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What constitutes a rational expression? Please give an example for reference. How would you explain this concept to someone unfamiliar with it?
Compute the discriminant of the quadratic equation 3x2+x+2=0. Briefly describe the number and type of solutions for this equation.
Polynomial Linear Operator. Show that T is a linear operator.Find the nullspace and range of T.
Why is this process more difficult than when the leading coefficient is equal to one? Give an example.
In an exponential smoothing model, if the smoothing constant (alpha) were equal to 0, then the forecast would be the same as the forecast for the naive model.
Forecast sales for week 5 using exponential smoothing with a smoothing constant of 0.4 . Assume the forecast for week 1 is perfect.
There were 77 birds on the endanger species list in 2005. This is 7 more than 5 times the number of reptiles list.
Determinants Prove: 1) if A, B are square and AB=I_n, then det B=1/det A 2) if A, B, S are square and B=(S^-1)AS, then det B=det A
Distributive property to rewrite expression then simplify expression. Rewrite each fraction with the Lowest Common Denominator.
Tetrahedral and Octahedral Groups.Let G=O be the group of rotations of a cube. Two regular tetrahedra can be inscribed in this cube
Draw a scatter plot and find the equation of the least square line for the given data. From the least square equation, find the percentage for year 1999.
Coin Combination Probability.Suppose you have 50 American coins totaling exactly $1.
In 2000, the average cost of tuition and fees at public four- year colleges was $3500, and in 2005 it was $5100.
Find real-values fundamental set of solutions of the general solution.Identify its equilibrium solution; classify the type and stability characteristics
A university bookstore recently sold a wirebound graph-paper notebook for $3.36 and a college-ruled notebook for $4.57.
Four different methods of solving a quadratic equation have been discussed: factoring, the square root property, completing the square.
Find the discount and proceeds on a 3,240 face value note for six months if the discount rate is 9.3%.
Obtain the solution of the differential equation with initial condition N(0) =2, assuming the parameters c=1 and ?=1/2.
Solve the system of simultaneous equations.Solve each system. State whether it is inconsistent or has infinitely many solutions
Eigen function and eigenvalues.Consider a linear operator A^with two sets of eigenfunctions and eigenvalues:
Use Y=196x-379,400 to estimate the number of radio stations on the air in 1975 and 1985.
Find three consecutive integers such that the product of -5 and the sum of the first two is 43 less than twice the second.
The profit for a company is determined by the equation y = 0.02x - 0.30, where y represents the profit and x represents the number of items sold.
Explain how you can find the difference 120-70 using mental math. Then name the difference.
Jackie, a 25 year old client, want to retire by age 65 with $2,000,000. How much would she have to invest annually, assuming a 6% rate of return?