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# Recent problems solved by 'stanbon'

stanbon answered: 57135 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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 Miscellaneous_Word_Problems/490929: this is miscellaneous i do not know what to categorize these problems at sorry. 1. 1/25 - x^2 2. which is not a factor of 3x^3 - 60 + 15x^2 - 12x a)x + 5 b)x - 2 c) x - 5 d) x + 2 3. ((5m + n) / (2))= 3 ((4m - 3n) / (9)) = -2 4. z^2 = 18 if you could show all work that would be great 1 solutions Answer 334366 by stanbon(57203)   on 2011-09-04 10:03:11 (Show Source): You can put this solution on YOUR website!1. 1/25 - x^2 Factor: [(1/5)-x] ================================= 2. which is not a factor of 3x^3 - 60 + 15x^2 - 12x Factor: 3[x^3+5x^2-4x-20] = 3[x^2(x+5)-4(x+5)] = 3(x+5)(x^2-4)] = 3(x+5)(x-2)(x+2) ------ a)x + 5 b)x - 2 c) x - 5 d) x + 2 Ans: x-5 is not a factor ================================== 3. ((5m + n) / (2))= 3 ((4m - 3n) / (9)) = -2 ----- 5m + n = 6 4m -3n = -18 ------------------------- Multiply thru the 1st equation by 3: 15m + 3n = 18 4m -3n = -18 ------------------ Add and solve for "m": 19m = 0 m = 0 ================================ 4. z^2 = 18 z = sqrt(18) or z = -sqrt(18) --- z = 3sqrt(2) or z = -3sqrt(2) =================================== Cheers, Stan H.
 Numbers_Word_Problems/490928: Word problems!! Can you help me solve: Find three consecutive integers whose sum divided by the difference between the third number and the first number will be 3 more than the middle number. Thank you!1 solutions Answer 334363 by stanbon(57203)   on 2011-09-04 09:55:27 (Show Source): You can put this solution on YOUR website!Find three consecutive integers whose sum divided by the difference between the third number and the first number will be 3 more than the middle number. ----- 1st: x-1 2nd: x 3rd: x+1 ------------------ Equation: (3x)/(2) = x+3 --- 3x = 2x+6 x = 6 ---- 1st: x-1 = 5 2nd: x = 6 3rd: x+1 = 7 ================= Check: (18)/2 = 6+3 9 = 9 =================== Cheers, Stan H.
 Travel_Word_Problems/490927: 1.how far is it in miles from the bus station to the hospital about how many miles is it from Hilo to captain cook 1 solutions Answer 334361 by stanbon(57203)   on 2011-09-04 09:49:59 (Show Source): You can put this solution on YOUR website!Incomplete questions.
 Problems-with-consecutive-odd-even-integers/490926: The sum of three consecutive odd integers the first being n+1.1 solutions Answer 334360 by stanbon(57203)   on 2011-09-04 09:48:51 (Show Source): You can put this solution on YOUR website!The sum of three consecutive odd integers the first being n+1. --- 1st: n+1 2nd: n+3 3rd: n+5 --- Sum = 3n+9 ============ Cheers, Stan H. ============
 Numbers_Word_Problems/490925: I have a word problem, hope you can help me solve. The problem reads: Find two numbers whose difference is 8 and 1/2 of whose sum is 16. Thank you! Cindy1 solutions Answer 334359 by stanbon(57203)   on 2011-09-04 09:47:07 (Show Source): You can put this solution on YOUR website!Find two numbers whose difference is 8 and 1/2 of whose sum is 16. ---- Equations: x - y = 8 (1/2)(x+y) = 16 ---- Rearrange: x - y = 6 x + y = 32 --- Add and solve for "x": 2x = 38 x = 19 ---- Solve for "y": x - y = 6 19 - y = 6 y = 13 ================= Cheers, Stan H.
 Probability-and-statistics/490910: Evaluate: C 11 6 Answers" 66 120 24 4621 solutions Answer 334358 by stanbon(57203)   on 2011-09-04 09:44:20 (Show Source): You can put this solution on YOUR website!Find the number of different arrangements that can be made out of the letters of the word „TRIANGLE‟ if the vowels are to come together. --- 11C6 = 11!/[(11-6)!*6!] = 462 ============================== Cheers, Stan H. ==============================
 Probability-and-statistics/490903: Find the number of different arrangements that can be made out of the letters of the word „TRIANGLE‟ if the vowels are to come together.1 solutions Answer 334356 by stanbon(57203)   on 2011-09-04 09:42:24 (Show Source): You can put this solution on YOUR website!Find the number of different arrangements that can be made out of the letters of the word „TRIANGLE‟ if the vowels are to come together. --- # of letters: 8 # of vowels: 3 ---- # of arrangements of the 3 vowels: 3! = 6 --- Now consider the "vowel arrangement" to be a single letter. --- # of arrangements of the "six" letters: 6! = 720 ------------ Total # of arrangements 6!*3! = 720*6 = 4320 ================ Cheers, Stan H.
 Inequalities/490793: Here is the problem: 2/3(x+7)-(x/4)>1/2(3-x)+(x/6) I come up with an answer of -38/9 I have seen a solution for this problem as -14/15 I don't understand how they came up with the solution. I have tried this problem several times1 solutions Answer 334318 by stanbon(57203)   on 2011-09-03 22:43:06 (Show Source): You can put this solution on YOUR website!2/3(x+7)-(x/4)>1/2(3-x)+(x/6) ---- Multiply thru by 12 to get: 8(x+7) - 3x > 6(3-x) + 2x --------------------------- 5x+56 > 18-4x 9x > -38 --- x > -38/9 =============== Cheers, Stan H.
 Numbers_Word_Problems/490788: the tens digit of a two number is three greater than the ones digit. the difference between twice the original number and half the number obtained after reversing the digits is 1081 solutions Answer 334316 by stanbon(57203)   on 2011-09-03 22:37:53 (Show Source): You can put this solution on YOUR website!the tens digit of a two number is three greater than the ones digit. the difference between twice the original number and half the number obtained after reversing the digits is 108 ---- Let the number be 10t+u ---- Equations: t = u + 3 2(10t+u)-(1/2)(10u+t) = 108 ----------------------------------- Modify: t = u+3 4(10t+u) - (10u+t) = 216 ---- 39t - 6u = 216 t = u+3 ------ Substitute and solve for "u": 39(u+3) - 6u = 216 33u = 216-3*39 33u = 99 u = 3 --- Solve for "t": t = u + 3 t = 6 ----- The number is 63 ======================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/490792: need help solving theequation using the quadratic formula x^2+6x-10=01 solutions Answer 334314 by stanbon(57203)   on 2011-09-03 22:31:30 (Show Source): You can put this solution on YOUR website!x^2+6x-10=0 ---- a = 1 ; b = 6 ; c = -10 ---- x = [-6 +- sqrt(36-4*1*-10)]/2 ----- x = [-6 +- sqrt(76)]/2 --- x = [-6 +- 2*sqrt(19)]/2 ============================= x = [-3+sqrt(19)] or x = -3-sqrt(19) ============================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/490790: Investment: \$20,000 Annual Income: \$1,280 x = T-Bills, 5% yeild y = T-Bonds, 7% yeild z = Corp Bonds, 9% yeild amount invested in t-bills must be 2 times the amount invested in Corp Bills. Find the amount in each investment. I have two of the three equations: x+y+z= 20,000 5x+7y+9z=128,000 What would the third equation be?1 solutions Answer 334313 by stanbon(57203)   on 2011-09-03 22:23:59 (Show Source): You can put this solution on YOUR website!Investment: \$20,000 Annual Income: \$1,280 x = T-Bills, 5% yeild y = T-Bonds, 7% yeild z = Corp Bonds, 9% yeild amount invested in t-bills must be 2 times the amount invested in Corp Bills. Find the amount in each investment. I have two of the three equations: x+y+z= 20,000 5x+7y+9z=128,000 What would the third equation be? y = 2*z ================ Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/490789: Richard has a piggy bank containing only dimes and quarters. He has seven more quarters than dimes. If the total value of the coins is \$3.85, how many dimes and quarters does Richard have?1 solutions Answer 334311 by stanbon(57203)   on 2011-09-03 22:20:16 (Show Source): You can put this solution on YOUR website!He has seven more quarters than dimes. If the total value of the coins is \$3.85, how many dimes and quarters does Richard have? -------------------------- Equations: q = d + 7 10d + 25q = 385 cents ------------------- Substitute for "q" and solve for "d": 10d + 25(d+7) = 385 10d + 25d + 175 = 385 35d = 210 d = 6 (# of dimes) ---- Solve for "q": q = d+7 q = 6+7 = 13 (# of quarters) ============================ Cheers, Stan H.
 Age_Word_Problems/490773: a culture started with 5000 bacteria. after 4 hours it grew to 5500.predict how many bacteria will be after 13 hours.1 solutions Answer 334309 by stanbon(57203)   on 2011-09-03 22:09:59 (Show Source): You can put this solution on YOUR website!---- A culture started with 5000 bacteria. After 4 hours it grew to 5500. A(t) = Ao*b^t 5500 = 5000*b^4 1.1 = b^4 b = 1.1^(1/4) ---- Equation: A(t) = 5000*1.1^(t/4) ------ Predict how many bacteria will be after 13 hours. A(13) =5000*1.1^(13/4) ------------------- A(13) = 6815.48 Round up to 6816 bacteria ====================================== Cheers, Stan H.
 Travel_Word_Problems/490780: This the answer a got for part A of the problem I submitted which is 1B 1.Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: -2, where C is a constant and r is the distance in miles that the object is from the center of the earth. 1A) Solve the equation w = Cr-2 for r. I do have the answer, so could please answer the question 1B, This is my question 1B. Suppose that an object is 150 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth 1 solutions Answer 334305 by stanbon(57203)   on 2011-09-03 21:43:46 (Show Source): You can put this solution on YOUR website!1.Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: -2, where C is a constant and r is the distance in miles that the object is from the center of the earth. 1A) Solve the equation w = C*r^(-2) for r. I do have the answer, so could please answer the question 1B, This is my question 1B. Suppose that an object is 150 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth ----------- w = C*r^(-2) 150 = C*3963^-2 ---- 150*3963^2 = C --- C = 2,355,805,350 ================ Cheers, stan H.
 Quadratic-relations-and-conic-sections/490770: Please help me remember how to solve the following: "Let R(x)=(-3x^2+2)/(x-1). R(x) has an oblique asymptote at: ?" (hint: answer is -3x-3) Thanks!1 solutions Answer 334300 by stanbon(57203)   on 2011-09-03 21:00:55 (Show Source): You can put this solution on YOUR website!"Let R(x)=(-3x^2+2)/(x-1). R(x) has an oblique asymptote at: ?" (hint: answer is -3x-3) ----- Use synthetic division: 1)....-3....0....2 ........-3...-3..|..-1 ------ (-3x^2+2)/(x-1) = -3x-3 - [1/(x-1)] ---- This shows the oblique asymptote is -3x-3 ============================================== Cheers, Stan H. =================
 Equations/490767: q=p-q/2, for p1 solutions Answer 334295 by stanbon(57203)   on 2011-09-03 20:42:34 (Show Source): You can put this solution on YOUR website!q=p-q/2, for p ---- (3/2)q = p ============== Cheers, Stan H.
 Equations/490768: solve and check 5y-10+y=7y+18-5y1 solutions Answer 334294 by stanbon(57203)   on 2011-09-03 20:41:19 (Show Source): You can put this solution on YOUR website!solve and check 5y-10+y=7y+18-5y ---- 6y - 10 = 2y + 18 4y = 28 y = 7 ----- Check: 5y-10+y=7y+18-5y 5*7 - 10 + 7 = 7*7 + 18 - 5*7 35 -3 = 49-17 32 = 32 ============= Cheers, Stan H.
 Polynomials-and-rational-expressions/490769: Factor 3y^2 + 7y + 4.1 solutions Answer 334292 by stanbon(57203)   on 2011-09-03 20:37:28 (Show Source): You can put this solution on YOUR website!Factor 3y^2 + 7y + 4. --- 3y^2 + 4y + 3y + 4 --- y(3y+4) + (3y+4) ---- = (3y+4)(y+1) ================= Cheers, Stan H.
 expressions/490534: 23(+3!)/21 solutions Answer 334137 by stanbon(57203)   on 2011-09-03 07:40:18 (Show Source): You can put this solution on YOUR website!23(+3!)/2 --- 23*6/2 --- = 23*3 --- = 69 ========== Cheers, Stan H.
 expressions/490535: (23+3!)/2 in detail steps1 solutions Answer 334135 by stanbon(57203)   on 2011-09-03 07:38:54 (Show Source): You can put this solution on YOUR website!(23+3!)/2 --- (23+6)/2 --- 29/2 = 14.5 ================ Cheers, Stan H.
 Permutations/490536: 8 guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is?1 solutions Answer 334133 by stanbon(57203)   on 2011-09-03 07:37:25 (Show Source): You can put this solution on YOUR website!8 guests have to be seated 4 on each side of a long rectangular table. 2 particular guests desire to sit on one side of the table and 3 on the other side. The number of ways in which the sitting arrangements can be made is? ---- Pick a side: 2 ways Arrange the 2 on one side: 2! = 2 Arrange the 3 on the other side: 3! = 6 ---- Pick 2 from the remaining 3: 3C2 = 3 ways Put them on the side with 2: 1 way Put the remaining person on the side with 3: 1 way -------------------- Total # of arrangements: 2*2*6*3*1*1 = 72 ============================================= Cheers, Stan H.
 Equations/490538: 28x + (-144)= 10 x +901 solutions Answer 334132 by stanbon(57203)   on 2011-09-03 07:32:10 (Show Source): You can put this solution on YOUR website!28x + (-144)= 10 x +90 --- Subtract 10x from both sides. Add 144 to both sides. --- 18x = 234 Divide both sides by 18 to get: x = 13 ========== Cheers, Stan H. ==========
 Angles/490537: one of the supplementary angle exeeds the other by 15 degree.find the measure of the supplementary angle1 solutions Answer 334129 by stanbon(57203)   on 2011-09-03 07:22:50 (Show Source): You can put this solution on YOUR website! one of the supplementary angle exeeds the other by 15 degree.find the measure of the supplementary angle ------ Angle: x Supplement: 180-x ------------ Equation: 180-x = x + 15 2x = 165 x = 82.5 (the angle) 180-82.5 = 97.5 degrees (supplement) ========================================= Cheers, Stan H.
 Probability-and-statistics/490443: Please help...i am taking an online stats class and am so confused on this problem..I have been working on it for so long Im getting a headache...thank you very much Assume that the population of heights of female college students is approximately normally distributed with mean µ of 64.64 inches and standard deviation đ of 6.02 inches. A random sample of 98 heights is obtained. Show all work. (A) Find the mean and standard error of the x distribution (B) Find p(x>63.75) 1 solutions Answer 334128 by stanbon(57203)   on 2011-09-03 06:59:19 (Show Source): You can put this solution on YOUR website!Assume that the population of heights of female college students is approximately normally distributed with mean µ of 64.64 inches and standard deviation đ of 6.02 inches. A random sample of 98 heights is obtained. Show all work. (A) Find the mean and standard error of the x-bar distribution. mean of the sample means = 64.64 ----------------- (B) Find p(x>63.75 If you really mean x and not x-bar you get: z(63.75) = (63.75-64.64)/6.02 = -0.1478 P(x > 63.75) = P(z > -0.1478) = 0.5587 -------------- But, if you mean P(x-bar > 63.75) you get: t(63.75) = (63.75-64.64)/[6.02/sqrt(98)] = -1.4635 --- P(xbar > 63.75) = P(t > -1.4635 when df = 97) = 0.9267 ============================ Cheers, Stan H.
 Probability-and-statistics/490487: A test consists of 90 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers.1 solutions Answer 334127 by stanbon(57203)   on 2011-09-03 06:46:06 (Show Source): You can put this solution on YOUR website!A test consists of 90 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers. ---- Binomial Problem with n = 90 and p(correct) = 1/5 --- mean = np = 90(1/5) = 18 Std = sqrt(npq) = sqrt(18*(4/5)) = 3.7947 ======================== Cheers, Stan H.
 Probability-and-statistics/490454: Given a level of confidence of 99% and a population standard deviation of 7, answer the following: (A) What other information is necessary to find the sample size (n)? (B) Find the Maximum Error of Estimate (E) if n = 74. Show all work. 1 solutions Answer 334101 by stanbon(57203)   on 2011-09-02 22:50:17 (Show Source): You can put this solution on YOUR website!Given a level of confidence of 99% and a population standard deviation of 7, answer the following: (A) What other information is necessary to find the sample size (n)? n = z*s/E Need to know "E" ---------------------------- (B) Find the Maximum Error of Estimate (E) if n = 74. E = 2.5758 * [7/sqrt(74)] --- E = 2.0960 ================ Cheers, Stan H.
 Percentage-and-ratio-word-problems/490473: soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360 pound mixture that is 15% protein?1 solutions Answer 334099 by stanbon(57203)   on 2011-09-02 22:35:27 (Show Source): You can put this solution on YOUR website!soybean meal is 18% protein; cornmeal is 9% protein. How many pounds of each should be mixed together in order to get 360 pound mixture that is 15% protein? ----------- Equation: protein + protein = protein 0.18x + 0.09(360-x) = 0.15*360 --- Multiply thru by 100 to get: 18x + 9*360 - 9x = 15*360 9x = 6*360 x = 240 lb (amt. of 18% meal needed) --- 360-x = 120 lb (amt. of 9% mean needed) ============ Cheers, Stan H. ============
 Inequalities/490455: Hi, I am having trouble solving this inequality: 2x≤5-7x<7+x The answer my textbook gives (in interval notation) is: (-1/4, 5/9] I have tried several different ways of solving this problem but have not been successful. I would greatly appreciate any help you can provide. Thank you!1 solutions Answer 334097 by stanbon(57203)   on 2011-09-02 22:28:12 (Show Source): You can put this solution on YOUR website!2x≤5-7x<7+x The answer my textbook gives (in interval notation) is: (-1/4, 5/9] ----------------------- Solve: 2x <= 5-7x 9x<=5 x <= 5/9 ------------------- Solve: 5-7x < 7+x 8x > -2 x > -1/4 -------------------- Solution -1/4 < x <= 5/9 ---- Cheers, Stan H.
 Percentage-and-ratio-word-problems/490470: a tablet of medication consists of two substances in the ratio of 9 to 5.if the tablet contains 140 milligrams of medication . how much of each substance is in the tablet1 solutions Answer 334093 by stanbon(57203)   on 2011-09-02 22:13:56 (Show Source): You can put this solution on YOUR website!a tablet of medication consists of two substances in the ratio of 9 to 5.if the tablet contains 140 milligrams of medication . how much of each substance is in the tablet --- 9 to 5 is the same as 9x to 5x Equation: 9x + 5x = 140 14x = 140 x = 10 ---- 1st substance: 9x = 90 mg 2nd substance: 5x = 50 mg ------------------ Cheers, Stan H.
 Functions/490469: Find the domain and range of f(x)=-3x^2+81 solutions Answer 334091 by stanbon(57203)   on 2011-09-02 22:11:09 (Show Source): You can put this solution on YOUR website!Find the domain and range of f(x)=-3x^2+8 --- Domain: All Real Numbers Range: All Real Numbers <= 8 ----------------- Cheers, Stan H.
 Linear-equations/490465: Find the general equation of each line; that is, write the equation in the form of Ax+By=C. Slope= 2; containing the point (-4,1) 1 solutions Answer 334089 by stanbon(57203)   on 2011-09-02 22:08:45 (Show Source): You can put this solution on YOUR website!Find the general equation of each line; that is, write the equation in the form of Ax+By=C. Slope= 2; containing the point (-4,1) ---- Form: y = mx+b 1 = 2(-4) + b b = 9 ---------- Equation: y = 2x + 9 --- Form Change: 2x - y = -9 ================= Cheers, Stan H.