The lisbon’s new heat pump cost $4,500. they bought it to replace their old furnace and air conditioner which cost about $2,800 a year to run. the heat pump will save them approximately 39% a year. in how many years will the heat pump pay for itself? round to the nearest tenth.

4.1 years.  

Step-by-step explanation:

We have been given that The Lisbon’s new heat pump cost $4,500. They bought it to replace their old furnace and air  conditioner which cost about $2,800 a year to  run. The heat pump will save them approximately  39% a year.

Yearly cost was 2800 at first and the pump will save 39% of 2800. So annual saving with new heat pump will be:

Let x be the number of years in which heat pump will pay for itself, so saving in x years will be:

Now let us equate the savings by new heat pump with cost of heat pump to find the number of years (x).

Therefore, the heat pump will pay for itself in 4.1 years.

b because it contains 40% of the possible results from the random list.  

0,1,2,3 v 4,5,6,7,8,9  

4 integers to 6 integers  

40% success vs 60% fail

step-by-step explanation:

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.