A water tank holds 1,200 gallons but is leaking at a rate of 5 gallons per week. A second water tank holds 1,500 gallons but is leaking at a rate of 9 gallons per week. After how many weeks will the amount of water in the two tanks be the same?

75 weeks takes for the amount of water in the two tanks be the same, if a 1200 gallons water tank leaking rate of 5 gallons per week and 1500 gallons water tank leaking rate of 9 gallons per week.

Step-by-step explanation:

             The given is ,

                   First water tank holds 1200 gallons and leaking at a rate of 5 gallons per week.

                  Second water tank holds 1500 gallons and leaking at a rate of 9 gallons per week.

Step:1

           The difference in the water level in tanks,

                      = Second tank - First tank

                      = 1500 - 1200

                      = 300 gallons

Step:2

         The difference in the rate of leaking of water in tanks,

                = Rate of leaking of second tank - rate of leaking of first tank

                = 9 - 5

                = 4 gallons per week

Step:3

          Weeks takes for the two tanks are same level of water,

                      =

                      =

                      = 75 weeks

Step:4

        Check for solution,

        Water at the first tank after 75 weeks,

                  = Total capacity - Amount of water leaked at 75 weeks

                  = 1200 - ( 5 × 75)

                  = 825 gallons

          Water at the second tank after 75 weeks,

                  = Total capacity - Amount of water leaked at 75 weeks

                  = 1500 - ( 9 × 75)

                  = 825 gallons

           Water at the first tank after 75 weeks = Water at the second tank after 75 weeks,

                825 gallons = 825 gallons

Result:

        75 weeks takes for the amount of water in the two tanks be the same, if a first water tank holds 1200 gallons at a leaking rate of 5 gallons per week and second water tank holds 1500 gallons at a leaking rate of 9 gallons per week.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0