Answer:
294.375 or 294.38
Step-by-step explanation:
Volume of a circle:
πr³
If the diameter of a circle is 10, the radius is 5 .
5³ = 125
125 x 3.14 = 392.5
392.5 x
= 294.375 or 294.38
Step-by-step explanation:
![\bf a=2\cdot (1+2+3....224)+225](https://tex.z-dn.net/?f=%5Cbf%20a%3D2%5Ccdot%20%281%2B2%2B3....224%29%2B225)
![\bf a=2\cdot \big[(1+224)\cdot 224 : 2\big]+225](https://tex.z-dn.net/?f=%5Cbf%20a%3D2%5Ccdot%20%5Cbig%5B%281%2B224%29%5Ccdot%20224%20%3A%202%5Cbig%5D%2B225)
![\bf a=2\cdot \big(225\cdot 224 : 2\big)+225](https://tex.z-dn.net/?f=%5Cbf%20a%3D2%5Ccdot%20%5Cbig%28225%5Ccdot%20224%20%3A%202%5Cbig%29%2B225)
![\bf a=2\cdot \big(225\cdot 112\big)+225](https://tex.z-dn.net/?f=%5Cbf%20a%3D2%5Ccdot%20%5Cbig%28225%5Ccdot%20112%5Cbig%29%2B225)
![\bf a=2\cdot 25200+225](https://tex.z-dn.net/?f=%5Cbf%20a%3D2%5Ccdot%2025200%2B225)
![\bf a=50400+225](https://tex.z-dn.net/?f=%5Cbf%20a%3D50400%2B225)
![\bf a=50625](https://tex.z-dn.net/?f=%5Cbf%20a%3D50625)
![\red{\boxed{\bf a=225^{2} \implies ~patrat ~perfect}}](https://tex.z-dn.net/?f=%5Cred%7B%5Cboxed%7B%5Cbf%20a%3D225%5E%7B2%7D%20%5Cimplies%20~patrat%20~perfect%7D%7D)
![\bf \sqrt{a}=\sqrt{225^{2}} \implies \purple{\boxed{\bf a = 225}}](https://tex.z-dn.net/?f=%5Cbf%20%5Csqrt%7Ba%7D%3D%5Csqrt%7B225%5E%7B2%7D%7D%20%5Cimplies%20%5Cpurple%7B%5Cboxed%7B%5Cbf%20a%20%3D%20225%7D%7D)
Answer:
A. 200 packages
Step-by-step explanation:
The number of packages per roll can be found by dividing the length of a roll by the length of tape needed for each package.
__
For each package:
(2.375 in/piece)×(4 piece/package) = 9.5 in/package
Per roll:
(1900 in/roll) / (9.5 in/package) = (1900/9.5) packages/roll
= 200 packages/roll
The machine can seal 200 packages with a roll of tape 1900 inches long.
Let X be the number of burglaries in a week. X follows Poisson distribution with mean of 1.9
We have to find the probability that in a randomly selected week the number of burglaries is at least three.
P(X ≥ 3 ) = P(X =3) + P(X=4) + P(X=5) + ........
= 1 - P(X < 3)
= 1 - [ P(X=2) + P(X=1) + P(X=0)]
The Poisson probability at X=k is given by
P(X=k) = ![\frac{e^{-mean} mean^{x}}{x!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-mean%7D%20mean%5E%7Bx%7D%7D%7Bx%21%7D%20%20%20%20)
Using this formula probability of X=2,1,0 with mean = 1.9 is
P(X=2) = ![\frac{e^{-1.9} 1.9^{2}}{2!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-1.9%7D%201.9%5E%7B2%7D%7D%7B2%21%7D%20%20%20%20)
P(X=2) = ![\frac{0.1495 * 3.61}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.1495%20%2A%203.61%7D%7B2%7D%20%20)
P(X=2) = 0.2698
P(X=1) = ![\frac{e^{-1.9} 1.9^{1}}{1!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-1.9%7D%201.9%5E%7B1%7D%7D%7B1%21%7D%20%20%20%20)
P(X=1) = ![\frac{0.1495 * 1.9}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.1495%20%2A%201.9%7D%7B1%7D%20%20)
P(X=1) = 0.2841
P(X=0) = ![\frac{e^{-1.9} 1.9^{0}}{0!}](https://tex.z-dn.net/?f=%20%5Cfrac%7Be%5E%7B-1.9%7D%201.9%5E%7B0%7D%7D%7B0%21%7D%20%20%20%20)
P(X=0) = ![\frac{0.1495 * 1}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B0.1495%20%2A%201%7D%7B1%7D%20%20)
P(X=0) = 0.1495
The probability that at least three will become
P(X ≥ 3 ) = 1 - [ P(X=2) + P(X=1) + P(X=0)]
= 1 - [0.2698 + 0.2841 + 0.1495]
= 1 - 0.7034
P(X ≥ 3 ) = 0.2966
The probability that in a randomly selected week the number of burglaries is at least three is 0.2966