3 years ago

Is 4.47 a rational number

Mathematics

1 answer:

bonufazy [111]3 years ago

6 0

I think 4.47 is a a rational number

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A fossil was analyzed and determined to have a carbon-14 level that is 80 % that of living organisms. the half-life of c-14 is 5

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Answer:

The fossil is 1860 years old.

Step-by-step explanation:

The equation for the amount of fossil has the following format:

$Q(t) = Q(0)e^{rt}$

In which Q(t) is the amount after t years, Q(0) is the initial amount and r is the rate of change.

Half-life of c-14 is 5730 years.

This means that $Q(5730) = 0.5Q(0)$

$Q(t) = Q(0)e^{rt}$

$0.5Q(0) = Q(0)e^{5730r}$

$e^{5730r} = 0.5$

$\ln{e^{5730r}} = \ln{0.5}$

$5730r = \ln{0.5}$

$r = \frac{\ln{0.5}}{5730}$

$r = -0.00012$

$Q(t) = Q(0)e^{-0.00012t}$

How old is the fossil?

This is t for which

$Q(t) = 0.8Q(0)$

$Q(t) = Q(0)e^{-0.00012t}$

$0.8Q(0) = Q(0)e^{-0.00012t}$

$e^{-0.00012t} = 0.8$

$\ln{e^{-0.00012t}} = \ln{0.8}$

$-0.00012t = \ln{0.8}$

$t = -\frac{\ln{0.8}}{-0.00012}$

$t = 1860$

The fossil is 1860 years old.

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two dice are rolled in succession. determine the probability that their sum is 8 or more, given that the first die is a 4 or mor

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Is y= 1/2x - 4 equal to 3x - 6y = 24

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Answer:

$\fbox{\begin{minipage}{4em}Yes, it is\end{minipage}}$

Step-by-step explanation:

3x - 6y = 24

Divide both sides by 6:

(3/6)x - (6/6)y = 24/6

Simplify:

(1/2)x - y = 4

Move y to the right side, 4 to the left side, and change sign of y and 4:

(1/2)x - 4 = y

Rearrange both sides:

y= (1/2)x - 4

Hope this helps!

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