Problem 2

A person with mass m1 = 74 kg person climbs a distance d from the base of a uniform ladder before the ladder starts to slip. The ladder has a mass m2 = 30 kg and length L = 7.0 m and rests against a smooth vertical wall at an angle θ = 65° with the floor. The coefficient of static friction between the floor and the ladder is 0.40. Use the symbolic notations given before using numerical substitutions.

A) Find the normal force N from the floor and the force of the wall Fw on the ladder when the man is on the ladder.

B) Find the distance d that the person climbs on the ladder before the ladder starts to slip.

Suppose you are taking a test in Math 1044, which is made up of 100 independent, identically distributed students. Your professor claims that the average score will be 72 with a standard deviation of 10 points. Let S be the normal approximation to the average score and use the Central Limit Theorem to answer the following questions. Please simplify answer in terms of the Φ function before entering them in a calculator.C

(a) How is S distributed and what is the CDF of S?

(b) Find the probability that the average score is below a 70.

(c) Find the probability that the actual average score is between 68 and 72.

(d) Find the probability that the average score is above a 74.

1. You are a teacher and want to analyze if your morning class has significantly different scores than your afternoon class. You have 12 students in both of your classes. Compute a t-test for independent samples on these scores from the last quiz you administered and then use the eight steps to test the null hypothesis that there is no difference between the two conditions. Do the two groups differ?
Morning class Afternoon class
87 86
98 73
75 79
88 56
76 72
85 70
92 87
56 59
89 64
85 77
84 74
92 72

a. Is the t-test the appropriate test for this study?

b. yes, state why, using examples to support your agreement or if no, state why not, using examples to support your disagreement

An independent sample t-test would be used if a professor at FIU wanted to compare his calculus classes scores from the past two semesters. Class 1 had 20 students and an average of 70 and SD of 15. Class 2 had 25 students and an average of 74 standard deviation of 25. You have to use alpha .05 to determine if class 1 and 2 had a difference between scores by using the degrees of freedom on a normal distribution table.

The PulseRates data set has pulse, height and weight for 90 patients who had an echocardiogram test in one of the clinic in Ottawa in the month of September. (a)[2] Fit a L-S regression line using height to predict the pulse rate (pulse rate is called the response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient)

(b)[2] Fit a L-S regression line using weight to predict the pulse rate (response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient) .

(c)[2] Fit a L-S regression line using height to predict the weight (response variable). What is the equation of the L-S regression line? . Does it make sense to use this line? Why? (Check the correlation coefficient) .

(d) What is the predicted value for weight for a patient whose height is 68.7 inches?[1] .

For 71.5 inches?[1] . For 83 inches ?[1] . Which of these seem to make sense?[1] . Can you predict the height if the weight is 156 lb

Refer to the accompanying data set and construct a 90​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.

Males   Females
87   77
74   92
51   56
60   65
54   54
61   83
51   78
77   85
49   89
62   55
74   34
59   68
66   81
76   79
80   79
63   66
64   66
96   80
45   58
85   61
72   82
62   85
73   72
71   75
53   85
64   92
57   86
77   93
73   92
63   95
64   68
96   89
57   85
67   80
59   77
59   53
67   100
71   73
86   75
60   77

A.Construct a 90​% confidence interval of the mean pulse rate for adult females.

___bpm<μ<___ bpm?

round one decimal place

B.Construct a 90​% confidence interval of the mean pulse rate for adult males.

_____bpm<μ<_____bpm?

C.

A.The confidence intervals do not​ overlap, so it appears that adult females have a significantly higher mean pulse rate than adult males.

B.The confidence intervals do not​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.

C.The confidence intervals​ overlap, so it appears that there is no significant difference in mean pulse rates between adult females and adult males.

D.The confidence intervals​ overlap, so it appears that adult males have a significantly higher mean pulse rate than adult females.

The global marketplace has witnessed an increased pressure from customers and competitors in manufacturing as well as service sector (Basu, 2001; George, 2002).Due to the rapidly changing global marketplace only those companies will be able to survive that will deliver products of good quality at cheaper rate and to achieve their goal companies try to improve performance by focusing on cost cutting, increasing productivity levels, quality and guaranteeing deliveries in order to satisfy customers (Raouf, 1994).

Increased global competition leads the industry to increasing efficiency by means of economies of scale and internal specialization so as to meet market conditions in terms of flexibility, delivery performance and quality (Yamashina, 1995). The changes in the present competitive business environment are characterized by profound competition on the supply side and keenindecisive in customer requirements on the demand side. These changes have left their distinctive marks on the different aspect of the manufacturing organizations (Gomes et al., 2006). With this increasing global economy, cost effective manufacturing has become a requirement to remain competitive.

To meet all the challenges organizations try to introduce different manufacturing and supply techniques. Management of organizations devotes its efforts to reduce the manufacturing costs and to improve the quality of product. To achieve this goal, different manufacturing and supplytechniques have been employed. The last quarter of the 20th century witnessed the adoption of world-class, lean and integrated manufacturing strategies that have drastically changed the way manufacturing firm’sleads to improvement of manufacturing performance (Fullerton and McWatters, 2002).

1. Due to COVID 19 emergency do you thinkagile supply chain is the right concept in this kind of situation? Give reason with example.

Critical Thinking

The global marketplace has witnessed an increased pressure from customers and competitors in manufacturing as well as service sector (Basu, 2001; George, 2002).Due to the rapidly changing global marketplace only those companies will be able to survive that will deliver products of good quality at cheaper rate and to achieve their goal companies try to improve performance by focusing on cost cutting, increasing productivity levels, quality and guaranteeing deliveries in order to satisfy customers (Raouf, 1994).

Increased global competition leads the industry to increasing efficiency by means of economies of scale and internal specialization so as to meet market conditions in terms of flexibility, delivery performance and quality (Yamashina, 1995). The changes in the present competitive business environment are characterized by profound competition on the supply side and keenindecisive in customer requirements on the demand side. These changes have left their distinctive marks on the different aspect of the manufacturing organizations (Gomes et al., 2006). With this increasing global economy, cost effective manufacturing has become a requirement to remain competitive.

To meet all the challenges organizations try to introduce different manufacturing and supply techniques. Management of organizations devotes its efforts to reduce the manufacturing costs and to improve the quality of product. To achieve this goal, different manufacturing and supplytechniques have been employed. The last quarter of the 20th century witnessed the adoption of world-class, lean and integrated manufacturing strategies that have drastically changed the way manufacturing firm’sleads to improvement of manufacturing performance (Fullerton and McWatters, 2002).

Consult chapter 7 of your text book or secondary available data on internet and answer the following questions.

Question:

1. Assess the reasons for using lean thinking (suitable examples),what are the benefits from Suppliers to end users?

The global marketplace has witnessed an increased pressure from customers and competitors in manufacturing as well as service sector (Basu, 2001; George, 2002).Due to the rapidly changing global marketplace only those companies will be able to survive that will deliver products of good quality at cheaper rate and to achieve their goal companies try to improve performance by focusing on cost cutting, increasing productivity levels, quality and guaranteeing deliveries in order to satisfy customers (Raouf, 1994).

Increased global competition leads the industry to increasing efficiency by means of economies of scale and internal specialization so as to meet market conditions in terms of flexibility, delivery performance and quality (Yamashina, 1995). The changes in the present competitive business environment are characterized by profound competition on the supply side and keenindecisive in customer requirements on the demand side. These changes have left their distinctive marks on the different aspect of the manufacturing organizations (Gomes et al., 2006). With this increasing global economy, cost effective manufacturing has become a requirement to remain competitive.

To meet all the challenges organizations try to introduce different manufacturing and supply techniques. Management of organizations devotes its efforts to reduce the manufacturing costs and to improve the quality of product. To achieve this goal, different manufacturing and supplytechniques have been employed. The last quarter of the 20th century witnessed the adoption of world-class, lean and integrated manufacturing strategies that have drastically changed the way manufacturing firm’sleads to improvement of manufacturing performance (Fullerton and McWatters, 2002).

Consult chapter 7 of your text book or secondary available data on internet and answer the following questions.

1. Assess the reasons for using lean thinking (suitable examples),what are the benefits from Suppliers to end users?

Implement the Tic-tac-toe game for variable board sizes, you may assume: 2 < s < 11, where s is the board size. Before the game starts the program will prompt for the board size. Note: the winning conditions are the same as the original Tic-tac-toe game in that you need to fill the entire row/column/diagonal to win.

Here are a few sample runs. The output is a bit different so that we can handle two-digit coordinates consistently. We expect (but you won’t lose any marks if you don’t) that you make extensive use of compound data types and string library. Note that our solution has less than 50 lines of code. You may assume that a user always enters a valid move.

You may use any functions/operators for this question.

Sample runs:

Size--> 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 1 0 X 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 13 0 X 2 3 4 5 6 7 8 9 10 11 12 O 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 2 0 X X 3 4 5 6 7 8 9 10 11 12 O 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 14 0 X X 3 4 5 6 7 8 9 10 11 12 O O 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 3 0 X X X 4 5 6 7 8 9 10 11 12 O O 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 15 0 X X X 4 5 6 7 8 9 10 11 12 O O O 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 4 0 X X X X 5 6 7 8 9 10 11 12 O O O 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 16 0 X X X X 5 6 7 8 9 10 11 12 O O O O 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 5 0 X X X X X 6 7 8 9 10 11 12 O O O O 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 17 0 X X X X X 6 7 8 9 10 11 12 O O O O O 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 6 0 X X X X X X 7 8 9 10 11 12 O O O O O 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 18 0 X X X X X X 7 8 9 10 11 12 O O O O O O 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 0 X X X X X X X 7 8 9 10 11 12 O O O O O O 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Winner: X

Size--> 9 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 X--> 0 X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 O--> 72 X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O 73 74 75 76 77 78 79 80 X--> 1 X X 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O 73 74 75 76 77 78 79 80 O--> 73 X X 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O 74 75 76 77 78 79 80 X--> 8 X X 2 3 4 5 6 7 X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O 74 75 76 77 78 79 80 O--> 80 X X 2 3 4 5 6 7 X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O 74 75 76 77 78 79 O X--> 7 X X 2 3 4 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O 74 75 76 77 78 79 O O--> 79 X X 2 3 4 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O 74 75 76 77 78 O O X--> 2 X X X 3 4 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O 74 75 76 77 78 O O O--> 74 X X X 3 4 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O 75 76 77 78 O O X--> 3 X X X X 4 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O 75 76 77 78 O O O--> 75 X X X X 4 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O O 76 77 78 O O X--> 4 X X X X X 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O O 76 77 78 O O O--> 76 X X X X X 5 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O O O 77 78 O O X--> 5 X X X X X X 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O O O 77 78 O O O--> 77 X X X X X X 6 X X 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O O O O 78 O O X--> 15 X X X X X X 6 X X 9 10 11 12 13 14 X 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O O O O 78 O O O--> 78 X X X X X X 6 X X 9 10 11 12 13 14 X 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 O O O O O O O O O Winner: O

Size--> 6 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 0 X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 1 X O 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 2 X O X 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 3 X O X O 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 4 X O X O X 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 5 X O X O X O 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 12 X O X O X O 6 7 8 9 10 11 X 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 13 X O X O X O 6 7 8 9 10 11 X O 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 14 X O X O X O 6 7 8 9 10 11 X O X 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 15 X O X O X O 6 7 8 9 10 11 X O X O 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 16 X O X O X O 6 7 8 9 10 11 X O X O X 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 O--> 17 X O X O X O 6 7 8 9 10 11 X O X O X O 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 X--> 24 X O X O X O 6 7 8 9 10 11 X O X O X O 18 19 20 21 22 23 X 25 26 27 28 29 30 31 32 33 34 35 O--> 25 X O X O X O 6 7 8 9 10 11 X O X O X O 18 19 20 21 22 23 X O 26 27 28 29 30 31 32 33 34 35 X--> 26 X O X O X O 6 7 8 9 10 11 X O X O X O 18 19 20 21 22 23 X O X 27 28 29 30 31 32 33 34 35 O--> 27 X O X O X O 6 7 8 9 10 11 X O X O X O 18 19 20 21 22 23 X O X O 28 29 30 31 32 33 34 35 X--> 28 X O X O X O 6 7 8 9 10 11 X O X O X O 18 19 20 21 22 23 X O X O X 29 30 31 32 33 34 35 O--> 29 X O X O X O 6 7 8 9 10 11 X O X O X O 18 19 20 21 22 23 X O X O X O 30 31 32 33 34 35 X--> 11 X O X O X O 6 7 8 9 10 X X O X O X O 18 19 20 21 22 23 X O X O X O 30 31 32 33 34 35 O--> 10 X O X O X O 6 7 8 9 O X X O X O X O 18 19 20 21 22 23 X O X O X O 30 31 32 33 34 35 X--> 9 X O X O X O 6 7 8 X O X X O X O X O 18 19 20 21 22 23 X O X O X O 30 31 32 33 34 35 O--> 8 X O X O X O 6 7 O X O X X O X O X O 18 19 20 21 22 23 X O X O X O 30 31 32 33 34 35 X--> 7 X O X O X O 6 X O X O X X O X O X O 18 19 20 21 22 23 X O X O X O 30 31 32 33 34 35 O--> 6 X O X O X O O X O X O X X O X O X O 18 19 20 21 22 23 X O X O X O 30 31 32 33 34 35 X--> 23 X O X O X O O X O X O X X O X O X O 18 19 20 21 22 X X O X O X O 30 31 32 33 34 35 O--> 22 X O X O X O O X O X O X X O X O X O 18 19 20 21 O X X O X O X O 30 31 32 33 34 35 X--> 21 X O X O X O O X O X O X X O X O X O 18 19 20 X O X X O X O X O 30 31 32 33 34 35 O--> 20 X O X O X O O X O X O X X O X O X O 18 19 O X O X X O X O X O 30 31 32 33 34 35 X--> 19 X O X O X O O X O X O X X O X O X O 18 X O X O X X O X O X O 30 31 32 33 34 35 O--> 18 X O X O X O O X O X O X X O X O X O O X O X O X X O X O X O 30 31 32 33 34 35 X--> 30 X O X O X O O X O X O X X O X O X O O X O X O X X O X O X O X 31 32 33 34 35 O--> 31 X O X O X O O X O X O X X O X O X O O X O X O X X O X O X O X O 32 33 34 35 X--> 32 X O X O X O O X O X O X X O X O X O O X O X O X X O X O X O X O X 33 34 35 O--> 33 X O X O X O O X O X O X X O X O X O O X O X O X X O X O X O X O X O 34 35 X--> 34 X O X O X O O X O X O X X O X O X O O X O X O X X O X O X O X O X O X 35 O--> 35 X O X O X O O X O X O X X O X O X O O X O X O X X O X O X O X O X O X O Winner: None

Size--> 3 0 1 2 3 4 5 6 7 8 X--> 0 X 1 2 3 4 5 6 7 8 O--> 1 X O 2 3 4 5 6 7 8 X--> 2 X O X 3 4 5 6 7 8 O--> 3 X O X O 4 5 6 7 8 X--> 4 X O X O X 5 6 7 8 O--> 5 X O X O X O 6 7 8 X--> 6 X O X O X O X 7 8 Winner: X