We're playing a game. I flip a coin. If it lands on Tails, I flip it again. If it lands on Heads, the game ends.

You win if the game ends on an even turn, and lose otherwise.

Define the following events:

A: You win the game

B: The game goes on for at least 4 turns

C: The game goes on for at least 5 turns

What are P(A), P(B), and P\(C)? Are A and B independent? How about A and C?

Consider the function defined by y = x\^(sin(x)\sin(x)). Observe its graph. Find an increasing function which passes through each of its local maximums, and another increasing function which passes through each of its local minimums.

Extra credit: You'll notice the graph isn't drawn for x-values which make sin(x) negative. This is because most of those values make the function undefined - though it is defined for infinitely many points in those intervals, it just also has infinitely many holes. Since it lacks continuity here, it has no true local maxes or local mins, and doesn't impact the original problem. We can nonetheless cheat and fill in the holes by expanding the function to these regions with y = x\^|sin(x)|\sin(x) (Using x\^-|sin(x)|\sin(x) should also be technically valid, but is being ignored because it's discontinuous with the rest of the graph and not as pretty, but will be mentioned in my solution). Doing so adds more local maxes and local mins. The new local mins should line up with your function that finds the local maxes for the original function - but, find a new function which hits all of the new local maxes.

(x/5)\^log_b(5) - (x/6)\^log_b(6) = 0

Index of my unnamed series of posted problems

|Date|Post |---|---| |2024-05-07 | Find a+b |2024-05-09 | What is the area of the shaded region? |2024-05-15 | Solve for x |2024-05-17 | Bounding a function |2024-05-22 | Coin-flipping game

An 8x5 rectangle. If the bottom left corner is considered (0, 0), then two lines are drawn within the rectangle, from (0, 4) to (8, 1) and from (1, 5) to (7, 0). The smaller two regions of the four these lines cut the rectangle into are shaded. What is their combined area?

!

The image is of a large unit square with five smaller disjoint shaded squares contained entirely within it. The five smaller squares are congruent. Four of them are at each corner of the large square. The fifth is in the center, rotated diagonally, so the center of each of its sides is touched by the vertex from one of the other four squares. You are given that the common length for the five smaller congruent squares is (a-sqrt(2)) / b, where a and b are positive integers. What is the value of a + b?

I read this article and still walked away feeling like I didn't understand the situation that well.

Is it $56 billion that he's already been paid, and he needs to return it? $56 billion he's partially been paid, and he can keep what he has, but won't get the rest? Something more complicated?

Sharing an Anki deck I made for learning the US presidents. I've always been mediocre at best when it came to remembering them, but in about a week with this deck I can now list them all, in order, including their years in office.

Card fronts will display either their order, name, or their years in office. Card backs will display all of that, in addition to their official white house portrait, political party, vice president(s), and the president who preceded and succeeded them. Also includes a note for presidents who died in office, detailing how they died. When using the deck I study it by attempting to remember both of the missing pieces of information from the front of the card. I put a fair amount of effort into trying to get the cards to look nice as well, and in particular trying to get elements of the card to stay in place when swapping between front and back - I don't like when things jump around.

I might share other decks in the future. I have decks I made for US/Canadian/Australian state/province/territory locations and capitals, but for all three of those I used maps from decks other people made, so I'm not sure on the etiquette of sharing something like that. I did make a chemical element deck from scratch that I'm pretty proud of and will probably share at some point, though - I'm just not sure if I'm done tinkering with it yet.

I'm pretty new to Anki but have enjoyed learning how to create nice decks. If you download this and find any sort of issues or bugs, please let me know.

Note that I'm using autohotkey v2, not v1.

I want to run two different autohotkey scripts. I want to trigger a hotstring in the first script, the output of which ends up being part of the hotstring trigger for the second script. Is this possible?

Here's a simplified version of my intended workflow.

Script 1: #Hotstring EndChars \ #Hotstring o #Hotstring ? ::iv::ǐ ::av::ǎ

Script 2: #Hotstring EndChars \ #Hotstring o #Hotstring ? ::nǐ::你 ::hǎo::好

So the idea is that I can type niv\ and the first script will convert it to nǐ - then I can immediately type \ and the second script will convert it to 你. So I type niv\\\ and my text goes from niv to nǐ to 你. I can then type hav\o\ and have my text go: h, ha, hav, hǎ, hǎo, 好. So I can do niv\ hav\o and get nǐ hǎo, or I can do niv\\\ hav\o\ and get 你 好. Both writing systems in a reasonably simple format.

There are reasons I want to set it up like this. The first script has dozens of functions beyond writing in pinyin/chinese, and I share it with another person - so I don't want to add potentially hundreds of random Chinese hotstrings to it, just the special pinyin characters. That's why I'm using two scripts.

But I also realize I could just make "niv" and "havo" their own hotstrings which go directly to 你 and 好 without the intermediate nǐ and hǎo. I don't want to do this mostly because I think the system I have in mind is prettier - type it correctly in pinyin first, then have it correctly convert to Chinese.

All of that aside: I've gathered that this is probably possible using some combination of SendLevel and #InputLevel - but I've tried a bunch of different combinations and ideas with it, and haven't successfully had one script trigger another yet. Even in simplified toy scripts, which is a little discouraging. Ideally I'd be able to do this with as few changes to the main script I share with another person as possible - the script that handles the Chinese can be as complicated as it needs to be though. Anyone know how to make this work?

Imgur album: https://imgur.com/a/ikTA97e

Those photos were taken under extreme magnification and bright light - the actual size is about the size of an uncooked grain of rice. Maybe smaller. This one was killed by freezing to preserve its form.

In the last few days I've started to see a lot of these - I can find one crawling across my desk every 5 or 10 minutes if I remember to look (Though I can't find where they're coming from at all). They don't move all that fast - they're frankly pretty easy to capture or squash.

In person I don't think they look very much like ants but in the closeup I think they kind of do. Also hoping they aren't termites.

Thanks for any help.

Edit: Here's a video of one scurrying across my desk too: https://imgur.com/a/ZC15gNZ

For example - if a popular TV show is about to have its season or series finale, or a sport league is about to have its championship game. Are there any websites that track these, without all the noise of less important shows or games, to keep track of?

ESPN.com does seem to track upcoming sporting events pretty well, but it's not that easy to tell which upcoming games are "big" for the league in question or not.

It seems like every shower has its own unique way of controlling water temperature and pressure. Of all the showers I've ever used, no two of which have ever been alike, I like my controls the least. Plus the faucet has started dripping lately.

Is this likely to be something I can replace on my own, without a plumber? To me, that means: Can I likely do this without damaging the wall, without having to mess with pipes, and without needing to do anything involving words like "hacksaw", "weld", or "plumbing torch"?

Basically I believe in my ability to buy a faucet and control thingie from Home Depot; to use screwdrivers, allen wrenches, pliers, and regular wrenches; to use things like plumbing tape, lubricants, and caulk; and to remember to turn the water off to the house.

Would a project like this likely require anything more complex than that? I tend to prefer shower controls that have separate knobs for hot and cold, but I figure going from a one-knob setup to a two-knob setup is definitely going to require reconfiguring the plumbing. Should sticking with a one-knob solution be okay?

I don't know if it matters but I live in Florida in the US, and this place was built in the 1980s. I doubt this matters, but my current controls work by turning the larger knob left or right for temperature, and the smaller knob for pressure.

My place does have some annoyances - like the front door is an uncommon size that's difficult to find replacements for at places like Home Depot. Is there any chance of me running into issues like that when it comes to things like the size of the pipe openings?

Thanks for any insight.

Edit: Thanks for all the replies. It's pretty clear now that this is something that could very easily end up a lot more involved and time consuming and property damaging than I'm comfortable with.

I'm mostly thinking about insurance here. I've been told conflicting information. I live in Florida.

I live with someone who has a driver's license and a car, but I don't have either. I've avoided getting one because I have no interest in car ownership, and I feel like if I started driving regularly I'd probably die - I have driven before but I really don't think it's something I'd ever get good at.

It's undeniable that having one would be convenient though - for rare occasions like emergencies at a minimum but also other scenarios.

I know almost nothing about how this stuff works. If I get a license, am I required to acquire and pay for insurance, even if I don't own a car or regularly drive? Or will the person I live with have to pay more for their insurance? Are there any other costs or downsides associated with it that I might not be thinking of?

Thanks.

What kind of cat is this? It was taken behind a Chinese food restaurant in southwest Florida.

The person who took the picture said it's a Bobcat, but other people who've seen it have said it doesn't really look like one, and is probably something non-native. Anyone know for certain?

Hollow Knight is an incredibly competent game on pretty much all fronts. In my opinion, Hollow Knight is a masterpiece and we will discuss all the things that make it so great in detail in this Hollow Knight retrospective. However - the one thing that I find most fascinating about Hollow Knight is an aspect of the game that is seldom discussed. The most fascinating aspect of Hollow Knight is that it exists in the first place - because to put it mildly - Hollow Knight’s existence should not be possible. Hollow Knight was developed by only three people, in roughly three years. Three people managed to produce a game that looks this beautiful, features a combat system with a skill ceiling this high, crafted a beautiful world this big, wrote lore that deep, and crafted gameplay this fluid. Three people did a job that puts most teams of 60 people that work for half a decade on a game to shame. How did three pull this off?

In this Hollow Knight retrospective, we are going to investigate this question. We are going to find out how it is possible that Hollow Knight even exists!

In late July, a couple of startling papers appeared on the arXiv, a repository of pre-peer-review manuscripts on topics in physics and astronomy. The papers claim to describe the synthesis of a material that is not only able to superconduct above room temperature, but also above the boiling point of water. And it does so at normal atmospheric pressures.

Instead of having to build upon years of work with exotic materials that only work under extreme conditions, the papers seem to describe a material that could be made via some relatively straightforward chemistry and would work if you set it on your desk. It was like finding a shortcut to a material that would revolutionize society.

The perfect time to write an article on those results would be when they've been confirmed by multiple labs. But these are not perfect times. Instead, rumors seem to be flying daily about possible confirmation, confusing and contradictory results, and informed discussions of why this material either should or shouldn't work.

In this article, we'll explain where things stand and why getting to a place of clarity will be challenging, even if these claims are right.

I just reached 112 myself.

I'm very much awaiting a time when users can block specific instances. I still don't want to check the option to hide NSFW content, because I do want to see NSFW content that may show up on non-porn communities. Just not really interested in seeing so much porn in All.

You can check on your settings page, btw, in the Blocks tab - count quickly with Ctrl+F.

About two weeks ago I believe there was some sort of update that let posts that are just youtube links open in-line on the lemmy feed as embeds, by clicking the post thumbnail. This was pretty great.

It seems to be back to the old behavior now, where you can't do that anymore. Why? What happened?

I've had this cactus for a few years, and for a while it's had a problem where it grows so tall that it can't stand up. You can see in the photo that I have it tied to some stakes to keep it upright - if not for those it would literally uproot itself in under a day.

Why might this be? I don't know all that much about houseplants. I water this cactus (and my other cactuses, which are not the same species) once every two weeks, about 1 to 1.5 cups of water. I use some cactus fertilizer like twice a year, pretty inconsistently. It lives perpetually indoors with those three light rods visible in the picture as its sole light source (On for 12 hours a day).

Given how little I know about proper plant care, I'm sure none of that is ideal - but is any of it the obvious culprit for why this happens? What should I be doing better?

Thanks for any help.

P.S. Those two nodules just above the lower string are brand new, and it's never branched out like that before - what should I expect them to become? Round bulbs? Branches? Flowers? Nothing at all? The tip top of the cactus being white is also very recent.