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3 years ago

13

a bag contains 9 green marbles, 3 red marbles, and 8 blue marbles. one marble is taken from the bag and put back after checking

its color. a second marble is then taken out. what is the probability that the first is blue and the second green?

1 answer:

grin007 [14]3 years ago

5 0

Answer:

17÷ 20 is the probability that the first is blue and the second is green

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The amount of substance left of a radioactive element of half life, $t_{\frac{1}{2}}$ after a time, t, is given by:

$N(t)=N_0\left( \frac{1}{2} \right)^ \frac{t}{t_{ \frac{1}{2} }}$

Given that <span>potassium-40 has a half life of approximately 1.25 billion years.

The number of years it will take for 0.1% of potassium-40 to remain is obtained as follows:

$0.1=100\left( \frac{1}{2} \right)^ \frac{t}{1.25}} \\ \\ \Rightarrow\left( \frac{1}{2} \right)^ \frac{t}{1.25}}=0.001 \\ \\ \Rightarrow\frac{t}{1.25}\ln\left( \frac{1}{2} \right)=\ln(0.001) \\ \\ \Rightarrow \frac{t}{1.25}= \frac{\ln(0.001)}{\ln\left( \frac{1}{2} \right)} =9.966 \\ \\ t=9.966(1.25)=12.5$

Therefore, </span><span>the maximum age of a fossil that we could date using 40k is 12.5 billion years.</span>

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