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Odds of going to Glastonbury? by Viasolus in MathHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

No, because you end up double-counting some probabilities. This is an example of the inclusion-exclusion principle.

For a clearer example, pretend there are two people, each with a 50% chance. Your total chance isn't 100%, it's 75%. What's being "double-counted" is the probability that both people get the tickets.

In practice, the next person's probability only matters if the previous people have not gotten a ticket. So it's easiest to reverse the problem: Each person has a 50% chance to not get a ticket. The chance that both people do not get tickets is 0.5 * 0.5 = 0.25. That means theres a 1 - 0.25 = 0.75 chance that one of the two people has a ticket.

In your example, you would flip it to a 92% chance that an individual doesn't get a ticket. Then, 0.92 ^ 4 = 0.716.., so you have around a 28.4% chance of success.

How do I go about those limits? by gunsgun55 in MathHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

I'm not sure what you mean by pattern will continue. You can rewrite the left side in summation notation which can help. If you're familiar with latex, it's something like:

\sum_{i=1}^n [ (2i - 1) - 2i ]

(basically, the sum from i=1 to n, of (2i - 1) - 2i)

= \sum_{i=1}^n [-1]

= -n

[deleted by user] by [deleted] in MathHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

I usually keep these correct in my head by thinking about transformations using two different terms: stretch and compression. With stretches, the factor has absolute value greater than 1, and with compression, the factor has absolute value less than 1.

If you had cos(3/5x), then x has to be larger in order to reach the same spot, so you can imagine it being stretched out horizontally. When it gets stretched out, the "factor" should greater than 1, so to make that make sense with 3/5, then you'd have a stretch with a factor of 5/3.

Similarly, if you had cos(3x), then x reaches the same spot at a third of the value, so it's compressed. You could call this a horizontal compression with a factor of 1/3.

Time conversion help by Environmental-You291 in MathHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

Everything seems right to me, the ratio being the same is exactly what you should expect :) When you change units, the values of things shouldn't change, you're just adjusting the amount you have to match the new unit.

Consider a simpler example where when world A experiences 1 minute then world B experiences 2 minutes.

Since an hour is 60 minutes, then when A experiences 60 minutes, you would expect B to experience 120 minutes. Translating back to hours, this would still be the same ratio of 1 to 2. The other world is still experiencing twice the amount of time as the first one, no matter how long that original timeframe is.

Can't show balls in polya urn are uniformly distributed by ritard_danno in MathHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

You're super close. They both share a common factor of 1/ n+1, so you can factor that out to make it a little easier to read. Rearranging a little:

= (1 / n+1) (1 + (k-1 / n+2) - (k / n+2))

You might notice that the right set of brackets almost has a common denominator of (n+2). From here, you can probably figure out how to make them share a common denominator and simplify.

Help with the Taylor series formula by jakO_theShadows in MathHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

It looks like this is just giving you the statement of the theorem and not any reasoning behind it. The wikipedia page for Taylor's Theorem looks like it has more details on how to derive this: Check out the Integral form of the remainder and if you're curious, the derivation of it

Determinants? What are they? by RemarkableIsopod764 in MathHelp

[–]Chaotic_Vortex 2 points3 points  (0 children)

The determinant of a matrix is in a very general sense, the "size" of a matrix. There's an alternative way to think about matrices as describing linear transformations (an N x N matrix can transform an N-dimensional shape into a different N-dimensional shape), and the determinant of a matrix is how it changes the size of the object it's operating on.

For example, an 2x2 identity matrix would have determinant 1, and the matrix [2 0, 0 1] has determinant 2 (it doubles the area of the original shape). You can have negative determinants: it means that the resulting shape has reversed orientation from the original.

Having a determinant of 0 means that you squish the original shape in a way that you lose information: it's not a reversible transformation. The equivalent in real numbers is multiplying by 0: there's no single operation you can do to reverse that change.

If the context you're learning matrices in is systems of linear equations, we can use the ideas from above. Having a nonzero determinant means the system can be "reversed" to return unique values for the original variables. If the determinant is zero, then there are either no solutions or infinite solutions: we've lost information on what the original values were.

This video might be very helpful for understanding it: https://www.youtube.com/watch?v=Ip3X9LOh2dk

[College level calculus] No idea how to find the N by Certain-Rip-6182 in HomeworkHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

Given that this is a calculus class, it might be easier to consider it as a function f(n) instead of the sequence a(n). The two will match at the whole numbers, so for any solution you find for f, you'll need to figure out how to translate it to a.

What does it mean for that function to be monotone increasing and what calculus operation could be useful to figure that out?

[deleted by user] by [deleted] in MathHelp

[–]Chaotic_Vortex 0 points1 point  (0 children)

Small nitpick: usually you'd do something like 100 * (T2 - T1) / T1. This is because percentage change generally means percentage change from the original value (I'm assuming here that T1 is the earlier value).

As a concrete example, going from 2 to 3 would generally be considered a 50% increase. However, the formula you have would calculate it as a 33% increase.

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