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Recent problems solved by 'stanbon'

stanbon answered: 57222 problems
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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

Angles/256495: I have this question on a homework sheet for review. We covered this topic earlier in the year but I cant remember the steps to take to solve. The question is "An angle is half the size of its compliment. What is the measure of the larger angle." I tried X+1/2=90 and got x=36. I was told that was wrong is the correct answer 54? Thanks! 1 solutions Answer 188604 by stanbon(57290)   on 2010-01-13 14:42:53 (Show Source): You can put this solution on YOUR website! "An angle is half the size of its compliment. What is the measure of the larger angle." -------------------------------------- Let the angle be "x". Its complement is 90-x ----- Equation: x = (1/2)(90-x) x = 45 - (x/2) (3/2)x = 45 x = 30 degrees ---- The complement is 90-30 = 60 degrees. ========================================== Cheers, Stan H.

Matrices-and-determiminant/256456: find M^-1 (inverse) M= 1 2 0 -1 2 1 0 3 1 M^-1 = 1 solutions Answer 188559 by stanbon(57290)   on 2010-01-13 12:06:35 (Show Source): You can put this solution on YOUR website! find M^-1 (inverse) M= 1 2 0 -1 2 1 0 3 1 M^-1 = -1 -2 2 1 1 -1 -3 -3 4 ====================== Cheers, Stan H.

Linear-systems/256461: 3x+5y=16 2x- y=2 1 solutions Answer 188557 by stanbon(57290)   on 2010-01-13 12:01:36 (Show Source): You can put this solution on YOUR website! 3x+5y=16 2x- y=2 ----- Solve the 2nd equation for "y": y = 2x-2 ------ Substitute into the 1st equation and solve for "x": 3x + 5(2x-2) = 16 13x -10 = 16 13x = 26 x = 2 --- Since y = 2x-2, y = 2*2-2 = 2 ---- Final Answer: (2,2) ========================= Cheers, Stan H.

Problems-with-consecutive-odd-even-integers/256462: The equation y=-1777x 27,153 can be used to predict the number of y of gun deaths in the United States x years after 2000, that is, x=0 corresponds to 2000, x=3 corresponds to 2003, x =5 corresponds to 2005 and so on. Predict the number gun deaths in 2005 and 2009. In what year will the number gun deaths be 9383? The predicted gun deaths in 2005 will be _____. The predicted gun deaths in 2009 will be ______. The predicted number of gun deaths will be 9383in the year _____. 1 solutions Answer 188553 by stanbon(57290)   on 2010-01-13 11:58:37 (Show Source): You can put this solution on YOUR website! The equation y=-1777x + 27,153 can be used to predict the number of y of gun deaths in the United States x years after 2000, that is, x=0 corresponds to 2000, x=3 corresponds to 2003, x =5 corresponds to 2005 and so on. Predict the number gun deaths in 2005 and 2009. ------------------------------------------------------------ The predicted gun deaths in 2005 will be _____. f(5) = -1777*5 + 27153 = 18268 ---- The predicted gun deaths in 2009 will be ______. f(9) = -1777*9 + 27153 = 11160 ---- The predicted number of gun deaths will be 9383in the year _____. -1777x + 27153 = 9383 -1777x = -17770 x = 10 --- Year = 2000+ 10 = 2010 =============================== Cheers, Stan H.

Probability-and-statistics/256420: 1000 tickets were sold at $2 each for three prizes of $250, $100, $50. Only one prize per selected ticket. Find the expected value? 1 solutions Answer 188551 by stanbon(57290)   on 2010-01-13 11:49:39 (Show Source): You can put this solution on YOUR website! 1000 tickets were sold at $2 each for three prizes of $250, $100, $50. Only one prize per selected ticket. Find the expected value? -------------------------------------------------------- Random number values: -2, 248, 98, 48 Corresponding probabilities: 997/1000, 1/1000, 1/1000, 1/1000 ---------------------------------------- Expected value: E(x) = (-2*997 + 248*1 + 98*1 + 48*1)/1000 --- E(x) = -1600/1000 = -$1.60 ============================= Cheers, Stan H.

Equations/256427: a man has a number of duks costing rs 10 each and three times as many chikens costing rs. 6 each . if total cost of ducks and chikens is rs.432.find the number of chikens the man has. 1 solutions Answer 188531 by stanbon(57290)   on 2010-01-13 10:41:42 (Show Source): You can put this solution on YOUR website! a man has a number of ducks costing rs 10 each and three times as many chickens costing rs. 6 each . if total cost of ducks and chikens is rs.432.find the number of chickens the man has. Equations: Quantity: c = 3*d Value: 6c + 10d = 432 ------------------------------ Substitute for "c" and solve for "d": 6(3d) + 10d = 432 28d = 432 d = ? ==== Comment: "d" should be a whole number. With the numbers you have posted it is not. ============================================== Cheers, Stan H.

Probability-and-statistics/256421: Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected? 1 solutions Answer 188530 by stanbon(57290)   on 2010-01-13 10:33:49 (Show Source): You can put this solution on YOUR website! Seven equally qualified students apply for a scholarship, but only five scholarships equal in value, can be given. How many ways can the five winners be selected? ------------ 7C5 = 7C2 = (7*6)/(1*2) = 21 ================================= Cheers, Stan H.

Quadratic-relations-and-conic-sections/256411: find the graph of the parabola y2(squared)+6y+8x+25=0 1 solutions Answer 188519 by stanbon(57290)   on 2010-01-13 09:23:08 (Show Source): You can put this solution on YOUR website! find the graph of the parabola y^2+6y+8x+25=0 ------------ Complete the square on the y-terms: y^2+6y+9 = -8x-25+9 (y+3)^2 = -8x-16 --- solve for "x": 8x = -(y+3)^2 - 16 --- x = (-1/8)(y+3)^2 - 2 ------ Graph the parabola: Vertex at (-2,-3) Opens to the left. --- If y = -3, x = -2 ----------------------- That is enough information to sketch the graph. =================================================== Cheers, Stan H.

Probability-and-statistics/256273: Can you please help me with this problem? The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 with a standard deviation of 0.41 ounces. a) What is the appropriate null and alternate hypothesis to determine if the packages are under filled? b) What is the p-value for the hypothesis test? c) Using α = 0.01, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem. d) Using α = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem. 1 solutions Answer 188516 by stanbon(57290)   on 2010-01-13 09:13:36 (Show Source): You can put this solution on YOUR website! The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 with a standard deviation of 0.41 ounces. a) What is the appropriate null and alternate hypothesis to determine if the packages are under filled? Ho: u >= 18 H1: u < 18 ------------------------------ b) What is the p-value for the hypothesis test? The test statistic is t = (17.78-18)/[0.41/sqrt(18)] = -0.22/0.09664 = -2.2765 --- So the p-value is P(t<-2.2765 when df = 17) = tcdf(-100,-2.2765,17) = 0.01802.. -------------------------- c) Using α = 0.01, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem. --- Since the p-value is greater than 1%, we fail to reject Ho. Based on this test we do not believe the rolled oats packages are under filled. ------------------------ d) Using α = 0.05, draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem. --- Since the p-value is less than 5% we reject Ho. Based on this test we conclude the rolled oats packs do not contain at least 18 ounces. ----------------- Cheers, Stan H.

Probability-and-statistics/256385: "In a certain game you roll 3 dice and are given 1 dollar for each 5 that is rolled. So on each play you may earn 0, 1, 2, or 3 dollars. What are your expected earnings per play?" 1 solutions Answer 188514 by stanbon(57290)   on 2010-01-13 09:00:38 (Show Source): You can put this solution on YOUR website! "In a certain game you roll 3 dice and are given 1 dollar for each 5 that is rolled. So on each play you may earn 0, 1, 2, or 3 dollars. What are your expected earnings per play?" ---------------------- P(no 5's) = (5/6)^3 = 125/216 P(1 five) = 3(1/6)(5/6)^2 = 75/216 P(2 fives) = 3(1/6)^2(5/6) = 15/216 P(3 fives) = (1/6)^3 = 1/216 ------------------------- E(x) = (0*125+1*75+2*15+3*1)/216 E(x) = (0 + 75 + 30 + 3)/216 = 108/216 = $0.50 ================================================= Cheers, Stan H.

Probability-and-statistics/256390: Seven white socks and four black socks are in a bag. Two socks are drawn at random, without replacement. What is the probability that they have the same color. Write your answer as a reduced fraction. 1 solutions Answer 188510 by stanbon(57290)   on 2010-01-13 08:48:26 (Show Source): You can put this solution on YOUR website! Seven white socks and four black socks are in a bag. Two socks are drawn at random, without replacement. What is the probability that they have the same color. Write your answer as a reduced fraction. ------- These are disjoint events. P(2 white or 2 black) = (7C2 + 4C2)/11C2 = (21 + 6)/55 = 27/55 ================================================================= Cheers, Stan H.

Numeric_Fractions/256325: please help me solve: i dont know how to make a line through the = sign but all the equals here have a line thru them: For all x=0 and y=0 (3x(negative small 2)y(pos.small 3))(small 2 outside par.) _________________________________________________________ xy 1 solutions Answer 188461 by stanbon(57290)   on 2010-01-12 21:48:31 (Show Source): You can put this solution on YOUR website! For all x not= to 0 and y not= to 0 (3x(negative small 2)y(pos.small 3))(small 2 outside par.) --- (3x^-2*y^3)^2 ------ = [3y^3/x^2]^2 --------------------- = [9y^6/x^4] ================== Cheers, Stan H.

Probability-and-statistics/256326: 10 questions test. you know the answer to 5 questions of true or false. You quess on the last 5. What is the probability that you will have at least eight correct answers. Express your answer as a common fraction. Hint look at the word (least) and think about combinations nCr. 1 solutions Answer 188459 by stanbon(57290)   on 2010-01-12 21:43:10 (Show Source): You can put this solution on YOUR website! 10 questions test. you know the answer to 5 questions of true or false. You quess on the last 5. What is the probability that you will have at least eight correct answers. Express your answer as a common fraction. Hint look at the word (least) and think about combinations nCr. -------------------- You need at least 3 correct from the 5. -- P(at least 3 of 5) = 1 - binomcdf(5,1/2,2) = 1 - 0.5 = 0.5 ===================== Cheers, Stan H.

Exponential-and-logarithmic-functions/256324: please help me find of the inverse this equation 1 solutions Answer 188457 by stanbon(57290)   on 2010-01-12 21:38:25 (Show Source): You can put this solution on YOUR website! find of the inverse this equation y=log3(x+2)-2 ------------------- Interchange x and y: --- x = log3(y+2)-2 --- Solve for "y" to get the inverse: log3(y+2) = x+2 --- y+2 = 3^(x+2) y = [3^(x+2)] - 2 ============================= Cheers, Stan H.

Numeric_Fractions/256322: please help me solve this :i dont know how the write the small 2 orthe small three used to signify square...so im just going to write small before the number i wanted to write in small which of the following gives 6a(small 2)b(small 3)-3a(small2)b in factored form? then they have choices 1 solutions Answer 188456 by stanbon(57290)   on 2010-01-12 21:34:36 (Show Source): You can put this solution on YOUR website! 6a(small 2)b(small 3)-3a(small2)b in factored form ---- 6a^2b^3 - 3a^2b --- Common factor: 3a^2b --- = 3a^2b(2b^2-1) --- = 3a^2b(sqrt(2)b-1)(sqrt(2)b+1) ===================================== Cheers, Stan H.

absolute-value/256318: |0.2x+1|=0.8 1 solutions Answer 188454 by stanbon(57290)   on 2010-01-12 21:30:23 (Show Source): You can put this solution on YOUR website! |0.2x+1|=0.8 ------------------- 0.2x+1 = 0.8 or 0.2x+1 = -0.8 --- 0.2x= -0.2 or 0.2x = -1.8 x = -1 or x = -9 ===================== Cheers, Stan H.

Numeric_Fractions/256319: hi please help me understand how to solve this equation: -2|3-4-5|=? 1 solutions Answer 188453 by stanbon(57290)   on 2010-01-12 21:26:55 (Show Source): You can put this solution on YOUR website! hi please help me understand how to solve this equation: -2|3-4-5|=? --- = -2|3-9| --- = -2|-6| = -2(6) = -12 ============ Cheers, Stan H.

Quadratic-relations-and-conic-sections/256119: How do you solve the equation x^2-6x-25=0 and write your answer in the form ab+i? 1 solutions Answer 188274 by stanbon(57290)   on 2010-01-12 15:13:49 (Show Source): You can put this solution on YOUR website! How do you solve the equation x^2-6x-25=0 and write your answer in the form ab+i? ------ Use the quadratic formula: x = [6 +- sqrt(36 - 4*1*-25)]/2 x = [6 +- sqrt(136)]/2 x = [6 +- 2sqrt(34)]/2 x = 3 + sqrt(34) or x = 3 - sqrt(34) ========================================= Cheers, Stan H.

Miscellaneous_Word_Problems/256112: a union contract requires at least one union steward for every 20 union employees or fraction thereof. regular union employees ear $120/day and union stewards earn $144/day. a company has a need for 50 total employees and has a daily payroll budget of $6072. how many of each type of employee will meet the company's needs and consume all the budget? 1 solutions Answer 188272 by stanbon(57290)   on 2010-01-12 15:09:31 (Show Source): You can put this solution on YOUR website! a union contract requires at least one union steward for every 20 union employees or fraction thereof. regular union employees earn $120/day and union stewards earn $144/day. a company has a need for 50 total employees and has a daily payroll budget of $6072. how many of each type of employee will meet the company's needs and consume all the budget? ---- Quantity Equation: e + (e/20) = 50 Value Equation: 120e + 144(e/20) = 6072 -------------------------- Multiply thru the Quantity equation by 120: 120e + 6e = 120*50 120e + 144(e/20) = 6072 -------------------------------- Subtract the 1st Eq. from the 2nd and solve for "e": 144(e/20)- 6e = 72 144e - 120e = 72*20 24e = 72*20 e = 3*20 e = 60 --- But there must be 1 steward for each 20 employees or fraction thereof and only 50 personnel are to be hired. So # of stewards is 3 and number of employees is 47 ------ Checking: 120*47 + 144*3 = $6072 ============================= Cheers, Stan H.

Mixture_Word_Problems/256069: the supply S of a commodity (in thousands of units), if the price is P dollars per unit, is given by the equation s= 0,3p+3 the demand D for that commodity(in thousands of units), if the price is p dollas per unit, is given by the equation d= -o,5p+9 the value of p for which s = d is called equilibrium price a) graph both equations in the same coordinate plane. (let the horizontal axis represent price and the vertical axis represent supply or demand in thousands of units) b) determine the equilibrium price c) what will happen at prices greater than this price? TUTORS i really need help with this because i dont even understand the problem either so i dont really know what procedure to apply :S:S anyway thans for any help that you can give me 1 solutions Answer 188257 by stanbon(57290)   on 2010-01-12 13:50:36 (Show Source): You can put this solution on YOUR website! the supply S of a commodity (in thousands of units), if the price is P dollars per unit, is given by the equation s= 0.3p+3 the demand D for that commodity(in thousands of units), if the price is p dollas per unit, is given by the equation d= -o.5p+9 the value of p for which s = d is called equilibrium price --------------------------------------------------------------------- a) graph both equations in the same coordinate plane. (let the horizontal axis represent price and the vertical axis represent supply or demand in thousands of units) -------------------------------------------------------- b) determine the equilibrium price Solve 0.3p+3 = -0.5p+9 0.8p = 6 p = 7.5 ------------------------------------------------------------ c) what will happen at prices greater than this price? As price rises demand goes decreases. Cheers, Stan H.

Travel_Word_Problems/256089: If I ran 5.5 mph for 6 1/2 min. how far did I travel? 1 solutions Answer 188256 by stanbon(57290)   on 2010-01-12 13:42:21 (Show Source): You can put this solution on YOUR website! If I ran 5.5 mph for 6 1/2 min. how far did I travel? --- 6 1/2 minutes is (13/2)/60 hrs. ================================= Equation: distance = rate*time distance = (5.5)(13/120) miles distance = 0.5958... miles ====================================== Cheers, Stan H.

Polynomials-and-rational-expressions/256095: Please please help me with this equation. 1 solutions Answer 188255 by stanbon(57290)   on 2010-01-12 13:37:49 (Show Source): You can put this solution on YOUR website! Where is the equal sign? Cheers, Stan H.

Functions/256093: Please help me with this. Listed below are 5 functions, each denoted g(x) and each involving a real number constant c>1. If f(x)=2x ( 2 exponent x), which of these 5 functions yields the greatest value for f(g(x)), for all x>1? g(x)=cx g(x)=c/x g(x)=x/c g(x)=x-c g(x)=logcx 1 solutions Answer 188254 by stanbon(57290)   on 2010-01-12 13:36:44 (Show Source): You can put this solution on YOUR website! Listed below are 5 functions, each denoted g(x) and each involving a real number constant c>1. If f(x)=2^x ( 2 exponent x), which of these 5 functions yields the greatest value for f(g(x)), for all x>1? g(x)=cx f[g(x)] = f[cx] = 2^(cx) goes to infinity as x gets larger ------------------------ g(x)=c/x f[g(x)] = f[c/x] = 2^(c/x) goes to 1 as x gets larger ------------------------- g(x)=x/c f[g(x)} = 2^(x/c) goes to infinity as x gets larger -------------------------- g(x)=x-c f[g(x)] = 2^(x-c) Goes to infinity as x gets larger ------------------------ g(x)=logcx f[g(x)] = 2^(log(cx)] goes to infinity as x gets larger ====================================== Cheers, Stan H.

Linear-systems/256092: how do I find the slope of 2x +3y =15 1 solutions Answer 188253 by stanbon(57290)   on 2010-01-12 13:20:33 (Show Source): You can put this solution on YOUR website! how do I find the slope of 2x +3y =15 -------- Put the equation in the slope-intercept form: 3y = -2x + 15 y = (-2/3)x + 5 ================== Cheers, Stan H.

Probability-and-statistics/256044: Jim is considering an MS degree in Info. Systems. He has applied to two universities. The acceptance rate for applicants with similar qualifications is 20% for University 1 and 45% for University 2. What is the probability that Jim will not be accepted at either university? 1 solutions Answer 188252 by stanbon(57290)   on 2010-01-12 13:17:38 (Show Source): You can put this solution on YOUR website! Jim is considering an MS degree in Info. Systems. He has applied to two universities. The acceptance rate for applicants with similar qualifications is 20% for University 1 and 45% for University 2. What is the probability that Jim will not be accepted at either university? ---- Assuming the events are independent: P(neither) = P(not #1)*P(not #2) = 0.20*0.55 = 0.11 ------------------------------------------------------ Cheers, Stan H.

Quadratic_Equations/256086: solve this x^2 + y^2 = 100 using completing the square or any other method tq :) 1 solutions Answer 188251 by stanbon(57290)   on 2010-01-12 13:09:54 (Show Source): You can put this solution on YOUR website! solve this x^2 + y^2 = 100 using completing the square or any other method --------------------------------------------------- The square is already complete. The solution is every point on a circle that has a radius of 10 and has its center at (0,0). Cheers, Stan H.

Exponential-and-logarithmic-functions/256084: solve 3^x=7^2 using both interpolation and logarithms. 1 solutions Answer 188247 by stanbon(57290)   on 2010-01-12 12:51:11 (Show Source): You can put this solution on YOUR website! solve 3^x=7^2 using both interpolation and logarithms. ----------------------------- Take the log of both sides and solve for "x": xlog(3) = log(49) x = [log(49)]/[log(3)] x = 3.5425 Cheers, Stan H.

Functions/256075: Please help me with this Point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB? 1 solutions Answer 188245 by stanbon(57290)   on 2010-01-12 12:45:01 (Show Source): You can put this solution on YOUR website! Point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of AB? ------------------- Draw the picture so you can see what you are doing. Plot the point: (-4,1) Draw the line x=2; it will pass thru (2,1) and (2,1) will be the mid-point of AB. ---- Let the coordinates of B be (x,y): (-4+x)/2 = 2 -4+x = 4 x = 8 -------- (1+y)/2 = 1 1+y = 2 y = 1 ------- The coordinate of B are (8,1) =================================== Cheers, Stan H.

Probability-and-statistics/256053: A box contains 131 similar transistors of which 70 are satisfactory, 43 gives too high a gain under normal operating conditions and 18 gives too low gain. Determine the probability when drawing two resistors in turn at random with replacment of having (a) two satisfactory (b) none with low gain (c) one satisfactory and one with high gain 1 solutions Answer 188212 by stanbon(57290)   on 2010-01-12 10:49:05 (Show Source): You can put this solution on YOUR website! A box contains 131 similar transistors of which 70 are satisfactory, 43 gives too high a gain under normal operating conditions and 18 gives too low gain. Determine the probability when drawing two resistors in turn at random with replacment of having (a) two satisfactory P(2 good) = 70C2/131C2 = 2415/8515 = 0.2836.. ----- (b) none with low gain P(no low gain) = 113C2/131C2 = 6328/8515 = 0.7432.. --------- (c) one satisfactory and one with high gain P(one high and one low) = 1-[P(2 good)+P(2 low)+P(2 high)] = 1 - [0.2836 + (1-0.7432)+ 43C2/131C2] = 0.6465 ================= Cheers, Stan H.

Linear_Algebra/256049: which pattern is not linear a. 1,6,11,16,21,... b. -1,7,15,23,31,... c. 1,21,31,41,... d. 1,3,9,27,81, 1 solutions Answer 188210 by stanbon(57290)   on 2010-01-12 10:34:40 (Show Source): You can put this solution on YOUR website! which pattern is not linear Comment: If there is a common difference, the sequence is linear. If there is a common multiple, the sequence is geometric ------------------------------------------------- a. 1,6,11,16,21,...common diff. of 5 , so it is linear ------------------------------ b. -1,7,15,23,31,...common diff. of 8, so it is linear ------------------------------ c. 1,21,31,41,...no common diff ------------------------------ d. 1,3,9,27,81.....common multiple of 3, so it is geometric ============================================ Cheers, Stan H.

Equations/256048: can you solve 2x+3/5=x-4/2. note that / means a fraction. 1 solutions Answer 188209 by stanbon(57290)   on 2010-01-12 10:30:09 (Show Source): You can put this solution on YOUR website! solve (2x+3)/5=(x-4)/2 --- Cross-multiply to get: 2(2x+3) = 5(x-4) 4x+6 = 5x-20 x = 26 =================== Cheers, Stan H.