The half-life of a radioactive substance is the time required for half of a sample to undergo radioactive decay, or for the quantity to fall to half its original amount. carbon 14 has a half-life of 5,730 years. suppose given samples of carbon 14 weigh (fraction 5/8) of a pound and (fraction 7/8) of a pound. what was the total weight of the samples 11460 years ago
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Amount of C-14 taken were 2.5 pounds and 3.5 pounds respectively.

Step-by-step explanation:

Radioactive decay is an exponential process represented by

where = Amount of the radioactive element after t years

= Initial amount

k = Decay constant

t = time in years

Half life period of Carbon-14 is 5730 years.

Now we take ln (Natural log) on both the sides

-ln(2) = -5730kln(e)

0.69315 = 5730k

Now we have to calculate the weight of samples of C-14 taken for the remaining quantities and of a pound.

pounds

Similarly for pounds

pounds

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

b because it contains 40% of the possible results from the random list.  

0,1,2,3 v 4,5,6,7,8,9  

4 integers to 6 integers  

40% success vs 60% fail

step-by-step explanation: