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3 years ago

6

10. In rolling 3 dice, are the events A: Sum divisible by 3 and B: Sum divisible by 5 mutually exclusive?

1 answer:

dalvyx [7]3 years ago

6 0

Answer: No, the events A and B are not mutually exclusive.

Step-by-step explanation:

We say any two events P and Q are mutually exclusive , if they are disjoint set such that their intersection is empty.

Given : In rolling 3 dice, we have two events

Event A: Sum divisible by 3

Event B: Sum divisible by 5

But the sum of all 3 dices can 15 and 15 is divisible by 3 and 5.

The intersection of events A and B have = {(5,5,5), (3,6,6), (6,3,6), (6,6,3),(5,4,6), (6,4,5), (4,6,5), (4,5,6), (6,5,4), (5,6,4)}

Hence, the events A and B are not mutually exclusive.

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An amusement park recently increased the cost of a family season pass. The original price was $150. The new price is $183. What

viva [34]

Answer:

1.22%

Step-by-step explanation:

150 x 1.22 = 183

6 0

3 years ago

the half life of c14 is 5730 years. Suppose that wood found at an archeological excavation site contains about 35% as much C14 a

Furkat [3]

Answer:

The wood was cut approximately 8679 years ago.

Step-by-step explanation:

At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:

$\frac{dm}{dt} = -\frac{m}{\tau}$ (Eq. 1)

Where:

$\frac{dm}{dt}$ - First derivative of mass in time, measured in miligrams per year.

$\tau$ - Time constant, measured in years.

$m$ - Mass of the radioactive isotope, measured in miligrams.

Now we obtain the solution of this differential equation:

$\int {\frac{dm}{m} } = -\frac{1}{\tau}\int dt$

$\ln m = -\frac{1}{\tau} + C$

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$ (Eq. 2)

Where:

$m_{o}$ - Initial mass of isotope, measured in miligrams.

$t$ - Time, measured in years.

And time is cleared within the equation:

$t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right]$

Then, time constant can be found as a function of half-life:

$\tau = \frac{t_{1/2}}{\ln 2}$ (Eq. 3)

If we know that $t_{1/2} = 5730\,yr$ and $\frac{m(t)}{m_{o}} = 0.35$ , then:

$\tau = \frac{5730\,yr}{\ln 2}$

$\tau \approx 8266.643\,yr$

$t = -(8266.643\,yr)\cdot \ln 0.35$

$t \approx 8678.505\,yr$

The wood was cut approximately 8679 years ago.

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3 years ago

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choli [55]

Answer:

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Step-by-step explanation:

8x15 is 120. The formula to find the area of a right triangle is base x height divided by two.
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2 years ago

Read 2 more answers

Suppose that A = PDP-1 . Prove that det(A) = det(D)

daser333 [38]

Answer:

Check.

Step-by-step explanation:

To prove it we need to know that for two matrices A and B we have that:

det(AB) = det(A)*det(B) and $det(A^{-1}) = \frac{1}{det(A)}$ . Now:

$A = PDP^{-1}$

$det(A) = det(PDP^{-1})$

$det(A) = det(P)*det(D)*det(P^{-1})$

$det(A) = det(P)*det(D)*\frac{1}{det(P)}$

$det(A) = det(P)*\frac{1}{det(P)}*det(D)$

$det(A) = det(D)$ .

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3 years ago

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Kisachek [45]

Answer:

1.368

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3 years ago