Therefore, the bones were 6612.5 years old at the time they were discovered.
<h3><u>Half life</u></h3>
Given that the radioactive element carbon-14 has a half-life of 5750 years, and a scientist determined that the bones from a mastodon had lost 57.5% of their carbon-14, to determine how old were the bones at the time they were discovered, the following calculation must be made:
- 50 = 5750
- 100 = 11500
- 57.5 = X
- 57.5 x 11500 / 100 = X
- 6612.5 = X
Therefore, the bones were 6612.5 years old at the time they were discovered.
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Answer:
x = 5/e
Step-by-step explanation:
ln x- ln 5= -1
We know that ln a - ln b = ln (a/b)
ln x- ln 5= -1
ln(x/5) = -1
Raise each side to the power of e
e^ ln(x/5) = e^-1
We know that e^-1 = 1/e
x/5 = 1/e
Multiply each side by 5
x/5 *5 = 1/e * 5
x = 5/e
Answer:
The system of inequalities is


Step-by-step explanation:
step 1
Find the equation of the dashed line with negative slope
The line passes through the points
(0,-2) and (-2,0)
Find the slope

Find the equation of the line in slope intercept form

we have

substitute

The solution of the inequality is the shaded area below the dashed line
therefore
The equation of the inequality A is

step 2
Find the equation of the dashed line with positive slope
The line passes through the points
(0,0) and (4,1)
Find the slope

Find the equation of the line (direct variation)

we have

substitute

The solution of the inequality is the shaded area above the dashed line
therefore
The equation of the inequality B is

therefore
The system of inequalities is


I dont know all of them sorry. But i think
Its d. If its a list of questions lol. But I could be wrong but i did the math 2 times.