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Blababa [14]
4 years ago
7

In 2008 election there was 28 blue states and 22 red states express the red and blue states as fractions in lowest terms of the

total number of states and also as decimals
Mathematics
1 answer:
Basile [38]4 years ago
8 0
Let's start with the blue states. Out of 50 states, 28 of them were blue.
Therefore, the fraction would be 28/50. Let's reduce it.
28/50=14/25 --> these are the lowest terms for this fraction
Use a calculator to find the decimal solution --> 14/25= .56

Now, let's do the red states. Out of the 50 states, 22 of them were blue.
22/50=11/25 --> lowest terms
Use a calculator --> 11/25= .43
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9. Determine how long it takes for 80% of the material to decay.
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Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.

The amount of a substance after t days is modeled by:

A(t) = A(0)e^{-kt}

In which:

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The half-life is of 8 days, hence A(8) = 0.5A(0), and this is used to find k.

A(t) = A(0)e^{-kt}

0.5A(0) = A(0)e^{-8k}

e^{-8k} = 0.5

\ln{e^{-8k}} = \ln{0.5}

-8k = \ln{0.5}

k = -\frac{\ln{0.5}}{8}

k = 0.08664339757

Hence:

A(t) = A(0)e^{-0.08664339757t}

The time it takes for 80% of the material to decay it t for which A(t) = 0.2A(0), hence:

0.2A(0) = A(0)e^{-0.08664339757t}

e^{-0.08664339757t} = 0.2

\ln{e^{-0.08664339757t}} = \ln{0.2}

-0.08664339757t = \ln{0.2}

t = -\frac{\ln{0.2}}{0.08664339757}

t = 18.6

It takes 18.6 days for 80% of the material to decay.

To learn more about exponential functions, you can take a look at brainly.com/question/24906920

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