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3 years ago

Suppose you roll a special 34-sided die. What is the probability that the number rolled is a "1" OR a "2"?

1 answer:

5 0

Rolling a 1 or a 2 are mutually exclusive events (if you roll a 1, you could not have rolled a 2, and vice-versa), so the probability here is additive:

P(1 or 2) = P(1) + P(2) = 1/34 + 1/34 = 2/34 = 1/17.

So the probability of rolling a 1 or a 2 is 1/17.

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HELP I NEED THOS FASSTTTT A What is the domain of the function?

Oxana [17]

Answer:

Step-by-step explanation:

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3 years ago

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Lim (n/3n-1)^(n-1) n → ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, e :

$\displaystyle e = \lim_{n\to\infty} \left(1+\frac1n\right)^n$

To make our limit resemble this one more closely, make a substitution; replace 9/(n - 9) with 1/m, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9m = n - 9, we see that m also approaches infinity as n approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

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3 years ago

Find the quotient: 8,358 ÷ 27 = ________. 309 r 15 309 r 26 310 r 15 310 r 26

Rus_ich [418]

Answer:

the answer is 309 r 15

Step-by-step explanation:

309 × 27 is 8343 and your left with 15

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3 years ago

A Boxerville Express commuter train leaves the station every 30 minutes. When Theo arrives at the station, a woman tells him she

Dmitrij [34]

Answer: D

The answe is just simply D because of the minutes when it adds up is almost the same as MPH

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3 years ago

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Fred has 230 animals at his zoo. Grace at 349 more animals in her zoo than Fred has. how many animals do they have altogether? T

WARRIOR [948]

Step-by-step explanation:

okay so im in 8th grade and i just worked the problem out and i got , 809 ,

first you add 230 + 349 to see how much she has in her farm

she has 579, then you add 579 because she has that many , and he has 230 so you add 579 +230 and tou get 809

work:

230

+349

----------

579

+230

---------

809

hope i helped!!

4 0

4 years ago