Early studies of probability were conducted by the Italian mathematician Girolamo Cardano (1501-1576). One of the many dice games that Cardano studied was played with six 6-sided dice. Each of these six dice had five blank faces and one face with a number. The numbers 1 through 6 each appeared on one of the six dice. All 6 dice were rolled at once, and the payoff to the gambler was based on the sum of the numbers showing on the up faces. What is the expected value of the sum obtained by rolling all 6 dice

Ariana starts with 100 milligrams of a radioactive substance. the amount of the substance decreases by 20% each week for a number of weeks, w. the expression 100(1−0.2)w finds the amount of radioactive substance remaining after w weeks. which statement about this expression is true? a) it is the difference between the initial amount and the percent decrease. b) it is the difference between the initial amount and the decay factor after w weeks. c) it is the initial amount raised to the decay factor after w weeks. d) it is the product of the initial amount and the decay factor after w weeks.