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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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 test/178623: 3. A bar graph is used to show and a line graph is used to show. Fill in the sentence. a. Changes b. comparisons 1 solutions Answer 133577 by stanbon(57282)   on 2009-01-26 17:49:33 (Show Source): You can put this solution on YOUR website!A bar graph is used to show comparison and a line graph is used to show changes. ================== Cheers, Stan H.
 Equations/178616: Hello. Inheriting money: Paul split an inheritance between two investments, one paying 7% annual interest and the other 10%. He invested twice as much in the 10% investment as he did in the 7% investment. If his combined annual income form the two investments was \$4,050, how much did he inherit? Thanks. H.C.1 solutions Answer 133576 by stanbon(57282)   on 2009-01-26 17:46:22 (Show Source): You can put this solution on YOUR website!Inheriting money: Paul split an inheritance between two investments, one paying 7% annual interest and the other 10%. He invested twice as much in the 10% investment as he did in the 7% investment. If his combined annual income form the two investments was \$4,050, how much did he inherit? ---------------------------------------------------------- Equation: 0.07x + 0.10(2x) = 4050 Multiply thru by 100 to get: 7x + 20x = 405000 27x 405000 x = 15000 (amt. invested at 7%) 2x = 30000 (amt. invested at 10%) Total amount invested = x + 2x = 45,000 ========================================== Cheers, Stan H.
 Numeric_Fractions/178598: can u please answer this problem for me -1/2*3/5*(-2/7)1 solutions Answer 133575 by stanbon(57282)   on 2009-01-26 17:37:56 (Show Source): You can put this solution on YOUR website!(-1/2)*(3/5)*(-2/7) = 6/70 = 3/35 ============ Cheers, Stan H.
 Numeric_Fractions/178599: Find the two roots of (x-3)^2 = 25 without changing (x-3)^2 to a trinomial.1 solutions Answer 133574 by stanbon(57282)   on 2009-01-26 17:33:38 (Show Source): You can put this solution on YOUR website!Find the two roots of (x-3)^2 = 25 (x-3)^2 - 25 = 0 Factor to get: (x-3 - 5)(x-3 + 5) = 0 (x-8)(x+2) = 0 x = 8 or x = -2 ================== Cheers, Stan H.
 Travel_Word_Problems/178600: The formula d=16t^2 gives the approximate distance in feet (d) traveled by a falling object in t seconds. Approximately how long would it take a baseball dropped from the top of the Gareway Arch in St. Louis to hit the ground if the arch is 630 feet high?1 solutions Answer 133572 by stanbon(57282)   on 2009-01-26 17:28:42 (Show Source): You can put this solution on YOUR website!The formula d=16t^2 gives the approximate distance in feet (d) traveled by a falling object in t seconds. Approximately how long would it take a baseball dropped from the top of the Gareway Arch in St. Louis to hit the ground if the arch is 630 feet high? ---------------------------- d = 16t^2 630 = 16t^2 t^2 = 630/16 Positive solution: t = sqrt630)/4 t = 6.27 seconds =================== Cheers, Stan H.
 Inequalities/178610: i need help with this inequality x+14<5 or -6x<-421 solutions Answer 133571 by stanbon(57282)   on 2009-01-26 17:24:09 (Show Source): You can put this solution on YOUR website!x+14<5 or -6x<-42 x < - 9 or x > 7 ===================== Cheers, Stan H.
 Finance/178611: 7/8+5/121 solutions Answer 133570 by stanbon(57282)   on 2009-01-26 17:22:04 (Show Source): You can put this solution on YOUR website! 7/8+5/12 lcd = 24 = 21/24 + 10/24 = 31/24 ==================== Cheers, Stan H.
 Inequalities/178607: Is there a solution for: 23-t <= 2 (t-9) -3 (t+2) thanks, Donnie1 solutions Answer 133569 by stanbon(57282)   on 2009-01-26 17:20:21 (Show Source): You can put this solution on YOUR website!Is there a solution for: 23-t <= 2 (t-9) -3 (t+2) 23 - t <= 2t - 18 -3t - 6 23 - t <= -t - 24 23 < = -24 That is false, so there is no solution fot the original equation ============================= Cheers, Stan H.
 Equations/178605: Find all solutions of the equation below. (If there are more answer boxes than answers, enter NONE in the extra boxes.) x4 - 4096 = 0 x = (smaller real solution) x = (larger real solution) x = (smaller imaginary part) x = (larger imaginary part) i dont understand! could someone help explain it to me thanks!!!1 solutions Answer 133568 by stanbon(57282)   on 2009-01-26 17:13:50 (Show Source): You can put this solution on YOUR website!x^4 - 4096 = 0 x^4 - 2^12 = 0 Factor to get: (x^2-2^6)(x^2+2^6) = 0 Factor to get: (x-2^3)(x+2^3)(x+8i)(x-8i) = 0 x = 8 or x = -8 or x = -8i or x = 8i ====================================== Cheers, Stan H.
 Expressions-with-variables/178606: This question is from textbook algebra 1 How do i solve 3x-6y=30 and how do i solve y=-6x+34 using the expressions involving variables, substitution?1 solutions Answer 133567 by stanbon(57282)   on 2009-01-26 17:09:11 (Show Source): You can put this solution on YOUR website! How do i solve 3x-6y=30 y=-6x+34 ----------- Modify to get: x - 2y = 10 y = -6x + 34 ----------- Substitute to solve for "y": y = -6(2y+10) + 34 y = -12y - 60 + 34 13y = -26 y = -2 ------------- Substitute to solve for "x": x -2*-2 = 10 x = 6 ============================ Ans: x = 6 and y = =2 ========================= Cheers, Stan H.
 Money_Word_Problems/178572: John invested \$11000, a portion earning a simple interest rate of 4.5% per year and the rest earning a simple intrest rate of 4% per year. After one year the total value of John's investment is \$11445.50. How much did John invest at 4.5% interest rate? And how much did John invest at 4% interest rate? HINT: the total value of John's investment includes both the amount he invested and the interest he earned.1 solutions Answer 133530 by stanbon(57282)   on 2009-01-26 15:11:30 (Show Source): You can put this solution on YOUR website!John invested \$11000, a portion earning a simple interest rate of 4.5% per year and the rest earning a simple intrest rate of 4% per year. After one year the total value of John's investment is \$11445.50. How much did John invest at 4.5% interest rate? And how much did John invest at 4% interest rate? -------------------- Equation: interest + interest = interest 0.045x + 0.04(11000-x) = 445.50 Multiply thru by 1000 to get: 45x + 40*11000 - 40x = 445500 5x = 5500 x = \$1100 (amt invested at 4.5%) 11000 - 1100 = \$9900 (amt. invested at 4% ============================================ Cheers, Stan H.
 Miscellaneous_Word_Problems/178530: Stan and Hilda can mow the lawn in 60 mins. if they work together. If hilda works twice as fast as Stan, how long does it take Stan to mow the lawn alone?1 solutions Answer 133488 by stanbon(57282)   on 2009-01-26 07:08:53 (Show Source): You can put this solution on YOUR website!Stan and Hilda can mow the lawn in 60 mins. if they work together. If hilda works twice as fast as Stan, how long does it take Stan to mow the lawn alone? --------- Together DATA: time = 60 min/job ; rate = 1/60 job/min -------------------------- Hilda DATA: time = x min/job ; rate = 1/x job/min ----------------------------- Stan DATA: time = 2x min/job; rate = 1/2x job/min ----------------------------- Equation: rate + rate = together rate 1/x + 1/2x = 1/60 60 + 30 = x x = 90 min ----------- Stan time = 2x = 180 min or 3 hrs. ===================== Cheers, Stan H.
 Numbers_Word_Problems/178532: if 1/3 is an added to the reciprocal of a number , the result is 3 more than 3 times the reciprocal of the original number. find the number /1 solutions Answer 133487 by stanbon(57282)   on 2009-01-26 07:03:47 (Show Source): You can put this solution on YOUR website!if 1/3 is an added to the reciprocal of a number , the result is 3 more than 3 times the reciprocal of the original number. find the number ----------- Let the number be "x": Equation: (1/x) + 1/3 = 3(1/x) + 3 2(1/x) = -8/3 1/x = -4/3 x = -3/4 ================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/178481: This question is from textbook blitzer college algebra 3x/5-x=x/10-5/21 solutions Answer 133469 by stanbon(57282)   on 2009-01-25 22:18:50 (Show Source): You can put this solution on YOUR website!(3x/5) - x = (x/10) - (5/2) Multiply thru by 10 to get: 15x - 10x = x - 25 4x = -25 x = -25/4 ========================= Cheers, Stan H.
 Linear-systems/178486: This question is from textbook Algebra II An organization wants to sell tickets to a concert. It plans on selling 300 reserved seat tickets and 150 general admission tickets. The price of a reserved seat ticket is \$2.00 more than a general admission ticket. If the organization wants to collect at least \$3750.00 what is the minimum price it can charge for the reserved seat tickets? i found that the reserved tickets will sell for \$9.00 and the general tickets for \$7.00 but i don't know how to make it an inequality or to graph that inequality. 1 solutions Answer 133464 by stanbon(57282)   on 2009-01-25 22:09:06 (Show Source): You can put this solution on YOUR website!An organization wants to sell tickets to a concert. It plans on selling 300 reserved seat tickets and 150 general admission tickets. The price of a reserved seat ticket is \$2.00 more than a general admission ticket. If the organization wants to collect at least \$3750.00 what is the minimum price it can charge for the reserved seat tickets? ------------------------------------------------ Value Equation: value + value = value 150x + 300(x+2) >= 3750 150x + 300x + 600 >= 3750 450x >= 3150 x >= \$7.00 (price range of general admission tickets) x+2 >= \$9.00 (price range of reserved seat tickets) =============================================== Cheers, Stan H.
 Linear-equations/178445: Studies have shown that the population of rats inside an average sized house grows exponentially depending upon the number of cats that can be found on the premises. A a function of time the population of rats is approximated by the equation: p(t)=P(K/C)^t Where K=4.2 is a constant derived from experiment P is the initial popuation of rats, C is the number of cats, and t is given in weeks. How many cats are necessary to stop the number of rats from increasing? Explain.1 solutions Answer 133453 by stanbon(57282)   on 2009-01-25 21:10:02 (Show Source): You can put this solution on YOUR website!Studies have shown that the population of rats inside an average sized house grows exponentially depending upon the number of cats that can be found on the premises. A a function of time the population of rats is approximated by the equation: p(t)=P(K/C)^t Where K=4.2 is a constant derived from experiment P is the initial popuation of rats, C is the number of cats, and t is given in weeks. How many cats are necessary to stop the number of rats from increasing? Explain. ----------------- p(t)=P(K/C)^t p(t) = P(4.2)/C)^t -------------------------- Since t is always increasing p(t) will = 4.2P when C = 4.2 cats. and p(t) will decrease if C is greater than 4.2 cats because the fraction K/C will be greater than zero but less than one; that will make p(t) a decreasing function.. ========================================= Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/178493: The cost of 12 oranges and 7 apples is \$5.36. 8 oranges and 5 apples cost \$3.68. what is the cost of each orange?1 solutions Answer 133449 by stanbon(57282)   on 2009-01-25 20:51:35 (Show Source): You can put this solution on YOUR website!The cost of 12 oranges and 7 apples is \$5.36. 8 oranges and 5 apples cost \$3.68. what is the cost of each orange? ------------------ Value Equation: 12R + 7A = 536 cents Value Equation: 8R + 5A = 368 cents ------------------------------------ Multiply thru the 1st equation by 2; Multiply thru the 2nd equation by 3: 24R + 14A = 1072 24R + 15A = 1104 ----------------------- Subtract 1st from 2nd to get: A = 32 (price of an apple) ---------- Substitute to solve for "R": 8R + 5*32 = 368 8R + 160 = 368 8R = 208 R = 26 (price of an orange) ================================= Cheers, Stan H.
 Linear-equations/178504: I am not sure where to start with this one. Graph 2x+5y-2>3y-10+2x1 solutions Answer 133447 by stanbon(57282)   on 2009-01-25 20:45:18 (Show Source): You can put this solution on YOUR website!Graph 2x+5y-2>3y-10+2x Subtract 2x from each side to get: 5y - 2 > 3y - 10 2y > 12 y > 6 ------------- Draw a dotted line thru all points where y = 6. Shade the half-plane ABOVE the line. The half-plane is the graph you want. ===================================== Cheers, Stan H.
 Quadratic_Equations/178495: use the following equation, where x and y are the measured in meters, to model a cross section of the Barringer Meteor crater, near Winslow, Arizona y=1/1800(x-600)(x+600) 1) assuming the lip of the crater is at y=0, how wide is the crater? 2) what is the depth of the crater?1 solutions Answer 133445 by stanbon(57282)   on 2009-01-25 20:41:07 (Show Source): You can put this solution on YOUR website! use the following equation, where x and y are the measured in meters, to model a cross section of the Barringer Meteor crater, near Winslow, Arizona -------------------------- y=1/1800(x-600)(x+600) 1) assuming the lip of the crater is at y=0, how wide is the crater? (1/1800)(x-600)(x+600) = 0 (x-600)(x+600 = 0 Positive solution: x = 600 meters ====================== 2) what is the depth of the crater? Assuming the crater is deepest in the center, let x = 300 meters;solve for y. y = (1/1800)(300-600)(300+600) y = (1/(1800)*-300*900 y = -150 meters ============================ Cheers, Stan H.
 Miscellaneous_Word_Problems/178480: The subway fare in a city is \$1.55. People eho use the subway may buy a monthly coupon book for \$12.00. The coupon book reduces the fare to \$0.95. Determine the number of fares in one month the subway must be used such that the total monthly cost without the coupon books is equal to the total monthly cost with the coupon book. Here is what I have thought of so far: i have decided on x to represent rides taken 1.55x=y what y should represent i don't know. Thanks.1 solutions Answer 133425 by stanbon(57282)   on 2009-01-25 19:07:39 (Show Source): You can put this solution on YOUR website!The subway fare in a city is \$1.55. People eho use the subway may buy a monthly coupon book for \$12.00. The coupon book reduces the fare to \$0.95. Determine the number of fares in one month the subway must be used such that the total monthly cost without the coupon books is equal to the total monthly cost with the coupon book. -------------------------------- Equation: total without the coupon books is equal to the total with the coupon book 1.55x = 12.00 + 0.95x 0.60x = 12 x = 20 (# of fares for which each plan results in equal cost) ==================== Cheers, Stan H.
 Rational-functions/178478: This question is from textbook Discovering Advanced Algebra I need assistance with this problem. Simplify the expression and identify values for which the expression is undefined...... I think that the undefined values for x are -3 and 0 and for y is 0 since those values would cause a denominator to become 0. Please confirm my logic and help with simplifying. THANKS1 solutions Answer 133422 by stanbon(57282)   on 2009-01-25 18:59:39 (Show Source): You can put this solution on YOUR website!Simplify the expression and identify values for which the expression is undefined...... ((2/y)-1)/((3/x)+1) I think that the undefined values for x are -3 and 0 and for y is 0 since those values would cause a denominator to become 0. ---------- The undefined value for x is 0; the undefined value for y is 0. ------------------- Simplifying: = [(2-y)/y] / [(3+x)/x] Invert the denominator and multiply to get: [(2-y)/y] * [x/(3+x)] = [x(2-y)]/[y(3+x)] ========================= Cheers, Stan H.
 Mixture_Word_Problems/178479: This question is from textbook algebra A health food store mixes a breakfast cereal containing granola and dried bananas. Plain granola costs \$6.00 per pound. Dried banana slices cost \$4.00 per pound. The store makes up 40 pounds of the new cereal and sells it at \$5.80 per pound. How much of each ingredient will go into the 40 pound mixture?1 solutions Answer 133416 by stanbon(57282)   on 2009-01-25 18:52:41 (Show Source): You can put this solution on YOUR website!Plain granola costs \$6.00 per pound. Dried banana slices cost \$4.00 per pound. The store makes up 40 pounds of the new cereal and sells it at \$5.80 per pound. How much of each ingredient will go into the 40 pound mixture? --------------- Equation: value + value = value 6x + 4(40-x) = 5.80*40 6x + 4*40 - 4x = 5.80*40 2x = 1.8*40 x = 36 lbs. (amt. of \$6 granola in the mixture) 40-x = 4 lbs.(amt. of \$4 banana slices in the mixture) ================================= Cheers, Stan H.
 Linear-systems/178469: Suzanne invested \$19,800 in two mutual fund accounts. During the subsequent year, on mutual fund earned 10% and the othe earned 6%. At the end of the year, the total interest earned was \$1,492.00. How much did she invest in each fund? 1 solutions Answer 133404 by stanbon(57282)   on 2009-01-25 18:04:25 (Show Source): You can put this solution on YOUR website!Suzanne invested \$19,800 in two mutual fund accounts. During the subsequent year, on mutual fund earned 10% and the othe earned 6%. At the end of the year, the total interest earned was \$1,492.00. How much did she invest in each fund? ------------------- Equation: interest + interest = interest 0.10x + 0.06(19,800-x) = 1492 Multiply thru by 100 to get: 10x + 6*19800 - 6x = 149200 4x = 149200 - 6*19800 x = \$7600 (amt. invested at 10%) 19800-x = 19800-7600 = \$12,200 (amt. invested at 6%) =============== Cheers, Stan H.
 Linear-systems/178467: Find the x and y intercepts of 7x-2y=-5, and then graph.1 solutions Answer 133402 by stanbon(57282)   on 2009-01-25 17:57:40 (Show Source): You can put this solution on YOUR website!Find the x and y intercepts of 7x-2y=-5, and then graph. ---------- x-intercept: Let y = 0, then x = -5/7 --------- y-intercept: Let x = 0, then y = 5/2 --------------------------- ============== Cheers, Stan H.
 Linear-equations/178461: write the equation of a line parallel to x+2y=7.which passes through the point(-5,-4) the answer I came up with was y=-1/2x-13/2 is this correct?1 solutions Answer 133399 by stanbon(57282)   on 2009-01-25 17:38:11 (Show Source): You can put this solution on YOUR website!Yes, correct. Cheers, Stan H.
 Expressions-with-variables/178339: 10u/9t divided by 14u/15tu how do I do this do I use the same fraction rules1 solutions Answer 133301 by stanbon(57282)   on 2009-01-24 22:18:47 (Show Source): You can put this solution on YOUR website!10u/9t divided by 14u/15tu ---------------------------------- Invert the denominator and multiply: [10u/9t] * [15tu/14u] Cancel factors common to a numerator and a denominator such as 2,3,t,u. = [5u/3] * [5/7] = 25u/21 =============== Cheers, Stan H.
 Linear-equations/178329: 1. Find the equation of a straight line that passes through a point (–1,3) such that it is perpendicular to straight line y - 2x = 5. 2. Sketch a graph for a quadratic function given as below: f (x) = x˛ - x - 6 1 solutions Answer 133299 by stanbon(57282)   on 2009-01-24 22:10:21 (Show Source): You can put this solution on YOUR website!1. Find the equation of a straight line that passes through a point (–1,3) such that it is perpendicular to straight line y - 2x = 5. ----------- The slope of the given line is 2 because y = 2x+5 ----------------------------------- The perpendicular line must have slope = -1/2 -------------------- Intercept: 3 = (-1/2)*-1 + b; b = = 3 - 1/2 = 5/2 -------------------------- Equation: y = (-1/2)x + (5/2) ================================== Cheers, Stan H. 2. Sketch a graph for a quadratic function given as below: f (x) = x˛ - x - 6
 Proportions/178330: 5/(x+3)-2/3=11 solutions Answer 133296 by stanbon(57282)   on 2009-01-24 22:04:03 (Show Source): You can put this solution on YOUR website!5/(x+3)-2/3=1 Multiply thru by 3(x+3) to get: 15 - 2(x+3) = 3(x+3) 15 = 5(x+3) x+3 = 3 x = 0 ============== Cheers, Stan H.
 Functions/178324: A Michigan orchard made 11,877 lb of Taffy apples, with approximatley 1 pound of taffy mixture for each 61.2 pounds of apples. To the nearest tenth of a pound, how many pounds of apples and how many pounds of taffy were used. How many pounds of taffy were used. How many pounds of apples were used. Round to the nearest tenth.1 solutions Answer 133295 by stanbon(57282)   on 2009-01-24 21:57:43 (Show Source): You can put this solution on YOUR website! A Michigan orchard made 11,877 lb of Taffy apples, with approximatley 1 pound of taffy mixture for each 61.2 pounds of apples. --- ratio is 1 taffy : 61.2 apple or x : 61.2x where x is lbs. of taffy -------------------- Equation: x + 61.2x = 11,877 62.2x = 11,877 x = 190.95 (# of lbs of taffy needed) 61.2x = 11.686.05 (# of lbs of apples needed) -------------------- Cheers, Stan H. To the nearest tenth of a pound, how many pounds of apples and how many pounds of taffy were used. How many pounds of taffy were used. How many pounds of apples were used. Round to the nearest tenth.