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Let b = r_0, r_1, r_2, ... be the successive remainders in the Euclidean Algorithm applied to a and b.
If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?
Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman?
A governor would like to find out how people in his state feel about state subsidized public art. How might a cluster sample be selected?
The height (h) (in feet) of an object that is dropped from the height of (s) feet is given the formula h=s-16t^2, where (t) is the time the object.
The formula for profit (P) is cost (C) minus overheard (O). Write an equation for profit and then translate it to solve for cost.
You have $5100. to invest in two different investments. Investment A pays 4% and investment B pays 6% You would like to earn $265. in interest.
If United States imports increased 20 percent and exports decreased 10 percent during a certain year, the ratio of imports to exports at the end of the year.
Future Values. Compute the future value of a $100 cash flow for the same combinations of rates and times as in problem 1.
A woman deposits $50,000 in a savings account with 4% continuously compounded interest. How many years must she wait until the balance has doubled?
You have exactly $537 to spend on parting gifts for your rich uncle's birthday party. You decide to get watches for the ladies.
Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2?
Time of flight. Using the information from Exercise 115 to determine how long Johnson was in the air. For how long was he more than 14 ft in the air?
If they take 2 hours to mow it when working together, then how long would it take Winston working alone?
Using the index "n" of the partial sums of a series as the domain, and the value of the corresponding partial sums of the series.
What is the optimal solution to the integer linear programming problem? State the value of the objective function Z = x or x.x.
What is the optimal solution? Z = ? Put your answer in the form xx with no additional numbers or symbols.
The period T (time in seconds for one complete cycle) of a simple pendulum is related to the length L (in feet) of the pendulum by the formula.
Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true.
How far can you see to the horizon from the top of Long’s Peak? Can you see Cheyenne, Wyoming (about 89 miles away)?
Prove that Z(G)=1. Use the fact that the group generated by "g" is less than or equal to C_G(g) for all "g" .
Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.
A 40-ounce can of cling peaches (remember that episode of All in the Family?) sells for $2.80. At the same rate, what would a 10-ounce can sell for?
A professor started a project with a group of students, 60% of whom were boys, due to some unavoidable reason.
The credit remaining on a phone card in dollars is a linear function of the total time in minutes. When graphed, the function gives a line with a slope of -0.13