The sum of chris and mike’s scores on a math quiz is 39. mike’s score is twice the sum of chris’ score and 3. find each student’s quiz score.

c=11, m=28

Step-by-step explanation:

c= Chris's score

m= Mike's score

c+m=39                 we know from the equation that their scores

                              add up to 39, so this equation is a good starting

                              point.

c+2(c+3)=39          we also know that Mike's score is twice the sum of Chris's

                              score and 3 so we can substitute that in for his score.

                              now we can solve.

c+2c+6=39             distribute

3c+6=39                 combine like terms

   -6  -6                  

3c=33                     addition property of equality

÷3  ÷3          

c=11                         multiplication property of equality

Now that we know Chris's score, we simply substitute that number in in our simple equation for earlier to find Mike's score.

11+m=39                  substituted in 11 for c

-11     -11                  

m=28                       addition property of equality

There you go! Don't worry, I had a lot of trouble with these types of problems too. That's why I'm so good at them now Hope this helps!

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.