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3 years ago

14

A certain rumor spreads through a community at the rate dy/dt= 2y(1−y) , where y is the proportion of the population that has he

ard the rumor at time t. At what time t is the rumor spreading the fastest?

1 answer:

ss7ja [257]3 years ago

3 0

Answer:

1/2 or 50% of the population has heard the rumor when it is spreading fastest.

Step-by-step explanation:

We need to take the derivative with respect to y from the r(y) = dy/dt = 2y(1-y) and equal to zero. At this condition we maximize the function and will get the maximum of the rumor spreading.

$\frac{d(r(y))}{dy}=2-4y=0$

Therefore we just need to find y:

$y=2/4=1/2$

So 1/2 or 50% of the population has heard the rumor when it is spreading fastest.

I hope it helps you!

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A tattoo enthusiast website claims that :

KATRIN_1 [288]

Answer:

The probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

Step-by-step explanation:

We have here a case where we need to use Bayes' Theorem and all conditional probabilities related. Roughly speaking, a conditional probability is a kind of probability where an event determines the occurrence of another event. Mathematically:

$\\ P(A|B) = \frac{P(A \cap B)}{P(B)}$

In the case of the Bayes' Theorem, we have also a conditional probability where one event is the sum of different probabilities.

We have a series of different probabilities that we have to distinguish one from the others:

The probability that a person has a tattoo assuming that is a Millennial is:

$\\ P(T|M) = 0.47$

The probability that a person has a tattoo assuming that is of Generation X is:

$\\ P(T|X) = 0.36$

The probability that a person has a tattoo assuming that is of Boomers is:

$\\ P(T|B) = 0.13$

The probability of being of Millennials is:

$\\ P(M) = 0.22$

The probability of being of Generation X is:

$\\ P(X) = 0.20$

The probability of being of Boomers is:

$\\ P(B) = 0.22$

Therefore, the probability of the event of having a tattoo P(T) is:

$\\ P(T) = P(T|M)*P(M) + P(T|X)*P(X) + P(T|B)*P(B)$

$\\ P(T) = 0.47*0.22 + 0.36*0.20 + 0.13*0.22$

$\\ P(T) = 0.204$

For non-independent events that happen at the same time, we can say that the probability of occurring simultaneously is:

$\\ P(M \cap T) = P(M|T)*P(T)$

Or

$\\ P(T \cap M) = P(T|M)*P(M)$

But

$\\ P(M \cap T) = P(T \cap M)$

Then

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

We are asked for the probability that a person is a Millennial given or assuming that they have tattoos or P(M | T). Solving the previous formula for the latter:

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

$\\ P(M|T) = \frac{P(T|M)*P(M)}{P(T)}$

We have already know that

$\\ P(T|M) = 0.47\;P(M) = 0.22\;and\;P(T) = 0.204$ .

Therefore

$\\ P(M|T) = \frac{0.47*0.22}{0.204}$

$\\ P(M|T) = 0.50686 \approx 0.51$

Thus, the probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

5 0

4 years ago

What is the value of b in the equation below? 9^-8 x 9^-2 = a^b

vfiekz [6]

Answer:

b= -10

Step-by-step explanation:

9^ -8 * 9^ -2

We know that a^b * a^c = a^ (b+c)

9^ (-8+-2)

9^ -10

We want it in the form a^b

a=9

b= -10

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3 years ago

Explain how you could use the conversion table to convert 700 centimeters to meters.

Kay [80]

Yes
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What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from a) 5 to 11? b)2 to 8? c)10

LenKa [72]

Answer: 1/2, 1/2, 1/4

Step-by-step explanation:

To find the fraction that the hour hand turns of a clockwise revolution, we have to find how long it is going then divide by 12

Ex. a) 11 - 5 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution

b) 8 - 2 = 6, 6/12 = 1/2 so the hour hand turns by 1/2 of a clockwise revolution

c) For this, we have to convert 1 into 13 as 1 - 10 is a negative number

13 - 10 = 3, 3/12 = 1/4 so the hour hand turns by 1/4 of a clockwise revolution

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