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3 years ago

Is 0.84 less than greater than or equal to one half

2 answers:

8 0

One half is 0.50, so compare 0.84 to 0.50. Which is true?

0.84 is greater than 0.50
0.84 equals 0.50
0.84 is less than 0.50.

LuckyWell [14K]3 years ago

8 0

0.84 is greater that 1/2

0.5 is 1/2 and 0.84 is greater than that so its greater that 1/2

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3 years ago

Element X decays radioactively with a half life of 12 minutes. If there are 200 grams of Element X, how long, to the nearest ten

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Answer:

It would take 24 minutes for the element to decay to 50 grams

Step-by-step explanation:

The equation for the amount of the element present, after t minutes, is:

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

In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.

Half life of 12 minutes

This means that $Q(12) = 0.5Q(0)$

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

$0.5Q(0) = Q(0)e^{-12r}$

$e^{-12r} = 0.5$

$\ln{e^{-12r}} = \ln{0.5}$

$-12r = \ln{0.5}$

$12r = -\ln{0.5}$

$r = -\frac{\ln{0.5}}{12}$

$r = 0.05776$

If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?

This is t when Q(t) = 50. Q(0) = 200.

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

$50 = 200e^{-0.05776t}$

$e^{-0.05776t} = 0.25$

$\ln{e^{-0.05776t}} = \ln{0.25}$

$-0.05776t = \ln{0.25}$

$0.05776t = -\ln{0.25}$

$t = -\frac{\ln{0.25}}{0.05776}$

$t = 24$

It would take 24 minutes for the element to decay to 50 grams

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4 years ago

A passenger train has tickets available for 12 window seats and 8 aisle seats. The next person to buy a ticket will be randomly

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