A 50.00 g sample of an unknown metal is heated to 45.00°C. It is then placed in a coffee-cup calorimeter filled with water. The calorimeter and the water have a combined mass of 250.0 g and an overall specific heat of 1.035 cal/g•°C. The initial temperature of the calorimeter is 10.00°C. The system reaches a final temperature of 11.08°C when the metal is added.

Sorry i dont understand the question can you rephase it?

Radon-222 or rn-222 has a half-life of 3.82 days. to determine the fraction of an original sample of rn-222 that remains unchanged after 7.646 days, we calculate the amount of rn-222 remaining after 7.646 days and divide it with the original amount. using 1 gram as a basis and using half-life calculation methods, we can determine that  0.249 or 0.25  grams of rn-222 will remain, and thus the fraction remaining is 0.25 or 1/4.