/r/askmath

This subreddit is for questions of a mathematical nature. Please read the subreddit rules below before posting.

- Explain your post - show your efforts and explain what you are specifically confused with.
**Don't just say "I don't get this, help"** - Stay on topic - this subreddit is for math questions; no how-to guides, or non math related questions
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Don't just post a question and say "HELP". Post your question and outline the steps you've taken to solve the problem on your own. Beginner questions and asking for help with homework **is okay**. Asking for solutions without any effort on your part, is **not okay**. Help others, help you!

- Give context and details to your question, not just the equation
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**Show your work!**Detail what you have tried and what isn't working- Re-read your post before hitting submit, does it still make sense

Basic Math Symbols

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °

Geometry Symbols

∠ ∟ ° ≅ ~ ‖ ⟂ ⫛

Algebra Symbols

≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳

Set Theory Symbols

∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟

Logic Symbols

¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣

Calculus and Analysis Symbols

∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ

Mathematical Greek Letters

𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔

/r/askmath

2

So i was trying to find out the probability of a dice landing on 1 when rolled x amount of times. My first thought was to take 1/6 times however many times but then i realized thats the probability that it lands 1 every time. So logically i just need to find the chance that it doesnt land 1 every time and subtract that to 1. Thus i got the equation: Chance = 1 - (5/6)^z or Chance = 1 - (1 - x/y)^z

Which is correct, but intuitively I thought this would work: Chance = z root of x/y

Could someone smarter than me explain why it does work and any better formulas for calculating this

0 Comments

2024/06/13

23:19 UTC

23:19 UTC

1

Hello! I ordered an uber and saw his rate being 4.88 of 7.167 trips, and was wondering how many people did rate him bad. what equation should I do to get these answers:

- how many people did rate him bad?
- how many stars they had to give him to make his rate being 4.88?

English is not my first language, correct me if im wrong and please explain like im a little kid

3 Comments

2024/06/13

22:40 UTC

22:40 UTC

0

If i have 1 plane (denoted on the picture as (0,0) and x pointing right and y pointing down, and another plane (lets call it main plane) denoted on the image as {R} how can i create a transformation matrix T 4x4 that transforms the point from the plane1 to the main plane. And follow up question what would it look like if the main plane was rotated 45 degrees?I know you dont have the exact mesurements but use variables.

2 Comments

2024/06/13

21:02 UTC

21:02 UTC

2

A piece of wood in the shape of a cube has a surface area of P square inches. The cube is cut in half through the center to form two identical rectangular prisms each with a square base. What is the surface area of one of these rectangular prisms, in terms of P?

A) 1/2 P B) 2/3 P C) 3/4 P D) P

I believe the answer key has B as the answer but I can't arrive at that answer. If I start with a cube that is 4 by 4 by 4, I get a surface area of 96 and therefore P=96. After the cut is made through the center forming 2 identical prisms with a square base is where I get lost. I made the assumption that one of the new rectangular prisms has dimensions 2 by 2 by 4 since it said each of them has a square base. But then the surface area of one of these new prisms would be 40 and 2/3 of 96 is not 40. I'm obviously doing something wrong here. Can someone please walk me through this problem?

4 Comments

2024/06/13

20:57 UTC

20:57 UTC

1

Sorry if this question is redundant, but I’m having a hard time with this concept.

A co-occurrence matrix is nxn and the diagonals show how often a value occurs and co-occurrence on the off-diagonal.

A covariance matrix, also nxn, measures how two random variables vary together. With variance on the diagonal and covariance on the off-diagonal.

If given a co-occurrence matrix, are we able to find the covariance somehow?

0 Comments

2024/06/13

19:48 UTC

19:48 UTC

0

Hello,

For the following inequality:

**4x + 3 < x - 6**

If I attempt to isolate the variable on the left side of the equation, the answer I get it is **x < -3**.

When I attempt to isolate the variable on the right side of the equation, I get **-3 > x**, which is as good as **x < -3**.

Why is it the case that doing different operations on the different numbers on each side should yield the same answer?

Thank you for your time.

7 Comments

2024/06/13

19:34 UTC

19:34 UTC

2

6 Comments

2024/06/13

18:03 UTC

18:03 UTC

2

I wanted to find out if there can be variables added to each

A is equal to of( B1 Given A) (B2 given A) (B3 given A)

If B1 is 25%, B2 is 30% and B3 is 35% then the probability of A is 65.875%

If you added in variables such as due to reasons each probability could only be verified at 90% so now there is a 10% variable in probability confirmation. (Could be bias, bad eyesight, second guessing data what ever)

B1 is 22.5% B2 is 27% and B3 is 31.5% Now the probability of A is 61.24%

Does this make sense so far? I'm trying to figure out if this formula is a thing. If it's confusing I can try and clarify but I'm trying to find out if a probability is affected by variables.

9 Comments

2024/06/13

17:35 UTC

17:35 UTC

2

If we consider the Gödel sentence of PA (G), for instance, then we know that G is true for a model of PA iff the Gödel sentence cannot be proven from PA, that is, it is unprovable. G is false, however, iff G is provable from PA. Another consequence of this is that for those structures where G is false PA is inconsistent. More importantly though, it seems (and this is where I may be mistaken) that that specific structure cannot be a model of PA since if the axioms of PA are true in this structure, then PA should not be inconsistent. Thus, G in any model of PA must be true albeit unprovable from PA.

On the other hand, if we consider the axiom of choice (AC), then we know from both Gödel and Cohen jointly that AC is independent of ZF since AC cannot be refuted as there is a model of ZF where AC is true (namely, Gödel’s inner model L), and AC cannot be proven as there is a model where AC is false. Together, these results show that AC is independent of ZF.

Given this, why is the Gödel sentence (for any axiom system) regarded as independent? It doesn’t seem to be independent because any structure where it can be proven (and thus false) is one where PA would have to be inconsistent, and thus all the axioms of PA cannot be true together, so this structure cannot be a model of PA. This also seems to be the reason that both sides of the bi-conditional need to be established in order for AC to be shown to be independent. If Gödel was only able to show his result (that is, AC cannot be refuted, and there is a model of ZF where it is true), then AC “could” have been Gödel-like similar to Con(PA).

As a side question, since both the Gödel sentence and AC are independent, is there a way of ranking them in a taxonomy or hierarchy since one’s truth value can be inferred (but not proven) and the other’s truth value is wholly non-inferable?

6 Comments

2024/06/13

17:13 UTC

17:13 UTC

1

If it helps to paint a scenario: I'm able to roll 3 six-sided dice. I want one of any of the three dice to be a 2 and another of any of the three dice to be a 3. The remaining dice can be any result, including a duplicate of 2 or 3.

How do I calculate the probability of this occurring?

When I write everything out in a table, 30 of 216 possible outcomes meet these criteria. I can't figure out the math behind it though.

Edit: thanks all

5 Comments

2024/06/13

16:04 UTC

16:04 UTC

0

Used to be good at this but I gives me a MASSIVE headache 🤣 I have liquid of 22,79% of activite substance I need to dilute it into 100 ml water and have a 0,9% solution Calculating in my head I need around 4ml of the 22,79% concentrate, right? Gonna have a camomile tea now. Help! 😩

3 Comments

2024/06/13

15:32 UTC

15:32 UTC

1

Probably a dumb question and might be the wrong subreddit, but it seems like there are two different answers to the question.

Let’s say a business has 22 sales days in April of this year and 21 sales days of last year. (22/21)-1 is roughly 4.76%

The business has revenue of $35,000 this year in April and $30,000 last year in April. Year-over-year growth ($35,000/$30,000)-1 is roughly 16.7%. Then you subtract the -4.76% to account for the extra sales day which = 11.91% adjusted sales growth.

However, if you take the average sales per day for both months it would be $35,000/22= $1,590.90 for this year and $30,000/21= $1,428.57 for last April. Then calculate the year-over-year growth ($1,590.90/$1,428.57)-1 = 11.36%.

My question is, why are those two values different and which one would be considered a more accurate way to calculate growth when adjusting for sales day changes?

2 Comments

2024/06/13

15:18 UTC

15:18 UTC

18

Title basically

Hi all! When we say the limit as x->c for some function f, we use an equals sign to show our answer but this usage of the equals sign doesn’t feel the same to me as when we say 1+1=2.

Am I wrong? Or is there a better definition of equality?

14 Comments

2024/06/13

15:13 UTC

15:13 UTC

4

I am working through Elementary Linear Algebra by Howard Anton, and I see the dot product x·y represented as matrix multiplication which I cannot make sense of. I see how x·y could be viewed under matrix multiplication as (x^T)y if x and y are column vectors, except for the fact that x·y is a scalar whereas, as a matrix product, (x^T)y is necessarily not a scalar, it is a 1x1 matrix.

What's going on here? Is it normal to consider a 1x1 matrix as a scalar? Is (x^T)y a rare example where the notation is self contradictory (transpose and matrix multiplication being matrix operations but the result being regarded as a scalar?).

Further, if this notation is accepted in this particular case, how can we be sure that any matrix product (A^T)B is to be considered a matrix and not a scalar? Is there something I have overlooked in the notation?

10 Comments

2024/06/13

13:49 UTC

13:49 UTC

2

Suppose we have an equation of 2s =3x , where both s & x are a function of time (t). Why is it that when we differentiate wrt to t, we get 2*ds/dt = 3*dx/dt?

11 Comments

2024/06/13

13:40 UTC

13:40 UTC

1

What kind of formula is this? When you want to find the probability that something is true or not. Suppose you are trying to determine the odds of if an event is happening or not. This is an extreme but just so you can understand where I'm coming from.

Question is the bank being robbed? If the bank were being robbed we would see certain things such as Bank robbers, the alarm going off, people laying on the floor or with there hands up. If a value was assigned to each category the more of these categories observed the higher the probability the bank is being robbed.

The silent alarm is going off :70% probability of a robbery.

Customers with their hands up: 90% probability the bank is being robbed

People who appear to be bank robbers: 98% probability the bank is being robbed.

If you see that both the silent alarm and that customers are on the floor there is a 90%+70% probability the bank is being robbed. And you combine them to say there is a 97% probability of the bank being robbed.

What is this probability determination called?

6 Comments

2024/06/13

13:34 UTC

13:34 UTC

0

I find Penrose/Lucas critique of AI very interesting. And frankly, it looks ironclad if one believes that Goedel's incompleteness is actually true.

Basically, what it boils down for me is, that algebra cannot understand certain things we understand with our brains.

But this 'thing', as it follows from Goedel's proof, is infinity, isn't it? For instance, it makes sense to me, that geometry was found to be a complete system, because it naturally has infinity in it - in the form of ideal straight lines, etc.

I did not look at Goedel's own proof, but I tried following simplified versions. And I could see that the proof relies on, I guess, Cantor's methods, e.g. something akin to 'the infinite hotel'.

But the problem I have with the 'infinite hotel' types of argument is that when you do shifting of infinite series, you can get all sorts of weird results, like the one with the sum of all natural numbers being -1/12.

So, my question is - is it possible that this is the weak point of Goedel's theorem? May it be

that with Cantor's methodology one imports into the logic some sort of a twisted understanding of infinity, which later leads to contradictions and thus confirms incompleteness?

24 Comments

2024/06/13

12:52 UTC

12:52 UTC

1

There's a theorem that states F = exp∫R(x)dx where R = 1/Q(∂P/∂y - ∂Q/∂x) and F is the integrating factor for the exact ODE P(x, y)dx + Q(x, y)dy = 0. But what if ∂P/∂y - ∂Q/∂x = 0?

2 Comments

2024/06/13

12:48 UTC

12:48 UTC

2

Hey folks.

I'm playing a computer game called Stationers where you are building a base on Mars (or other planets). Part of the game is setting up a breathable atmosphere for your character which requires two or more gasses in a specific ratio.

To mix gasses you use a type of valve called a mixer, which has two inputs and one output and a dial that you can change the incoming ratio of the two inputs.

The base I want to build will need to have 70% nitrogen (N), 25% oxygen (O) and 5% carbon dioxide (D). I figure I can combine in mixer A the o2 and co2, then in mixer B take the output of A and add in the nitrogen.

So what percentages should I put in mixer A and B to get my 70/25/5 ratio of gasses? I'm trying to figure out the formula for that but it's escaping me currently.

6 Comments

2024/06/13

12:39 UTC

12:39 UTC

2

Inner products on a finite dimensional Hilbert space can always be written in the form:

<v, w> = g_ij v*^i w^j,

(I don’t know a proof for this but I think it’s the case?)

Is the equivalent statement true for infinite dimensional Hilbert spaces? I.e. if I have a Hilbert space of functions defined on some n dimensional manifold, all possible inner products can be written as

<f, g> = int f*(x) g(x) s(x) d^n x,

Where s(x) is some scalar function that serves as a measure with d^n x

It seems that every possible inner product that I can think of can be written in this form (including “distributional” functions like the delta function for s(x)), but I’m sure if this were a fact, there would be some theorem proving it. It seems somewhat related to the Riesz representation theorem and Riesz-Markov theorem, as well as a fact I have seen floating around, but never proved, which is that infinite dimensional Hilbert spaces are inner product isomorphic to L^2 on some measure space (I’ve seen the proof they are isomorphic to l^2 ).

16 Comments

2024/06/13

11:54 UTC

11:54 UTC

1

I needed a fast way of getting the radon transform of an image. The wiki article says that the 2d fourier transform is related to the radon transfrom. and shows how to use it to take the inverse radon transform.

I tried doing what they did but in reverse again to get the forwards radon transform but my answer is not entirely real. I dont know were i went wrong. my code and intermediate images: https://github.com/jktechs/radon-transform/tree/main .

The reason for the extra transforms is that by using the FFT low frequency data is on the edges while it is supposed to be in the middle.

0 Comments

2024/06/13

11:16 UTC

11:16 UTC

1

5 Comments

2024/06/13

10:50 UTC

10:50 UTC

1

Does it take the same time to go from beat A to beat B if we decrease/increase the BPM continously or discretely? And if it doesn't, is there much error between the two?

4 Comments

2024/06/13

09:25 UTC

09:25 UTC

1

Hi,

I have come across an engineering question, that requires me to show that one Laurent Polynomial is always larger than another one (assuming complex inputs on the unit circle).

From my understanding this is termed "Majorization".

Do you guys have any basic-literature recommendations that discuss/introduce the theory behind the topic of polynomial majorization?

0 Comments

2024/06/13

08:56 UTC

08:56 UTC

1

the problem i am working on:

here are the variables:

Here is what I got from the problem 19 :

0 Comments

2024/06/13

04:40 UTC

04:40 UTC