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The air in the room 50 ft by 20 ft by 8 ft tests 0.2% carbon dioxide. Starting at t=0, outside air testing 0.05% carbon dioxide is admitted to room. How many cubic feet of this outside air should b
A DNA chain is string of As, Ts, Gs, and Cs. How many DNA chains are there of length 12 which have the following properties? Has string of 10 or more consecutive Gs.
Suppose that the risk free rate is 3.5%. Determine the premium of one-year call option with strike price of $38.50, if the profit of the buyer of the call is $4.78 and stock spot price is $44.34 at
Find out the current i at any time t after the switch is closed. 3 Determine the maximum current that can be obtained from the simple circuit?
Determine the relation between recursion and induction? How do you go about finding an explicit (closed-form) formula for a recursion relation?
Prove the following Theorem. If (X,d) is a metric space, then there is bounded metric on X which is equivalent to d. recall: When we say a metric p is bounded, we mean that there exists an M >0
Find the value of k so that the given differential equation is exact. (y^3 + kxy^4 ? 2x) dx + (3xy^2 + 24x^2(y^3)) dy = 0.
Find out whether the given differential equation is exact. If it is exact, solve it. (y ln y ? e?xy) dx + (1/y + x ln y) dy = 0.
The following data can be employed to approximate the integral: M = ?3? ÷ 2 0 cos x dx N1(h) = 2.356194 N1(h ÷ 2) = -0.4879837 N1(h ÷ 4) = -0.8815732 N1(h ÷ 8) = -0.97091
Show that the following equation has a solution of the form u(x,y) = e^(ax+by). Find the constants a and b: u_xx + u_yy = 5e^(x-2y)
A copper pipe, employed for plumbing from the water main to a house, is 5 meters long and has a circular cross-section 2.8 cm in diameter. There is a 2 cm diameter hole in the center of the cross-s
Carry out eulers method twice to approximate to this solution on interval [0, 0.5], first with step size h = 0.25, then with step size h = 0.1. Compare the three decimal-place values of the two app
Determine an example of a family {Un : n is an element of N} of open sets of R for which the intersection from n=1 to infinity Un is not open.
In the US Senate, each of 100 Senators has one vote, and vice president of US can vote also if it is necessary to break tie. If simple majority is required to pass a bill, what constitutes a winnin
Determine the directional derivative on the surface z=f(x,y)=3(x^2)(y^3) at the point (7,2) in the direction of vector i + j ? Round off to the nearest integer.
Which of the following isn't the credit risk faced by a trader who purchases a call option?
Assume A is a matrix with pivot position in every row. Is it true that the columns of A form a linearly indpendent set? If so, explain why. If false give a counter example.
Determine the smallest natural number N such that any amount n>=N can be paid using $2 and $5 bills by using strong induction.
A production procedure produces 90% non-defective parts. A sample of 10 parts from production process is chosen. Determine the probability that the sample will contain 2 to 6 defective parts?
Employ your answer to part a to write down revenue as a function of price. c) Graph the revenue function in part b. Find the price that maximizes revenue. What is the revenue at this price?
A bicycle pedal is pushed straight downwards by the foot with 26 Newton force. The shaft of the pedal is 20 cm long. If the shaft is \pi / 5 radians past horizontal, determine the magnitude of the
After considering lines of equal objective function value (the contour lines or topographical lines in figure 2.2 on page 18), why is necessary that a linear model will have either a single maximum
Let s denote the success of the read operation, f denote the failure of read operation, F denote the failure of an error recovery, S denote a success of an error recovery, and A denote an abort mess
Suggest a three-person voting system with voters A, B, and C. The winning coalitions are {A, B, C}, {A, B}, {A, C}. Find out the Banzhaf power index for this voting system.
In the US Senate, each of 100 Senators has one vote, and vice president of the US can vote also if it is necessary to break a tie. If simple majority is needed to pass a bill, what constitutes a wi