The total amount Serena earns is the sum of her regular wage and the tips. The amount she earns from the wage is equal to 9h. This total should be more than or equal to $110. This is mathematically expressed as,
9h + 15 ≥ 110
Step One
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Find the length of FO (see below)
All of the triangles are equilateral triangles. Label the center as O
FO = FE = sqrt(5) + sqrt(2)
Step Two
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Drop a perpendicular bisector from O to the midpoint of FE. Label the midpoint as J. Find OJ
Sure the Pythagorean Theorem. Remember that OJ is a perpendicular bisector.
FO^2 = FJ^2 + OJ^2
FO = sqrt(5) + sqrt(2)
FJ = 1/2 [(sqrt(5) + sqrt(2)] \
OJ = ??
[Sqrt(5) + sqrt(2)]^2 = [1/2(sqrt(5) + sqrt(2) ] ^2 + OJ^2
5 + 2 + 2*sqrt(10) = [1/4 (5 + 2 + 2*sqrt(10) + OJ^2
7 + 2sqrt(10) = 1/4 (7 + 2sqrt(10)) + OJ^2 Multiply through by 4
28 + 8* sqrt(10) = 7 + 2sqrt(10) + 4 OJ^2 Subtract 7 + 2sqrt From both sides
21 + 6 sqrt(10) = 4OJ^2 Divide both sides by 4
21/4 + 6/4* sqrt(10) = OJ^2
21/4 + 3/2 * sqrt(10) = OJ^2 Take the square root of both sides.
sqrt OJ^2 = sqrt(21/4 + 3/2 sqrt(10) )
OJ = sqrt(21/4 + 3/2 sqrt(10) )
Step three
find h
h = 2 * OJ
h = 2* sqrt(21/4 + 3/2 sqrt(10) ) <<<<<< answer.
1 gallon = 8 pints, so 2 gallons = 16 pints.
If each container can hold one pint, then she will need 16 containers.
Answer: 1/3
Explanation:
1/12 of the squad are suspended:
1/12 x 24 = 24/12 = 2
So 2 player are suspended
24 - 2 = 22 player
And some are injured leaving 14 left to play:
22 - 14 = 8 players injured
So 8/24 is the fraction of injured player.
But 8/24 = 1/3 so we can say 1/3 of the whole squad are injured.
Multiply numerators:
-4*-5=20
Multiply denominators:
9*8=72
20/72= 10/36
10/36= 5/18
Final answer: 5/18
