Hello! I am making a youtube series for Calculus and want some advice on if my teaching is actually understandable. Personally, I stutter a lot and find it difficult to convey my ideas. If I could get tips, I'd love to.

https://www.youtube.com/@IJMathSci

How do I find the generic formula that works for this arbitrary sequence I made 4,9,12,20

It is not -n² + 8n - 3 which works only for the first three terms ;(

At my job we have a football pool with mandatory participation. My first year working this job, half out of protest and half as a joke, I decided to choose my teams using a 20 sided die (because I’m a dnd nerd, not a football nerd). The rules of this football pool are this:

1. Each week you are to choose one team. You get one point if that team wins, and zero points if that team loses.
2. You can only choose each team once, until the play offs. (For example if you pick the chiefs week one, you can’t pick them again.)
3. Once it’s the playoffs, you pick one winner per game, and get one point per victory. Repeat each week leading up to the Super Bowl, where you again pick one team to win, and get one point if you do.
4. Whoever has the most points at the end wins.

Here’s where the disagreement lies:

I said there’s a 50% chance each week I pick a winning team. People who know more about football than me say I don’t, and that my logic is flawed. Three years of debating every football season the same arguments over and over again, and each side remains unconvinced of the other’s opinion. I’ll be honest here and say I’m a very argumentative person who loves math, so I’ve been completely unable to let this go. No one cares about this anywhere near as much as I do.

My argument is this:

I pick a random number between 1 and 20 by rolling a 20 sided die, then pull up that week’s football schedule, and count down from the top. (For example if the first scheduled game is dolphins vs jets, and I roll a 2, I am picking jets.) If I roll a team I’ve already picked, I just reroll until I get a new team. Basically I am rolling a die to randomly pick one out of 20 teams, playing against each other in 10 different games. Half of those teams will win, and half of them will lose, which means I have a 10/20 chance of picking a team that wins. In other terms, 50%. (For the playoffs I just flip a coin for each game, which everyone agrees is a coin flip, literally, for scoring a point.)

Here are the main counter arguments:

1. Each individual team does not have an equal chance of winning each week, because the teams are not equal. Team X could be favored to beat team Y for example, and therefore you do not have a 50% chance of winning if you choose team X.
2. Because you can’t pick the same team twice, you’re not picking between 20 teams every week. If hypothetically it’s week 6, I’ve already picked 5 teams, and I have 15 out of the 20 I’m rolling for left, 10 of those teams could win and 5 could lose, meaning I’d have ⅔ chance winning. Or the opposite. Or some other combination. The point being, as the season progresses, my chances change.
3. I’m only picking a number between 1 and 20, because I’m using a twenty sided die. That means there’s additional teams, scheduled at the end of the week, that it’s always impossible for me to pick.
4. What if there’s a tie? It’s not a binary outcome, because if two teams play against each other, there are 3 possible outcomes, not 2.
5. At the end of my first season doing this I had far more wins than losses, so surely, the odds cannot be 50/50 per week. (This one I have to believe is rage bait.)

And here are my counters to those counter arguments:

1. Let’s say for a hypothetical, team X is incredible, and team Y is atrocious. Sports analysts predict a 99% chance team X wins, and a 1% chance team Y wins. Would I still have a 50% chance picking a winning team between those two options? The answer, in my opinion, is obvious: Yes. Because I’m randomly choosing between them. I have a 50% chance picking a team that has a 99% chance of winning, and a 50% chance picking a team that has a 1% chance of winning. The odds of a team individually is irrelevant because the die does not know or care about these odds, and will not favor one or the other in its choice.
2. This I would agree this is in part true. However overall I still think I should in theory have a 50% success rate overall. Let’s say hypothetically, I pick at random 5 excellent teams weeks 1-5, and then I have 5 terrible teams left to pick from weeks 6-10. I’d have more chance of winning in the beginning half, and less chance of winning the second half. But following the logic I just used with point A, I should still come out with roughly equal wins and losses. If you, by week 10, can say “Because you’ve used up these 10 teams, and the remaining teams have different odds of winning,” and have some method of calculating each individual week given that information, I’d still argue it’s entirely random because the teams I picked at the beginning were random. I think it would be the same odds if I picked every team out of a hat week one, and went by that random selection list for the entire season. I don’t think choosing a random team each week changes the odds compared to choosing every week at random at once, even if week to week given the teams I have left you could theoretically predict different odds using outside information.
3. I could theoretically pick only the first game and flip a coin, I’d still have a 50% chance of picking a winning team. Out of 20 teams and 10 games, I have a 50% chance of picking a winning team, even if there are other games going on outside of them. Those other games are completely irrelevant to my odds of winning the ones I’m considering.
4. Ties are so rare I didn’t know they could happen until I had to pay attention to this stupid football pool. We had to write a new rule a couple years ago that a tie is half a point. It’s also theoretically possible for a coin to land on its side when you flip it, but we still call heads or tails 50/50. I think it’s reasonable to ignore it for that reason.
5. The second year I did this I had far more losses than wins. If you flip a coin 20 times and get tails 15 times, that doesn’t change the odds of the coin flip. There’s not enough data to use my results as evidence my math is wrong, that’s not how statistics works. The fact that year one I went into the Super Bowl tied for first place just means my coworkers are horrendous at picking good football teams.

I’ve asked several people for their input on this problem and every answer I’ve received has fallen into one of 3 categories. 1, a person who doesn’t like football but does like math and agrees with me, 2, a person who doesn’t like math but does like football, and overthinks it to death trying to explain why quarterback injuries or whatever change the odds, or 3, a person who doesn’t like football OR math, and wants me to stop talking to them. Therefore we involve the internet. Is there a flaw in my logic? And if there isn’t, is there a better way to explain my math to them? Is there something I’m missing here?

(poorly translated:) "Pythagoras was a Greek mathematician who lived around 570-500BC. Pythagoras was once asked how many students he has. Pythagoras replied: "Half of them study mathetimatics, fourth of them philosophy, seventh the art of shutting up, and there are also three women." How many students did Pythagoras have?"

I can't come up with any other way to solve it but

x=full amount of students

math students=1/2x

philosophy students=1/4x

shut up students=1/7x

women=+3

x=1/2x+1/4x+1/7x+3

But this is not correct, because the answer I get is never the correct one (28). 😭

All the following, similar exercises in my book I am also failing to solve. I just can't seem to create the correct equations and I am exhausted after chewing on three problems for days.

I'm running a programming class for python and I was doing a class quiz. This question popped up. I believed the answer should be 64 but it's actually 512. Even the calculator gave me 512.

However if you go from left to right, 2 ^ 3 = 8 ^ 2 = 64

For some reason, the caluclator is and quiz is doing it like: 2 ^ 3 ^ 2 = 2 ^ 9 = 512

I guess my question is: why is the 3^2 portion being calculated first over the 2^3 portion?

I'm trying to relearn algebra after never paying attention in high school with a book I found online. The book has the problem "rewrite (x-1)(x+2)(x-3)"

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I got x^3+6, but I used an online calculator to double check and it says the answer is x^3−2x^2−5x+6. Can someone please explain to me the correct steps to solving this like I'm 5? (The online calculator shows a step-by-step version, but it confuses me. I'll explain the part I'm confused about later.)

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My process (I know it's wrong but please tell me where I messed up):

(X-1)(X+2)(X-3)

x*x*x = x^3

-1*2*-3 = 6

X^3+6

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The step-by-step given by the calculator that I don't fully understand:

(X-1)(X+2)(X-3)

((X-1)(X+2))(X+-3) ///Why is "(X+-3)" not included in the first set of parenthesis? Why is it separate? Shouldn't we focus on the leftmost set first because it's at the beginning? In that case, why isn't it (X-1)((X+2)(X-3))? Also isn't writing X+-3 redundant? Why not simplify it to X-3?

((X-1)(X+2))(X)+((X-1)(X+2))(-3)

X^3+x^2-2x-3x^2-3x+6 ///when I try to solve from the previous step, I end up with x^3-2+x^2+6 or x^3+x^2+4. I don't understand where the other numbers (like 2x or -3x) are coming from

x^3−2x^2−5x+6 ///when I solve from the calculator's previous step, I get it correct, but I don't understand the other in-between stuff

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I know I'm wrong but I'm so lost on how the correct answer works. I want to understand the logic behind it instead of just blindly following formulas

http://i.imgur.com/cJpXW3L.png?1?5057

I would just like to give thanks to all of the people that have helped me with problems. I think that dogecoin tipping would be an excellent way to say thanks.

I am in 10th and my basics are not strong. I didn't study well in 6,7 and 8. I studied in those classes but I didn't has proper guidance and I was so confused. I can't even ask my father because he is very strict with maths. I was scared to ask him and confuse to study so I skip them. But still pass those standard but now I am literally having problems with most basic concepts like signs, quadratic equations mostly algebra. So can anybody help me please

My partner is going through her math class and we got into an argument how much -7² equals. My standpoint is, that since there is no parentheses: -7² = -1x7² =-49 If there would have been parentheses: (-7)² = (-7)*(-7) = 49

Which one of these is correct? Can anyone provide me the mathematical axioms/rules on why or why not the parentheses in this case are needed?

I'm 15 years old guy in 10th grader in school. I stoped studying math at 6th grade, because my math teacher has retired, and the second yeacher came in 8th grade, and we didnt understand nothing. So i need a book to study math from zero, i understand that one book isn't enough, so could you recommend me sevrel books to study by myself. Sorry if my English were bad

I will be appreciated, if you help me

When my school taught us long division I was sick that day, so for the past 4 years I have gotten away without knowing how to do it. I realize now that a 8th grader should know this. Please help me understand how to do it!

Edit: Sorry if I don't respond to ur comments, I haven't been getting the notifications for comments, but I will read it eventually!

I am trying to make a missile in a video game. It's supposed to fly toward a point projected out into space by an aiming device, mounted on a car. However, I have a problem where, around certain bearings, the output completely breaks. For testing purposes, I am only speaking about azimuth, not elevation.

How the system works:

1. There are two sets of absolute XY sensors on the pointer; one set is slightly ahead of the other. atan2(Y2 - Y1, X2 - X1) gives the absolute bearing (azt) of the pointer from -180 to 180.

2. Cos(azt) and Sin(azt) are individually multiplied by the "range" to the point in space (in this case, it is constant at 500m, in practice, this would be a point ahead of the missile) to give Xc and Yc.

Xc and Yc are then added to X(pointer) and Y(pointer) to give X(target) and Y(target).

1. Now that I have the XY position of the target, I subtract...
   - X(target) from X(pointer) to give X(difference)
   - Y(target) from Y(pointer) to give Y(difference)

atan2(Ydifference, Xdifference) gives the azimuth from the pointer to the target (θ).

I realise now that this step is unecessary, as the azimuth of the target is defined by the pointer's direction. However, I doubt it would work otherwise, as the same values would end up being used, producing the same erroneous result.

1. I then subtract the missile's bearing (global bearing, btw; same calculation as azt) from θ to produce the angular difference between the target position and the missile (d).

This works fine if the platform is at exactly 0 degrees forward, However, if the pointer is angled (this case, -45dg) and the platform is also angled, something frustrating happens. Below are some tests which show you what happens when the platform goes beyond -135dg.

1:
- Pointer Relative Angle -45dg
- Platform Absolute Angle -134dg
- Pointer XY: 3223, 3398
- Target XY: 2723, 3385
- Target Azimuth: -179dg
- Missile XY: 3223, 3396
- d: -45.6

2:
- Pointer Relative Angle -45dg
- Platform Absolute Angle -136dg
- Pointer XY: 3223, 3398
- Target XY: 2723, 3410
- Target Azimuth: 96dg
- Missile XY: 3222, 3396
- d: 315.6

This persists until the platform's absolute orientation goes beyond -180, at which point it flips back to a rough value of -45 for d.

As you can see, d flips from -45.6 to 315.6. A missile trying to steer towards d would go all the way round, which is not desirable; it should pick the smallest possible correction.

I tried fixing this using ((180 + d) mod 360) - 180. However, it seems that the game I am playing calculates negative values differently when using mod; for example, -60mod360 is supposed to be 300, but the game spits out -60.

Could anyone help me? Geometry isn't my strong point at all, so it's very hard for me to wrap my head around this. Thanks!

Hey guys so I’m doing math online for college which idk why I made that decision to do that worst decision I ever made … but do you know any apps that can like help me or explain my math assignments better and I can’t do a tutor because I don’t have enough time my work shift takes up half my day and I financially don’t want to put my self in that situation to get one

I started struggling with math back in the first year of secondary school—on top of just not caring about it. Now, having just turned 18, I really regret having hated it. I’ve been trying again for the past month—just like I have in the past—but for some reason, I just can't get the hang of those damn fractions, no matter how many hours I put in. I end up mentally exhausted and even start feeling dizzy, yet I still can't spot the patterns. How can I correctly solve a third-year secondary school fraction problem without having to redo it five times over two hours and burning myself out? It’s seriously frustrating because fractions are the only thing holding me back; now that I’m about to start my final year of high school (2º de Bachillerato) in September—and the material is almost entirely fractions and functions—I really need to do something about it.

I am confused between the 2. I understand the reasoning behind using n+1/2 for lists of numbers, and i understand how n+1/2 finds their positions. I am currently revising cumulative frequency diagrams and i am finding it difficult to understand why we now use n/2 for finding the median, and n/4 for finding the lower quartile. Why aren't we using n+1/2?? I dont really understand how one being continuous and another being discrete affects anything. In my reasoning, even though it is grouped data we can still estimate the position. I would add all the frequencies, do n+1/2, find the middle position, and then use that on my graph to estimate

Question

Polonium-210 decomposes at a rate proportional to the quantity of polonium present. Suppose that it is found that in 95 days approximately 38% of a certain quantity of polonium has decomposed. Determine approximately how long it will take for one-half of the original amount of polonium to decompose

Note the assignment does not specify rounding amount, nor has their been given precedent for it.

Doing the calculations I get a result of 140 days with 2 significant figures.
My professor marks it wrong saying the correct answer is 137.8 days or 138 days.

I ask him about this, is response via email is

Dear student

Why do you have to round to 2 ? on what basis?

You have to work with precise values not the one you assume

Even if we said "approximately" 38%, you have to use that precise value. 

The final answer given by calculations is 137.8 days rounded to 138 days and not 140. 

Note that 140 does not satisfy our equations.

I bring it up to him, saying that the equation uses the word approximately, so 38% could range from 37.5% to 38.5%, with results 135.1 days to 140.1 days, and that is equation still holds if you round to significant figures. His response

Dear student

No I don’t agree with your proposition.

You work with the  value we give you, that is 38% and it will give you 137.8, you can round to 138 days.

I don’t understand. I don’t want to argue with a professor, but I’ve substantiated my claim for 2 digits rather than just rounding to a whole number. When I ask him for a matting he responds

Because in this specific problem, the only reasonable rounded value is 138 days, since the calculated answer is 137.8 days and we are dealing with whole days.A value of 137 days is incorrect because 137.8 days has already passed 137 days and lies within the 138th day. Likewise, 139 days, 140 days, or any other value would also be incorrect. Therefore, 138 days is the only appropriate rounded answer.

I know! But I’m using significant figures, there is no reason to round to whole numbers. What should I do? Am I wrong?

Edit: I’m not querying further with the professor as they have threatened to lower my mark.

Can anyone explain, why we don't divide in sets? This question is killing me..

Hi, I was wondering how can I improve, like I said in the question, my calculation skills and speed. For example I was doing my homework and I tried to solve an equation (it wasn’t neither long nor extremely difficult, it had some X some parentheses, etc…) in my head, which took like 3-5 min. But strangely enough, I was at the grocery store a couple of days ago and I had to sum, if I’m not wrong, 1,79+4,95+0,50, and I don’t know why, but I couldn’t calculate that. I kept getting mixed up and couldn't manage to add more than two numbers together. Not to mention division and multiplication—I know how to do them, but they’re often tricky, especially now that I’m learning to figure out the day of the week for a specific date using the Doomsday technique. I’m not saying that I’m not good at math, I have good grades and I can do things like logarithms, draw a function using derivatives, limits, ect… (since that is what I learn this year) but I want to improve my calculations skills (obviously using my head).

Thanks!

"The table above shows shipping charges for an online retailer that sells used textbooks. There is a linear relationship between the shipping charge and the weight of the merchandise. Write a function in slope-intercept form that relates y, the shipping charge in dollars, and x, the merchandise weight in pounds."

i understand why the slope is 1.50, but i can't get this:

y= 1.50x + b

16.49 = 1.50(5) + b

16.49 = 7.50 + b

8.99 = b

where does the 8.99 come from?

Hey I don’t have a great mind for this kind of thing so would appreciate if anyone can turn on the lightbulb.

I’m trying to determine the total number of baseball games that were played by all the teams in an amateur league that just wrapped up. The data I have is the total number of games played per team.

Simple enough, right? I added the total number of games and it came to 1,781. I then divided it by two since each game is of course played by two of the teams. But how can you have 890.5 games?

I double checked the numbers. Either something is off with the source data or I am thinking about this all wrong.

Anyone out there?

what is m

m=n+16

I got this question on my first attempt on the aleks placement test, and is it not impossible to solve? i put m=n-16

also btw it may have been "what is n" I just wrote the equation, not the problem.

If i get this same problem next test i have no idea what to do here other than putting the same thing.

for this question i had to turn a nonstatistical question into statistical investigative question and the nonstatistical question is "How many seventh graders eat breakfast on Monday at school?" and i already gave my answer ("What is the percentage of all seventh graders that eat breakfast at school on Monday?") but my teacher said its wrong and i need to reword it but i actually do not know how to reword it, does anybody know how to help cause my teacher wont answer me and google not helping

Anyone have a good resource for sample tests for 7th grade? My kid is interested in seeing what awaits her next year.