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Problem 1: Let f(x) = 5x2 - 7x + 8 and g(x) = 1 - 3x.
a. Find the difference function (f - g)(x) and simplify the result. Show work.
b. Find (g - f)(-1). Show work.
c. Find (fg)(-1). Show work.
Problem 2: The cost, in dollars, for a company to produce x widgets is given by C(x) = 4700 + 5.20x for x > 0, and the price-demand function, in dollar per widget, is p(x) = 40 - 0.02x for 0 < x < 2000.
a. Find and interpret C(500).
b. Find and interpret C(500). (Note that C(x) is average cost function.)
The volume of a square-based rectangular cardboard box needs to be 1000 cm^3. Determine the dimensions that require the minimum amount of material to manufacture all six faces.
Facebook reports that the average number of Facebook friends worldwide is 175.5 with a standard deviation of 90.57. If you were to take a sample of 25 students, what is the probability that the mean number Facebook friends in the sample will be 19..
Find the resultant sum of the complex numbers.
Kendra pawned her guitar for $100. Her guitar was valued at $150. If Kendra paid the pawnbroker $150. to get her guitar back after one month, what annual percent interest rate did she end up paying?
Ken borrowed $6,000 for 4 years at a rate of 7% simple interest per year. How much interest will Ken have to pay after paying back the borrowed amount?
Find the mass of the lamina and the coordinates of the centre of mass.
The measure of angle A is 66 degrees and side c = 60 yd.
The relationship between the numbers of calculators x a company sells per day and the price of each calculator p i given by the equation x = 1300-100p. At what price should the calculators be sold if the daily revenue is to be $4,000?
Which of the following would be a valid tensor equation? You should indicate if the equation is valid; and if it is not valid, you should state why.
Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.
Calculate the probability that a student with an A on the midterm examination will obtain a final grade of A?
One card is drawn from a well-shuffled deck of 52 cards (no jokers). Find the probability of drawing a card above an 8(count an ace as high).
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