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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, >>Next

 Functions/562202: (x)/(x^(2)+9x+20)-(4)/(x^(2)+7x+12)1 solutions Answer 364479 by stanbon(57203)   on 2012-01-24 22:03:04 (Show Source): You can put this solution on YOUR website! (x)/(x^(2)+9x+20)-(4)/(x^(2)+7x+12) ----------------------- x/[(x+4)(x+5)] - 4/[(x+3)(x+4)] ----------------------- least common denominator: (x+4)(x+3)(x+5) ----------------------- Rewrite each fraction with the lcm as its denominator: [x(x+3) - 4(x+5)]/lcm ------ [x^2+3x-4x-20]/lcm ------- = (x^2-x-20)/ lcm ------------ = [(x-5)(x+4)] / [(x+3)(x+4)(x+5)] ===================================== Cheers, Stan H. =====================
 Probability-and-statistics/562030: Mike has 30 jellybeans. 10 are blue,8 are red, 6 are green, and the rest are yellow. What is the probability when Mike picks 2 that it won't be blue? 1 solutions Answer 364428 by stanbon(57203)   on 2012-01-24 18:58:12 (Show Source): You can put this solution on YOUR website!Mike has 30 jellybeans. 10 are blue,8 are red, 6 are green, and the rest are yellow. What is the probability when Mike picks 2 that it won't be blue? --- # that are not blue:20 P(2 not blue) 20C2/30C2 = 190/435 ====================================== Cheers, Stan H.
 Probability-and-statistics/562002: how many different meal choices are there if each meal must consist of one main dish one side dish and a desert1 solutions Answer 364427 by stanbon(57203)   on 2012-01-24 18:54:44 (Show Source): You can put this solution on YOUR website!insufficient information
 Probability-and-statistics/561912: In a scientific study there are 12 guinea pigs, 5 of which are pregnant. If 3 are selected at random without replacement, find the probability that none are pregnant. Enter your answer as a fraction. I can find the probability that all are pregnant but I cant seem to be able to solve this problem. I would really appreciate if someone can guide me step by step how to solve it. Thank you, in advance =]1 solutions Answer 364425 by stanbon(57203)   on 2012-01-24 18:52:38 (Show Source): You can put this solution on YOUR website!In a scientific study there are 12 guinea pigs, 5 of which are pregnant. If 3 are selected at random without replacement, find the probability that none are pregnant. Enter your answer as a fraction. --------- Binomial Problem with n = 3 and p(not pregnant) = 7/12 ------ P(x = 0) = 3C3*(7/12)^3*(5/12)^0 = (7/12)^3 = 0.1985 =================================== Cheers, Stan H. ========
 Probability-and-statistics/561937: A stack of cards contains 7 hearts numbered 1 through 7, and 9 clubs numbered 1 through 9. If two cards are drawn at random with replacement, what is the probability of drawing a 2 of any suit on the first draw and the same card on the second draw?1 solutions Answer 364415 by stanbon(57203)   on 2012-01-24 18:24:19 (Show Source): You can put this solution on YOUR website!A stack of cards contains 7 hearts numbered 1 through 7, and 9 clubs numbered 1 through 9. If two cards are drawn at random with replacement, what is the probability of drawing a 2 of any suit on the first draw and the same card on the second draw? --- P(2 on 1st draw) = 2/16 = 1/8 -- P(2 on 2nd draw) = 2/16 = 1/8 ---- P(2 on both draws) = (1/8)^2 = 1/64 ============== Cheers, Stan H. ================
 Probability-and-statistics/561981: Ok so the question is this: Two cards are drawn in succession from a standard deck of 52 cards. Find the probability that an ace and a jack, in that order, are drawn. 1 solutions Answer 364413 by stanbon(57203)   on 2012-01-24 18:16:06 (Show Source): You can put this solution on YOUR website!Two cards are drawn in succession from a standard deck of 52 cards. Find the probability that an ace and a jack, in that order, are drawn. ---- # of ways to pick an ace: 4 # of ways to pick a jack: 4 --- # of ace/jack pairs = 16 ---- # of random pairs: 52C2 = 1326 ----- P(ace/jack) = 16/1326 = 0.0098 =============================== Cheers, Stan H.
 Polynomials-and-rational-expressions/561703: 1/2 + 2/y = 1/4 + 4/7 Tried: multiplying both sides by (2+y) ex: (2+y)(3/2+y)=(5/4+y)(2+y)1 solutions Answer 364353 by stanbon(57203)   on 2012-01-24 09:25:44 (Show Source): You can put this solution on YOUR website!1/2 + 2/y = 1/4 + 4/7 ------ Multiply thru by 4*7*y = 28y to get: 14y + 56 = 7y + 16y 14y + 56 = 23y 9y = 56 y = 6.2222... Cheers, Stan H. ============
 Square-cubic-other-roots/561701: what is the answer to this equation 2 cubed times 3 squared plus 3 times 14 minus 41 solutions Answer 364351 by stanbon(57203)   on 2012-01-24 09:22:02 (Show Source): You can put this solution on YOUR website!2 cubed times 3 squared plus 3 times 14 minus 4 ---- 2^3*3^2+3*14-4 ---- 8*9+42-4 --- 72 + 38 --- = 110 ============ Cheers, Stan H.
 Geometry_Word_Problems/561702: what is 2 feet more than 1/3 of 3 feet ?1 solutions Answer 364349 by stanbon(57203)   on 2012-01-24 09:18:49 (Show Source): You can put this solution on YOUR website!what is 2 feet more than 1/3 of 3 feet ? ---- Ans (1/3)3+2 = 1+2 = 3 ------------------------ Cheers, Stan H. --------------
 expressions/561681: Is y-m*x=b the same as y=mb+x?1 solutions Answer 364348 by stanbon(57203)   on 2012-01-24 09:16:51 (Show Source): You can put this solution on YOUR website!Yes --- Cheers, Stan H.
 Permutations/561684: How many different ways can 10 students be seated in 10 different seats? How do I know which method to use?1 solutions Answer 364341 by stanbon(57203)   on 2012-01-24 08:22:17 (Show Source): You can put this solution on YOUR website!How many different ways can 10 students be seated in 10 different seats? How do I know which method to use? --- Just think of doing it. ten choices on the 1st seat 9 choices on the 2nd seat 8 choices on the 3rd seat. etc. --- Ans: 10! = 3,628,800 ways ----- Hint: On most of these "selection" problems you have to think of doing the selections one at a time. You can't just think of 10 people walking into a room with 10 chairs and sitting down. Cheers, Stan H.
 Quadratic-relations-and-conic-sections/561628: Given y=x^2+3x-28. How do I algebraically find: The vertex, The x and y intercepts, and write the equation in vertex and factor form. This makes absolutely no since to me at all, and I'm super confused. PLEASE HELP ME! 1 solutions Answer 364338 by stanbon(57203)   on 2012-01-24 08:14:58 (Show Source): You can put this solution on YOUR website!Given y=x^2+3x-28. How do I algebraically find: The vertex, The x and y intercepts, and write the equation in vertex and factor form. ---- Complete the square: y = x^2+3x + 9 -9-28 --- y = (x+3)^2-37 ---- Vertex: (-3,-37) ------------------------ y-intercept: Use the form y = x^2+3x-28 Let x = 0, then y = -28 ------------------------------- x-intercepts: Solve x^2-3x-28 = 0 Factor: (x-7)(x+4) = x = 7 ; x = -4 -------------------- Cheers, Stan H. ===============
 Geometry_Word_Problems/561586: Find the number of sides of a regular polygon if the measure of each interior angle is 17 times the measure of each exterior angle.1 solutions Answer 364304 by stanbon(57203)   on 2012-01-23 22:09:41 (Show Source): You can put this solution on YOUR website!Find the number of sides of a regular polygon if the measure of each interior angle is 17 times the measure of each exterior angle. ------ interior angle: 17x exterior angle: x ---- Equation: x + 17x = 180 18x = 180 x = 10 degrees ---- Sum of ALL the exterior angles is 360 degrees ---- # of exterior angles = 360/10 = 36 --- # of sides = # of exterior angles = 36 ======================================================= Cheers, Stan H. =============
 Mixture_Word_Problems/561580: A tank holds 140 liters of a chemical solution. Currently, the solution has a strength of 40%. How much of this solution should be drained and replaced with 80% solution to get a final strength of 60%1 solutions Answer 364301 by stanbon(57203)   on 2012-01-23 22:05:43 (Show Source): You can put this solution on YOUR website!A tank holds 140 liters of a chemical solution. Currently, the solution has a strength of 40%. How much of this solution should be drained and replaced with 80% solution to get a final strength of 60% -------------------------------------------------- active - active + active = active 0.40*140 - 0.40x + 1*x = 0.60*140 ---- Multiply thru by 100 to get: 40*140 - 40x + 100x = 60*140 60x = 20*140 x = (1/3)140 --- x = 46 2/3 liters (amt. of 40% that must be replaced) ============================= Cheers, Stan H. =================
 Triangles/561578: If a second side length is three times as long as the first side, what is the range of possible values for the third side lenght?1 solutions Answer 364300 by stanbon(57203)   on 2012-01-23 21:59:19 (Show Source): You can put this solution on YOUR website!If a second side length is three times as long as the first side, what is the range of possible values for the third side length? ----- 1st side: x 2nd side: 3x ------- x+3x <(3rd side)< 3x-x ============================ Cheers, Stan H. ================
 Linear-equations/561577: Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution". x - y = 6 x = y + 21 solutions Answer 364295 by stanbon(57203)   on 2012-01-23 21:55:37 (Show Source): You can put this solution on YOUR website!Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution". x - y = 6 x = y + 2 ---- Substitute for "x" and solve for "y": (y+2) - y = 6 2 = 6 ----- That happend because we assumed there was an (x,y) pair that saisfied both equations. There is no such point. --- The equations are inconsistent. Cheers, Stan H. ===================
 Probability-and-statistics/561539: How many ways can 5 keys be arranged on a key ring? I want to know every detail steps to solve this kind (keys on key rings) of question. Thank you very muchh!!1 solutions Answer 364282 by stanbon(57203)   on 2012-01-23 20:53:11 (Show Source): You can put this solution on YOUR website!Ans: 4! = 24 ----------------- Cheers, Stan H.
 Probability-and-statistics/561506: Use one of these words or phrases to complete each sentence: certain, impossible, very likely, not likely, more likely, less likely. 1) the probability of tossing a coin and getting an outcome of heads or tails is ______. 2) an outcome of 2 or 4 on a 1-6 number cube is ____ than an outcome of any odd number. 3) an outcome of tossing a coin and getting an outcome of tails is ___ than rolling a 1-6 number cube and getting an outcome of 3. 4) the probability of tossing a coin and getting an outcome of heads and tails is ___. 5) an outcome of an odd number on a 1-6 number cube is __ than an outcome of 3 or 5. 6) the probability of tossing a coin and getting an outcome of heads and tails is __ than the probability of flipping a coin ang getting an outcome of heads or tails. 7) it is ___ that peron was born during the month of February 8) it is ___ that a persons age is a one-digit or a two-digit number.1 solutions Answer 364280 by stanbon(57203)   on 2012-01-23 20:51:53 (Show Source): You can put this solution on YOUR website!Use one of these words or phrases to complete each sentence: certain, impossible, very likely, not likely, more likely, less likely. 1) the probability of tossing a coin and getting an outcome of heads or tails is certain. ------------------ 2) an outcome of 2 or 4 on a 1-6 number cube is less likely than an outcome of any odd number. ------------------ 3) an outcome of tossing a coin and getting an outcome of tails is more likely than rolling a 1-6 number cube and getting an outcome of 3.more likely -------------------- 4) the probability of tossing a coin and getting an outcome of heads and tails is certain. -------------------- 5) an outcome of an odd number on a 1-6 number cube is more likely than an outcome of 3 or 5. -------------------- 6) the probability of tossing a coin and getting an outcome of heads and tails is impossible; than the probability of flipping a coin ang getting an outcome of heads or tails. ----------------------------- 7) it is less likely that person was born during the month of February. ----------------------------- 8) it is more likely that a persons age is a one-digit or a two-digit number. ================================== Cheers, Stan H. ==================================
 Probability-and-statistics/561523: .A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed, what percentage of sample means are less than 691 solutions Answer 364279 by stanbon(57203)   on 2012-01-23 20:40:23 (Show Source): You can put this solution on YOUR website!A final exam in Math 160 has a mean of 73 with standard deviation 7.73. Assume that a random sample of 24 students is selected and the test score of the sample is computed. Assuming the scores are normally distributed, what percentage of sample means are less than 69 --- mean of all samples of size 24: 73 std of all samples of size 24: 7.73/sqrt(24) = ----------------- t(69) = (69-73)/[7.73/sqrt(24)] = -2.535 ----- P(x < 69) = P(z < -2.535) = tcdf(-100,-2.535,23) = 0.0093 ================================ Cheers, Stan H. ================
 Equations/561509: What is the vertex of g(x)=x^2+9x+181 solutions Answer 364278 by stanbon(57203)   on 2012-01-23 20:28:18 (Show Source): You can put this solution on YOUR website!What is the vertex of g(x)=x^2+9x+18 --- Vertex occurs at x = -b/(2a) = -9/(2*1) = -4.5 ----- g(-4.5) = (-4.5)^2+9(-4.5)+18 = -2.25 ---------------------------------------- Vertex(-4.5 , -2.25) ======================== Cheers, Stan H. ==================
 �t�e�s�t/561477: Illana is 2 more than three times Ben's age. The sum of their ages is 54 years old. What is Ben's age?1 solutions Answer 364275 by stanbon(57203)   on 2012-01-23 19:44:36 (Show Source): You can put this solution on YOUR website!Illana is 2 more than three times Ben's age. I = 3B + 2 ----------------------- The sum of their ages is 54 years old. I + B = 54 ----------------------- What is Ben's age? Substitute for "I" and solve for "B" 3B+2 + B = 54 4B = 52 Ben age = 13 years ------------------------- Solve for I: I = 3B + 2 Illana = 39 + 2 = 41 years =============================== Cheers, Stan H. ===============================
 Probability-and-statistics/561438: Five separate awards are to be presented to selected students from a class of size 30. a) How many different outcomes are possible if a student can receive any number of awards? b) How many different outcomes are possible if each student can receive at most one award?1 solutions Answer 364273 by stanbon(57203)   on 2012-01-23 19:38:49 (Show Source): You can put this solution on YOUR website!Five separate awards are to be presented to selected students from a class of size 30. a) How many different outcomes are possible if a student can receive any number of awards?::: The 1st student may or may not receive each of the 5 awards: 2^5 = 32 ways The 2nd student the same: 32 ways The 3rd student the sam: 32 ways Total # of ways = 32^3 = 32768 ------------------------------------------ b) How many different outcomes are possible if each student can receive at most one award? 1st student 5 2nd student 4 3rd student 3 Total 5*4*3 = 60 ways ========================= Cheers, Stan H.
 Probability-and-statistics/561452: In a probability experiment a 1-6 number cube is rolled once. Find the theoretical probability (P) of each event. Express your answer as a fraction in simplest form. 1) P (2) 2) P ( 3 or 5) 3) P (odd number) 4) P ( 2, 3, or 4) 5) P ( prime number) 6) P (composite number)1 solutions Answer 364269 by stanbon(57203)   on 2012-01-23 19:31:42 (Show Source): You can put this solution on YOUR website!In a probability experiment a 1-6 number cube is rolled once. Find the theoretical probability (P) of each event. Express your answer as a fraction in simplest form. 1) P (2) = 1/6 2) P ( 3 or 5) = 2/6 3) P (odd number) = 3/6 4) P ( 2, 3, or 4) = 3/6 5) P ( prime number) = 2/6 6) P (composite number) = 0 ================================ Cheers, Stan H. ===========
 Probability-and-statistics/561456: In standard normal distribution what is the probability of randomly sleeting a value between-2.555and-0.745 round to four decimal places1 solutions Answer 364268 by stanbon(57203)   on 2012-01-23 19:27:25 (Show Source): You can put this solution on YOUR website!In standard normal distribution what is the probability of randomly sleeting a value between-2.555and-0.745 round to four decimal places --- Using a TI-84 you get: normalcdf(-2.555,-0.745) = 0.2228 ========================= Cheers, Stan H. =====================
 Probability-and-statistics/561458: In a probability experiment a painted cube is rolled once. One side of the cube is painted red, two sides are painted yellow, and three sides are painted green. Find the theoretical probability (P) of each event. 1) P (yellow) 2) P (green) 3) P ( red) 4) P ( yellow or green) 5) P (blue) 6) P ( red or yellow or green) 1 solutions Answer 364267 by stanbon(57203)   on 2012-01-23 19:24:56 (Show Source): You can put this solution on YOUR website!In a probability experiment a painted cube is rolled once. One side of the cube is painted red, two sides are painted yellow, and three sides are painted green. Find the theoretical probability (P) of each event. 1) P (yellow) = 2/6 ---------------------- 2) P (green) = 3/6 ---------------------- 3) P (red) = 1/6 ------------------------------ 4) P ( yellow or green) = (2+3)/6 = 5/6 ----------------------------------------- 5) P (blue) = 0 ------------------------------- 6) P (red or yellow or green) = (1+2+3)/6 = 1 ================================================= Cheers, Stan H. ===============
 Probability-and-statistics/561454: A player pays \$1 to play and wins \$2 if the dart lands in the sections marked B. If B = 6/13, how much money will the player make or lose after 36 turns?1 solutions Answer 364266 by stanbon(57203)   on 2012-01-23 19:21:29 (Show Source): You can put this solution on YOUR website!A player pays \$1 to play and wins \$2 if the dart lands in the sections marked B. If B = 6/13, how much money will the player make or lose after 36 turns? --- Expected gain = 2*(6/23) + -1(7/23) = 0.2174 dollars ----- So the player can expect to win 21.74 cents each time he plays. ---- In 36 games he can expect to win 36*21.74 cents = \$7.83 =============== Cheers, Stan H,
 Probability-and-statistics/561146: Compute the probability of drawing, without replacement, 3 odd numbers in a row from the set {1, 2, ... 11}. Round your answer to three decimal places.1 solutions Answer 364199 by stanbon(57203)   on 2012-01-23 12:45:34 (Show Source): You can put this solution on YOUR website!Compute the probability of drawing, without replacement, 3 odd numbers in a row from the set {1, 2, ... 11}. Round your answer to three decimal places. ---- There are 6 odd numbers. # of ways to pick 3 odd is 6C3 = 20 --- # of ways to randomly pick 3 is 11C3 = 165 --- P(pick 3 odd) = 20/165 = 0.1212 ================================== Cheers, Stan H. ===================
 Linear-equations/561171: Susan invested part of her 1800 savings at 9% annum and the remainder at 6% per annum. In one year, the 9% investement earned 102 more than the ^% investement. How much did she invest at each rate?1 solutions Answer 364195 by stanbon(57203)   on 2012-01-23 12:40:16 (Show Source): You can put this solution on YOUR website!Susan invested part of her 1800 savings at 9% annum and the remainder at 6% per annum. In one year, the 9% investement earned 102 more than the ^% investement. How much did she invest at each rate? --------------------- Equation: 0.09x - 0.06(1800-x) = 102 ---- Multiply thru by 100 to get: 9x - 6*1800 + 6x = 10200 -------- 14x = 21000 x = \$1500 (amt invested at 9% 1800-x = \$300 (amt invested at 6%) ===================================== Cheers, Stan H. =================
 Geometry_Word_Problems/561175: find the length of the hypotenuse of a right triangle with legs measuring 6 inches and 8 inches. using pythagorean theorem 1 solutions Answer 364192 by stanbon(57203)   on 2012-01-23 12:35:37 (Show Source): You can put this solution on YOUR website!find the length of the hypotenuse of a right triangle with legs measuring 6 inches and 8 inches. using pythagorean theorem --- h^2 = 6^2 + 8^2 h = sqrt(36+64) h = 10 inches ====================== Cheers, Stan H. ======================
 Equations/561174: How do you identify the vertex and exis of symmetry of an equation?1 solutions Answer 364191 by stanbon(57203)   on 2012-01-23 12:30:56 (Show Source): You can put this solution on YOUR website!How do you identify the vertex and axis of symmetry of an equation? --------------- Vertex occurs at (-b/(2a) , f(-b/(2a)) ------- The axis of symmetry is x = -b/(2a) if the parabola opens up or down. The axis of symmetry is y = -b/(2a) if the parabola opens right or left. ================ Cheers, Stan H. ===================
 Linear_Equations_And_Systems_Word_Problems/561161: A poll found that a particular group of people read an average of 10.1 books per year. The pollsters are 99% confident that the result from this poll is off by fewer than 1.32 books from the actual average x. Express this situation as an inequality involving absolute value, and solve the inequality for x to determine the interval in which the average is likely to fall1 solutions Answer 364186 by stanbon(57203)   on 2012-01-23 12:26:00 (Show Source): You can put this solution on YOUR website!A poll found that a particular group of people read an average of 10.1 books per year. The pollsters are 99% confident that the result from this poll is off by fewer than 1.32 books from the actual average x. Express this situation as an inequality involving absolute value, and solve the inequality for x to determine the interval in which the average is likely to fall ---------- --- |10.1-x|<= 1.32 ------ -1.32 <= 10.1-x <= 1.32 -11.32 <= -x <= -8.78 ---------- Multiply thru by -1 to get: -------------- 8.78 <= x <= 11.32 ======================== Cheers, Stan H.