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In algebra, we often have to solve simultaneous differential equations. If the equations are linear and independent, there is a unique solution when the number of equations equals the number of variables. If there are only two variables and two equations, it's easy, but as the number of equations and unknowns increases, the problem becomes more difficult. Imagine, for example trying to solve 100 equations in 100 unknowns. That's an unthinkably difficult manual exercise, but a good computer program can do it in less than a second. Suppose you want the solution to this pair of equations: 2 * x + y = 1 4 * y = 12 In the first equation, the coefficient of x is 2 and the coefficient of y is 1. In the second equation, the coefficient of x is 0, and the coefficient of y is 4. The right-side values are 1 and 12, respectively. It's easy to solve this pair of equations by hand. The second equation says y = 12/4 = 3, and substituting this back into the first equation gives x = (1-3)/2 = -1.
A company is evaluating two competing investments. Investment X has a cost of $100,000 and a NPV estimated at $35,000. Investment Y has a cost of $220,000 and a NPV estimated at $35,500. Taking everything into account, you would recommend the company..
Grantran Metrics is considering new equipment to run their service function for their customers. This equipment would run faster and less expensively than equipment currently in place. This would be best characterized as:
Duggins Veterinary Supplies can issue perpetual preferred stock at a price of $72.50 per share with an annual dividend of $4.50 a share. Ignoring flotation costs, what is the company's cost of preferred stock, rps?
Gontier Corporation stock currently sells for $64.93 per share. The market requires a return of 12 percent on the firm’s stock. If the company maintains a constant 5.5 percent growth rate in dividends, what was the most recent dividend per share paid..
Suppose you are considering either working through school or taking out loans. If you work at a 20 hour job at $15 per hour over 50 weeks per year, you can make $15,000, but it will take 5 years to graduate. How many years will it take to pay back th..
A firm is trying to decide whether to produce a new product. In order to produce this product, the firm would have to invest $4,906,000 in machinery and $490,600 in net working capital. The machinery would be depreciated using the 5-year depreciation..
Paychex Inc. (PAYX) recently paid a $0.86 dividend. The dividend is expected to grow at a 15 percent rate. The current stock price is $62.91. What is the return shareholders are expecting?
A firm is expected to pay a dividend of $2.35 next year and $2.65 the following year. Financial analysts believe the stock will be at their price target of $105 in two years. Compute the value of this stock with a required return of 11.3 percent.
You own a stock portfolio invested 30 percent in Stock Q, 25 percent in Stock R, 10 percent in Stock S, and 35 percent in Stock T. The betas for these four stocks are 1.47, 0.85, 0.63, and 1.14, respectively. What is the portfolio beta?
SolarTech Inc. is expected to pay a $2.50 dividend at year end, the dividend grows at a constant rate of 5.50% a year, and the common stock currently sells for $67.50 a share. The before-tax cost of debt is 7.50%, and the tax rate is 40%. The company..
Solve the following equations
Solving the expression by using order of operations
Factor algebraic expression.
write a function rule for the area of a rectangle whose length is 6ft. more than its width?then find the area of a
From 1997 through 2004, the value of US exports to Mexico was as shown below. Data are in billions of dollars. Fit a linear trend equation to the time series. Using this equation, determine the trend estimate for 2012.
Apply the simplex method to solve the problem.
a rock is thrown upward from the edge of a 50 m cliff overlooking lake superior with an initial velocity of 17.2 ms.
Find the solution for x
The number of tickets sold each day for an upcoming performance of Handelâ??s Messiah is given by N(x)=-0.4^2+12x+10, where x is the number of days since the concert was first announced. When will daily ticket sales peak and how many tickets will ..
When we square a product, we square each factor in the product. For example, (3b)^2= 9b^2. Explain why we cannot square a sum by simply squaring each term of the sum.
Find the LCM of the denominators
What are like terms? Explain how the distributive property is used to combine like terms. Please use a problem from pages 458 - 459 #'s 41 - 62 as your example for this question.
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