Answer:
a) add a dummy stroke to make the problem as an assignment problem of adding 5 strokes to 5 swimmers. see first attachment.
b) applying the Hungarian method.
4.8 0 0.9 4.1 2.5
10.3 0 9.1 1.6 8.7
4.8 0 10.4 1.9 5.1
2.8 0 3.2 2.1 4.7
0 0 0 0 0
Deduct the smallest element in each column from the other elements of the column.
2 0 0 2.5 0
7.5 0 8.2 0 6.2
2 0 9.5 0.3 2.6
0 0 2.3 0.5 2.2
0 0 0 0 0
Which implies:
2 8.2 2.5 6.2
7.5 9.5 0.3 2.6
2 2.3 0.5 2.2
33.8 + 34.7 + 28.5 + 29.2 = 126.2
David = Back Stroke
tony = Breast Stroke
Chris = Butterfly
Carl = Free Style
%= (exact-appropriate)/exact
so 279.45-250.55 divided by 279.45
basically .103417 nearest tenth is 10.3%
i believe
Answer:
4 Soccer balls and 6 Basketballs
Step-by-step explanation:
You can solve this problem by setting up a system of equations. Letting x be Soccer balls and y be Basketballs. Remember, Money goes with, Money goes with Money, meaning that for this problem the first equation that can be made is $248 = $28y + $20x with Y being basketballs and x being soccerballs. Next is a little more difficult. You will be creating the equation y=3x-6 because it is 6 less than 3 times the amount of x or Soccer balls. From here you can plug in the equations into a graphing calculator and graph it and see where the two lines intersect. This would be at (4, 6). When I said to let x equal Soccer Balls and y equal basketballs that is where I got the 4 soccer balls and 6 basketballs.
The solutions appear to be
{π/2, 2π/3, 4π/3}.
_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0
This has solutions
sin(x) = 1
x = π/2and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}
Answer:
...
Step-by-step explanation:
1.) if supplement then its equal to 90, so subtract from 90
2.) 90-72= 18, so the asnwer is 18
39+2x+1=90
40+2x=90
2x=50
x=25
3.) x-24+29=296
x+5=296
x=291
4.)vertical angles so congruent, 107
5.) 83+4x+1=180
84+4x=180
4x=96
x=24
