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mand is 18,200 rolls. When the demand increases to 26,200 rolls, the supply is 20,000 and the price is $1.24 per roll. Let x be the quantity in thousands of rolls. The table below gives the price-supply and price-demand equations. Price Equations for Toilet Paper Type Equation Price-Supply P = -0.04x + 2.04 Price-Demand P = 0.025x + 1.495 QUESTION 1 Find the supply at a price of $2 per roll. 1000 rolls 10,000 rolls 1 roll 5000 rolls QUESTION 2 Find the demand at a price of $2 per roll. 20.2 rolls 202 rolls 20,200 rolls 500 rolls QUESTION 3 Use the substitution method to find the equilibrium quantity. Round x to the nearest tenth first and then convert to thousands. Include the units in your answer. QUESTION 4 What is the equilibrium price? Write the answer in dollars and cents, rounding to the nearest cent.

er-example (if false). (a) If |f | is integrable on [a, b], then f is also integrable on [a, b]. (b) If f = F ′ for some function F on [a, b], then f is continuous on [a, b]. (c) If g is continuous on [a,b], then g = G′ for some G on [a,b]. (d) If G(x) = ???? x g is differentiable at p ∈ (a, b), then g is continuous at p.

ind ε when p = 8 .The supply for a particular item is given by the function S ( x ) = 15 + 7 x . Find the producer's surplus if the equilibrium price of a unit $ 99 .

producer's surplus if the equilibrium price of a unit $ 99 .A retailer anticipates selling 7600 units of its product at a uniform rate over the next year. Each time the retailer places an order for x units, it is charged a flat fee of $ 100 . Carrying costs are $ 38 per unit per year. How many times should the retailer reorder each year and what should be the lot size to minimize inventory costs? What is the minimum inventory cost? For a particular commodity, the demand function is q = 1 4 ( 400 − p 2 ) . a . Find ε when p = 8 .A hotel rents 240 rooms at a rate of $ 60 per day. For each $ 1 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.

tal-revenue and​ total-cost functions, find the total​ profit, the maximum value of the total​ profit, and the value of x at which it occurs. Upper R left parenthesis x right parenthesis equals 1300 x minus x squared​, Upper C left parenthesis x right parenthesis equals 3000 plus 30 x The total​ profit, ​P(x)equals negative x squared plus 1270 x minus 3000. ​(Simplify your answer. Do not​ factor.)

C D Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with ∠DAB = x, and ∠ABC = 90◦ , and AD = BC. Say the perpendicular bisector to DC meets the perpendicular bisector to AB at P. Then P A = P B and P C = P D. So the triangles P AD and P BC have equal sides and are congruent. Thus ∠P AD = ∠P BC. But P AB is isosceles, hence ∠P AB = ∠P BA. Subtracting, gives x = ∠P AD − ∠P AB = ∠P BC − ∠P BA = 90◦ . This is a preposterous conclusion – just where is the mistake in the “proof” and why does the argument break down there?

2)(x - 3)(x + 3) d. (x2 - 4)(x2+ 9) Value: 1 The table below shows the cost of purchasing a standard stapler at five office supply stores, A through E. If the median cost of purchasing a standard stapler for these stores was $17.99, which of the following could NOT have been the cost of the stapler for Store A? staplergraph.jpg a. $19.95 b. $18.95 c. $16.95 d. $19.25 Value: 1 If equation image indicator then x = a. 7 b. 1/5 c. 5 d. 1/7 Value: 1 A six−sided die, with sides numbered 1,2, 3,4,5, and 6, is tossed. What is the probability of tossing a number less than three? a. 1/3 b. 0 c. 1/2 d. 1/4 Value: 1 If 6m + 4 = 8m, then 4m = a. 6 b. 2 c. 8 d. 4 Value: 1 In the xy-plane, what is the y-intercept of the graph of the equation equation image indicator? a. 2 b. 4 c. 16 d. There is no y-intercept. Value: 1 Which of the following equations has both 2 and −4 as solutions? a. x2 + 6x + 8 = 0 b. x2 - 2x - 8 = 0 c. x2 + 2x - 8 = 0 d. x2 - 2x + 8 = 0 Value: 1 The perimeter of a square is 20 ft. If you increase the length of the square by 2 feet and decrease the width by 1 foot, what is the area, in square feet, of the new figure? a. 22 b. 28 c. 35 d. 40 Value: 1 (3x-2y4)-3 = a. equation image indicator b. equation image indicator c. equation image indicator d. equation image indicator Value: 1 A softball is tossed into the air upward from a first floor balcony. The distance of the ball above the ground at any time is given by the function, distance function.png, where h(t) is the height of the softball above the ground (in feet) and t is the time (in seconds). What was the maximum height, in feet, of the softball above the ground after it was thrown? a. 28 b. 30 c. 32 d. 34 Value: 1 A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening? a. 20 b. 50 c. 70 d. 80 Value: 1 The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank? a. 21 b. 15 c. 19 d. 9 Value: 1 In the xy−coordinate plane shown below, point P has coordinates (8, −6). Which of the following is an equation of the line that contains points O and P? O and P graph.jpg a. equation image indicator b. equation image indicator c. equation image indicator d. equation image indicator Value: 1 The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9? a. 54 b. 6 c. 2/3 d. 3/2 Value: 1 A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees planted in each row and each row must be complete before it is planted, how many trees will be left over after planting? a. 21 b. 11 c. 0 d. 55