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Two weather tracking stations are on the equator 159 miles apart. A weather balloon is located on a bearing of N 38°E from the western station and on a bearing of N 14°E from the eastern station. How far is the balloon from the western station?
Modelling the Rules of a Game. Alex and Mark are playing a game. The goal is to get to 100. The first player picks a whole number from 1 to 10, inclusive, and then the second player picks a whole number from 1 to 10 and adds it to the score so far..
Explain what the index of a subgroup and a coset of a group are. Also, prove that if N is a subgroup of a group G such that [G: N] = 2, and if "a" and "b" are elements of G,
how to find the sum of each series?
Calculate the value of the sample correlation coefficient between weekly sales & shelf space.
What are the possible orders of subgroups of S4? Prove that S4 has at least one subgroup of each of these orders. What are the elements of these subgroups?
Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x).
Let G be the group of symmetries of a cube, including the orientation-reversing symmetries. Describe the elements of G geometrically.
Calculate the probability, A random variable T is selected that is uniformly distributed over the interval
Discrete probability distribution
Find the volume of a triangle with sides y = 2, y = x+1, y = 11-x. The vertices are (5, 6), (1, 2) and (9, 2). Find the volume by rotating about y-axis:
Assume that a watermelon dropped from a tall building falls y=16t^2 in t sec. Find the watermelon's average speed during the first 3 sec of fall and the speed at the instant t=3sec.
The points (1,2) and (7,12) lie on a line. Find the coordinates of a third point on the line. how can you use the idea of slope.
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