The amount of caffeine consumed from a glass of Diet Pepsi is proportional to the number of ounces that was drank. The table below shows the amount of caffeine consumed by three different people and the corresponding number of ounces of Diet Pepsi that they each drank. Amount of Caffeine (mg) 27 45 72 Amount of Diet Pepsi (oz) 3 5 8 What is the unit rate (or constant of proportionality)? Write an equation to represent this proportional relationship. Make sure to define the variables you used.

Constant of proportionality: k=3

Equation: c=3d

Step-by-step explanation:

By definition, Direct proportion equations have the following form:

Where "k" is the Constant of proportionality.

In this case, let be "c"  the the amount of caffeine consumed  (in mg) from a glass of Diet Pepsi and "d" the number of ounces that was drank.

So, the equation that represents this relationship will have this form:

Then, the first step is to find the Constant of proportionality "k".

Knowing that:

We can substitute values into the equation:

Now, solving for "k", we get:

Therefore, we can write the following equation that represents that proportional relationship:

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.

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb