Gunfighters A, B, and C are to fight a three-cornered pistol duel. All know that A’s chance of hitting the target is 0.3, C’s is 0.5, and B never misses. They are to fire at their choice of target in succession in the order of A, B, and C, cyclically (but a hit man loses his turn and is no longer shot at) until only one man is left unhit. What should A’s strategy be? a. Shoots B first b. shoots the ground c. shoot C first d. Shoot himself

You and a friend are spending two days in the woods; you both enjoy hiking. HOWEVER, each of you believes with probability π a bear in the woods may have ingested a brick of cocaine.If a bear is high on cocaine, anyone hiking will surely be attacked. Each of you receives −c for being attacked by a bear on blow, 0 to staying at your cabin, and 1 for a day’s worth of hiking (c > 0).If either of you is attacked by the cocaine bear on the first day, then you both know the cocaine bear exists and whoever hikes will surely be attacked on the second day, and hence no one will hike, receiving 0.If at least one person hikes and is not attacked on the first day then you know the forest is safe for sure and will hike on the 2nd day, earning 1.If neither of you hike, then on the second day you have the same belief as the first (π), and hike if and only if −πc + 1 − π ≥ 0 (i.e., your expected utility from hiking is higher than not hiking).(HINT: you need to consider both the case where −πc+1−π ≥…

5 Compute A² and A³. Make a prediction for A5 and An: b 22 4= [1] and 4 = [²2] A A .

A botanist wants to determine if a fertilizer is effective in Which of the following is a valid conclusion? the growth of plants. He randomly selects 100 of the same type of seedling and randomly assigns them to two groups: one that uses the fertilizer, and one that does not. He makes sure the plants all have the same amount of water, soil, and light for two months. At the end of two months, he measures the heights of the plants and finds that the ones receiving the fertilizer are O Inferences can be made for all plants, and the conclusion can be drawn that the fertilizer will help all plants grow taller. O Inferences cannot be made for all plants, and the conclusion cannot be drawn that the fertilizer will help these plants grow taller. Inferences can be made for these types of plants, significantly taller. and the conclusion can be drawn that the fertilizer will help these types of plants grow taller. Inferences cannot be made for these types of plants, 29 and the conclusion cannot…

Solve the following using Cramer's rule. A family of 3 people went out for dinner in a restaurant. The cost of two dosai, three idlies and two vadais is Php150. The cost of the two dosai, two idlies and four vadais is Php200. The cost of five dosai, four idlies and two vadais is Php250. The family has Php350 in hand, and they ate 3 dosai and six idlies and six vadais. Will they be able to manage to pay the bill within the amount they had ? Let "x", "y" and "z" be the cost of 1 dosa, 1 idly and 1 vada respectively. 2x + 3y + 2z = 150 2x + 2y + 4z = 200 5x + 4y + 2z = 250

The boxplots for the grade scores in the midterm exam in a Calculus I class for two different classes is attachedClass 1: Q1= 65 M= 70 Q3 = 80Class 2: Q1= 60 M= 70 Q3 = 75Which class is likely to have a greater percentage of students with grades smaller or equal to 70? Class 2 Class 1      It is impossible to tell. Neither Both classes are about equal. Which class has 50% percentage of students with grades between 70 and 80? Class 2 Both classes are about equal.      Neither It is impossible to tell. Class 1 For which class did 25% of students receive grades between 60 and 70? Both classes are about equal. Class 1      Class 2 Neither It is impossible to tell.

Let a = (2, 3, 4) and b = (-2,0, 5). Find a x b

Please solve A,B,C,D AND E

Given a. u + v b. w-v c. w. u (2, 6), u = (-1,4), and u = (3,-7), find each of the following. - d. 2. (u – v)

On a certain hole, a golfer knows that he has a 70% chance of reaching the green (putting surface) in one stroke, 20% in two strokes, 8% in three, and 2% in four or more. If he reaches the green on his first stroke, he has an 80% chance of putting the golf ball in the cup on his second stroke. If he does not reach the green on his first stroke, then he has a 30% chance of putting the golf ball in the cup on his second stroke. What is the probability that the golfer will reach the green in one stroke and put the ball in the cup on his second stroke? 0.09 0.21 0.56 0.80