Precalculus Questions - Final Test

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WebAssign 131-FinalReview (Homework) Current Score : 5 / 72 Sarah Saad MTH131-SP2018, section 01, Spring 2018 Instructor: Mojtaba Sirjani Due : Wednesday, May 2 2018 12:00 PM EDT 1. –/2 pointsHarMathAp11 0.3.061. If $P is invested for n years at a rate i (as a decimal), compounded annually, the future value that accrues is given by S = P(1 + i)n, and the interest earned is I = S − P. Find S and I for the given P, n and i. (Round your answers to the nearest cent.) $1200 for 4 years at 16% S = $ I = $ 2. –/1 pointsHarMathAp11 0.4.053. Rationalize the denominator and then simplify. 5 11 3. –/1 pointsHarMathAp11 0.4.076. Suppose it has been determined that the sales at a gallery decline after the end of an advertising campaign, with daily sales given by S = 9000(2−0.1x) where S is in dollars and x is the number of days after the campaign ends. What are the daily sales 40 days after the end of the campaign? $ 4. –/2 pointsHarMathAp11 0.5.070. Suppose a company's revenue R (in dollars) from the sale of x units of its product is given by R = 350x. Suppose further that the total costs C (in dollars) of producing those x units is given by C = 70x + 20,000. (a) If profit is revenue minus cost, find an expression for the profit from the production and sale of x units. P= (b) Find the profit received if 4500 units are sold. P=$ 5. –/2 pointsHarMathAp11 0.5.071. A rental truck costs $50.45 for a day plus 54¢ per mile. (a) If x is the number of miles driven, write an expression for the total cost C, in dollars, of renting the truck for a day. C= (b) Find the total cost of the rental if it was driven 194 miles. C=$ 6. –/1 pointsHarMathAp11 0.6.006. Factor by grouping. 2y − 10 − x2y + 5x2 7. –/4 pointsHarMathAp11 0.6.020. Factor each expression as a product of binomials. (a) 10x2 − 99x − 63 (b) 10x2 − 27x − 63 (c) 10x2 + 61x − 63 (d) 10x2 + 9x − 63 8. –/1 pointsHarMathAp11 0.6.030. Factor completely. x5 + 12x4 + 36x3 9. –/1 pointsHarMathAp11 0.7.001. Simplify the fraction. 12x2y7 4x2z 10.–/1 pointsHarMathAp11 0.7.009. Perform the indicated operation and simplify. 9x − 45 · 7x − 21 x−3 8x − 40 11.–/1 pointsHarMathAp11 0.7.023. Perform the indicated operation and simplify. a a−2 − a−2 a 12.–/1 pointsHarMathAp11 0.7.038. Simplify the complex fraction. 7 + 5 3y y 1 1 + 4 5y 13.–/1 pointsHarMathAp11 0.7.047.MI. Rationalize the denominator of the fraction and simplify. 5− x 5+ x 14.–/1 pointsHarMathAp11 0.7.049. Rationalize the numerator of the fraction and simplify. 5x + h − 5x h 15.–/1 pointsHarMathAp11 1.1.029. Solve S = P + Prt for t. t= 16.–/2 pointsHarMathAp11 1.1.037. Solve the inequality. 5(x − 1) − 6 > 8x + 1 Graph the solution. 17.–/1 pointsHarMathAp11 1.1.043. A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 − 1800x dollars. After how many months will the value of the building be $412,800? x= months 18.–/1 pointsHarMathAp11 1.1.047. Burnem, Inc. manufactures blank CDs and sells them to a distributor in packs of 500 CDs. Burnem's total cost and total revenue (in dollars) for x packs of 500 CDs are given by the following equations. Total cost = 4x + 4873 and Total revenue = 15x How many packs of 500 CDs must Burnem sell to break even? x= packs 19.–/2 pointsHarMathAp11 1.1.059. For a certain product, the revenue is given by R = 70x and the cost is given by C(x) = 50x + 1200. To obtain a profit, the revenue must be greater than the cost. For what values of x will there be a profit? x> Graph the solution. 20.–/2 pointsHarMathAp11 1.2.023. If f(x) = x − 8x2 and h ≠ 0, find the following and simplify. (a) f(x + h) = (b) f(x + h) − f(x) = h 21.2/4 points | Previous AnswersHarMathAp11 1.2.037.MI. For f(x) = 6x and g(x) = x6, find the following. (a) (f + g)(x) 6x+x6 (b) (f − g)(x) 6x−x6 (c) (f · g)(x) (d) (f/g)(x) , x≠0 22.–/2 pointsHarMathAp11 1.3.031. Write the equation of the line that passes through the given point and has the given slope. (−1, 5) with slope − Graph the line. 3 4 23.–/1 pointsHarMathAp11 1.3.035.MI. Write the equation of the line described. Through (3, 3) and (−1, −5) 24.–/1 pointsHarMathAp11 1.5.011. Solve the system of equations by substitution. (Give an exact answer. Do not round.) 2x − y = 2 5x + 6y = 8 (x, y) = 25.–/6 pointsHarMathAp11 1.5.037.MI. A concert promoter needs to make $58,100 from the sale of 1820 tickets. The promoter charges $30 for some tickets and $35 for the others. Let x represent the number of $30 tickets and y represent the number of $35 tickets. (a) Write an equation that states that the sum of the tickets sold is 1820. (b) Write a formula for how much money is received from the sale of $30 tickets? $ (c) Write a formula for how much money is received from the sale of $35 tickets? $ (d) Write an equation that states that the total amount received from the sale is $58,100. (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $58,100. x = y = 26.–/3 pointsHarMathAp11 1.6.019. A manufacturer sells belts for $13 per unit. The fixed costs are $1600 per month, and the variable cost per unit is $9. (a) Write the equations of the revenue R(x) and cost C(x) functions. R(x) = C(x) = (b) Find the break-even point. It takes units to break even. 27.0/1 points | Previous AnswersHarMathAp11 1.6.044.MI. Find the market equilibrium point for the following demand and supply functions. Demand: Supply: p = −2q + 324 p = 8q + 2 (q, p) = 30210,183.2 28.0/1 points | Previous AnswersHarMathAp11 2.1.039.MI. Multiply both sides of the equation by the LCD and solve the resulting quadratic equation. (Enter your answers as a comma-separated list.) x+ 4 =5 x x= 4 29.0/1 points | Previous AnswersHarMathAp11 2.1.045.MI. If the profit from the sale of x units of a product is P = 115x − 300 − x2, what level(s) of production will yield a profit of $1950? (Enter your answers as a comma-separated list.) x= 1 units 30.1/4 points | Previous AnswersHarMathAp11 2.2.003. Consider the following equation. y = 8 + 8x − x2 (a) Find the vertex of the graph of the equation. (x, y) = (b) Determine if the vertex is a maximum or minimum point. maximum minimum (c) Determine what value of x gives the optimal value of the function. x= (d) Determine the optimal (maximum or minimum) value of the function. y= 31.–/2 pointsHarMathAp11 2.2.031. The daily profit from the sale of a product is given by P = 12x − 0.1x2 − 200 dollars. (a) What level of production maximizes profit? units (b) What is the maximum possible profit? $ 32.2/2 points | Previous AnswersHarMathAp11 2.4.013. Decide whether each function whose graph is shown is the graph of a cubic (third-degree) or quartic (fourthdegree) function. (a) cubic quartic (b) cubic quartic 33.–/4 pointsHarMathAp11 2.4.033. If k(x) = 2 x+4 1−x if x < 0 if 0 ≤ x < 1 , find the following. if x ≥ 1 (a) k(−8) (b) k(0) (c) k(1) (d) k(−0.002) 34.–/1 pointsHarMathAp11 4.1.001.MI. Graph the inequality. y ≤ 4x − 3 35.–/1 pointsHarMathAp11 5.1.029.MI. If $2000 is invested for x years at 8%, compounded quarterly, the future value that will result is represented by the following equation. S = 2000(1.02)4x What amount will result in 6 years? (Round your answer to the nearest cent.) $ 36.–/1 pointsHarMathAp11 5.2.039. Write the expression as the sum or difference of two logarithmic functions containing no exponents. log3(x 3 x + 8) 37.–/1 pointsHarMathAp11 5.2.043. Use the properties of logarithms to write the expression as a single logarithm. log5(x + 6) + 1 log5(x) 3 38.–/2 pointsHarMathAp11 5.2.051.MI. Use a change-of-base formula to evaluate each logarithm. (Round your answers to four decimal places.) (a) log6(17) (b) log3(0.54) 39.–/1 pointsHarMathAp11 5.2.063. Use the fact that the loudness of sound (in decibels) perceived by the human ear depends on intensity levels according to L = 10 log(I/I0) where I0 is the threshold of hearing for the average human ear. Find the loudness when I is 10,000 times I0. This is the intensity level of the average voice. L= dB 40.–/1 pointsHarMathAp11 5.3.007. Solve the equation. Give your answer correct to 3 decimal places. 10,000 = 1500e0.09x x= 41.–/1 pointsHarMathAp11 5.3.015. Solve the equation. log4(9x + 19) = 3 x= 42.–/2 pointsHarMathAp11 5.3.043. If $8500 is invested at 12.6% compounded continuously, the future value S at any time t (in years) is given by the following formula. (Round your answers to two decimal places.) S = 8500e0.126t (a) What is the amount after 18 months? S=$ (b) How long before the investment doubles? t= yr
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