Inradius = area of triangle / semi-perimeter
Semiperimeter = ( 6 + 5 + 4.5) /2 = 7.75
Area = sqrt [ 7.75 * (7.75 - 6) * (7.75 - 5) * (7.75 - 4.5) ] ≈ 11
Inradius = 11 / 7.75 ≈ 1.42 cm
6 vowels 20 consonants
Assuming we can have repeats of vowels / consonants
(20) * (6) * (20) * (6) =
120 * 120 =
14400 plates
(8x^2 - 4x) / ( 4x - 2)
[(4x)(2x - 1)] / [ 2 (2x - 1) ]
(4x) / 2 =
2x
8 /12 = x /24 cross-multiply
24 * 8 =12 * x
192 = 12 * x
192 / 12 = x = 16 cups
( 5 + 8 + 10+ 16 + 18 + 28 + 30 + x ) / 8 = x - 4.5
(115 + x) = 8 ( x - 4.5)
115 + x = 8x - 36
115 + 36 = 8x - x
151 = 7x
151 / 7 = x
Factors of 60 =
1,2,3,4,5,6,10,12,15,20,30,60
P (< 3) = 2 /12 = 1 / 6
A graph seems the way to go, here
https://www.desmos.com/calculator/04zmr3pddp
The smallest value occurs when x = 0
And that value = sqrt (2) + sqrt (8) = sqrt (2) ( 1 + 2) = 3sqrt (2)
Just 10
Choose "GE" and then any 1 of the remaining 10
Let the total cost = C
Caleb contributes (8/13) C
Paul contributes (8/13)C - 6
(8/13)C + (8/13)C - 6 = C
(16/13)C - C = 6
(3/13)C = 6
C = 6 (13/3) = $26
Caleb contributes (8/13)(26) = $16
Paul contributes 16 - 6= $10
[ (111 - - 36) / 7 ] + 1 =
[(147) / 7 ]+ 1 =
21 + 1 =
22
