/r/askmath

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

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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!

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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

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Geometry Symbols

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Algebra Symbols

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

Set Theory Symbols

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

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

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

1

Say I have the following set of data:

3x+2y+1205z=352000

2x+2y+1150z=323000

2x+2y+1107z=165000

3x+2y+1200z=190000

3x+2y+1224z=300000

For context, this pertains to home sales. The coefficients of x, y and z are the number of bedrooms, number of bathrooms, and area of the floor space respectively. and the constant is the final selling price. Should this data be represented another way?

How does one find a way to "best fit" these equations to understand how future sales might look based on their metrics? Would this involve regression analysis and if so how? Can these equations be simplified further by removing 2y since that 2y is present in all equations? Ideally, I'd like to be able to solve this using WolframAlpha.

0 Comments

2024/11/07

22:21 UTC

22:21 UTC

1

The data is positive integers z, n and subsets A1, A2, . . . , Az

of the set {1, 2, . . . , 2n}. We will say that a pair of numbers (x, y) is good if x < y,

x, y ∈ {1, 2, . . . , 2n}, and there is exactly one index i ∈ {1, 2, . . . , z}, for

of which exactly one of the numbers x, y belongs to Ai. Evaluate in how many subsets can x be and in how many y can be. Remember that there is only one subset where there is either y or x in every other there are both or none. Then prove that there can be at most n^2 good pairs no matter what subsets are we given.

I tried using the formula for combination and got 2n^2-n but well that doesnt get me anything. Any help appreciated...

0 Comments

2024/11/07

21:34 UTC

21:34 UTC

1

My home pantry has limited space, and I want to eliminate the need to stock one ingredient by combining two other ingredients.

Consider three baking ingredients (descriptors and percentages vary across locales; use these as assumptions):

- Bread flour, which is 12.7% protein
- All-purpose flour, which is 11.7% protein
- Vital wheat protein, a high-gluten additive that packs a whopping 76.6% protein

Bread flour can be replaced using all-purpose flour and a small amount of vital wheat protein; however, bread is finicky, and the replacement combo should:

- contain the same percent of protein as the bread flour it is replacing, and
- equal the volume of the bread flour initially called for.

I would appreciate recommendations on a formula that meets my needs. Bonus points and my lifelong respect for a formula or spreadsheet tool that allows the protein percentages to be variables.

Thanks to the community for your help.

1 Comment

2024/11/07

20:07 UTC

20:07 UTC

1

Hey

So I'm currently learning about strong induction with The Book of Proof by Richard Hammack, and I am stuck on this example. Why do we choose S_k-5 which then gives us k>=6??

I understand why the statement is true, but I don't understand where the 5 comes from, and how I could replicate the pattern for similar exercises.

Any explaination will be very much appreciated :)

3 Comments

2024/11/07

20:06 UTC

20:06 UTC

1

Its been a while since i touched any math.

I need to get an estimation on the combinations/permutations for a bucket of x items when picking in any combination. For the sake of example say bucket has 3 items: item1, item2, item3 and any number of items can be picked

Pick possibilities:

- Item1
- Item2
- Item3
- Item1 + Item2
- Item2 + Item3
- Item3 + Item1
- Item1 + Item2 + Item3

I know 3! is 6 but wondering what I am missing to end up with 7. Do I have the wrong idea for what a factorial is supposed to be? How do we model the pick possibilities into an equation given any x [ 0 ... 1000 ]

1 Comment

2024/11/07

20:01 UTC

20:01 UTC

7

5 Comments

2024/11/07

20:00 UTC

20:00 UTC

0

I just took the Accuplacer college placement test and I was one question off from passing the Arithmetic section.

This question bothered me because I had no idea where to start..

6[4+2(1-3)]

..

How do I solve this and what type of math question is this?

7 Comments

2024/11/07

18:57 UTC

18:57 UTC

4

Proof that the function is Injective function using ∀x1,x2∈X,f(x1)=f(x2)⇒x1=x2 f:R⇒R*+(all positive real numbers without 0) x⇒(e^x +2)/e^-x

I tried a lot to make them x1=x2, but I couldn't. Maybe I have a problem with working with( e) if someone could help me, and I would be thankful

7 Comments

2024/11/07

18:34 UTC

18:34 UTC

2

1 Comment

2024/11/07

17:24 UTC

17:24 UTC

2

When writing the range of a function like (a, b) or [a, b], which value should be put first - the value that is lower, or the value that corresponds to the lower limit of the domain?

For instance, 1/ √ (x), keeping to real numbers only. The domain would be (0, ∞), but as the domain tends up the range tends down. So would the range be (0, ∞) or (∞, 0)?

3 Comments

2024/11/07

16:35 UTC

16:35 UTC

1

I need help to appear intelligent at work!

Say you have a population of people.

10% have characteristic a, 20% have characteristic B, 5% have characteristic c.

People can have more than one characteristic.

What is the average number of people who will not have any characteristics?

I was leaning to using the format:

P(A or B) = P(A) + P(B) - P(A&B)

But I don't think that covers the nuances.

2 Comments

2024/11/07

16:06 UTC

16:06 UTC

1

I'm really dumb and I need an information for an item I'm creating for my rpg

I want to know how slower would time perception be than usual if 2 days feel like one year

Like: it's (number)x slower because (math) 🤓☝️

2 Comments

2024/11/07

14:47 UTC

14:47 UTC

1

So, the problem I set out to solve is this: Determine the complex Fourier Series of the function for the given interval: f(x)=e^(−|x|) , −1<x<1

I solved it and arrived at the following:

own working with answer at bottom

however, the given memo reaches this :

Basically, my in\pi term is replaced with n^2pi^2 in the memo. After I did all the working out, I fed the problem into the math chatgpt, and it came up with the same answer as me, though I don't know if that really proves anything.

Can someone please help me figure out if my answer is correct, or if the memo is correct?

0 Comments

2024/11/07

14:43 UTC

14:43 UTC

2

A probability mass function can be represented as a probability vector and then multiplied by a stochastic matrix, e.g., a transition matrix as in a Markov chain.

Is there an equivalent operation for continuous probability density functions?

1 Comment

2024/11/07

14:16 UTC

14:16 UTC

1

I want to normalize the data in this table (https://docs.google.com/spreadsheets/d/1BePh2uKC-p-22yQzBBr9wF1-d\_U9AA6ynWvdv081uvM/edit?usp=sharing) but I'm not sure how

One method I used was to get the maximum and the minimum values of the distributions and then

(X-Min)/(Max-Min)

The other method that I used was to get each value in each table of distributions times 100 and then dividing it by the maximum value

(X*100)/Max

But I'm not sure that I'm doing this correctly. Is this a good way to normalize data values? Which method is better? If none, can you suggest any others?

3 Comments

2024/11/07

13:56 UTC

13:56 UTC

4

I'm trying to prove to myself that as a nonogram/Picross puzzle gets larger, the probability that a randomly generated puzzle of that size is clued ambiguously approaches 1.

If we depict an n x n nonogram as an n x n binary matrix, with 1 representing filled squares and 0 representing unfilled squares, the presence of either of these two 4 x 4 matrices will cause the whole puzzle to be clued ambiguously, regardless of what appears in the rest of the puzzle.

Therefore, a lower bound on the proportion of n x n nonograms that are clued ambiguously will be the proportion of n x n binary matrices that contain one of those two 4 x 4 submatrices.

Calculating this seems to be where I'm making a mistake. My logic is as follows:

There are 2^(n^2) possible n x n binary matrices. Where n >= 4, if we fix a 4 x 4 submatrix at any given position, then there will be 2^(n^2-16) possible n x n matrices that contain it in that position. In a 5 x 5 matrix, you can "fit" this 4 x 4 submatrix in 4 possible positions. In a 6 x 6 matrix, it would fit in 9 possible positions. In general, it will fit in (n-3)^2 possible positions.

Therefore, my lower bound for proportion of n x n matrices that contain each of the specified 4 x 4 submatrices, where n > 4, is 2^(n^2-16) * (n-3)^2/2^(n^2) . Cancelling the 2^(n^2-16) from the top and the bottom gives (n-3)^2/2^16.

But surely this must be wrong? If n > 259, then this proportion exceeds 1! Any help unpicking my mistake would be much appreciated.

Edit: I've realised the mistake in the above, this 9 x 9 matrix for example would be double-counted. I haven't a clue how to get the right answer though!

5 Comments

2024/11/07

11:54 UTC

11:54 UTC

20

x² + x + 1 = 0 (mod 6)

Multiplying both sides by 4

4x² + 4x + 4 = 0 (mod 6)

Adding 3 to both sides (4+3 = 7 = 1 mod 6) to complete the square

4x² + 4x + 1 = 3 (mod 6)

(2x+1)² = 3 (mod 6)

In modulo 6, the unique solution to a² = 3 is a = 3 because 3² = 9 = 3 mod 6

2x+1 = 3 (mod 6)

Subtracting 1 and then dividing by 2

2x = 2 (mod 6)

x = 1 (mod 6)

However, when we substitute 1 into the original equation, we get 3 = 0, which is not correct. I'm struggling to find the error in this proof.

9 Comments

2024/11/07

11:12 UTC

11:12 UTC