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How many proper subsets of {1, 2, 3, 4, 5} contain the numbers 1 and 5? How many of them do not contain the number 2? Justify your answers.
Use truth tables to prove that an implication is always equivalent to its contrapositive. Site an example where this is so.
How many bit strings of length 6 are there which begin with a 0 and end with a 1? Explain.
An auto insurance company classifies its customers in three categories: poor, satisfactory, and preferred.
Of 100 clock radios with digital tuners and/or CD players sold recently in a department store, 70 had digital tuners and 90 had CD players.
Automata theory involves the study of mathematical objects called automata and the computational problems that can be solved using them.
What is the difference between combinations and permutations? What are some practical applications of combinations? Permutations?
Solve the two-dimensional wave equation for a quarter-circular membrane, the boundary condition is such that u=0 on the entire boundary.
Approximate y(1) using Euler's method and step sizes of 0.2. Perform these calculations by hand. What is the exact value of y(1)?
Using the bisection method, find the positive root of 2x(1 + x^2)^-1 = arctan x. Using this root as x0.
Show that the series state solution for the initial value problem approaches the steady state solution of the initial value problem as t ?8.
Use a fixed-point iteration method to find an approximation to 3v25 that is accurate within 10-4.
How to estimate the abosolute and relative maximum and average errors in the total of the above rounded data?
Determine the flow Qt : R^2 into R^2 for the nonlinear system: x' =f(x) with
Write down the conditions required for the spline S(x) to fit the data and have 6 continuous derivatives, i.e. S(x) E C^6[x0,xn].
Lobsters cannot survive more than 30 hours in refrigeration. How many half-hour breaks can the driver take and still deliver the lobsters alive?
Determine the order of each differential equation, and whether or not the given functions are solutions of that equation on some interval of x values.
What factors other than admission price influence annual attendance and thus should be considered in the forecast?
On the following terms could you please give my an English text description – in your own words.
Using the numbers 3, 3, 8 and 8 once and only once, obtain the target number of 24. (You have to use 3 twice and 8 twice - 3 x 8 = 24 is not acceptable).
Suppose that a population develops according to the logistic equation: dP/dt = 0.15P - 0.003P^2
Having trouble researching the number of deaths in the US each year due to each of the following medical conditions.
The average numbers of home runs hit by the Boston Red Sox per game are.
Determine if the following functions satisfy local or uniform Lipschitz condition.
Verify that it is the solution to the differential equation x^2 y'' + x y' + _x^2 y = 0, satisfying y(0)=1, y'(0)=0.