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One of my cats, Shpuntik (Шпунтик), is a fussy eater. Givehim the same dish more than once in an interval of 3 days and hewon't eat it! I...

Question

One of my cats, Shpuntik (Шпунтик), is a fussy eater. Givehim the same dish more than once in an interval of 3 days and hewon't eat it! If I have an assortment of 5 dish types (10 canseach), how many menus can I make for the next 10 days? Assume thatShpuntik is getting one can a day.

One of my cats, Shpuntik (Шпунтик), is a fussy eater. Give him the same dish more than once in an interval of 3 days and he won't eat it! If I have an assortment of 5 dish types (10 cans each), how many menus can I make for the next 10 days? Assume that Shpuntik is getting one can a day.



Answers

Alexis's cat eats 3 cans of cat food every 5 days. Alexis is going away for 30 days. A friend has offered to feed her cat. How many cans of cat food must Alexis leave for her cat while she is away?

So in this province talking about getting a cat over 10 days with an automated future. Eso if we have 10 days and the cat eats half a cup a day, um, twice a day, that means he's gonna eat one cup a day, so he's gonna eat. Uh, here we go. Gonna eat 10 cups in the 10 days he gave us a hint. It said, um, a cup is 14.4 cubic inches s so we can go ahead and say that this is going to be 144 cubic inches of cat food we'll need for those 10 days. That's our That's the answer we're looking for. So the shape of the feeder, we have a cylinder which the volume of a cylinder is pie r squared times h, and we have a cone on the bottom and the volume of a cone or anything with a point on the top will be one third times the base, which is a circle. So we pi r squared times the height of the count. Okay, there's a little bit in the picture. It looks like there's a little bit of the cone on the bottom taking off. But let's just go ahead and assume that the point is at the four inches. Okay, so we just need to plug in our values. Eso the radius of the cylinder and the radius of the cone is 2.5 inches. So we have pi times 2.5 inches, squared times the height of our cylinder. Eso the height of the cylinder was 7.5. Okay, we still have our one third your stuff pie. We're gonna have again 2.5 squared and we're gonna have the four inches for the bottom cone. Okay? Nobody seemed toe. Find out what this is, so if we just plug that into a calculator so we'll have pie times 2.5 squared. And just make sure you're keeping track of You're making sure you're only squaring the 2.5. Don't square the pie to the volume of our cylinder is already gonna be 147. So if that cylinders full, it doesn't matter what the cone is. That 1 47 will feed the cat by itself. Eso We could still calculate this because it's still be useful just for practice. So just to make sure you get the right numbers, it'll be 1 47 and some change. But we were just making sure it could feed the cap. So, um, let's do ah pie developed by three times 2.5 squared. So the count itself will give us around 26 extra eso. If the count was pulled to that would also give us enough to feed the cat. So that's just extra. But just feeling the cylinder on top with the 1 47 cubic inches, that would be plenty to feed the cap for the 10 days. Okay, thank you very much.

One bag of cat food feeds your cat for 25 days. How many bags of cat food do you need for 365 days? So this is a division problem. I'm gonna set it up like a long division problem. So I have 300 and 65 divided by 25 and then start my long division process. Um, 25 cannot go into three, but it can go into 36 1 time. Subtract, I get 1 15 So I know that 25 times four is 100 so I have a remainder of 15. So what does that mean? About 14. 15? Well, what that means is that 14 times 25. So this is how many bags and this is how many days it'll last. If I'm also play this, then 14 bags will Onley last me 350 days. But my question is not asking that it's asking me how many I would need for 365 days. So this remainder is telling me that I'm 15 days short of 365 so I can buy 1/2 a bag. Can't buy 1/4 of a bag. I can only buy an extra bag, so I need to buy 15 bags of cat food toe last meat a year. Because, yes, that will go over. If I do that math, I am gonna go, like, 10 days over. But that's how many bags I'm gonna need to last me 365 days or for a year. So your answer should be 15 bags of cat food.

We have a total of 17 dinners on the menu, and a husband and wife shall abbreviated as H and W each have to choose a meal. So we're going to be choosing a total of two meals, one for the husband and one for the wife. How many different ways can this be done? Well, in this case, it's not just going to be a normal combination that is in a combination. The order does not matter, but here the order does matter. That is, if the husband gets spaghetti and the wife gets a sandwich that's completely different from the husband getting a sandwich and the wife getting spaghetti. So the order is going to matter in this case, making this a permutation. It's very important to remember that in permutations, order does matter, whereas in combinations it does not. So with that established, let's set up our permutation. That is because of the permutation of 17 total meals. Commute two. That is two different choices in order. One for the husband, one for the wife and if you solve this well, we can solve it a little bit by hand with the formula from the book, which will make this equal to 17 factorial over 17 minus two. Factorial this formula. Just come straight out of the book, substituting n and R for 17 and two, respectively. Now we can simplify a little bit, that is 17. Factorial is 17 times 16 times, well, 15 all the way through zero or 15 factorial. This is divided by 17 minutes to is 15 so 15 factory and these 15 factorial is will cancel, leaving us with just 17 times 16 which is equal to 272. There's 272 different ways for this husband and wife to get their meals.

Okay, so basically, here you have a 60 mil liter container of medicine, and the cat has to take two doses a day, and each dose is one mil leader. So we could just say in one day one day they're using up to male leaders. Well, to figure out how many days it would take, you just divide 60 divided by the two, and you get 30 days. Well, it turns out if you start September 1st for the first day in the on September 30th that would be your last day of giving her the medicine. You be out by them. So it would take 30 days, and that they would be, Ah, September 30th. Then it ask us about, um when you have to call if you have to call two days before and you need you need the medicine on October 1st. If he called two days before October 1st, that would be September 29. I would say you have to call in the morning in the A. M. Um, that be the latest you could call it. That would be that if they count that day plus September 30th they count that day that would be two days. Um, just on practical. I would I would think it be better to call. Sept 28. I think the actual answer would be you have to call by September 29 if they count that as a day. And then it had the second day, September 30th so that by the first you would have your medicine.


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