Member: Rom

Quote:
We have 19 smarties in a bag left. 6 spills on the floor. What are the chances of 4 out of that 6 being blue, if there were 2 red 6 blue 5 brown 3 yellow and 3 green in the bag?

let p = Pr[smartie in the bag is blue] = 6/19

then the number of blue smarties out of the 6 spilled is a binomial random variable

Pr[k blue smarties out of 6 spilled] = Choose(6,k) p ^k(1-p) ^(6-k)

Choose(n,k) is "n choose k", or n!((n-k)!k!)

Pr[0, 1, ... 6] = (0.102598, 0.284117, 0.327828, 0.20174, 0.0698331, 0.0128923, 0.000991713)

Pr[4 of 6 spilled were blue] = 0.0698331

RomApr 12, 2014

+6251

Quote:
The problem is: (3t + 4)^5
Instead of simply expanding, my instructor wants me to use Pascal's Triangle.

Neat question.

(a+b) ⁿ can be written as

Sum[k={0,n} Choose(n,k) a ^kb ^n-k]

i.e. Choose(n,0) b ⁿ+Choose(n,1) a b ^n-1 + ... Choose(n,n-1) a ^n-1b + Choose(n,n) a ⁿ

Now you're probably thinking ok wth is "Choose"?

This is the binomial coefficient, "n choose k" and they are the values of a given row in Pascal's triangle. Come down n rows and go over k elements in the triangle and you get the Binomial coefficient corresponding to "n choose k" = Choose(n,k) = Binomial(n,k) (different names for the same thing).

So in this case if you look at the n=5 row (really the 6th row, the first row is n=0) of Pascal's triangle you see it's

1 5 10 10 5 1

in other words

Choose(5,0)=Choose(5,5) = 1
Choose(5,1)=Choose(5,4) = 5
Choose(5,2)=Choose(5,3) = 10

so (a+b) ⁵ = 1*a ⁵ + 5 a ⁴ b + 10 a ³ b ² + 10 a ² b ³ + 5 a b ⁴ + 1 b ⁵

now let a=3t and b=4 and substitute those into the formula above and simplify things and you're done

RomApr 8, 2014

+6251

25% off means that the shoes are priced at (1 - 25%)=75% of their original price.

75% = 0.75

So if the original price was P0 the sale price is

P = 0.75 P0

RomApr 4, 2014

+6251

one sneaky trick you can use is to go over to the other forum and do your latex there, MHF has a very nice rendering engine now, and take a screen shot.

Crop it down and save it and upload it here.

RomApr 4, 2014

+6251

Clipboard01.jpg

RomApr 3, 2014

+6251

What is your purpose in posting here?

RomMar 31, 2014

+6251

Mathematicians are many things.

Psychologists is not generally one of them.

RomMar 27, 2014

+6251

14.50 = 0.75 x

x = 14.50 / 0.75

14.50 / 0.75 =

x = 19 1/3 = 19.3333 etc.

RomMar 27, 2014

+6251

Quote:
3 to the power of x equals 30. how to solve?

3 ^x=30

take logs of both sides

x log(3) = log(30)

x = log(30)/log(3) = log(3*10)/log(3) = (log(3)+log(10))/log(3) = 1 + 1/log(3)

RomMar 25, 2014

+6251

product rule
chain rule
addition rule
quotient rule

RomMar 25, 2014

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