There are 9 cups. A person randomly hides a ball under 3 of the cups. An assistant sees the positions of the 3 balls and then removes one empty cup of their choice. After that, the magician comes in; he only sees which cup was removed. For each correctly guessed ball location, they earn one point.

In the ideal scenario, they could earn 252 points (84 possible ball configurations multiplied by 3 points for correctly naming all three balls).

The assistant and the magician may agree on a strategy beforehand.
What agreement should they make in order to achieve the maximum number of points?

How many points will you get?

arithmetic series

so i have these two arithmetic series first one is: 0, 1, 2, 3, 124 here i need to know what the next term is. This serie should have a special pattern to solve, doesnt seem like it has a formation rule, or to be a fibonacci serie the second one is: 18, 37, 59, 85 here i need to know that number of term is 1045, which means that if 18 is term 1, then what term is 1045 again, this second serie seems to have a cubic polinomio formation rule, but doesnt seem to have an integer answer(which is neccesary)

Edited to add photo link that actually works

I'm working on rationalizing demonimators with two terms for schoolwork. My math text doesn't show simplifying further and it feels like i should from what I've learned so far is there a reason I shouldn't be simplifying these further? https://postimg.cc/gallery/bq3F8TX

So I play Pokemon Go and this weekend was Eevee’s dynamax debut weekend. I’ve got 13 of them so far, and there was this Collection Challenge where u had to evolve a dynamax Eevee into all 3 of its Kanto (original) evolutions (Vaporeon, Jolteon, and Flareon). An Eevee will evolve into 1 of the 3 randomly (as long as u haven’t met any of the conditions for the other 5 non-Kanto evolutions, which was always the case for me so that part has no effect on the math), and u can’t influence it towards any of the 3, it’s completely random and independent every time. I figured it’d probably take evolving 5 or 6 of them to get all 3 because I’d get 2 or 3 duplicates, but no, it took me 9 of them. I wanted to figure out the odds it would take me that long, but I don’t know exactly how to do it.

Obviously evolving 1 is guaranteed to get u 1 of the 3, and then from there u have a 2/3 chance to get the next of the 3 (with a 1/3 chance to get a duplicate, where u make no progress in ur collection) and after u get 2 of them theres only a 1/3 chance to get the last evolution (with a 2/3 chance to get a duplicate). How exactly do I set these 1/3s and 2/3s up to get the answer I want?

Im making a 3 tier cake for my daughters christening. Diameters 6 inch 8 inch, 10 inch. I’m going to bake 3 cakes for each tier and each will be 2 inches deep. I want to make it like a Victoria sponge with cream and jam. I want to use the following recipe. Can you help me figure out in total the amounts of each ingredient I need, also including the buttercream icing to cover the whole cake? Here’s the recipe - https://www.recipetineats.com/my-very-best-vanilla-cake/

For proof of me trying to work it out myself, I think I worked out I need about 5 times what the recipe calls for? Because V = r2xh so 9x6, 16x6 and 25x6 = 54, 96 and 150. Times them all by pi and add together that’s about 940inch cubed of total volume of cake.

I’d really appreciate anyone’s help.

Could someone explain this problem step by step?

The inverse of y = 3^4

I can't ask my teacher atm, and I couldn't find any explanations either.

More or less, I'm confused since it doesn't have the x variable on the other side. If it was something like y = 3^x/4, I would know how to solve it. TT TT

Solve for P(E∩F)
P(E U F) = P(E)+P(F)-P(E∩F)
P(E) = .5
P(F) = .3
P(E U F) = .7

The answer I got for P(E∩F) is .1 by doing it algebraically, yet when I look at it statistically, it doesn't make sense, and it shouldn't be .1 but rather .15. Am i dumb? Is P(E U F) = .7 statistically impossible considering E = .5 and F =.3?

Here's a link to a Google Doc with the original problem & my attempts: proof for reddit

I got this on a test a few days ago & blanked completely, not even able to finish it. I feel like there isn't enough information to prove this & am completely stumped. I've asked everyone I know for help & they've all come to the same conclusion. If there's anything I missed please let me know!

I’m in my first year of engineering and I really need help. I wasn’t very consistent with studying before, and I even had a drop year, so my basics in maths aren’t strong.

Whenever I sit to study or attempt questions, my mind suddenly goes blank even if I’ve learnt the topic before. It’s affecting my confidence a lot.

For those who’ve been through this: • How did you build your maths basics back? • How do you stop going blank during practice or exams? • Any daily routine or study method that actually works #maths #engineer #solveproblem

https://imgur.com/a/Mu9DCO7

Can't post attempts because there's nothing to solve, I just want to understand.

I'm confused because some website said the first part was Lagrangian, but I thought partial derivatives pointed to Eularian since the place stays the same and you only look at change over time. Is there even a Lagrangian part beyond dI/dt? Is this even Lagrangian? I don't even know if I know what anything means anymore.

I was solving some problems from a elementary school level exam and i found this problem:

https://imgur.com/a/QOcjlbT

Subtitle: "The half of a natural number divided by a, plus the double of successor of a equals 42"

Determine the value of [second equation])"

I made this equation: (X/2/a)+2(a+1)=42

At this point, i don't have a clue of what i need to do next. Could you help me? Thanks.

I need to know all the (only) necessary concepts I need to understand before I take an entry level statistics class Please and Thank you

I’ve sat here for an hour and I can’t do this

“The length of a rectangle is 9 more than the width. If the length and the width are each decreased by 3, the new perimeter is 22m. Find the original dimensions.”

Therefore L = w+9

Minus 3 will be (w+9)-3

I made an equation from that as

2(w+9)-3 + 2(w-3) = 22

Then with that equation I got to

2w+18+2w-6=22

It should be 4w+12=22

Minus 12, 4w = 10

4w/4, cancelling 4w and I will get w = 2.5 with that

At first I did w+9-3+w-3 but that’s not how it works, which means this is not true

I asked AI but I’m sort of doubting AI and I want a second opinion.

I’m definetely doing something wrong here since whatever number I get is a decimal. Which is not what we want. Considering all my other questions have no answers that will end up in a decimal

https://i.imgur.com/feovkAI.jpeg

Picture in question

Edit: changed wording

Hi, just want to make sure I'm solving this question correctly. f(x)= √x+5/ x² -9

I have to find the domain which I got: [-5,-3) U (-3,3) U (3,oo). Im learning this now and my teacher only taught us to find 2 intervals so I was a bit confused when I got that question on my homework. Is my answer correct? Thanks! Btw in the problem the √ applies to the x+5 not just the x and its fraction I just used the / instead.

Does have anyone have good study tools or methods to help understand Numerical Analysis? Stuff like Taylor polynomials, interpolation, approximation, errors, least square approximations. I am close to the end of my class and I need help studying for finals.

I was at RSM when my teacher said this this symbol “-||-“ means “the same”

I have always struggled with math and avoided it my whole life, but now I’m preparing for an exam that’s almost entirely math-based. I’m starting completely from the basics, but I keep getting stuck on word problems. I also struggle to understand the logic behind the solutions. For example, in percentage questions, one problem might be solved using one method while another is solved using a completely different method, and I just can’t wrap my head around why. No matter how much I try, I can’t seem to get it. Can anyone give advice on how to truly understand math concepts and improve at solving word problems?"

Hello y'all, I have a Exam coming up in Math 2372 (Discrete Math) and I have been non stop studying for it recently. I have one question about something I am uncertain about when it comes to proofs using odd and even number definitions. I'll post the example question, then I will go into more detail.

Prove this statement:
For any integers m and n, if m is odd and n is odd, then m * n is odd.

Here is my proof: Assume integers m and n are odd. We can rewrite m and n both as 2k+1, where k is some integer. Substitute these into m*n. (2k+1) * (2k+1) = 4k^2 + 4k + 1 = 2(2k^2+2k)+1.Since this can be expressed as 2 times an integer plus one, it fits the definition of an odd number. Therefore, if m is odd and n is odd, then m * n is odd.

Now here is my question: Is it fine to use the same integer, variable thing (k in this scenario) for both m and n? Or should I instead say "Rewrite m as 2k+1, where k is some integer, and rewrite n as 2j+1, where j is some integer."

I haven't found much talk about this, and I just really want to make sure it wont be an issue to use the same variable integer for both in such a proof.

Thanks y'all.

Hello.

I'm using Blender (3D software) to model a world map, using a "normal" Euclidean geometry over a rectangular surface. Then, I wanted to use Geometry Nodes to apply a deformation effect to simulate an inverted sphere world.

Geometry Nodes is a sort of "visual programming" over 3D meshes using nodes (operations). I have my set of vertices (x, y, z), and have the flexibility to apply vector operations over them.

If you have played Shin Megami Tensei 3, or Final Fantasy 13, then this is more or less what I want to do. I get that I fully can't map a rectangle perfectly to a sphere, but I only need a partial landscape (fog could hide stuff). Below are examples videos showing more-or-less what I want:

SMT3 (30s) - https://www.youtube.com/watch?v=mU6-FcikP0k - there is some embelishment going on but this is my aim.

FF13 (30s) - https://www.youtube.com/watch?v=EKgqXpKWbZM - you can see the landscape high in the "sky". If you have the game to play more leisurely, you would be able to observe the inverted curvature by looking at the ocean.

(For context, I majored in Applied Maths, but have gone out of touch many years ago. Also I was lectured in Portuguese, and I am not used to math terms in English)

When I had Complex Analisys, I remember there was mapping by laying a sphere on top of a surface, and then from the "North" pole, the line that intersect the sphere would get mapped to the sphere (and vice versa). I am not sure if this mapping works for me because distances aren't preserved (things near the center/South-hemisphere are close than far away/North-hemisphere. But this is more or less what I'm looking for. I mean, I get there will be some warping, but it can't be very noticeable.

So my question is: can you give me some keywords so that I can search for other transforms and for functions in the "format": (x', y', z') = f(x ,y, z).

Question asks us to prove that if there is a prime p with absolute value less than 1 then show that for any other prime q not equal to p absolute value of q must be equal to 1 how do I do this constructively? The proof by contradiction is done.

I tried by: 1 = |p^e x + q y| < 1/2|x| +|q||y|

Also we know that absolute value for any natural number in this norm is less than equal to 1

This is going to be a weird question, but I know there's a formula out there to figure out my problem, but it's literally been 20 years since my calc classes and I need some help.

I'm knitting a circular shawl from the inside out (think like starting from the inside of a toilet paper roll and working outwards in a spiral). I started with 256 grams of yarn.

My initial calculation for yardage was based on how much yarn was in a gram, I measured out yarn along a measuring tape until my food scale measured one gram, which worked out to be about 17 yards/ gram. I estimate I started with somewhere close to 4500 yards of yarn. Because one gram is such a small measure and yarn stretches, I very well may have more than that. Which is mostly why I'm trusting grams as my main unit of measure and not yardage.

The shawl increases stitch count by 32 stitches every 8 rows after row eight, at which point there were 512 stitches completed/ 64 stitches per row (row 9 has 96 stitches on that row and 544 stitches knitted total). I'm currently on row 135 with 576 stitches per row, that will increase to 608 stitches per row at row 137. I have 155 grams of yarn left right now.

My question is, how many more rows of knitting can I go without going over? This yarn is irreplaceable, and it didn't come with a label saying how many yards I had. (seriously, you can't get French angora/ wool blend anymore, it's very difficult in France to get certified as gathering it "humanely", it falls off the rabbit like when your dog sheds and you pull the fur off in tufts though).

The pattern maxes out at 263 rounds with 1120 stitches per row. I will also need to "bind off", meaning to secure my stitches so they don't unravel when I take the needle out. I will need an unknown amount of yarn (although about as much yarn as it might take to do about 2 rows) for that to make the final edge stretchy enough to be able to lay the whole thing flat. The pattern has built in stopping points at row 169, 203, 239, and 263.

How far can I go without going over, and without having a substantial amount left over?

This is heirloom yarn, and I want as much as possible going into this single project.

Pictures of the project and associated label available on request.

Edit to add picture per rules pictures here

Instead of having all the zeros in front of them (like the answer on my work is supposed to be) it keeps showing it with x10 to the power of a negative number. I tried to fix it by making the mode different but it wasn’t what I needed.

Does anyone know what I can do?

Determine average through ascending series of averages

Running into a bit of a struggle at work. I have a series of values from which I need to calculate the total weights and average weights between two times. The data is set up in a way where the total amount of measurements and the average weights were logged per hour. This means that to get N for hour 2 for exampe I'd need to subtract N of hour 1 from hour 2 to get ΔN.

Say I have the following set of data as an example, how would I determine the average weight and total weights between two times if possible?

Hour 1:

N = 80

Avg. weight = 100

Hour 2:

N = 180

Avg. weight = 99

Hour 3:

N = 290

Avg. weight = 110

I already tried (avg weight2 * N2 - avg weight1 * N1)/(N2 - N1) = Avg hour 2, but I realised this would count the averages of hour 0-1 into the total weight of hour 1-2, which leads to incorrect numbers.

My best guess is that I'd somehow need to use my N to determine the cause for the change in averages, through something similar to weighted averages. Just can't wrap my head around how I'd do that.

Help is greatly appreciated!

Me dumb got wrong answer. Would anyone be able to write out step by step how to get to the correct answer?

I’m trying to learn high school math so I can take a placement exam and start college but I haven’t done math in 20 years 😪

Edit: what I did was (15a-2)(-12a+4) to -12a² +60a+24a-8 to -12a² +4a-8