which table shows a positive correlation?

Explanation:

Step1: Understand positive correlation

Positive correlation means as (x) increases, (y) also increases.

Step2: Analyze the first table

In the first table, (x) values are (1,2,2,4,5) and (y = 5) for all (x). (y) is constant as (x) changes. So no positive correlation.

Step3: Analyze the second table

For (x = 1,y = 10); (x=2,y = 18); (x = 3,y=31); (x = 4,y = 37); (x=5,y = 52). As (x) increases ((1\to2\to3\to4\to5)), (y) increases ((10\to18\to31\to37\to52)).

Step4: Analyze the third table

For (x = 1,y = 24); (x=2,y = 15); (x = 3,y=13); (x = 4,y = 9); (x=5,y = 6). As (x) increases, (y) decreases. So no positive correlation.

Step5: Analyze the fourth table

In the fourth table, (x = 8) for all values and (y) changes. (x) is constant as (y) changes. So no positive correlation.

Answer:

The second table.