2800 + 2481 + 2105 + 1975 + 2732 + x) / 6

2042 = (12093 + x) / 6

Cross multiply :

6 * 2042 = 12093 + x

12252 = 12093 + x

x = 12252 - 12093

x = 159

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is