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A. Let d ∈ N and V := {0, 1} d ; thus, V is the set of all 0-1 sequences of length d. The graph on V in which two such sequences form an edge if and only if they differ in exactly one position is called the d-dimensional cube. Determine the average degree, number of edges, diameter, girth and circumference of this graph. (Hint for the circumference: induction on d).
B. Let G be a graph containing a cycle C, and assume that G contains a path of length at least k between two vertices of C. Show that G contains a cycle of length at least √ k. Hint [1]: Consider how the path intersects C. Where can you see cycles, and can they all be short?
Price the European option to swap gold for silver that matures in 6 months. suppose the storage cost, as a rate, of gold is .05 and of silver is .06. What is the exchange option worth?
the time spent in days waiting for a heart transplant in two states for patients with type a blood can be approximated
Determine the area of the largest rectangle that can be inscribed in a semicircle of radius 8". Figure shows that the area can be written as A =(2x)y, if (x,y) is the point of the upper right corner of the rectangle.
If the water level is rising at a rate of 15000 centimeters per minute when the height of the water is 4500 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.
How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
A is the amount of material remaining from an initial amount I at a given time t and k is negative constant determined by the nature of the material.
Suppose that the average outstanding credit card balance for young couples is $650 with a standard deviation of $ 420. If a couple is selected at random, what is the probability the outstanding credit card balance exceeds $ 700?
Mary and Tom park their cars in an empty parking lot with n≥2 consecutive parking spaces (i.e, n spaces in a row, where only one car fits in each space). Mary and Tom pick parking spaces at random. (All pairs of parking spaces are equally likely.)..
a college student invests 8000 in an account that pays interest annually. if the student would like this investment to
A father and his son can clean the house together in 4 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long it takes the son to clean alone.
find the maximum depth using the given function.suppose the function dt t2nbsp- 14t models the depth of a scuba diver
Starbucks cashiers take thousands of orders each day. Samples of the accuracy in the orders are listed below. One hundred orders taken by each cashier were carefully examined and the number of errors counted.
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