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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209, >>Next

 Reduction-of-unit-multipliers/192685: This question is from textbook algebra 1/2 an incremental development This spring, the numberbof flowers that could be seen was 360 percent greater than the year before. If 22,000 could be seen the year before, how many flowers could be seen this spring? 1 solutions Answer 144619 by stanbon(57250)   on 2009-04-22 22:14:34 (Show Source): You can put this solution on YOUR website!This spring, the numberbof flowers that could be seen was 360 percent greater than the year before. If 22,000 could be seen the year before, how many flowers could be seen this spring? Equation: x = (360%)(22000) x = (360/100)*22000 x = 3.6*22000 x = 79,200 ================= Cheers, Stan H.
 Linear-equations/192682: Show algebraically that segment A (2,0) A' (0,2) is parallel to segment C (8,12) C' (12,8) I dont understand that question. Could someone help with this? Thank you.1 solutions Answer 144618 by stanbon(57250)   on 2009-04-22 22:09:42 (Show Source): You can put this solution on YOUR website!Show algebraically that segment A (2,0) A' (0,2) is parallel to segment C (8,12) C' (12,8) ------------------------- Check the slopes: AA': (2-0)/(0-2) = 2/-2 = -1 --------------------------------------- CC': (8-12)/(12-8) = -4/4 = -1 ------------------------------------ Since the slopes are the same, the lines are parallel. Cheers, Stan H.
 Exponential-and-logarithmic-functions/192676: I am having so much trouble with solving logarithmic equations. I dont understand what happens. I know to cancel out but i just really need some help.1 solutions Answer 144616 by stanbon(57250)   on 2009-04-22 21:31:41 (Show Source): You can put this solution on YOUR website!Post some of your problems. Cheers, Stan H.
 Equations/192650: please multiply and simplify this 5(3x^2-6x-7-(4x^2+8x-15) thank you1 solutions Answer 144615 by stanbon(57250)   on 2009-04-22 21:25:24 (Show Source): You can put this solution on YOUR website!please multiply and simplify this 5(3x^2-6x-7-(4x^2+8x-15) -------------------------------------- = 15x^2 - 30x -35 - 4x^2 - 9x + 15 = 11x^2 -39x -20 ======================= Cheers, Stan H.
 Equations/192664: i need help with x squared minus 2x plus 1 equal 241 solutions Answer 144611 by stanbon(57250)   on 2009-04-22 21:03:01 (Show Source): You can put this solution on YOUR website!help with x squared minus 2x plus 1 equal 24 ----------------------------------------- x^2 - 2x + 1 = 24 x^2 -2x - 23 = 0 Use the quadratic formula to get: x = [2 +- sqrt(4 - 4*1*-23)]/2 x = [2 +- sqrt(4 + 92)]/2 x = [2 +- sqrt(96)]/2 x = [2 +- 4sqrt(6)]/2 x = 1 + 2sqrt(6) or x = 1 - 2sqrt(6) ======================================== Cheers, Stan H.
 Rational-functions/192666: how do u work out a problem like this it says find the least common denominator 2.......3 ----- ----- x-3 2x+3 if u could explain how to work this out i would really appreciate it 1 solutions Answer 144610 by stanbon(57250)   on 2009-04-22 20:50:12 (Show Source): You can put this solution on YOUR website!find the least common denominator 2.......3 ----- ----- x-3 2x+3 --------------------------------------------- The least common denominator is the smallestini algebraic expression into which the various denominators can be evenly divided. ---------------- For example if you have 1/2 + 2/5, the lcd is 2*5 = 10 ------------ The lcd of 1/20 + 1/16 you have to see the factors of 20 and of 16: 20 = 2^2*5 16 = 2^4 ------------- The lcd must have each of these different factors to there highest power. The lcd is 5*2^4 = 5*16 = 80 ----------------------------------- So with algebraic expressions The lcd of x^2-9 and x^2+5x+6 = ? Factor each one: x^2 - 9 = (x+3)(x-3) x^2+5x+6 = (x+3)(x+2) The lcd is (x+2)(x+3)(x-3) ------------------------------ Using Google you may be able to see more examples of lcd problems. ----------------------- Cheers, Stan H.
 Quadratic-relations-and-conic-sections/192645: I do not understand how to solve this problem: Write the equation of the parabola with vertex (-2,-2) and directrix y=0. I know that the form should be y=a(x-k)^2+k and that it should be a(x+2)^2-2 but I don't get how to get the a. Answer to problem is: -(1/8)(x+2)^2-21 solutions Answer 144608 by stanbon(57250)   on 2009-04-22 20:25:23 (Show Source): You can put this solution on YOUR website!Write the equation of the parabola with vertex (-2,-2) and directrix y=0. I know that the form should be y=a(x-k)^2+k and that it should be a(x+2)^2-2 but I don't get how to get the a. Answer to problem is: -(1/8)(x+2)^2-2 ------------------------------------------- Starting with (x-h)^2 = 4p(y-k) Since the vertex is (-2,-2) you get (x+2)^2 = 4p(y+2) ----------------------- Since the directrix is the x-axis and the vertex is 2 below it, p = -2 So (x+2)^2 = 4(-2)(y+2) ------------- Solving for y you get: -8(y+2) = (x+2)^2 y = (-1/8)(x+2)^2 -2 ============================== Cheers, Stan H.
 Quadratic_Equations/192529: This question is from textbook saxon algebra 2 Write a quadratic equation whose roots are 6+4i and 6-4i. My answer is x^2-12x+40=0 Is this correct?1 solutions Answer 144552 by stanbon(57250)   on 2009-04-22 12:16:13 (Show Source): You can put this solution on YOUR website!Write a quadratic equation whose roots are 6+4i and 6-4i ----- y = [(x-6)+4i] * [(x-6)-4i] y = (x-6)^2 - (4i)^2 y = x^2 - 12x + 36 + 16 y = x^2 -12x + 52 ------------------------- Cheers, Stan H.
 Exponents/192531: I sent this question along with 3 others yesterday and still haven't gotten a respond, please help me Simplify; express answer with only positive exponents. (a^-2/3b^1/2)(a^3/2b^2/3) 1 solutions Answer 144549 by stanbon(57250)   on 2009-04-22 12:11:10 (Show Source): You can put this solution on YOUR website!Simplify; express answer with only positive exponents. (a^(-2/3)b^(1/2))(a^(3/2)b^(2/3)) ---------------- = a^(-2/3 + 3/2)*b(1/2 - 2/3) --- = a^(-4/6 + 9/6)*b^(3/6 - 4/6) --- = a^(5/6) * b^(-1/6) = a^(5/6) / b^(1/6) ========================= Cheers, Stan H.
 Volume/192544: This question is from textbook Elementary and Intermediate Algebra 112. Volume of a cube. Find the exact volume of a cube with sides of length 3_ meters. 1 solutions Answer 144548 by stanbon(57250)   on 2009-04-22 12:03:38 (Show Source): You can put this solution on YOUR website!Volume of a cube. Find the exact volume of a cube with sides of length 3_ meters. -------------------------- V = s^3 --- Your problem: V = 3^3 = 27 cu. meters ============================= Cheers, Stan H.
 Equations/192546: I am having difficulty with equations. Could someone please help. 8x + 7 => 5x - 14 Thanks for the help. 1 solutions Answer 144547 by stanbon(57250)   on 2009-04-22 12:01:43 (Show Source): You can put this solution on YOUR website!8x + 7 => 5x - 14 Subtract 5x from both sides to get: 3x + 7 >= -14 Subtract 7 from both sides to get: 3x >= -21 Divide both sides by 3 to get: x >= -7 ================ Cheers, Stan H.
 Quadratic-relations-and-conic-sections/192550: I have a question concerning having the x=3,-3 and the y=4,-4. My question is how do i determine if this is ellipse or hyperbola. One is either x2/9+y2/16 or x2/9 - y2/16. How do i figure this out?1 solutions Answer 144544 by stanbon(57250)   on 2009-04-22 11:59:19 (Show Source): You can put this solution on YOUR website!You can't. You must have more information. Cheers, Stan H.
 Rational-functions/192552: 2. Choose the least common multiple of x(x2 5x + 6) and x3(x2 + 4x  21). x2(x2  2)(x2  3)(x2 + 7) (x3  2)(x3  3)(x3 + 7) x3(x  2)(x  3)(x + 7) x3(x3  6)(x + 7)1 solutions Answer 144543 by stanbon(57250)   on 2009-04-22 11:57:20 (Show Source): You can put this solution on YOUR website!Choose the least common multiple of x(x2 5x + 6) and x3(x2 + 4x  21). Factors: x , x-3, x-2, x^3, x+7, x-3 ---------------- lcm = x^3(x-2)(x-3)(x+7) ------------------------- Cheers, Stan H. x2(x2  2)(x2  3)(x2 + 7) (x3  2)(x3  3)(x3 + 7) x3(x  2)(x  3)(x + 7) x3(x3  6)(x + 7)
 Radicals/192556: For each pair of functions, find f(g(x)) and g(f(x)). 31)f(x)=3x+5,g(x)=x^2+1 32)f(x)=x^2-5x+2,g(x)=2x 34)f(x)=-2x^2,g(x)=x+41 solutions Answer 144541 by stanbon(57250)   on 2009-04-22 11:52:26 (Show Source): You can put this solution on YOUR website!For each pair of functions, find f(g(x)) and g(f(x)). 31)f(x)=3x+5,g(x)=x^2+1 f[g(x)} = f[x^2+1] = 3(x^2+1) + 5 = 3x^2 + 3 + 5 = 3x^2 + 8 g[f(x)] = g[3x+5] = (3x+5)^2 + 1 = 9x^2 + 30x + 26 ========================================================== The others follow the same procedure ------------------------------------- Cheers, Stan H.
 Probability-and-statistics/192538: High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. A Boeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as Low (under 88 decibels), Medium (88 to 91 decibels), or High (92 decibels or more). There are three flight phases (Climb, Cruise, Descent). Research question: At α = .05, is the cockpit noise level independent of flight phase? Noise Level Climb Cruise Descent Row Total Low 6 2 6 14 Medium 18 3 8 29 High 1 3 14 18 Col Total 25 8 28 61 1 solutions Answer 144540 by stanbon(57250)   on 2009-04-22 11:49:03 (Show Source): You can put this solution on YOUR website!Run a Chi-Sq test on the 3 by 3 set of data. Cheers, Stan H.
 Probability-and-statistics/192540: A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = .05, does vehicle type vary by mall location? Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total Car 44 49 36 64 193 Minivan 21 15 18 13 67 Full-sized Van 2 3 3 2 10 SUV 19 27 26 12 84 Truck 14 6 17 9 46 Col Total 100 100 100 100 400 1 solutions Answer 144538 by stanbon(57250)   on 2009-04-22 11:47:08 (Show Source): You can put this solution on YOUR website!A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = .05, does vehicle type vary by mall location? Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total Car........... 44....... 49.......... 36...... 64.... 193 Minivan....... 21....... 15.......... 18.......13..... 67 Full-sized Van 2......... 3........... 3....... 2..... 10 SUV........... 19 ........27......... 26...... 12..... 84 Truck......... 14......... 6......... 17....... 9 .....46 Col Total 100 100 100 100 400 ------------ Enter the 5 by 4 set of data into a matrix and run a Chi-Sq Test on it. I used a TI calculator and got the following: Ho: Row and Column factors are Independent Ha: they are dependent --- Test Statistic: Chi-Sq = 24.532 p-value: 0.0172.. ----------- Since the p-value is less than 5%, reject Ho. Row and column factors are dependent Cheers, Stan H.
 Probability-and-statistics/192516: Probability Distribution 1. Decide whether the random variable is discrete or continuous. a. The number of oil spills off the East Coast b. The number of touchdowns in the 2007 Super Bowl c. The temperature in degrees Fahrenheit on December 31 in New York City d. The blood pressure of Statistic student in a class one hour after the final exam e. The age of the youngest student in an English grammar class Binomial Probability Find the indicated binomial probabilities. Round to the nearest 3 decimal places. 4. Hot Shot Battery manufactures batteries in batches of 15 with a defective rate of 10% a. What is the probability that exactly 2 will be defective? b. What is the probability that between 2 and 4 inclusive will be defective? c. What is the probability that no batteries will be defective? d. Find the mean  e. Find the variance 2 5. A Multiple-choice test has 15 questions with each having 4 possible answers with one correct. Assume a student answers every question. a. What is the probability of getting exactly 5 correct answers? b. What is the probability of getting less than 6 correct answers? 1 solutions Answer 144532 by stanbon(57250)   on 2009-04-22 09:27:34 (Show Source): You can put this solution on YOUR website!Probability Distribution 1. Decide whether the random variable is discrete or continuous. a. The number of oil spills off the East Coast discrete -------------------- b. The number of touchdowns in the 2007 Super Bowl discrete -------------------- c. The temperature in degrees Fahrenheit on December 31 in New York City continuous -------------------- d. The blood pressure of Statistic student in a class one hour after the final exam discrete -------------------- e. The age of the youngest student in an English grammar class discrete ------------------------ Binomial Probability Find the indicated binomial probabilities. Round to the nearest 3 decimal places. 4. Hot Shot Battery manufactures batteries in batches of 15 with a defective rate of 10% a. What is the probability that exactly 2 will be defective? 15C2(0.1)^2(0.9)^13 = 0.267 ------------------------------- b. What is the probability that between 2 and 4 inclusive will be defective? binomcdf(15,0.1,4) - binomcdf(15,0.1,1) = 0.438 ------------------------------- c. What is the probability that no batteries will be defective? (0.9)^15 = 0.206 ------------------------------- d. Find the mean  np = 15*0.1 = 1.5 ------------------------------- e. Find the variance 2 npq = 1.5*.9 = 1.35 ------------------------------- 5. A Multiple-choice test has 15 questions with each having 4 possible answers with one correct. Assume a student answers every question. a. What is the probability of getting exactly 5 correct answers? 15C5(1/4)^5(3/4)^10 = 0.165 ------------------------------- b. What is the probability of getting less than 6 correct answers? binomcdf(15,0.25,5) = 0.852 =============================== Cheers, Stan H.
 Functions/192508: z^2=-36 I got 6 and negative 6. It that correct. It should say z squared equals negative 36. Please help1 solutions Answer 144531 by stanbon(57250)   on 2009-04-22 08:18:25 (Show Source): You can put this solution on YOUR website!z^2=-36 I got 6 and negative 6. It that correct. ----- z^2+36 = 0 (z + 6i)(z - 6i) = 0 z = -6i or z = 6i ======================= Cheers, Stan H.
 Quadratic_Equations/191651: 9*(x+2/x+3)^2 - 6*(x+2/x+3)+1 = 01 solutions Answer 144530 by stanbon(57250)   on 2009-04-22 08:14:27 (Show Source): You can put this solution on YOUR website!9*(x+2/x+3)^2 - 6*(x+2/x+3)+1 = 0 ---------- Let w = (x+2/x+3) 9w^2 - 6w + 1 = 0 (3w -1)(3w - 1) = 0 w = 1/3 --------------- (x+2)/(x+3) = 1/3 Cross-multiply x+2 = 3x+9 2x = -7 x = -7/2 ============== Cheers, Stan H.
 Functions/192504: I am having trouble determining whether this is a function or not. Can someone help please. y=-2x-1 yes or no1 solutions Answer 144529 by stanbon(57250)   on 2009-04-22 08:09:51 (Show Source): You can put this solution on YOUR website!It is a function Cheers, Stan H.
 Percentage-and-ratio-word-problems/192507: a book has 40 pages. 10 pages were read in an hour. write in a fraction how much of the book was read.1 solutions Answer 144528 by stanbon(57250)   on 2009-04-22 08:08:25 (Show Source): You can put this solution on YOUR website!a book has 40 pages. 10 pages were read in an hour. write in a fraction how much of the book was read. ---------------- 10/40 = 1/4 = 0.25 = 25% ----------------------------- Cheers, Stan H.
 Quadratic_Equations/192506: (x^2-2x)(x+3)=neg.2x(x+1)1 solutions Answer 144527 by stanbon(57250)   on 2009-04-22 08:03:24 (Show Source): You can put this solution on YOUR website!(x^2-2x)(x+3)=neg.2x(x+1) ------ x^3 + 3x^2 -2x^2 -6x = -2x^2 -2x ---- x^3 + 3x^2 -4x = 0 x(x^2 + 3x - 4) = 0 x(x+4)(x-1) = 0 x = 0 or x = -4 or x = 1 ============================ Cheers, Stan H.
 Functions/192505: Is this a function. I don't know how to determine y=-3x-3 yes or no1 solutions Answer 144526 by stanbon(57250)   on 2009-04-22 07:48:46 (Show Source): You can put this solution on YOUR website! Is this a function. I don't know how to determine y=-3x-3 ---------------- If for each x value there is only one y value, the equation is a function. --- It is a function. ----- Cheers, Stan H.
 test/192451: 38. Suupose that in a one-tail hypothesis test where you reject H0 only in the upper tail, you compute the value of the test statistic Z to be +2.00. What is the P-value Answer is 0.0228 39. In problem 38, what is your statistical decision if you tested the null hypothesis at the 0.05 level of significance?1 solutions Answer 144525 by stanbon(57250)   on 2009-04-22 07:46:09 (Show Source): You can put this solution on YOUR website!38. Suupose that in a one-tail hypothesis test where you reject H0 only in the upper tail, you compute the value of the test statistic Z to be +2.00. What is the P-value Answer is 0.0228 --- p-value = the probability that z is greater than the test statistic. P-value = P(z > 2.00) = 0.02275.... ----------------------------------------------- 39. In problem 38, what is your statistical decision if you tested the null hypothesis at the 0.05 level of significance? Since the p-value is less than 5%, reject Ho. Comment: The p-value being less than 5% means the same as saying the test statistic falls in the rejection interval. ==================================================== Cheers, Stan H.
 Quadratic_Equations/192499: I am thinking of three consecutive negative numbers. If i multiply the first with the second and then subtract three times the third, the result is 57. What are the numbers?1 solutions Answer 144520 by stanbon(57250)   on 2009-04-22 07:15:42 (Show Source): You can put this solution on YOUR website!I am thinking of three consecutive negative numbers. If i multiply the first with the second and then subtract three times the third, the result is 57. What are the numbers? -------------------- 1st: x-1 2nd: x 3rd: x+1 ------------ Equations: x(x-1)-3(x+1) = 57 x^2-x-3x-3 = 57 x^2-4x-60 = 0 (x-10)(x+6) = 0 Negative solution: x = -6 (2nd) x-1 = -7 (1st) x+1 = -5 (3rd) =================== Cheers, Stan H.
 Polynomials-and-rational-expressions/192459: I am not understanding quadratic equations. Please help. Explain: 2h^2 - h- 3 = 0 By using the zero factor property. I am clueless.1 solutions Answer 144496 by stanbon(57250)   on 2009-04-21 20:59:09 (Show Source): You can put this solution on YOUR website!Explain: 2h^2 - h- 3 = 0 By using the zero factor property. ------------------------------------------------- 2h^2 -3h + 2h - 3 = 0 h(2h-3) + (2h-3) = 0 (2h-3)(h+1) = 0 h = 3/2 or h = -1 ======================= Cheers, Stan H.
 test/192454: A chocolate company uses machines to package candies, the packages are labeled as 8 ounces, the company wants packages to contain 8.17 ounces so that virtually none of the packages contain less than 8oz. A sample of 50 packages is selected and the packing is stopped is there is evidence that the mean amount is different from 8.17oz. Suppose that the mean amount dispensed in a sample of 50 packages is 8.159oz with a sample standard deviation of 0.051oz. A. Is there evidence that the population mean amount is different from 8.17oz? (use a 0.05 level of significance) B. Compute the p-value and interpret its meaning.1 solutions Answer 144495 by stanbon(57250)   on 2009-04-21 20:54:10 (Show Source): You can put this solution on YOUR website!A chocolate company uses machines to package candies, the packages are labeled as 8 ounces, the company wants packages to contain 8.17 ounces so that virtually none of the packages contain less than 8oz. A sample of 50 packages is selected and the packing is stopped is there is evidence that the mean amount is different from 8.17oz. Suppose that the mean amount dispensed in a sample of 50 packages is 8.159oz with a sample standard deviation of 0.051oz. A. Is there evidence that the population mean amount is different from 8.17oz? (use a 0.05 level of significance) Ho: u >= 8.17 Ha: u < 8.17 B. Compute the p-value and interpret its meaning. I ran a T-test and got the following results: test statistic: t = -1.52513... p-value: = P(t < -1.52513) = 0.0668... --------------- Since the p-value is greater than 5%, fail to reject Ho. ============================================================= Cheers, Stan H.
 Rational-functions/192442: What are the points of discontinuity, holes, vertical asymptotes,x-intercept, and horizontal asymptote of the problem f(x)= x^2+x-6 _________ -4x^2-16x-121 solutions Answer 144480 by stanbon(57250)   on 2009-04-21 19:52:27 (Show Source): You can put this solution on YOUR website!What are the points of discontinuity, holes, vertical asymptotes,x-intercept, and horizontal asymptote of the problem f(x)= (x^2+x-6) / (-4x^2-16x-12) --- Factored Form: f(x) = [(x+3)(x-2)] / [-4(x+3)(x+1)] ------------------------------------ Pts of discontinuity: x = -3 and x = -1 ----------------------------- holds: x = -3 because (x+3) is a factor of numerator and denominator --------------------------------- vertical asymptote at x = -1 ----------------------------------- horizontal asymptote = x^2/-4x^2 = -1/4 ----------------------------------- x-intercept: Let y = 0 ; solve for "x" x = 2 ========================================= Cheers, Stan H.
 Quadratic_Equations/192438: Sweet Harmony Crafts has determined that when x hundred Dobros are built, the average cost per Dobro can be estimated by C(x)=.1x^2-.7x+2.425 where C(x) is in hundreds of dollars. What is the minimum average cost per Dobro and how many Dobros should be built to achieve that minimum? 1 solutions Answer 144477 by stanbon(57250)   on 2009-04-21 19:39:53 (Show Source): You can put this solution on YOUR website!Sweet Harmony Crafts has determined that when x hundred Dobros are built, the average cost per Dobro can be estimated by C(x)=.1x^2-.7x+2.425 where C(x) is in hundreds of dollars. What is the minimum average cost per Dobro and how many Dobros should be built to achieve that minimum? ----------------------------------- C(x)=.1x^2-.7x+2.425 where C(x) is in hundreds of dollars. --------- Minimum occurs when x = -b/2a = -[-0.7/(2*0.1)] = 3.5 hundred ---------- C(3500) = 1.22 million hundred = 1.22*10^8 = 122,000,000 [# of Dobros] --------------------- Cheers, Stan H.
 Quadratic_Equations/192433: How do you solve (x-9)(x+1)(x-1)=01 solutions Answer 144473 by stanbon(57250)   on 2009-04-21 19:19:07 (Show Source): You can put this solution on YOUR website!solve (x-9)(x+1)(x-1)=0 ---------------- x = 9 or x = -1, or x = 1 =============================== Cheers, Stan H.