Answer:
Total possible number of outcomes = C(24,6) [24 choose 6]
=24!/(6!18!)
= 134596
Out of which there is only one winning combination.
Therefore we conclude:
P(win 20000)=1/134596
P(lose 1)=134595/134596
and hence the expected value is:
20000*(1/134596)+(-1)*(134595/134596)
=-114595/134596
=-0.8514 (rounded to four places after decimal)
Step-by-step explanation:
Hope this helped!
let's convert the mixed fractions to improper fractions firstly.
![\bf \stackrel{mixed}{2\frac{3}{8}}\implies \cfrac{2\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{19}{8}}~\hfill \stackrel{mixed}{4\frac{1}{2}}\implies \cfrac{4\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{9}{2}} \\\\\\ \stackrel{mixed}{3\frac{1}{8}}\implies \cfrac{3\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{25}{8}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B3%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%208%2B3%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B19%7D%7B8%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B4%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B9%7D%7B2%7D%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bmixed%7D%7B3%5Cfrac%7B1%7D%7B8%7D%7D%5Cimplies%20%5Ccfrac%7B3%5Ccdot%208%2B1%7D%7B8%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B25%7D%7B8%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
Answer:
x1=4
x2=8
Step-by-step explanation:
1- Factor the equation.
2- solve a Single Variable Equation
3- Parabola, Finding the Vertex
The original volume of the balloon is given by:
V1 = (4/3) * (pi) * (r ^ 3)
Where,
r: radius of the sphere.
Substituting values:
V1 = (4/3) * (pi) * (1 ^ 3)
V1 = (4/3) * (pi) * (1)
Then, the volume of the current sphere is:
V2 = (4/3) * (pi) * ((1 + 2 * (1)) ^ 3)
V2 = (4/3) * (pi) * ((1 + 2) ^ 3)
V2 = (4/3) * (pi) * ((3) ^ 3)
V2 = (4/3) * (pi) * (27)
The relation of volumes is:
V2 / V1 = ((4/3) * (pi) * (27)) / ((4/3) * (pi) * (1))
V2 / V1 = 27/1
Answer:
The ratio of the current volume of the balloon to the original volume of the balloon is:
27: 1
1980
660 --> 12
X --> 36
________
36 / 12 = 3
X = 3
660 x 3 = 1980
