repost cuz need explanations | Mathematics | Page 1

calm trout Jun 5, 2023, 5:47 AM

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grave totem Jun 5, 2023, 5:51 AM

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calm trout

I'm pretty sure for the first one, you can just multiple the proabbilities

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so find the probability of both 20 c coins landing heads

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which you can also find by multiplication

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the probability of landing heads assuming it's fair coin is 50%

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so it's 1/2

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since you do this twice, that's 1/2 * 1/2

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which is 1/4

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now for landing at least one 10 c coins

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you could either create a sample space or use the binomial distrbution equation or whatever it's called

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something like this

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and checking which ones have at least one head

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which is 7/8

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and now thinking about it

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you don't really need a sample space for this

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the only case where "at least one of the heads landing" tails is not true

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is when when land all tails

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which only happens once in a sample space like this

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and in general the number of outcomes in this case will be 2^n (since each time you flip a coin, two more possibilities can happen for each possibility)

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so the first flip is only 2 outcomes

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the second flip, there is 2 more outcomes, that will branch off of those two initial outcomes

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so 2 will branch off of the first outcome

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2 will branch off of the second outcome

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hence we now have 4

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and so on

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so it's just multiplying by 2 each flip

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so the general equation could be written as ```
1/(2^n - 1)

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anyways the probability is 7/8 for at least landing a head on one of the three 10 c flips)

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the probability of both happening is just the product of the two probabilities

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this is assuming the two events are independent

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which you can probably assume in this case since there isn't much reason to believe the events aren't dependent considering it's coin flips

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so 1/4 * 7/8

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7 / 32

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for the second one you can kind of imagine a right triangle

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and the reason we want to set this up

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is because we want to find that base length

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because the lid is slightly bigger than the bottom of the bucket

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you can think of the lid as being equal to the base

calm trout Jun 5, 2023, 6:03 AM

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mhm

grave totem Jun 5, 2023, 6:03 AM

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plus some value on the left and right side

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which are presumably equal

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so let's say that the "red" line is equal to "x"

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using the pythagorean theorem we can set up

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$$x^2 + 30^2 = 31^2$$

limber topazBOT Jun 5, 2023, 6:04 AM

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MoistBrain

grave totem Jun 5, 2023, 6:04 AM

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and from here solving for x will give you

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$$x = \sqrt{31^2 - 30^2}$$

limber topazBOT Jun 5, 2023, 6:05 AM

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MoistBrain

grave totem Jun 5, 2023, 6:05 AM

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and we can think of the lid as 18 + x + x

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since it's a bit bigger than the base by "x" amount

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on the left and right side

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which is why we add it twice

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so that'll give you

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$$18 + 2\sqrt{31^2 - 30^2}$$

limber topazBOT Jun 5, 2023, 6:06 AM

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MoistBrain

grave totem Jun 5, 2023, 6:06 AM

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from here you want to factor out 2

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$$2(\sqrt{31^2 - 30^2} + 9$$

limber topazBOT Jun 5, 2023, 6:06 AM

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MoistBrain

calm trout Jun 5, 2023, 6:10 AM

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3rd one?

grave totem Jun 5, 2023, 6:11 AM

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calm trout 3rd one?

you add the vectors up

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you can do that by putting the tail of one vector on the head of the other

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and seeing where it ends up

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so you can like move the tail of vector "c" to the head of vector "p"

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just kind of do it more accurately than this lol

calm trout Jun 5, 2023, 6:13 AM

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i dont understand lmao

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tf

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is

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going

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on

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what do you think

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the answer si?

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is?

grave totem Jun 5, 2023, 6:14 AM

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honestly not sure

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either "k" or "l" kind of hard to tell

#repost cuz need explanations