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Recent problems solved by 'stanbon'

stanbon answered: 57214 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 , 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, >>Next

Linear_Equations_And_Systems_Word_Problems/411188: Hi can i get some help with this question.? The product of 6 and nine times a number is the same as the difference of ten times the number 2. What is the number? 1 solutions Answer 289029 by stanbon(57282)   on 2011-02-18 19:11:41 (Show Source): You can put this solution on YOUR website! The product of 6 and nine times a number is the same as the difference of ten times the number and 2. What is the number? ------------------------- Equation: 6(9x)= 10x-2 54x = 10x-2 44x = -2 x = -1/22 ------ Cheers, Stan H.

Exponential-and-logarithmic-functions/410935: ln5-lnx=3 I tried: ln(5-x)=3 1 solutions Answer 288877 by stanbon(57282)   on 2011-02-17 22:46:39 (Show Source): You can put this solution on YOUR website! ln5-lnx=3 --- ln(5/x) = 3 ---- 5/x = e^3 --- x/5 = e^-3 x = 5*e^(-3) ---- x = 0.2489 ============== Cheers, Stan H. ==============

Linear-equations/410934: Determine the linear function for a graph that is a line containing the points (-1,-1) and (3,-9) 1 solutions Answer 288874 by stanbon(57282)   on 2011-02-17 22:41:55 (Show Source): You can put this solution on YOUR website! Determine the linear function for a graph that is a line containing the points (-1,-1) and (3,-9) --------------------- slope = (-9--1)/(3--1) = -8/4 = -2 ----- Equation Form: y = mx + b solve for "b": -1 = -2(-1)+b -1 = 2 = b b = -3 ----- Equation: y = -2x - 3 ================ Cheers, Stan H.

Expressions-with-variables/410926: Barry runs up the down escalator in 9 seconds. He can run down the down escalator in 6 seconds. The escalator is 36 feet long. How fast is the escalator moving? Find Barry's speed running down the escalator when it isn't moving. 1 solutions Answer 288873 by stanbon(57282)   on 2011-02-17 22:37:31 (Show Source): You can put this solution on YOUR website! Barry runs up the down escalator in 9 seconds. He can run down the down escalator in 6 seconds. The escalator is 36 feet long. How fast is the escalator moving? Find Barry's speed running down the escalator when it isn't moving. ---- Down escalator DATA: time = 6 seconds ; distance = 36 ft; rate = 36/6 = 6 ft/sec ----- Up escalator DATA: time = 9 seconds ; distance = 36 ft. rate = 36/9 = 4 ft/sec ----- Equations: Barry rate + stair rate = 6 ft/sec Barry rate - stair rate = 4 ft/sec ---- Add to get: 2*Barry rate = 10 ft/sec Barry's rate when escalator is not moving = 5 ft/sec ------- Cheers, Stan H. =============

Age_Word_Problems/410885: I'm having trouble writing equations that models how old in years each of us will be, when our ages add up to 150 years old. I had to use three people's ages 8,28,30. Explain the reasoning which helped you develop your equation? 1 solutions Answer 288855 by stanbon(57282)   on 2011-02-17 21:35:28 (Show Source): You can put this solution on YOUR website! I'm having trouble writing equations that models how old in years each of us will be, when our ages add up to 150 years old. I had to use three people's ages 8,28,30. Explain the reasoning which helped you develop your equation? ---- Those three person's ages do not add up to 150 years old. --- You might use 40,60, and 50 but not 8,28 and 30. ---- If you use a = 40, b = 60, and c = 50 you would get 3 equations: --- a + b + c = 150 a = b-20 c = b+10 --------- That's an example. ---------------------------- Cheers, Stan H. ====================

Miscellaneous_Word_Problems/410882: Suppose you bought supplies for a party. Three rolls of streamers and 15 balloons cost $30. Later, you bought 2 rolls of streamers and 4 baloons for $11. How much did each roll of streamers cost? How much did each balloon cost? (could you also explain how you got the answer?) 1 solutions Answer 288854 by stanbon(57282)   on 2011-02-17 21:23:52 (Show Source): You can put this solution on YOUR website! Three rolls of streamers and 15 balloons cost $30. Later, you bought 2 rolls of streamers and 4 baloons for $11. How much did each roll of streamers cost? ----- Equations: 3s + 15b = 30 dollars 2s + 4b = 11 dollars -------------- Multiply thru 1st by 4 Multiply thru the 2nd by 15 ------- 12s + 60b = 120 30s + 60b = 165 ---- Subtract and solve for "s": 18s = 45 s = 5/2 dollars streamers cost $2.50 ========================== Cheers, Stan H. ==============

Exponents/410879: When rewriting an exponential expression with a negative exponent and a positive base to an expression containing only a positive exponent, does the sign of the base change? And why not 1 solutions Answer 288851 by stanbon(57282)   on 2011-02-17 21:17:20 (Show Source): You can put this solution on YOUR website! When rewriting an exponential expression with a negative exponent and a positive base to an expression containing only a positive exponent, does the sign of the base change? And why not ---------------------- Example y = 3^(-x) ---- Answer to your question. No; the negative in the exponent means "invert the base". It does not mean "take the negative of the base". ================================ Cheers, Stan H. ===========

Linear_Equations_And_Systems_Word_Problems/410874: cory has $24.00 more than twice as much as stan does. together they have $150. how much money does each have. 1 solutions Answer 288847 by stanbon(57282)   on 2011-02-17 21:12:52 (Show Source): You can put this solution on YOUR website! Cory has $24.00 more than twice as much as stan does. together they have $150. how much money does each have. --- Let Stan have "x" dollars Then Cory has "2x+24" dollars ------ Equation: x + 2x+24 = 150 3x = 126 x = $42 (Stan has) ---- 2x+24 = 2*42+24 = 84+24 = $106 (Cory has) ======================================= Cheers, Stan H. =============

logarithm/410866: what is the range of log4(x+8)+2. 1 solutions Answer 288843 by stanbon(57282)   on 2011-02-17 21:06:52 (Show Source): You can put this solution on YOUR website! what is the range of ------- log4(x+8)+2 --- The range is "All Real Numbers". ============================== You won't see this on your calculator but log4(x+8)+2 approaches -inf as x approaches -8 ---- Cheers, Stan H.

Human-and-algebraic-language/410855: can someon help me solve the following rational equation: x+1 over 1 = 3 over 2 1 solutions Answer 288836 by stanbon(57282)   on 2011-02-17 20:49:35 (Show Source): You can put this solution on YOUR website! solve the following rational equation: x+1 over 1 = 3 over 2 ----- (x+1)/1 = 3/2 --- Cross-multiply to get: 2(x+1) = 3 2x+2 = 3 2x = 1 x = 1/2 -------------- Cheers, Stan H. ===============

Square-cubic-other-roots/410856: Please help me simplify this expression: 1 solutions Answer 288831 by stanbon(57282)   on 2011-02-17 20:27:39 (Show Source): You can put this solution on YOUR website! sqrt(98)-sqrt(2) --- = sqrt(49*2) - sqrt(2) --- = 7sqrt(2) - sqrt(2) --- = 6sqrt(2) ============== Cheers, Stan H. ==============

Probability-and-statistics/410853: The hypothesis that the number of hours worked is related to student grade point average is a _____ hypothesis. Null, One-tailed test, Two-tailed test or Test of proportions 1 solutions Answer 288829 by stanbon(57282)   on 2011-02-17 20:25:29 (Show Source): You can put this solution on YOUR website! The hypothesis that the number of hours worked is related to student grade point average is an alternate hypothesis in a test of independence. Null, One-tailed test, Two-tailed test or ---- It's a Right-tail test. ========================== Cheers, Stan H. ===========

Miscellaneous_Word_Problems/410834: I am HORRIBLE with percents, so if you can please help, please and thanks! Thirty-three pints of acid solution contain 3 pints of pure acid. Find the number of pints of pure acid that must be added to the 33 pints so that the resulting solution is 25% pure acid. 1 solutions Answer 288820 by stanbon(57282)   on 2011-02-17 19:54:16 (Show Source): You can put this solution on YOUR website! Thirty-three pints of acid solution contain 3 pints of pure acid. Find the number of pints of pure acid that must be added to the 33 pints so that the resulting solution is 25% pure acid. ----- Equation: acid + acid = acid 3 + x = 0.25(33+x) ---- Multiply thru by 100 to get: 300 + 100x = 25*33 + 25x 75x = 525 x = 11 pints (amt. of pure acid needed) =============== Cheers, Stan H. ==========

Exponents-negative-and-fractional/410835: Please help me solve this expression: (-27)^4/3 1 solutions Answer 288819 by stanbon(57282)   on 2011-02-17 19:50:03 (Show Source): You can put this solution on YOUR website! solve this expression: (-27)^4/3 ---- 1st: take the cube root root to get: (-3)^4 --- 2nd: raise to the 4th power to get: --- = 81 =========== Cheers, Stan H. ===========

Exponents-negative-and-fractional/410837: Please help me solve this expression: 125^-1/3 1 solutions Answer 288817 by stanbon(57282)   on 2011-02-17 19:47:58 (Show Source): You can put this solution on YOUR website! Please help me solve this expression: 125^-1/3 ---- The negative in the exponent means "invert". That 3 in the denominator of the exponent means "take the cube root". ---- These instructions may be followed in any direction. If you 1st invert you get: (1/125)^(1/3) If you then take the cube root you get: 1/5 ==== Cheers, Stan H. ====

Exponential-and-logarithmic-functions/410808: Divide (x^6-8x^3+12)/x^3-2 1 solutions Answer 288805 by stanbon(57282)   on 2011-02-17 19:08:23 (Show Source): You can put this solution on YOUR website! Divide (x^6-8x^3+12)/x^3-2 ------------------------- Factor to get: (x^6-6x^3-2x^3+12)/(x^3-2) --------------------------------- [x^3(x^3-6)-2(x^3-6)]/(x^3-2) ----- [(x^3-6)(x^3-2)]/(x^3-2) ----- Cancel to get: = x^3-6 ============= Cheers, Stan H. ===============

Inverses/410809: Hi having a difficult time trying to explain this problem to my child... the question says," What numbers belong in the blanks in the following equation? What is the value of a ?" a ÷ 6 ·__ = 5 ·__ 1 solutions Answer 288804 by stanbon(57282)   on 2011-02-17 19:04:27 (Show Source): You can put this solution on YOUR website! What numbers belong in the blanks in the following equation? What is the value of a ?" a ÷ 6 ·__ = 5 ·__ ----- Equation: a/6 = 5 ---- Multiply both sides of the equation by 6 to solve for "a": ---- 6(a/6) = 6*5 ----- a = 30 ============= Cheers, Stan H. ==========

Rational-functions/410803: find the vertical asymtote, horizontal asymtote, and graph the equation f(x)=(3x-3)/ (x^2+3x) 1 solutions Answer 288801 by stanbon(57282)   on 2011-02-17 19:00:39 (Show Source): You can put this solution on YOUR website! find the vertical asymtote, horizontal asymtote, and graph the equation f(x)=(3x-3)/ (x^2+3x) --- Factor: f(x) = [3(x-1)]/[x(x+3)] ---- vertical asymptotes at x = 0 and at x = -3 --- Horizontal asymptote at y = 0x^2/x^2 = 0 --- Graph: ------------------------ Cheers, Stan H. ========

Sequences-and-series/410797: I have to find the "nth" term in a sequence. The series of numbers is -2,-10,-50, -250... I have to find the fifth and ninth term in this sequence. I have come across several equations and they are: and This is a question on a take home quiz and don't necessarily want the answer, I just need help on what each of the variables stands for.(Example: A(n) is the nth term you want to find) Please help A.S.A.P. and Thank You! Sincerely, -In Need of Help 1 solutions Answer 288800 by stanbon(57282)   on 2011-02-17 18:56:08 (Show Source): You can put this solution on YOUR website! I have to find the "nth" term in a sequence. The series of numbers is -2,-10,-50, -250... I have to find the fifth and ninth term in this sequence. This is a geometric sequence because each successive term is 5 times the previous term. --- Formula: The nth term formula is a(n) = a(1)*r^(n-1) ---- In your sequence a(1) is -2 and r is 5 --- Find a(5) Find a(9) ================== Cheers, Stan H. This is a question on a take home quiz and don't necessarily want the answer, I just need help on what each of the variables stands for.(Example: A(n) is the nth term you want to find)

Numbers_Word_Problems/410793: You are choosing between tow plans at a discount warehouse. Plan A offers an annual membership fee of $300 and you pay 70% of the manufacturer’s recommended list price. Plan B offers an annual membership fee of $40 and you pay 90% of the manufacturer’s recommended listed price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? What will be the cost of each plan? I was absent the day of class and basically I was told by a class mate to take both plan A and plan B, set them equal to each other and solve. Also Prove. I do not have the text book, money is short for me now. Please help. A step by step action so I can go about the rest of this homework. Thank you :)! 1 solutions Answer 288798 by stanbon(57282)   on 2011-02-17 18:46:18 (Show Source): You can put this solution on YOUR website! You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $300 and you pay 70% of the manufacturer’s recommended list price. A(x) = 300 + 0.7x where x is cost of purchased products. -------------------------------- Plan B offers an annual membership fee of $40 and you pay 90% of the cost of purchased products. B(x) = 40 + 0.90x --------------------------------------- How many dollars of merchandise would you have to purchase in a year to pay the same amount under both plans? Solve for "x": 300 + 0.70x = 40 + 0.90x 0.20x = 260 ---- x = $1300 ============================== What will be the cost of each plan? A(1300) = 300+ 0.7*1300 = $1210 --- B(1300) = 40 + 0.9*1300 = $1210 ==================================== Cheers, Stan H. ========

absolute-value/410790: What is the absolute value for |-3-1|? 1 solutions Answer 288796 by stanbon(57282)   on 2011-02-17 18:33:38 (Show Source): You can put this solution on YOUR website! What is the absolute value for |-3-1|? ------ |-3-1| = |-4| = 4 ------------------------------------- Cheers, Stan H. ==========

Problems-with-consecutive-odd-even-integers/410788: Find three consecutive odd interrgers such that the product of the first and the second exceeds the third by eight. 1 solutions Answer 288795 by stanbon(57282)   on 2011-02-17 18:31:11 (Show Source): You can put this solution on YOUR website! Find three consecutive odd integers such that the product of the first and the second exceeds the third by eight. ----- 1st: 2x-1 2nd: 2x+1 3rd: 2x+3 ------------ Equation: (2x-1)(2x+1)-(2x+3) = 8 ----- 4x^2-1 -2x-3 = 8 --- 4x^2-2x-12 = 0 --- 2x^2-x-6 = 0 ---- 2x^2-4x+3x-6 = 0 ---- 2x(x-2) + 3(x-2) = 0 ---- (x-2)(2x+3) = 0 -------- x = 2 or x = -3/2 =========================== If x = 2: 1st: 2x-1 = 3 2nd: 5 3rd: 7 ------ If x = -3/2 1st: 2x-1 = -4 2nd: -2 3rd: 0 Note: These are all EVEn numbers. ------- So the only answer is 3,5,7 ========================================= Cheers, Stan H. ============

Miscellaneous_Word_Problems/410776: Rachelle spends 330 min/wk exercising. Her ratio of time spent on aerobics to time spent on weight training is 6 to 5. How many minutes per week does she spend on aerobics? Howmany miutes per week does she spend on weight training? (could you also explain how you got the answer?) 1 solutions Answer 288794 by stanbon(57282)   on 2011-02-17 18:20:12 (Show Source): You can put this solution on YOUR website! Rachelle spends 330 min/wk exercising. Her ratio of time spent on aerobics to time spent on weight training is 6 to 5. ------ 6 to 5 is the same as 6x to 5x, where 6x is aerobic time and 5x is weight training time. ------------- How many minutes per week does she spend on aerobics? How many minutes per week does she spend on weight training? ------ Equation: 6x + 5x = 330 min 11x = 330 x = 30 min ---- 6x = 6*30 = 180 min (aerobic time) --- 5x = 5*30 = 150 min (exercise time) ==================================== Cheers, Stan H. ===============

Equations/410772: Subsitituion of this prblem and can you show me the steps please y=3+x 2x+y=8 1 solutions Answer 288783 by stanbon(57282)   on 2011-02-17 18:04:44 (Show Source): You can put this solution on YOUR website! y=3+x 2x+y=8 ----- Substitute for "y" and solve for "x": 2x + 3+x = 8 3x = 5 x = 5/3 --------- Solve for "y": y = 3+x y = 3 + (5/3) y = 14/3 ================ Cheers, Stan H. =============

Exponents/410771: parentheses 5 to the third power divided by 3 to the fourth power parentheses raised to the third power 1 solutions Answer 288782 by stanbon(57282)   on 2011-02-17 17:58:39 (Show Source): You can put this solution on YOUR website! parentheses 5 to the third power divided by 3 to the fourth power parentheses raised to the third power -------------------- (5^3/3^4)^3 ---- = (5^9/3^12) ---- = 3.6751... ==================== Cheers, Stan H. ====================

Polynomials-and-rational-expressions/410767: What is the greatest common factor of negative 128? 1 solutions Answer 288780 by stanbon(57282)   on 2011-02-17 17:53:49 (Show Source): You can put this solution on YOUR website! What is the greatest common factor of negative 128? ----- You cannot have a "common factor" when there is only one number. ------------------------ Cheers, Stan H. =============

Systems-of-equations/410766: x+y=6 Systems of equations in two variables x-y=4 1 solutions Answer 288777 by stanbon(57282)   on 2011-02-17 17:47:47 (Show Source): You can put this solution on YOUR website! Systems of equations in two variables ----------- x+y=6 x-y=4 ------ Add and solve for "x": 2x 10 x = 5 -------- Solve for "y": x+y = 6 5+y = 6 y = 1 -------- Cheers, Stan H. ========================

test/410756: If f(x)= 6sinx + 4cosx What is the derivative of f(x)? What is the derivative of f(5)? 1 solutions Answer 288775 by stanbon(57282)   on 2011-02-17 17:35:49 (Show Source): You can put this solution on YOUR website! If f(x)= 6sinx + 4cosx What is the derivative of f(x)? f'(x) = 6cos(x) - 4sin(x) ---- I assume you mean f'(5): f'(5) = 6cos(5) - 4sin(5) f'(5) = 6*1.7020 - 4*-0.9589 f'(5) = 14.048 ------------------------- Cheers, Stan H. ========================

test/410750: If f(x)= 8/(x^(1/2)) - 6x^(-2) - 8x What is the derivative of f(x)? 1 solutions Answer 288772 by stanbon(57282)   on 2011-02-17 17:25:20 (Show Source): You can put this solution on YOUR website! If f(x)= 8/(x^(1/2)) - 6x^(-2) - 8x ------------------------ f(x) = 8(x^(-1/2)) - 6x^(-2) - 8x ---- f'(x) = (-4)(x^-(3/2)) + 12x^(-3) - 8 ---- f'(x) = -4/x^(3/2) + 12/x^3 - 8 ================================= Cheers, Stan H. ==========

Radicals/410707: I need help on how to solve this problem: Find the inverse function: 1. 4x-2y=8 1 solutions Answer 288755 by stanbon(57282)   on 2011-02-17 15:57:29 (Show Source): You can put this solution on YOUR website! Find the inverse function: 4x-2y=8 ---- 1st: Interchange x and y to get: 4y - 2x = 8 --- 2nd: Solve for "y": 4y = 2x+8 y = (1/2)x + 2 --- That is the inverse function. =================== Cheers, Stan H. ===================

Functions/410709: f(x)= 6/x+3 g(x)= 2/3x find (f o g)(x) and (g o f)(x) I don't think I know how to set this up when there are fractions involved. Please help, if possible. 1 solutions Answer 288754 by stanbon(57282)   on 2011-02-17 15:54:58 (Show Source): You can put this solution on YOUR website! f(x)= 6/x+3 g(x)= 2/3x ----------------- (f o g)(x) = f[(2/3)x] = 6/[(2/3)x+3] ------------------ (g o f)(x) = g[6/(x+3)] ---- = (2/3)[6/(x+3)] --- = 4/(x+3) ============== Cheers, Stan H. ==============