Strontium is a radioactive material that decays with a continuous rate (k) of -0.0244. If there are 30 grams of strontium present today and it decays continuously, how much will be present in 20 years?

18.42 g

Step-by-step explanation:

Using the exponential growth / Decay function :

A = Pe^kt

A = final amount ; P = initial amount, t = number of years ; t = 20

A = 30e^-(0.0244 * 20)

A = 30e^-0.488

A = 30 * 0.6138528

A = 18.415586

Strontium present after 20 years will be :

18.42 g

Given:

Probability that the Yankees wins a game is

P(A) = 0.46

Probability that the Yankees loses a game is

P(A') = 1 - P(A') = 1 - 0.46 = 0.54

Probability that the Yankees scores 5 or more runs in a game is

P(B) = 0.59

Probability that the Yankees scores fewer than 5 runs in a game is

P(B') = 1 - P(B) = 1 - 0.59 = 0.41

Probability that the Yankees wins and scores 5 or more runs is

P(A⋂B) = 0.39

Applying the De Morgan's law, the probability that the Yankees scores fewer than 5 runs and they loses the game would satisfy:

1 - P(A'⋂B') = P(A) ⋃ P(B) = P(A) + P(B) - P(A⋂B)

or

1 - P(A'⋂B') = 0.46 + 0.59 - 0.39

or

1 - P(A'⋂B') = 0.66

=> P(A'⋂B') = 1 - 0.66 = 0.34

Applying the Bayes theorem, the probability that the Yankees would score fewer than 5 runs, given they lose the game:

P(B'|A')  = P(A'⋂B')/P(A')

or

P(B'|A') = 0.34/0.54 = 0.630

Hope this helps!

:)