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sesenic [268]
3 years ago
5

You pick a card at random. Without putting the first card back, you

Mathematics
1 answer:
Inga [223]3 years ago
8 0

First, we need the probability of picking an odd number.

There are 5 cards in total, and 3 odd cards (3, 5, and 7).

That means that the probability that we'll draw an odd card would be \frac{3}{5}.

Then, we have 4 cards left, and 2 even cards (4 and 6), meaning that the probability that we draw an even card will be \frac{2}{4} or \frac{1}{2}.

To find the probability that these would happen in consecutive draws, we just multiply the probabilities together.

\frac{3}{5}*\frac{1}{2}=\frac{3}{10} or 0.3.

To convert this into a percentage, we multiply the decimal by 100.

0.3*100=30.

So the probability of picking an odd number and then picking an even number is 30%.

Hope this helps!

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Answer:

(a) The solution to the differential equation is x = A_0Coswt + Ce^(-kx)

(b) The initial condition t > 0 will not make much of a difference.

Step-by-step explanation:

Given the differential equation

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(a) To solve the differential equation, first separate the variables.

dx/(x - A) = -kdt

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ln(x - A) = -kt + c

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Now, we put A = A_0Coswt

x = A_0Coswt + Ce^(-kx) (Where C is constant.)

And we have the solution.

(b) Since temperature t ≠ 0, the initial condition t > 0 will not make much of a difference because, Cos(wt) = Cos(-wt).

It is not any different from when t < 0.

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