Which two quantitative variables would show a positive correlation if graphed on a scatterplot? (The number of items in a family’s refrigerator and the number of days since the family’s last visit to the grocery store; the age of a child and the size of the child’s vocabulary; a student grades in math and the number of student’s first name; the population of a town and the height of its mayor)

The two quantitative variables that would show a positive correlation if graphed on a scatterplot would be the age of a child and the size of the child’s vocabulary.

As children get older, they typically develop and expand their vocabulary, resulting in a positive correlation between age and vocabulary size.

The other pairs of variables do not have a clear positive correlation:

• The number of items in a family's refrigerator and the number of days since the family's last visit to the grocery store may have a negative correlation (more days since a visit could mean fewer items).
• A student's grades in math and the number of letters in the student's first name has no logical correlation.
• The population of a town and the height of its mayor do not have a direct relationship, making it unlikely to have a positive correlation as well.