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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 , 57210..57239 , 57240..57269, >>Next

 Rectangles/354620: A football field is rectangular with a perimeter of 1040 feet. the length is 200 feet more than the width. Find the length and the width of the field. (hint: p=2l+2w)1 solutions Answer 253366 by stanbon(57342)   on 2010-10-11 12:09:42 (Show Source): You can put this solution on YOUR website!A football field is rectangular with a perimeter of 1040 feet. the length is 200 feet more than the width. Find the length and the width of the field. (hint: p=2l+2w) ------------------- Let the width be "w". Then the length is "w+200" ---- P = 2(l+w) 1040 = 2(w+200 + w) ---- 520 = 2w+200 2w = 320 w = 160 (width) l = w+200 = 360 (length) ======================= cheers, Stan H.
 Rational-functions/354621: What is the lcd for "13/2x+2, 2/3x^2+6x+3"1 solutions Answer 253364 by stanbon(57342)   on 2010-10-11 12:05:25 (Show Source): You can put this solution on YOUR website!What is the lcd for "13/2x+2, 2/3x^2+6x+3" ------------------- Factor the denominators: 2x+2 = 2(x+1) ---- 3x^2+6x+3 = 3(x^2+2x+1) = 3(x+1)^2 ----- The LCD must have each of the factors in their highest power. LCD = 2*3*(x+1)^2 ====================== Cheers, Stan H.
 Rational-functions/354616: I have a huge problem with graphing equations. In my homework I need to graph linear systems and estimate the solution for this equation: y= -3x+2 y= 2x-3 My answer for where the two lines crossed was (-1,-3) but I don't know if that's right. 1 solutions Answer 253363 by stanbon(57342)   on 2010-10-11 12:00:13 (Show Source): You can put this solution on YOUR website!In my homework I need to graph linear systems and estimate the solution for this equation: y= -3x+2 y= 2x-3 My answer for where the two lines crossed was (-1,-3) but I don't know if that's right. ------------------- Put that x/y pair into each equation and see if your "solution" is really a solution. --- Putting it into the 1st equation you would get -3 = -3(-1) = 2 -3 = 3+2 That is wrong so (-1,-3) is not the correct solution. ---- --- I think (1,-1) is the correct answer. Checking: y = -3x+2 -1 = -3*1+2 -1 = -1 ---- y = 2x-3 -1 = 2*1-3 -1 = 2-3 -1 = -1 ------- The pair 1,-1 checks out in both equations, so that pair is the solution. ================================ Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/354614: an expression for the product of an even integer and an odd integer is: A) n^2 B) 4n^2 -1 C) 4n^2 + 1 D) 4n^2 +2n E) 4n^2+4n+1 The answer is D, but I don't understand the question or how they came about the answer.1 solutions Answer 253359 by stanbon(57342)   on 2010-10-11 11:52:55 (Show Source): You can put this solution on YOUR website! an expression for the product of an even integer and an odd integer is: A) n^2 B) 4n^2 -1 C) 4n^2 + 1 D) 4n^2 +2n E) 4n^2+4n+1 The answer is D, --------------------- The even must be a multiple of 2: 2n The odd must be one more than or one less then a multiple of 2: 2n+1 ---- Product = 2n(2n+1) = 4n^2+2n ============================== Cheers, Stan H.
 Probability-and-statistics/354602: Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. In bridge, exactly 3 kings and exactly 3 queens?1 solutions Answer 253357 by stanbon(57342)   on 2010-10-11 11:50:17 (Show Source): You can put this solution on YOUR website!Find the probability of the following card hands from a 52-card deck. In poker, aces are either high or low. A bridge hand is made up of 13 cards. In bridge, exactly 3 kings and exactly 3 queens? P(3 k and 3 q or 13) = [4C3/52C][44C7/46C7] (pick 3 k from 4 out of 52)(pick 3 q from 4 out of 48)(pick 7 from 44 out of 46) =================== Cheers, Stan H.
 Probability-and-statistics/354607: Mike can make 60% of his attempts from the foul line. Jake can make 70% of his attempts from the foul line. A. If each man shoots once what is the probability that they both make a basket? B. If each man shoots once what is the probability that at least on of them will make a basket? C. If he shoots 4 times, what is the probability that Jake makes all 4 shots D. If he shoots 4 times what is the probabilty that mike misses all 4 shots?1 solutions Answer 253355 by stanbon(57342)   on 2010-10-11 11:39:47 (Show Source): You can put this solution on YOUR website!Mike can make 60% of his attempts from the foul line. Jake can make 70% of his attempts from the foul line. A. If each man shoots once what is the probability that they both make a basket? The events are independent: Ans: 0.6*0.7 = 0.42 ------------------------- B. If each man shoots once what is the probability that at least on of them will make a basket? Ans: (at least one make it) = 1 - P(both miss) = 1 - 0.4*-0.3 = 1- 0.12 = 0.88 ------------------------- C. If he shoots 4 times, what is the probability that Jake makes all 4 shots Ans: 0.7^4 = 0.2401 ============== D. If he shoots 4 times what is the probabilty that mike misses all 4 shots? Ans 0.4^4 = 0.0256 ======================= Cheers, Stan H.
 Travel_Word_Problems/354447: Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as fast as Stan, how long would it take Stan to mow the lawn alone? 1 solutions Answer 253277 by stanbon(57342)   on 2010-10-10 22:33:30 (Show Source): You can put this solution on YOUR website!Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as fast as Stan, how long would it take Stan to mow the lawn alone? ------------ Together rate = 1/40 job/min Hilda time = x: Hilda rate = 1/x job/min Stan time = 2x; Stan rate = 1/(2x) job/min ------------------------------ Equation: rate + rate = together rate 1/x + 1/2x = 1/40 ----- Multiply thru by 40x to get: 40 +20 = x x = 60 minutes ---- Stan time = 2x = 2 hrs ============================ Cheers, Stan H.
 Probability-and-statistics/354410: In an ESP experiment, participants are required to predict the color (red or black) of a card drawn randomly from a complete deck. If a participant correctly identifies the color for 38 out of 64 trial, is that person performing significantly better than chance? Test at .05 significance level.1 solutions Answer 253276 by stanbon(57342)   on 2010-10-10 22:27:00 (Show Source): You can put this solution on YOUR website!In an ESP experiment, participants are required to predict the color (red or black) of a card drawn randomly from a complete deck. If a participant correctly identifies the color for 38 out of 64 trial, is that person performing significantly better than chance? Test at .05 significance level. ============ Ho: p = 1/2 Ha: p is not equal to 1/2 ---- p-hat = 38/64 = 0.5938 ------ z(0.5938) = (0.5938-0.5000)/sqrt[0.5*0.5/64] = 1.5 --- p-value = 2*P(z>1.5) = 2*0.0668 = 0.1336 ---- Since the p-value is greater than 5% fail to reject Ho. The person is not performing significantly better than chance. -------- Cheers, Stan H.
 Probability-and-statistics/354373: Find the minimum sample size you should use to assure that your estimate of p hat will be within the required margin of error around the population p. Assume the Margin of error is 0.08 with a confidence level of 95%. From a prior study, p hat is estimated to be 0.2.1 solutions Answer 253242 by stanbon(57342)   on 2010-10-10 20:12:12 (Show Source): You can put this solution on YOUR website!Find the minimum sample size you should use to assure that your estimate of p hat will be within the required margin of error around the population p. Assume the Margin of error is 0.08 with a confidence level of 95%. From a prior study, p hat is estimated to be 0.2. ---- Since E = z*sqrt(pq/n) --- n = [z/E]^2*pq ---- n = [1.96/0.08]^2*0.2*0.8 --- n = 97 when rounded up =========================== Cheers, Stan H.
 Mixture_Word_Problems/354378: How many liters of a 20% acid solution must be mixed with a 60% solution to obtain 40 liters of a 35% solution?1 solutions Answer 253237 by stanbon(57342)   on 2010-10-10 20:04:14 (Show Source): You can put this solution on YOUR website!How many liters of a 20% acid solution must be mixed with a 60% solution to obtain 40 liters of a 35% --------------------- Equation: acid + acid = acid 0.20x + 0.60(40-x) = 0.35*40 ---- Multiply thru by 100 to get: 20x + 60*40 - 60x = 35*40 -40x = -25*40 x = 25 liters (amt. of 20% solution needed in the mixture) ---- Cheers, Stan H.
 Complex_Numbers/354382: -3i-x+(2i)^4=3+2i/2-i x=all complex numbers Solve for x Thank You in advance!!!1 solutions Answer 253235 by stanbon(57342)   on 2010-10-10 19:59:50 (Show Source): You can put this solution on YOUR website!-3i-x+(2i)^4=3+2i/2-i --- -3i - x + 16 = 3 + i -i ------- x = 13-3i =================== Cheers, Stan H.
 Complex_Numbers/354377: (4)/(x^2-4)+(2x)/(x-2)+2/(x+2)=01 solutions Answer 253232 by stanbon(57342)   on 2010-10-10 19:55:19 (Show Source): You can put this solution on YOUR website!(4)/(x^2-4)+(2x)/(x-2)+2/(x+2)=0 ------------ Multiply thru by x^2-4 to get: 4 + 2x(x+2) + 2(x-2) = 0 --- 4 + 2x^2+4x + 2x-4 = 0 2x^2 + 6x -2 = 0 ----- x^2 + 3x -1 = 0 --- x = [-3 +- sqrt(9 -4*-1)]/2 --- x = [-3 +- sqrt(13)]/2 ============================= Cheers, stan H.
 Rational-functions/354356: Does anyone have a good website that can explain functions and graphs in plain English. I am having a hard time getting started with this pre-calculus stuff. Any information would be greatly appreciated. You have all been a great help so far. My textbook does not do a good job for me, so it is frustrating. Thank you!1 solutions Answer 253230 by stanbon(57342)   on 2010-10-10 19:31:46 (Show Source): You can put this solution on YOUR website!Search "functions and graphs" with Google or some other search engine. Cheers, Stan H.
 Geometry_Word_Problems/354358: A truck is traveling on a road and another truck is traveling on an overpass above it. Both the trucks are traveling in opposite directions. Describe the type of lines formed by the paths of the trucks. Explain your reasoning.1 solutions Answer 253229 by stanbon(57342)   on 2010-10-10 19:26:05 (Show Source): You can put this solution on YOUR website!parallel
 Probability-and-statistics/354342: A division has 20 employees, 12 males and 8 females. how many ways can they choose a president, a vice president, and a secretary in that order, if the president has to be a female and the other officers must be male?1 solutions Answer 253228 by stanbon(57342)   on 2010-10-10 19:24:15 (Show Source): You can put this solution on YOUR website!A division has 20 employees, 12 males and 8 females. how many ways can they choose a president, a vice president, and a secretary in that order, if the president has to be a female and the other officers must be male? ---------------- # of ways to choose a president: 8 # of ways to choose a vp: 12 # of ways to choose a sec: 11 ----------------------- Total # of ways: 8*12*11 = 1056 ---------------------------- Cheers, Stan H.
 Probability-and-statistics/354335: A supplier contract calls for a key dimension of a part to be between 1.95 and 2.05 cm. The supplier has determined that the standard deviation of its process which is normally distributed, is 0.10 cm. a. If the mean is 1.98, what fraction of parts will meet specifications? b. If the mean is adjusted to 2.00, what fraction of the parts will meet specifications? c. How small must the standard deviation be to ensure that no more than 2% of parts are nonconforming, assuming the mean is 2.oo?1 solutions Answer 253226 by stanbon(57342)   on 2010-10-10 19:07:37 (Show Source): You can put this solution on YOUR website!A supplier contract calls for a key dimension of a part to be between 1.95 and 2.05 cm. The supplier has determined that the standard deviation of its process which is normally distributed, is 0.10 cm. a. If the mean is 1.98, what fraction of parts will meet specifications? --- z(1.95) = (1.95-1.98)/0.1 = -.3000 z(2.05) = (2.05-1.98)/0.1 = 0.7 --- P(1.95< x <1.98) = P(-0.3 < z < 0.7) = normalcdf(-0.3,0.7) = 0.3759 ---------------------------------------------------- b. If the mean is adjusted to 2.00, what fraction of the parts will meet specifications? Same procedure as used in part a. ---------------------------------------------------- c. How small must the standard deviation be to ensure that no more than 2% of parts are nonconforming, assuming the mean is 2.oo? --- z-value with a left-tail of 1% and a right tail of 1% invNorm(0.01) = +/-2.3264 ---- Solve :: (1.95-2)/s = -2.3264 s = 0.0215 ------------------- (2.05-2)/s = 2.3264 s = 0.0215 -------------------------- ====================== Cheers, Stan H.
 Probability-and-statistics/354126: In a survey of 3224 U.S adults, 1515 said flying is the most stressful form of travel.1 solutions Answer 253141 by stanbon(57342)   on 2010-10-10 12:40:14 (Show Source): You can put this solution on YOUR website!No question
 Probability-and-statistics/354174: Find P(A or B) for the folowing: P(A)=0.64, P(B)=0.64, and P(A and B)=0.46. P(A or B) =1 solutions Answer 253140 by stanbon(57342)   on 2010-10-10 12:39:14 (Show Source): You can put this solution on YOUR website!Find P(A or B) for the folowing: P(A)=0.64, P(B)=0.64, and P(A and B)=0.46. P(A or B) = P(A)+P(B)-P(A and B) = 0.64 + 0.64 - 0.46 = 0.82 ======== Cheers, Stan H.
 Inequalities/354159: How do I solve the following inequality using interval notation? 1/x-3 <= 1/x-51 solutions Answer 253139 by stanbon(57342)   on 2010-10-10 12:35:36 (Show Source): You can put this solution on YOUR website! How do I solve the following inequality using interval notation? 1/(x-3) <= 1/(x-5) ------ x cannot be 3 and it cannot be 5. ------ Solve the equality. 1/(x-3) = 1/(x-5) --- x-5 = x-3 No solution: So no solution for the equality part of the problem. ----------------- Draw a number line and plot x = 3 and x = 5. --- Test values in the resulting intervals to find inequality solutions. --- 1/(x-3)<1/(x-5) -- If x = 0 you get 1/-3 < 1/-5: true, so solution in (-inf,3) If x = 4 you get 1/1 < 1/-1: false If x = 10 you get 1/7 < 1/5: true, so solutions in (5,+inf) ------ Cheers, Stan H.
 Rate-of-work-word-problems/354147: sue can sholver snow from her driveway in 40 minutes. tom can do the same job in 50 minutes. How long would it take sue and tom to shovel the driveway if they worked together?1 solutions Answer 253138 by stanbon(57342)   on 2010-10-10 11:55:18 (Show Source): You can put this solution on YOUR website!sue can shovel snow from her driveway in 40 minutes. tom can do the same job in 50 minutes. How long would it take sue and tom to shovel the driveway if they worked together. --- Sue rate = 1/40 job/min Tom rate = 1/50 job/min --------------- Together rate = 1/x job/min --------------------------------- Equation: rate + rate = together rate 1/40 + 1/50 = 1/x 50x + 40x = 40*50 90x = 2000 x = 22.222 minutes (time to do the job together) -------------------------- Cheers, Stan H.
 Travel_Word_Problems/354154: when fritz drives to work his trip takes 48 minutes, but when he takes the train it takes 40 minutes. find the distance fritz travels to work if the train travels an average of 6 mph faster than his driving.1 solutions Answer 253137 by stanbon(57342)   on 2010-10-10 11:50:33 (Show Source): You can put this solution on YOUR website!when fritz drives to work his trip takes 48 minutes, but when he takes the train it takes 40 minutes. find the distance fritz travels to work if the train travels an average of 6 mph faster than his driving. --- Drive DATA: time = 48 min ; distance = x miles ; rate = x/48 miles per minute ---------------- Train DATA: time = 40 min ; distance = x miles ; rate = x/40 miles per min ----- Equation: train rate - drive rate = 6/60 miles per minute x/40 - x/48 = 1/10 --- Multiply thru by 10*48*40 to get: 10*48x - 10*40x = 48*40 80x = 48*40 x = 24 miles ================== Cheers, Stan H.
 Equations/354148: I needhelp setting up this word problem. You have to sell 50 tickets to a fair. Student tickets cost \$3 and adult tickets cost \$5. Let t represent the number of student tickets you sell. Write and simplify an expression in terms of t for the total amount of money you raise for selling 50 tickets. Then use the expression to determine how much money you raise if you sell all 50 tickets and 28 of them are student tickets. I have figured out that if I sell 28 student tickets I will sell 22 adult tickets and I will raise \$194. 50-28=22 28(3) + 22(5) = 194 I just can't figure out what the first equation is.1 solutions Answer 253136 by stanbon(57342)   on 2010-10-10 11:43:44 (Show Source): You can put this solution on YOUR website!I needhelp setting up this word problem. You have to sell 50 tickets to a fair. Student tickets cost \$3 and adult tickets cost \$5. Let t represent the number of student tickets you sell. Write and simplify an expression in terms of t for the total amount of money you raise for selling 50 tickets. Then use the expression to determine how much money you raise if you sell all 50 tickets and 28 of them are student tickets. I have figured out that if I sell 28 student tickets I will sell 22 adult tickets and I will raise \$194. 50-28=22 28(3) + 22(5) = 194 ---------------- Quantity Equation: t + a = 50 ---- If t = 28, a = 22 Value is 3*28 + 5*22 = \$194 ---- Cheers, Stan H. ----
 Polynomials-and-rational-expressions/354152: Please solve: 2(x+2)-2(x-4)=x+71 solutions Answer 253135 by stanbon(57342)   on 2010-10-10 11:36:57 (Show Source): You can put this solution on YOUR website!Please solve: 2(x+2)-2(x-4)=x+7 ----- 2x+4-2x+8 = x+7 12 = x+7 x = 5 ------- Cheers, Stan H.
 Probability-and-statistics/354144: Birthweights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. What is the probability that a randomly chosen infant has a birthweight between 115 oz. and 130 oz.?1 solutions Answer 253134 by stanbon(57342)   on 2010-10-10 11:35:16 (Show Source): You can put this solution on YOUR website!Birthweights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. What is the probability that a randomly chosen infant has a birthweight between 115 oz. and 130 oz.? ---- z(115) = (115-110)/15 = 1/3 --- z(130) = (130-110)/15 = 4/3 ----- P(115 < x < 130) = P(1/3 < z < 4/3) = 0.2782 =============== Cheers, Stan H.
 Probability-and-statistics/353975: all male jury of 12 peopke is chosen for a trial. The defense lawyer claims the jury must have been chosen in a biased manner because 50% of the city;s adult residents are women and yet jury contains no women. Assess the claim by answering the following: If the jury were randomly chosen from the city's adult population , what is the probability that the jury would have a) no females, b) at least one female?1 solutions Answer 253119 by stanbon(57342)   on 2010-10-10 08:53:00 (Show Source): You can put this solution on YOUR website!all male jury of 12 peopke is chosen for a trial. The defense lawyer claims the jury must have been chosen in a biased manner because 50% of the city's adult residents are women and yet the jury contains no women. Assess the claim by answering the following: If the jury were randomly chosen from the city's adult population , what is the probability that the jury would have a) no females, P(x = 0 of 12) = (1/2)^12 = 0.0002441 ------------------- b) at least one female? P(at least one) = 1 - P(no female) = 1 - 0.0002441 = 0.999756... ------------------ Cheers, Stan H.
 Probability-and-statistics/353976: The probabilty that a health nurse will fina a client at home on a particular day is 0.7. What is the probabilty that one twon home vists made by the nurse in a day, she will find both clients at home?1 solutions Answer 253118 by stanbon(57342)   on 2010-10-10 08:48:25 (Show Source): You can put this solution on YOUR website!The probabilty that a health nurse will find a client at home on a particular day is 0.7. What is the probabilty that on two home vists made by the nurse in a day, she will find both clients at home? -------------- Ans: 0.7^2 = 0.49 ==================== Cheers, Stan H.
 Probability-and-statistics/354050: X= 7, 8, 9, 10, 11, 12, 13 and the corresponding p(X)= 0.05, 0.08, 0.10, 0.14, 0.28, 0.21, 0.14 The random variable X is the size of a popular shoe purchased. Suppose 3 randomly selected customers each purchase a pair of these sneakers. What is the probability that exactly two of three buy size 11 sneakers?1 solutions Answer 253117 by stanbon(57342)   on 2010-10-10 08:44:24 (Show Source): You can put this solution on YOUR website!X = 7, 8, 9, 10, 11, 12, 13 and the corresponding p(X)= 0.05, 0.08, 0.10, 0.14, 0.28, 0.21, 0.14 The random variable X is the size of a popular shoe purchased. Suppose 3 randomly selected customers each purchase a pair of these sneakers. What is the probability that exactly two of three buy size 11 sneakers? -------------------- Binomial Problem with n = 3 and p = 0.28 --- P(x = 2) = 3C2*(0.28)^2*(0.72) = binompdf(3,0.28,2) = 0.1693 ================= Cheers, Stan H.
 Sequences-and-series/354103: how does one solve piecewise functions f(x)x+4 if x is greater or less than -4 -(x+4) for x is less than -41 solutions Answer 253115 by stanbon(57342)   on 2010-10-10 08:30:24 (Show Source): You can put this solution on YOUR website! how does one solve piecewise functions f(x) = x+4 if x is greater or less than -4 -(x+4) for x is less than -4 ------------ You don't "solve" them. --- By they way, what you typed is a contradiction. Did you mean to type "less than -4" twice? ------------- Cheers, Stan H.
 Age_Word_Problems/354104: 25 years ago, Hailey was five more than one-third as old as Jason was. Today, Jason is twenty six less than two times the age of Hailey. How old is Jason? How do I figure this out.1 solutions Answer 253114 by stanbon(57342)   on 2010-10-10 08:27:18 (Show Source): You can put this solution on YOUR website!25 years ago, Hailey was five more than one-third as old as Jason was. Today, Jason is twenty six less than two times the age of Hailey. How old is Jason? --------------- Let Jason's age be J Let Hailey's age be H ----------------- Equations: (H-25) = (1/3)(J-25) J = 2H-26 ------------------ Substitute for "J" and solve for "H". --- H-25 = (1/3)(2H-26-25) 3H-75 = 2H-51 H = 24 (Hailey's age now) ---- Since J = 2H-26, J = 48-26 = 22 (Jason's age now) ===================================================== cheers, Stan H.
 Rational-functions/354090: how to find range of f(x)=x(square)-3x+2/(x+1) algebraically?1 solutions Answer 253113 by stanbon(57342)   on 2010-10-10 08:23:04 (Show Source): You can put this solution on YOUR website!how to find range of f(x)=x(square)-3x+2/(x+1) algebraically? -------- f(x) = x^2-[(3x+2)/(x+1)] ----- Range??? x^2 is always >=0 -- (3x+2)/(x+1) has a vertical asymptote at x=-1 so all Real Numbers are subtracted from x^2. -------- Graph: ------------ Range is "All Real Numbers" Cheers, Stan H.
 logarithm/354092: What would be the value of X so that |x-5|-2 has a positive answer1 solutions Answer 253112 by stanbon(57342)   on 2010-10-10 08:05:45 (Show Source): You can put this solution on YOUR website!What would be the value of X so that |x-5|-2 has a positive answer --- Solve |x-5| - 2 > 0 --- |x-5) > 2 ----- x-5 >2 or x-5 < -2 --- x > 7 or x < 3 =================== Cheers, Stan H.