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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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 Equations/101292: This question is from textbook Algebra 2 with Trigonometry hey could you please help me with this question : "The yearly changes in the population of a city for three consecutive years are, respectively, 20% increase, 30% increase, and 20% decrease.What is the total percent change from the beginning to the end of the third year?" i will appreciate your help, my math teacher refused to help....if you could give me other examples it would be great. it can be other type of problem, thank you!1 solutions Answer 73794 by stanbon(57237)   on 2007-09-30 13:15:11 (Show Source): You can put this solution on YOUR website!"The yearly changes in the population of a city for three consecutive years are, respectively, 20% increase, 30% increase, and 20% decrease.What is the total percent change from the beginning to the end of the third year?" ---------------- Let the population start at "x". After a 20% increase the population is 1.20x After a 30% increase the population is (1.30)[1.20x] After a 20% decrease the population is (0.80)(1.30)[1.20x = 1.248x That would be a gain of 24.8% =============== Cheers, Stan H."The yearly changes in the population of a city for three consecutive years are, respectively, 20% increase, 30% increase, and 20% decrease.What is the total percent change from the beginning to the end of the third year?"
 percentage/101327: What percent of a yard is a foot?1 solutions Answer 73793 by stanbon(57237)   on 2007-09-30 13:04:17 (Show Source): You can put this solution on YOUR website!What percent of a yard is a foot? 1 ft./3 ft. = (1/3)= 33.3% ====================== Cheers, Stan H.
 Linear-equations/101307: A 30% salt solution is prepared by mixing a 20% salt solution and a 45% salt solution. How many litres of each must be used to produce 60 L of the 30% salt solution? 1 solutions Answer 73767 by stanbon(57237)   on 2007-09-30 10:57:36 (Show Source): You can put this solution on YOUR website!A 30% salt solution is prepared by mixing a 20% salt solution and a 45% salt solution. How many litres of each must be used to produce 60 L of the 30% salt solution? ------------- Let amt of 20% solution be "x" L ; amt of active ingredient = 0.20x L ---------------- Amt of 45% solution is "60-x" L ;amt active is 0.45(60-x)= 27-0.45x L --------------------- Amt of 30% mixture is 60 L; amt active is 18 L --------------------- EQUATION 0.20x + 27 - 0.45x = 18 -0.15x = -7 x = 46.67 L (amt of 20% solution) 60-x = 13.33 L (amt of 45% solution) =============== Cheers, Stan H.
 Miscellaneous_Word_Problems/101308: KOJO IS TWICE AS OLD AS ESI WHO IN TURN IS 5 YEAR OLDER THAN KWEKU. IF THEIR TOTAL AGE IS 47,HOW OLD IS EACH OF THEM 1 solutions Answer 73766 by stanbon(57237)   on 2007-09-30 10:50:03 (Show Source): You can put this solution on YOUR website!KOJO IS TWICE AS OLD AS ESI WHO IN TURN IS 5 YEAR OLDER THAN KWEKU. IF THEIR TOTAL AGE IS 47,HOW OLD IS EACH OF THEM ----------------- Let Kweku be "x" yrs. old. Then ESI is "x+5" yrs old And KOJO is 2(x+5) yrs old ------------------------ EQUATION: x + x+5 + 2x+10 = 47 4x+15 = 47 4x = 32 x = 8 (Kweku's age) x+5 = 13 (ESI's age) 2x+10 = 26 (Kojo's age) ============================== Cheers, Stan H.
 Mixture_Word_Problems/101300: 5floz. of a 2% alcohol solution was mixed with 11floz. of a 66% alcohol solution. Find the concentrationof the new mixture. I need to know how to set the problem up! thanks1 solutions Answer 73765 by stanbon(57237)   on 2007-09-30 10:43:58 (Show Source): You can put this solution on YOUR website!5floz. of a 2% alcohol solution was mixed with 11floz. of a 66% alcohol solution. Find the concentration of the new mixture. ----------------- 5 fl oz of 2% has 0.02*5 = 0.10 oz active ingredient 11 fl oz of 66% has 7.26 oz of active ingredient ----------------- A mixture of the two would give you 16 fl oz with 7.26+0.10 oz = 7.36 oz of active ingredient or 7.36/16 = 46% concentration. ------------------------ Cheers, Stan H.
 Complex_Numbers/101302: what is the solution to this problem 2x^2-(square root 7)x-10=01 solutions Answer 73764 by stanbon(57237)   on 2007-09-30 10:35:12 (Show Source): You can put this solution on YOUR website!2x^2-(square root 7)x-10=0 2x^2-(sqrt7)x-10=0 a=2, b= -sqrt7, c=-10 ------------ x = [sqrt7 +- sqrt(7 - 4*1*-10)]/2 x = [sqrt7 +- sqrt(7 +40)]/2 x = [sqrt7 +- sqrt(47)]/2 x = 4.751 or x = -2.105 ================ Cheers, stan Y.
 Numeric_Fractions/101301: what is the percent of \$150 out \$1,000 dollars1 solutions Answer 73763 by stanbon(57237)   on 2007-09-30 10:25:56 (Show Source): You can put this solution on YOUR website!what is the percent of \$150 out \$1,000 dollars ----------------- 150/1000= 15/100 = 15% ================= Cheers, Stan H.
 Travel_Word_Problems/101250: An airplane is headed N 65 degrees E with an air speed of 500 miles per hour. A tail wind is blowing in the direction of N 35 degrees E at 80 miles per hour. Find the actual speed and direction of the airplane. Round off answers to one decimal.1 solutions Answer 73761 by stanbon(57237)   on 2007-09-30 08:24:25 (Show Source): You can put this solution on YOUR website!An airplane is headed N 65 degrees E with an air speed of 500 miles per hour. A tail wind is blowing in the direction of N 35 degrees E at 80 miles per hour. Find the actual speed and direction of the airplane. Round off answers to one decimal. ------------------ x-vector: 500cos(65)+80cos(35) = 276.841 y-vector: 500sin(65)+80sin(35) = 499.04 ------------- resultant: r = sqrt(276.841^2+499.04^2) = 570.685 (actual speed) theta = tan^-1(499.04/276.841)= 60.981 degrees (actual direction) --------------- Cheers, Stan H.
 Quadratic_Equations/101267: In the equation x2+mx+k =0, what relation exists between m and k if one of the roots is twice the other?1 solutions Answer 73758 by stanbon(57237)   on 2007-09-30 08:02:05 (Show Source): You can put this solution on YOUR website!In the equation x2+mx+k =0, what relation exists between m and k if one of the roots is twice the other? -------------- Let one of the roots be "r" and the other root "2r". Then (x-r)(x-2r)= x^2+mx+k=0 x^2-(3r)x+2r^2 = x^2+mx+k m=-3r and k=2r^2 ============================ Cheers, Stan H.
 Exponents-negative-and-fractional/101269: 1/3(X-4)+ 5/6(X+2)= X+3 Thanks.1 solutions Answer 73756 by stanbon(57237)   on 2007-09-30 07:58:29 (Show Source): You can put this solution on YOUR website!1/3(X-4)+ 5/6(X+2)= X+3 --------- Multiply thru by 6 to get rid of those fractions: 2(x-4) + 5(x+2) = 6(x+3) 2x-8+5x+10 = 6x+18 x = 16 =========== Cheers, Stan H.
 Miscellaneous_Word_Problems/101263: 1.FIVE TIMES A NUMBER IS 4 MORE THAN THE NUMBER. FIND THE NUMBER. 2.THE DIFFERENCE BETWEEN TWO NUMBERS IS 10 AND THEIR SUM IS 24. FIND THE NUMBERS 1 solutions Answer 73754 by stanbon(57237)   on 2007-09-30 06:41:19 (Show Source): You can put this solution on YOUR website!1.FIVE TIMES A NUMBER IS 4 MORE THAN THE NUMBER. FIND THE NUMBER. 5x = x+4 4x=4 x=1 -------------- 2.THE DIFFERENCE BETWEEN TWO NUMBERS IS 10 AND THEIR SUM IS 24. FIND THE NUMBERS x-y=10 x+y=24 --------- Add the equations to get: 2x=34 x=17 Substitute to get: 17+y=24 y = 7 =========== Cheers, Stan H.
 Trigonometry-basics/101251: let z1=8(cos5pi/4 + isin5pi/4) and z2=2(cos5pi/12 + isin5pi/12) Find each of the following in the form a+bi a. z1/z2 b. (z2)^61 solutions Answer 73753 by stanbon(57237)   on 2007-09-30 06:38:31 (Show Source): You can put this solution on YOUR website!let z1=8(cos5pi/4 + isin5pi/4) and z2=2(cos5pi/12 + isin5pi/12) Find each of the following in the form a+bi a. z1/z2 = (4)(cos[(15pi-5pi)/12 + isin[same]) = 4(cos[(5/6)pi] + isin[same]) = -3.464 + 2i ====================== b. (z2)^6 = (2^6)(cos[6[5pi/12]] + isin[same]) = 64(cos[(5/2)pi] + isin[same]) = 0 +64i ================= Cheers, Stan H.
 Polynomials-and-rational-expressions/101252: Find all the positive values for k for which each of the following can factored. x^2+x-k. please explain to me how to solve this problem and thank you in advance.1 solutions Answer 73752 by stanbon(57237)   on 2007-09-30 06:28:39 (Show Source): You can put this solution on YOUR website!Find all the positive values for k for which each of the following can factored. x^2+x-k. ------------- I will assume this means "factored in the Real Number System". You have a quadratic with a=1,b=1,c=-k The discriminant is b^2-4ac The quadratic has Real Number roots (and therefore Real Number factors) if b^2-4ac>=0 ------- So 1^2-4*1*(-k)>=0 1+4k>=0 4k<=1 k<=1/4 ------------- The quadratic will have Real Number factors if k<=1/4 ================== Cheers, Stan H.
 Trigonometry-basics/101253: Convert the rectangular point (-8,8sqrt3) to polar coordinates with r>0. Also give two additional ways to represent this point in polar coordinates for which r<0 and -2pi *and* r>0 and -2pi1 solutions Answer 73751 by stanbon(57237)   on 2007-09-30 06:23:07 (Show Source): You can put this solution on YOUR website!Convert the rectangular point (-8,8sqrt3) to polar coordinates with r>0. r=sqrt(8^2+(8sqrt3)^2)= sqrt(256)= 16 theta = tan^-1((8sqrt3)/-8)=tan^-1(-sqrt3)=120 degrees or (2/3)pi polar form: (16,(2/3)pi) ----------------------- (-16,(5/3)pi) Also give two additional ways to represent this point in polar coordinates for which r<0 and -2pi (-16,(-pi/3)) ------------------ *and* r>0 and -2pi (16,((-4/3)pi)) ============= Cheers, Stan H.
 Polynomials-and-rational-expressions/101256: Divide (6x3 - 5x2 - 13x + 13) ÷ (2x + 3) Please help. I need step by step help on this one. I have tried on my own and I cannot get the answer. Thank you so much.1 solutions Answer 73750 by stanbon(57237)   on 2007-09-30 06:15:07 (Show Source): You can put this solution on YOUR website!Hopefully you know the process. Quotient: 3x^2-7x+4 Remainder: 1 ============ Cheers, Stan H.
 Linear-systems/101260: ravish sold his motor cycle to vineet at a loss of 28% vineet spent rs. 1680/-on its repair and sold the motor cycle to rahul for rs. 35910, thereby making a profit of 12.5% find the cost price of the motor cycle for ravish.1 solutions Answer 73749 by stanbon(57237)   on 2007-09-30 05:43:58 (Show Source): You can put this solution on YOUR website!ravish sold his motor cycle to vineet at a loss of 28% vineet spent rs. 1680/-on its repair and sold the motor cycle to rahul for rs. 35910, thereby making a profit of 12.5% find the cost price of the motor cycle for ravish. --------------------- Let ravish cost price = "x" Sold to vineet for 0.72x Vineet value after repair: 0.72x-1680 Sold to rahul at 12.5% profit: (1.125)(0.72x-1680)=35910 0.72x-1680= 31920 0.72x = 33600 x=46666.67 ================= Cheers, Stan H.
 Linear-systems/101261: a defective briefcase costing rs.800 is being sold at a loss of 8% if the price is further reduced by 5% find its selling price.1 solutions Answer 73748 by stanbon(57237)   on 2007-09-30 05:34:58 (Show Source): You can put this solution on YOUR website!a defective briefcase costing rs.800 is being sold at a loss of 8% if the price is further reduced by 5% find its selling price. --------------------- 1st selling: 800(1-0.08) =800(0.92) = 736 rs -------------- Final selling: 736(1-0.05) 736(0.95)= 699.20 rs ==================== Shorter way to do it: 800*0.92*0.95 = 699.20rs ==================== Cheers, Stan H.
 Trigonometry-basics/101255: Let u=<-1,3> and v=<4,-6>. Find each of the following: a. 3u-2v b. The normalization of v1 solutions Answer 73747 by stanbon(57237)   on 2007-09-30 05:24:27 (Show Source): You can put this solution on YOUR website!Let u=<-1,3> and v=<4,-6>. Find each of the following: a. 3u-2v = 3(-1,3)-2(4,-6)=(-3-8.9+12)=(-11,21) b. The normalization of v: |v|= sqrt(4^2+6^2) = sqrt52 = 2sqrt13 So, norm of v = (4/(2sqrt13),-6/(2sqrt13)) =============== Cheers, Stan H.
 Trigonometry-basics/101254: Write in trig form: -6 + 6sqrt3i1 solutions Answer 73746 by stanbon(57237)   on 2007-09-30 04:57:54 (Show Source): You can put this solution on YOUR website!Write in trig form: -6 + 6sqrt3i ----------------------------- Conversion formulas: r = sqrt(a^2+b^2) theta = tan^-1(b/a) ------------------- Your Problem: r = sqrt((-6)^2+(6sqrt3)^2)= sqrt(36+108)= 12 ----- theta = tan^-1(6sqrt3/-6) = tan^-1(-sqrt3)=(2/3)pi -------------- Trig form: -6+6sqrt3i = 12(cos((2/3)pi) + isin((2/3)pi) ============ Cheers, Stan H.
 Age_Word_Problems/101257: Vicky is now 4 times as old as Cristy. five years ago,the sum of their ages was 45. how old are they now1 solutions Answer 73745 by stanbon(57237)   on 2007-09-30 04:46:41 (Show Source): You can put this solution on YOUR website!Vicky is now 4 times as old as Cristy. five years ago,the sum of their ages was 45. how old are they now ----------------- NOW DATA: Let Cristy be "x" yrs. old Then Vicky is "4x" yrs. old -------------- 5 yrs ago DATA: Christy was "x-5" Vicky was "4x-5" ------------------- EQUATION: (x-5)+(4x-5)=45 5x-10=45 5x = 55 x = 11 (Christy's age NOW) 4x= 44 (Vicky's age NOW) =============== Cheers, Stan H.
 Finance/101233: An investor receives \$600 annually from two investments. He has \$500 more invested at 8% than at 6%. What is the amount invested at each rate?1 solutions Answer 73717 by stanbon(57237)   on 2007-09-29 21:27:08 (Show Source): You can put this solution on YOUR website!An investor receives \$600 annually from two investments. He has \$500 more invested at 8% than at 6%. What is the amount invested at each rate? ------------ Let amt invested at 6% be "x" dollars Amt invested at 8% is "x+500" --------------- EQUATION: x + x+500 = 600 2x = 100 x = \$50 (amt invested at 6%) x+500 = \$550 (amt invested at 8%) =============== Cheers, Stan H.
 Volume/101236: Tony was making spaghetti for his son's graduation party. The recipe calls for 2lbs of ground beef for 8 servings. If he needs 120 servings, how many pounds of ground beef should he buy?1 solutions Answer 73712 by stanbon(57237)   on 2007-09-29 21:19:37 (Show Source): You can put this solution on YOUR website!Tony was making spaghetti for his son's graduation party. The recipe calls for 2lbs of ground beef for 8 servings. If he needs 120 servings, how many pounds of ground beef should he buy? -------------- x/120 = 2/8 x = 120(2/8) x = 30 lbs (amount needed to make 120 servings) ========== Cheers, Stan H.
 Functions/101231: Brain Freeze can't remember. Given functions F and G dtermine the domain of f+g: f(x)=5x-8,g(x)=5/x-2 Thank you for you help 1 solutions Answer 73701 by stanbon(57237)   on 2007-09-29 20:49:27 (Show Source): You can put this solution on YOUR website!dtermine the domain of f+g: f(x)=5x-8,g(x)=5/x-2 --------------- f+g = 5x-8 + 5/(x-2) Domain : all Real Numbers except x=2. ============ Cheers, Stan H.
 Functions/101232: My book from Granthum U does not show how to do this one. Find functions f and g so that h(x)=(f'g)(x) Thanx1 solutions Answer 73700 by stanbon(57237)   on 2007-09-29 20:42:49 (Show Source): You can put this solution on YOUR website!h(x)=6/x^2 + 8 --------- I'll assume your problem is as follows: h(x) = [6/x^2] + 8 -------------------- You want f{g(x)]=h(x) Let g(x)= 1/x^2 Then Let f(x)=6x + 8 ---------- Then f[g(x)] = f[1/x^2] =6(1/x^2)+8 = [6/x^2]+8 =h(x) ============== Cheers, Stan H.
 Age_Word_Problems/101056: This question is from textbook translate each into an equation: if 8 is added to the variable T , the sum is equal to the varible B1 solutions Answer 73697 by stanbon(57237)   on 2007-09-29 20:27:16 (Show Source): You can put this solution on YOUR website!if 8 is added to the variable T , the sum is equal to the varible B T+8 = B =========== Cheers, Stan H.
 Quadratic_Equations/101124: i want to ask how to solve this problems . i want u to explain me the whole question n then give a solution to it. my ques is show that my=x^2-4(x-1) meets the curve y=x^2-3x+2 at two distinct points for all non zero values of m.i would be very grateful to u if u solve this ques for me.this ques is nt from text book. 1 solutions Answer 73691 by stanbon(57237)   on 2007-09-29 19:25:59 (Show Source): You can put this solution on YOUR website!show that my=x^2-4(x-1) meets the curve y=x^2-3x+2 at two distinct points --------------------- y = x^2-4x+4 y = x^2-3x+2 ------------------ Substitute to get: x^2-4x+4 = x^2-3x+2 x= 2 ---------- Substitute to solve for y: y = 2^2-4*2+4 y = 0 ---------- The curves meet at the point (2,0) ----------- Cheers, Stan H.
 Linear-systems/101072: Can someone help me with this? Six pears and three apples cost \$3.90. Two pears and five apples cost \$3.30. How much does one pear cost? Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations. Let p = the cost of one pear Let a = the cost of one apple a. Write a system of equations that can be used to determine the cost of pears and apples. b. Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer 1 solutions Answer 73689 by stanbon(57237)   on 2007-09-29 19:09:15 (Show Source): You can put this solution on YOUR website!Six pears and three apples cost \$3.90. Two pears and five apples cost \$3.30. How much does one pear cost? Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations. Let p = the cost of one pear Let a = the cost of one apple a. Write a system of equations that can be used to determine the cost of pears and apples. 6p + 3a = 3.90 2p + 5a = 3.30 ----------------- Multiply the 2nd equation by 3 to get: 6p + 15a = 9.90 -------------- Subtract the 1st from this last to get: 12a = 6 a = 0.50 (cost of one apple) --------------- Substitute that into 6p + 3a = 3.90 6p + 3*0.5 = 3.90 6p + 1.5 = 3.90 6p = 2.40 p = 0.60 (price of one pear) ========================== Cheers, Stan H. b. Determine the cost of one pear and one apple.
 Miscellaneous_Word_Problems/101181: From a group of 6 juniors and 8 seniors on the student council, 2 juniors and 4 seniors will be chosen to make up a 6-person committee. How many different 6-person committees are possible?1 solutions Answer 73685 by stanbon(57237)   on 2007-09-29 18:56:58 (Show Source): You can put this solution on YOUR website!From a group of 6 juniors and 8 seniors on the student council, 2 juniors and 4 seniors will be chosen to make up a 6-person committee. How many different 6-person committees are possible? --------------------- # of ways to pick 2 juniors = 6C2 # of ways to pick 4 seniors = 8C4 ------------------- # of ways to to pick the student council with 2 juniors and 4 seniors = 6C2 * 8C4 = 1050 ================ Cheers, Stan H.
 Linear-equations/101214: Find the slope and y-intercept of the line: Ax + By = C1 solutions Answer 73683 by stanbon(57237)   on 2007-09-29 18:45:16 (Show Source): You can put this solution on YOUR website!Find the slope and y-intercept of the line: Ax + By = C -------------- Put the equation in the slope-intercept form: y = (-A/B) + (C/B) --------- slope =A/B y-intercept = C/B ===================== Cheers, Stan H.
 Linear-equations/101215: Find the slope of the line through the following pairs of points. (-5, -3) and (-5, 2)1 solutions Answer 73682 by stanbon(57237)   on 2007-09-29 18:42:33 (Show Source): You can put this solution on YOUR website!Since the two points have the same x value the graph of the line is a vertical line; the slope is undefined. The equation of the line is x=-5. =============== Cheers, Stan H.
 Graphs/101213: Graph the function: f(x)= -/x-1/ +2 ** /= absoulute value1 solutions Answer 73680 by stanbon(57237)   on 2007-09-29 18:40:47 (Show Source): You can put this solution on YOUR website!Graph the function: f(x)= -/x-1/ +2 Cheers, Stan H.