Given:
Given that the pie chart shows the relative frequency distribution resulting from a survey of 6000 US rural households with internet connections in a certain year.
We need to determine the total number of households with each type of internet in the survey.
Cable modem:
Since, the relative frequency distribution for cable modem is 0.142
The total number of households that use cable modem is given by

Thus, 852 households use cable modem.
DSL:
Since, the relative frequency distribution for DSL is 0.092
The total number of households that use DSL is given by

Thus, 552 households use DSL.
Dialup:
Since, the relative frequency distribution for dialup is 0.747
The total number of households that use dialup is given by

Thus, 4482 households use dialup.
Others:
Since, the relative frequency distribution for others is 0.019
The total number of households that use others is given by

Thus, 114 households use others.