Answer:
53.33% or 0.5333
Step-by-step explanation:
you have to count how many tiles in total then the amount of vowel tiles. you then put that in to a fraction of vowels over consonants then convert that into a percentage
The sum of the series is 999/1000 .
<h3>What is a Series ?</h3>
A series is a sequence of expression in a certain pattern.
The series of n terms is given
![\rm \frac{1^2+1*2+2^2}{1^3*2^3} + \frac{2^2+2*3+3^2}{2^3*3^3} +...+\frac{9^2+9*10*10^2}{9^3*10^3}](https://tex.z-dn.net/?f=%5Crm%20%5Cfrac%7B1%5E2%2B1%2A2%2B2%5E2%7D%7B1%5E3%2A2%5E3%7D%20%2B%20%5Cfrac%7B2%5E2%2B2%2A3%2B3%5E2%7D%7B2%5E3%2A3%5E3%7D%20%2B...%2B%5Cfrac%7B9%5E2%2B9%2A10%2A10%5E2%7D%7B9%5E3%2A10%5E3%7D)
nth term of the series is given by
![\rm T_n = \rm \dfrac{n^2 + n(n+1)+ (n+1)^2}{n^3*(n+1)^3}](https://tex.z-dn.net/?f=%5Crm%20T_n%20%3D%20%5Crm%20%5Cdfrac%7Bn%5E2%20%2B%20n%28n%2B1%29%2B%20%28n%2B1%29%5E2%7D%7Bn%5E3%2A%28n%2B1%29%5E3%7D)
On simplification it can be written as
![\rm T_n = \rm \dfrac{3n^2 + 3n+1}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{3n(n +1)+1}{n^3*(n+1)^3}\\\\\\T_n = \rm \dfrac{ (n +1)^3 - n^3}{n^3*(n+1)^3}\\\\T_n = \rm \dfrac{ 1}{n^3} - \dfrac{1}{(n+1)^3}](https://tex.z-dn.net/?f=%5Crm%20T_n%20%3D%20%5Crm%20%5Cdfrac%7B3n%5E2%20%2B%203n%2B1%7D%7Bn%5E3%2A%28n%2B1%29%5E3%7D%5C%5C%5C%5CT_n%20%3D%20%5Crm%20%5Cdfrac%7B3n%28n%20%2B1%29%2B1%7D%7Bn%5E3%2A%28n%2B1%29%5E3%7D%5C%5C%5C%5C%5C%5CT_n%20%3D%20%5Crm%20%5Cdfrac%7B%20%28n%20%2B1%29%5E3%20-%20n%5E3%7D%7Bn%5E3%2A%28n%2B1%29%5E3%7D%5C%5C%5C%5CT_n%20%3D%20%5Crm%20%5Cdfrac%7B%201%7D%7Bn%5E3%7D%20-%20%5Cdfrac%7B1%7D%7B%28n%2B1%29%5E3%7D)
The sum of terms from 1 to 9 is given by
∑ (
)
= ![\rm \dfrac{1}{1^3} - \dfrac{1}{2^3} + \dfrac{1}{2^3} - \dfrac{1}{3^3}+ .......... + \dfrac{1}{9^3} - \dfrac{1}{10^3}](https://tex.z-dn.net/?f=%5Crm%20%5Cdfrac%7B1%7D%7B1%5E3%7D%20-%20%5Cdfrac%7B1%7D%7B2%5E3%7D%20%2B%20%5Cdfrac%7B1%7D%7B2%5E3%7D%20-%20%5Cdfrac%7B1%7D%7B3%5E3%7D%2B%20..........%20%2B%20%5Cdfrac%7B1%7D%7B9%5E3%7D%20-%20%5Cdfrac%7B1%7D%7B10%5E3%7D)
= (1/1³) - (1/10³)
= 999/1000
Therefore the sum of the series given is 999/1000
To know more about Series
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Answer:
The equation of the boundary of the region is (x+2)² + (y-1)² = 25
Step-by-step explanation:
The satellite is positioned at (-2,1) and can sense the presence within 5 miles of its position.
The boundary of the region is a circle with center (-2,1) and radius 5.
The equation of the circle with center (h,k) and radius r is given by
(x-h)²+(y-k)²=r²
The equation of the circle with center (-2,1) and radius 5 is given by
(x+2)²+(y-1)²=5²=25
(x+2)² + (y-1)² = 25 is the required equation of the boundary of the region.
1cc is 1ml, or .001 liters.
1cc of water also has a mass of 1g