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deff fn [24]
3 years ago
7

Does (-2)^n/( 3^n+1) converge or diverge?

Mathematics
1 answer:
hodyreva [135]3 years ago
3 0
\left|\dfrac{(-2)^n}{3^n+1}\right|=\dfrac{2^n}{3^n+1}

As n\to\infty, the sequence a_n=\left(\dfrac23\right)^n converges to zero.

If you're talking about the infinite series

\displaystyle\sum_{n\ge0}\dfrac{(-2)^n}{3^n+1}

well we've shown by comparison that this series must also converge because we know any geometric series \sum\limits_n r^n will converge as long as |r|.
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Answer the following question
FromTheMoon [43]

Answer:

Letters as in the attached image.
Triangles ABC and ADC are congruent by SSS. From that, corresponding angles are congruent, in parcicualre B and D, both measuring 94°.
Final angle is obtained by difference. The internal angles of a quadrilater add to 360, so the remaining is 360-90-94-94 =82°

7 0
2 years ago
In a certain Algebra 2 class of 30 students, 14 of them play basketball and 10 of them play baseball. There are 14 students who
Veseljchak [2.6K]

Answer:

In a certain Algebra 2 class of 30 students, 22 of them play basketball and 18 of them play baseball. There are 3 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?

I know how to calculate the probability of students play both basketball and baseball which is 1330 because 22+18+3=43 and 43−30 will give you the number of students plays both sports.

But how would you find the probability using the formula P(A∩B)=P(A)×p(B)?

Thank you for all of the help.

That formula only works if events A (play basketball) and B (play baseball) are independent, but they are not in this case, since out of the 18 players that play baseball, 13 play basketball, and hence P(A|B)=1318<2230=P(A) (in other words: one who plays basketball is less likely to play basketball as well in comparison to someone who does not play baseball, i.e. playing baseball and playing basketball are negatively (or inversely) correlated)

So: the two events are not independent, and so that formula doesn't work.

Fortunately, a formula that does work (always!) is:

P(A∪B)=P(A)+P(B)−P(A∩B)

Hence:

P(A∩B)=P(A)+P(B)−P(A∪B)=2230+1830−2730=1330

7 0
3 years ago
A squirrel can run at a maximum speed of 4 miles per hour.
Vsevolod [243]

Answer:  

36 miles per hour if you were trying to multiply it.

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Anybody know the answer?
marysya [2.9K]
I'd start by writing an equation for each of the right triangles. (Pythagorean theorem)

y² + 9² = z²
x² + z² = (4+9)²
4² + y² = x²

we want to find z so combine the equations by substituting the other variables x,y out.

substitute y² for (x² - 4²) in 1st equation.

(x² - 4²) + 9² = z²

now by rearranging the 2nd equation we can substitute x² for (13² - z²)

(13² - z²) - 4² + 9² = z²
169 - z² - 16 + 81 = z²
234 - z² = z²
234 = 2z²
234/2 = z²
117 = z²
√(117) = z
√(9*13) = z
3√(13) = z

13 goes in the box




































6 0
3 years ago
you have 280 gallons of a solution that is 20% salt. how much water should be added to dilute the solution down to 14% salt
Readme [11.4K]
19.6 gallons of water need to be added.....
I think
5 0
4 years ago
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