Exploring Relationships Between x, y & z

In summary, the lists show the relationship between the value of x, y, and z. The nth term for each sequence is given by: a(x) = 3n, b(y) = 30-2n, and c(z) = 11-\frac{1}{2}n. The formula for z in terms of x and y is z = \frac{1}{2}(52-x-y). However, there are other possible solutions such as z(x,y) = y/4 +
  • #1
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The lists below show the relationship between value of x, y & z.
List A, x: 3, 6, 9, 12, 15,...
List B, y: 28, 26, 24, 22, 20,...
List C, z: 10.5, 10, 9.5, 9, 8.5,...
Find
a) a fomula for z in terms of x and y,
b) the nterm of each sequence.

I can see the pattern in A, B & C but i just am not sure how to connect them.
 
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  • #2
the nth term for each is givn below:
a(x): 3n
b(y): 30-2n
c(z): 11-0.5(n)

so...z = 11-0.5(n) = (22-n)/2 = (22-4n+3n)/2 = (22-4n +x)/2 = (8+22-2n-2n+x-8)/2
= (30-2n-2n+x-8)/2 = (y+x-2n-8)/2 = y/2 + x/2 - n -4 = z
 
  • #3
There are many possible solutions.

For example z(x,y) = y/4 + 7/2 will also work just fine.
 
  • #4
Thanks guys. For (a), my book said that the answer is [tex]z = \frac{1}{2}(52-x-y)[/tex]
 

1. How do you define the relationship between x, y, & z?

The relationship between x, y, and z can be defined as a statistical correlation or association between the variables. This means that as one variable changes, there is a corresponding change in the other variables as well.

2. What methods do you use to explore relationships between x, y, & z?

There are several methods that can be used to explore relationships between x, y, and z. These include statistical analysis, data visualization, and regression analysis. Each method provides different insights into the relationship between the variables.

3. How do you determine if there is a significant relationship between x, y, & z?

To determine if there is a significant relationship between x, y, and z, statistical tests such as correlation or regression analysis can be used. These tests measure the strength and direction of the relationship between the variables and provide a p-value to determine if the relationship is statistically significant.

4. Can you explore relationships between more than three variables?

Yes, it is possible to explore relationships between more than three variables. However, as the number of variables increases, the analysis becomes more complex and may require more advanced statistical methods.

5. How do you interpret the results of exploring relationships between x, y, & z?

The interpretation of the results will depend on the specific analysis and the variables being explored. Generally, a strong positive correlation between x and y indicates that as x increases, y also increases. On the other hand, a strong negative correlation means that as x increases, y decreases. It is important to carefully consider the variables and their relationship in order to properly interpret the results.

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