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3 years ago

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The Magic Dragon has 2013 heads. Leo the Brave is cutting off the Dragon's heads at a speed of 5 heads per minute. The Dragon's

heads are growing back at a speed of 2 heads per minute. How many heads will the Dragon have in an hour? How long will the "fight" last?

1 answer:

aivan3 [116]3 years ago

3 0

Answer: The answer is 1833 heads and 11 hours, 11 minutes.

Step-by-step explanation: Given that the Magic Dragon has 2013 heads. The brave Leo is cutting off the Dragon's heads at a speed of 5 heads per minute. But, the Dragon's heads are growing back at a speed of 2 heads per minute.

So, the number of heads of Dragon that are decreasing per minute = 3.

Therefore, after 1 hour, i.e., 60 minutes, The number of heads of the Dragon

= 2013 - 60 × 3 = 2013 - 180 = 1833 heads.

Now, the fight will last until all the heads of the Dragon are cut. Let the fight lasts for 'x' minutes, then

$2013-x\times 3=0\\\\\Rightarrow 3x=2013\\\\\Rightarrow x=\dfrac{2013}{3}=671.$

Hence the fight lasts for 671 minutes, i.e., 11 hours and 11 minutes.

Thus, the Dragon will have 1833 heads after 1 hour and the fight will last for 11 hour and 11 minutes.

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<u>Solving Equations Using Successive Approximations</u>

We need to find the solution to the equation

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The difference between the results is 0.25, we need further steps to reach a good solution (to the nearest tenth)

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$\boxed{x=2.4}$

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Use the law of total probability:

$P(Y^{c})=P(Y^{c}|X)P(X)+P(Y^{c}|X^{c})P(X^{c})$

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Thus, the proportion of women who are tested, get a negative test result is 0.82.

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Use the Bayes' theorem:

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$=0.20$

Thus, the proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

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