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MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Gymnastics Case Study

The Canada Games represents the highest level of national competition for up and coming Canadian athletes. Alternating between winter and summer, the competition is held once every two years. Niagara will be the proud host of the 2022 Canada Summer Games. In this case study, your group will explore the athletes’ information and achievements as given in the “Gymnastics” data sheet to make summaries and inferences.

Gymnastics Events

Artistic gymnastics has been part of the Canada Winter Games since the inaugural Games in 1967 in Quebec City and features both Men’s and Women’s competition.

 

Women's Artistic Gymnastics Apparatus Events

Men's Artistic Gymnastics Apparatus Events

Vault

Uneven bars

Beam 

Floor

Floor

Pommel horse

Rings

Vault

Parallel bars

Horizontal bars

Team Competition

Each team consists of 6 athletes from the same province/territory. Each athlete competes on every apparatus. The best 4 scores in each apparatus are added together for the team score.

Individual All-Around Finals

The top 3 gymnasts per province/territory from the Team Competition competes in the Individual All-Around Finals, with a total of up to 36 participants based on scores obtained in the preliminary competition. Each athlete competes on every apparatus. The scores in each apparatus are added together for the individual score.

Apparatus Finals

The top 8 gymnasts in each event (with a maximum of 2 per province/territory) from the Team Competition will compete in the Apparatus Finals Competition.

 

Question 2

The floor exercise is a commonly shared event between the Women’s and Men’s Artistic Gymnastics programs. Let’s compare the floor exercise scores of the female gymnasts and male gymnasts. To do this, we will consider the 2007, 2011, and 2015 results as sample data.

Part A: Individual All-Around Finals

We will first look at the floor exercise scores in the Individual Female All-Around Finals and in the Individual Male All-Around Finals.

i. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Female All-Around Finals.

ii. Find the sample mean and sample standard deviation for the floor exercise scores in the Individual Male All-Around Finals.

iii. Construct a 95% confidence interval for the difference in population mean floor exercise scores between female and male gymnasts in the Individual All-Around Finals. (Hint: Use the results of i. and ii. and use the t-distribution.)

iv. Using the confidence interval in part iii., can we infer at the 5% significance level that the population mean floor exercise score in the Individual All-Around Finals is different for female gymnasts and male gymnastics?

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12.95
14:00
12.55
14:00
13.1
19:41
13.4
1904
11.8
Spe
13.1
1941
12.9
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12.9
13.2
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12.85
14:00
13.9
13.1
12.7
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12.4
12.95
12.05
12.75
12.7
13.2
12.15
13.15
12.5
12.65
12.65
12.75
12.5
14.0
12.45
14:40
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12.3
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12.7
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12.6
12.35
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12.3
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12.5
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12.15
12
11.9
12.5
11.6
4
12
11.2
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11.75
11.2
12
11.9
11.65
11.6
11.4
11.2
L
Parallel
Bars
13.45
13.25
12.85
12.85
12.6
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13.
JA OF
13.95
13.15
13
=
13
13.2
12.2
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11.85
10.6
12.05
12.05
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12.2
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11.55
11.3
10.05
10.05
12.1
158
12.5
12.35
11.55
11.3
11.05
11.2
11.9
11.55
11:39
10.3
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10.35
19:39
10.2
10.05
12.05
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11.5
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12.05
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12.3
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14:1
12.7
11.45
40 46
12.15
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12.4
14.05
11.95
11.45
12.15
12.65
12.35
12:30
11.
11.5
11.9
11.95
11.5
10.9
9.6
9:0
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10.05
10
8.6
9.25
10.65
6.55
8.9
9.25
5.55
8.9
12.9
13.15
12.35
12.25
13.15
12.6
14:0
12
4
12.4
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11.
2
11.4
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11.7
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11.95
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11.1
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11.75
11:29
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11.4
11.75
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10.85
10:00
10.85
10:00
11.5
11:9
11.4
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10.55
11.85
9.75
9.8
4.2
M
Horizontal
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13.8
12.35
14.05
14.1
13.05
3:00
13.05
19:00
12.3
14:3
12.8
14:0
13.35
19:09
11.5
12.3
4
13.3
11.45
12.5
1285
12.85
500
12.9
14:0
12.3
11.15
11.3
11.9
14.06
11.05
10.05
11.05
10.25
10.2
10.65
6.4
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13.75
9:19
9.6
5.05
9.95
10.4
13.55
12.45
12.15
11.45
12.65
11.8
12.25
12
12.25
12.2
11.15
11.8
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10.9
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11.9
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11.35
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10.6
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11.15
11.35
10.85
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11.6
11:0
11.1
10.8
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11.85
11:09
10.75
19:19
10.85
9:09
3.05
8.3
9.5
8.3
8.4
12.95
12.8
12.7
12.6
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12.2
14:4
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14:19
11.4
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12
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11.55
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11.6
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11.5
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11.5
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11.15
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10.8
10.8
10.4
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0:99
10.75
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2.7
5.15
6.4
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Final Score
82.234
81.3
80.217
79.45
Tome
78.867
0:004
78.584
B:www
77.367
11:301
76.834
76.55
75.067
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74.9
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74.867
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74.4
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74.184
73.934
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73.734
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73.35
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72.117
74 08
71.85
60 024
69.934
69.
2684
68.684
654
65.1
64.817
64.8
63.784
62.5
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60.45
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59.684
09:004
58.234
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55.917
29:91
55.467
DONOT
54.134
SOM
47.45
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40.05
T
79.35
19:00
77.2
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76.95
19:90
76.25
75.85
75.8
75.5
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75.35
75.3
74.85
ABE
74.85
74 65
74.65
74.5
73.15
72.55
72.35
14:39
71.6
70.75
20:0
70.5
70.15
10:19
69.9
00.0
69.65
00:00
69.05
09:00
68
67.05
07:09
67.05
07:09
66.4
66.25
61.25
26
59.65
20:00
59.45
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57.7
ora
51.95
91:99
39.95
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31.9
17.7
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76.65
75.4
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74.25
74.05
73.45
73.4
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72.95
14:00
72.6
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71.75
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70.9
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70.85
20:00
70.55
10:00
70.4
10:4
70.25
70.2
69.85
09:00
69.65
DON
69.6
09.
69.4
69.15
Dane
69.1
67.85
66.75
100:10
66.25
00:40
65.15
09
65.15
65.1
109-1
64.6
63.1
56.95
55.5
55.1
51.45
21.75
21.4
11.05
O
Rank
2
3
4
5
6
=
8
9
10
11
7
12
77
13
14
14
→
15
16
17
17
40
18
10
19
20
21
21
22
22
22
23
24
25
26
=
28
70
€9
S
35
=
=
4
5
=
6
7
=
8
5
9
10
77
11
12
13
14
15
16
=
=
=
19
20
20
21
=
22
€
26
28
29
7
35
=
=
=
4
5
6
1
=
8
19
9
10
11
12
2
18
=
=
20
29
21
5
22
24
28
29
30
31
31
32
94
33
99
34
35
36
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15
20
16
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25
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51
52
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54
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55
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60
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61
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64
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65
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67
68
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78
78
79
79
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81
01
82
02
83
83
84
84
85
85
86
86
87
87
88
88
89
89
90
90
91
91
92
92
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93
04
94
DE
95
06
96
07
97
08
98
99
99
100
100
101
101
102
102
102
103
104
204
105
200
106
107
108
109
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Games
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2015 Artistic
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2015 Artistic
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2011 Artistic
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2011 Ant
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2011 Artistic
2011 Antiatio
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2011 Artistic
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All Around
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All Around
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All Around
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Female
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Come
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ALARVUT
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2011 Artistic - All Around
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Gender
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E
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Last Name
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PA
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25
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G
Age
15
14
14
=
17
2
15
29
13
19
16
=
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14
=
16
=
14
16
10
17
17
12
15
16
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16
19
17 14.05
22
14:00
13.9
17
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18
19
16
10
16
10
16
19
17
17
13.95
19:00
13.6
19:0
10
16
15
15
14.55
14:00
13.8
19:0
14.3
13.25
19.29
12.95
14:00
14.2
13.75
19:19
13.4
TONY
14.05
14.09
13.65
13.25
13.25
13.4
TON
13.15
13.19
14.1
14:1
14.35
12.85
13.2
13.15
12.8
18 12.05
13
12.9
13.15
14
17
11.9
2
16
12.5
11
12.2
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12.4
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11.3
14
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14.4
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13.5
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13.15
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13.15
19:19
12.65
13.55
13.35
13.35
77
13.4
13.15
14.05
11.95
12.05
12.05
427
13.7
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12.6
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12.5
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12.8
12.5
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12.65
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11.8
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15
14.5
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14.8
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13.5
13.5
13.2
13.2
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13.2
13.2
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13.5
13.5
14.25
14.25
13.8
13.8
144
14.4
134
13.4
12.8
13.8
13.35
13.15
133
13.3
12.8
12.8
12.2
13.2
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12.65
428
12.5
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12.95
11.85
12.35
13.2
12.75
11.5
12.6
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11.55
I
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14.55
14.5
14.2
ve
13.8
14.35
Spe
13.7
11944
13.85
14.3
14
=
11.5
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12.45
14:40
13.7
19:1
12.3
16.0
11.45
11:40
13.3
19.9
11.15
11:19
13.15
19:19
12.75
12.10
11.05
11.09
13.25
13.29
9.25
9.25
11.3
10.95
10.65
10.6
10
10.55
9.45
7.1
5.
7.95
12.
12
13.6
12.6
13.3
12.9
12.7
13.35
12.65
13.9
Dom
10.7
11.45
LEVO
12.3
14
11.
11.75
11.2
11.75
10.85
422
12.2
724
12.1
10.75
ZOF
11.05
10.07
10.05
DAF
9.15
DOF
10.05
9.75
45
10.45
Dive
7
9.4
8.55
7
6.7
7.95
9.3
7.75
Se
7.25
2
5.35
3.65
13.65
14.0
12.8
13.95
13.2
13.2
12.55
12:59
13.1
13.1
14.45
12
12
12.1
13.1
12.1
12.1
11.65
12.75
12.5
12.5
144
11.1
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11.4
102
10.2
12.15
11.35
10.7
44.6
11.6
442
11.3
44
11
8.9
9.05
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7.1
9.15
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14.75
14.1
13.65
13.75
14.7
13
13.3
20
12.5
12.7
DE
13.8
19:0
6.75
7.7
5.3
13.6
19.0
13.1
19:1
12.4
12.4
13.8
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14.55
17.00
12.25
12.20
13.0
12.3
12.3
12.25
14:40
12.45
12:40
11.35
11.35
11.9
11.9
12.65
12.1
10.95
10.85
11.1
8.2
19€
10.3
19:0
9.9
9.35
9:39
9.5
8.85
www
7.6
7:0
12.7
14.1
13.05
9:00
13.9
19:9
14.6
12.65
2:00
13.85
3:00
13.5
19:9
14.3
Akce
13.1
13.1
12.85
2:00
14.3
14:0
13.2
19:€
12.3
14:3
12.7
14:1
12.5
14.0
12.4
14:4
12.4
12.9
15.05
12.55 15.05
13.35
14.05
11.7
1.15
11.15
9.9
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12.05
128
12.6
44.46
11.15
740
11.2
12.25
12.35
40 FE
10.55
11.6
700
12.2
TOF
10.5
9.4
10.25
75
CE
9.65
7
8.45
7.6
9.3
8.7
15.3
14.45
14.4
14.9
14.35
14.35
14.35
14.35
14.25
14.25
13.85
12.25
13.7
13.7
15
19
13.45
14.55
13.85
12.9
12.95
14.3
14.3
137
13.7
14.65
133
13.3
131
13.1
K
Floor
15
14.85
15.2
14.25
13.85
19:00
S
13.6
119.9
13.7
Hom
14.05
14:00
12.7
en
14.05
14:00
13.65
19:09
13.25
19.40
13.25
19.40
13.55
19.99
12.95
12.99
13.55
13.55
13.05
13.09
11.85
11:09
13.2
19:4
11
13.8
13.8
12.25
12.1
12.1
12.1
11.6
11.9
12.05
10.75
19:10
11.2
10.55
11.1
10.45
9.6
13.85
14.25
14.8
14
14.5
13.75
TO
13.55
19:00
12.55
13.2
15.2
13.7
15.1
13.35
20
13.25
20
12.95
14:59
13.4
13.4
13.35
133
13.3
122
12.3
12 EE
13.55
700
12.8
12.4
757
13.1
12.3
700
12.6
12 65
12.65
11.9
405
10.2
12.05
12.05
14:09
11.7
10.4
10.75
2:0
9.8
9.6
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10.75
9.75
9.55
9.05
14.65
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14.
15.35
14.6
14.3
14.75
13.65
13.7
13.
14.25
13.8
141
14.1
136
13.6
14
14
14.25
132
13.2
144
13.25
137
13.7
13.15
13.05
12.45
13.45
424
12.4
12.2
13.3
12.75
127
13.7
134
13.4
127
116
11.6
11.6
12.7
42
13
124
12.4
45
11.45
10.2
10
11
10.9
10.35 10.35
9.55 11.75
9.6
11.3
10.25
10.3
10.6
10.9
122
12.2
126
12.6
14.65
11.55
Final Score
59.55
58.65
58.35
56.15
55.95
20:00
54.90
54.40
54.35
54.30
34:00
53.45
09:40
53.35
53.39
53.25
99.29
53.25
99.40
53.10
99.10
52.95
34.90
52.55
34.99
52.15
51.75
50.25
30:40
49.85
49:09
49.70
49.70
49.30
49.30
49.05
49.05
48.35
46.85
45.85
45.05
43.70
10:10
43.65
1410:00
42.30
174.00
40.40
MOTO
39.90
29:00
37.00
37:00
36.45
20:40
25.50
25.05
29:00
55.
99:10
54.85
37:00
54.45
SW.YO
54.35
37.00
54.25
ww.40
53.70
99:10
52.85
04:09
51.85
91:09
51.85
91:09
91:20
50.70
50.35
50.15
50.15
49.40
49.00
49 05
48.95
AD TE
48.75
49 25
48.35
47.25
47.35
ADF
47.25
46. 30
46.70
70.00
46.20
45.75
TE OF
45.65
www
44.15
42 46
43.15
700
40.80
700
40.50
39.40
39.10
Come
38.30
20:00
35.50
20:00
35.40
20.00
32.80
20
58.05
99:09
57.85
31.0
57.70
57.30
56.85
56.85
56.15
56.15
55.80
55.80
55.50
55.50
55.40
55.40
55.05
55.05
54.75
54.75
54 55
54.55
54 45
54.45
54.30
54.30
54.10
54.10
53.70
53.70
53. 30
53.30
52 55
52.55
52 25
52.35
51.50
51.50
51 45
51.45
64 46
51.15
50 55
50.55
50. 35
50.35
40 BE
49.85
40 10
49.10
49 50
48.50
44 75
44.75
44 45
44.45
42.35
41.75
41.35
41.10
40.35
39.70
38.35
M
Rank
3
4
5
2
6
=
7
2
8
=
9
10
11
20
12
12
13
19
14
14
15
15
16
19
17
+
18
19
19
19
20
20
21
21
22
22
23
23
24
24
25
26
27
55
20
29
31
32
33
35
36
4
=
3
=
4
=
5
6
=
7
=
8
=
9
=
9
=
11
!!
12
13
14
15
16
16
17
70
18
10
19
20
20
21
20
22
55
23
=
24
7
25
77
26
=
27
7
28
7
29
=
30
=
31
32
33
34
35
36
=
=
4
5
5
6
16
7
2
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
17
18
18
19
19
20
20
21
21
22
22
22
23
24
24
25
25
26
26
27
27
28
28
29
30
31
32
33
34
35
36
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13.8 141 14.1 136 13.6 14 14 14.25 132 13.2 144 13.25 137 13.7 13.15 13.05 12.45 13.45 424 12.4 12.2 13.3 12.75 127 13.7 134 13.4 127 116 11.6 11.6 12.7 42 13 124 12.4 45 11.45 10.2 10 11 10.9 10.35 10.35 9.55 11.75 9.6 11.3 10.25 10.3 10.6 10.9 122 12.2 126 12.6 14.65 11.55 Final Score 59.55 58.65 58.35 56.15 55.95 20:00 54.90 54.40 54.35 54.30 34:00 53.45 09:40 53.35 53.39 53.25 99.29 53.25 99.40 53.10 99.10 52.95 34.90 52.55 34.99 52.15 51.75 50.25 30:40 49.85 49:09 49.70 49.70 49.30 49.30 49.05 49.05 48.35 46.85 45.85 45.05 43.70 10:10 43.65 1410:00 42.30 174.00 40.40 MOTO 39.90 29:00 37.00 37:00 36.45 20:40 25.50 25.05 29:00 55. 99:10 54.85 37:00 54.45 SW.YO 54.35 37.00 54.25 ww.40 53.70 99:10 52.85 04:09 51.85 91:09 51.85 91:09 91:20 50.70 50.35 50.15 50.15 49.40 49.00 49 05 48.95 AD TE 48.75 49 25 48.35 47.25 47.35 ADF 47.25 46. 30 46.70 70.00 46.20 45.75 TE OF 45.65 www 44.15 42 46 43.15 700 40.80 700 40.50 39.40 39.10 Come 38.30 20:00 35.50 20:00 35.40 20.00 32.80 20 58.05 99:09 57.85 31.0 57.70 57.30 56.85 56.85 56.15 56.15 55.80 55.80 55.50 55.50 55.40 55.40 55.05 55.05 54.75 54.75 54 55 54.55 54 45 54.45 54.30 54.30 54.10 54.10 53.70 53.70 53. 30 53.30 52 55 52.55 52 25 52.35 51.50 51.50 51 45 51.45 64 46 51.15 50 55 50.55 50. 35 50.35 40 BE 49.85 40 10 49.10 49 50 48.50 44 75 44.75 44 45 44.45 42.35 41.75 41.35 41.10 40.35 39.70 38.35 M Rank 3 4 5 2 6 = 7 2 8 = 9 10 11 20 12 12 13 19 14 14 15 15 16 19 17 + 18 19 19 19 20 20 21 21 22 22 23 23 24 24 25 26 27 55 20 29 31 32 33 35 36 4 = 3 = 4 = 5 6 = 7 = 8 = 9 = 9 = 11 !! 12 13 14 15 16 16 17 70 18 10 19 20 20 21 20 22 55 23 = 24 7 25 77 26 = 27 7 28 7 29 = 30 = 31 32 33 34 35 36 = = 4 5 5 6 16 7 2 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 22 23 24 24 25 25 26 26 27 27 28 28 29 30 31 32 33 34 35 36
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