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Mrac [35]
3 years ago
12

You made a deal with Ms.Williams to read 100 pages every night. You know that it takes you 32 minutes to read 16 pages. How long

will it take you to read the 100 pages you promised Ms.Williams? Please help me with my homework ;(
Mathematics
1 answer:
AnnyKZ [126]3 years ago
5 0
Put the problem into a proportion to make it easier to solve.

32        x
      =
16       100

You can use cross products to simplify this proportion.  Multiply 32 by 100, and set that number equal to 16 *x.  

Your equation should now look like this
3200=16x

You are trying to get the variable alone on one side, so you should divide both sides by 16.

If this is performed correctly, then your final answer should be 

x=200.

It will take you 200 minutes (3 hours 20 mins) to read the pages that you promised Ms. Williams

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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
liq [111]

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)

So

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

So

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

How old is the fossil?

This is t for which

Q(t) = 0.8Q(0)

So

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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Step-by-step explanation:

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