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4 years ago

5

When rolling two standard six-sided dice, what is the probability that the sum of the dice will be even or a multiple of 3? (sho

w your work)

1 answer:

aliya0001 [1]4 years ago

8 0

Answer:

2/3

Step-by-step explanation:

List all the possible sums. If it helps, make a table:

$\left[\begin{array}{ccccccc} &1&2&3&4&5&6\\1&2&3&4&5&6&7\\2&3&4&5&6&7&8\\3&4&5&6&7&8&9\\4&5&6&7&8&9&10\\5&6&7&8&9&10&11\\6&7&8&9&10&11&12\end{array}\right]$

There are 36 total possible sums. Of those, 18 are even, and 6 are odd but multiples of 3.

Therefore, the probability is:

P = (18 + 6) / 36

P = 24 / 36

P = 2 / 3

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$\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}$

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Assume a solution of the form

$y_p=e^x(a\sin x+b\cos x)$

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${y_p}''=2e^x(a\cos x-b\sin x)$

Substituting into the ODE gives

$2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x$

$-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x$

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