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 Miscellaneous_Word_Problems/221465: It takes a train 7 seconds to pass by a stationary observer and 26 seconds to travel the length of a station 380 meters long. What is the speed of the train and its length? 1 solutions Answer 166169 by ankor@dixie-net.com(15652)   on 2009-10-04 20:10:00 (Show Source): You can put this solution on YOUR website!It takes a train 7 seconds to pass by a stationary observer and 26 seconds to travel the length of a station 380 meters long. What is the speed of the train and its length? : let s = speed of the train in meters/sec : 7s = length of the train : time of the front of the train passing the platform It passes the platform 26-7 = 19 sec : s = s = 20 meters/sec : Train length = 7s 7(20) = 140 meters long : The speed of train in km/hr = = 72 km/hr
 Linear_Equations_And_Systems_Word_Problems/221258: Diophantus a greek mathematician is considered by many as the "Father of Algeria" because of his works in the syncopation of algebra. In his epitaph, the following is scripted. "A sixth of his life was spent in childhood. A twelfth as a youth, and a seventh as a bachelor. Five years after his marriage, his son was born but died four years before his own death at half his age".1 solutions Answer 166132 by ankor@dixie-net.com(15652)   on 2009-10-04 18:00:17 (Show Source): You can put this solution on YOUR website!Diophantus passed one-sixth of his life in childhood, one-twelfth in youth, one-seventh more as a bachelor. Five years after his marriage, a son was born who died four years before his father, at half his father's [final] age. How old was Diophantus when he died. : Let x = his final age : a lengthy but simple equation Final age = child + youth + bach + marriage + son's age + 4 x = x + x + x + 5 + x + 4 : Common denominator of 12*7 = 84 x = x + x + x + 5 + x + 4 : x = x + 9 : x - x = 9 : x = 9 : x = 84 is his final age : Check: 14 + 7 + 12 + 5 + 42 + 4 = 84
 Human-and-algebraic-language/221446: A colonel, on attempting to draw up his regiment in the form of a solid square, finds that he has 30 men left over, and that he would require 25 soliders in his regiment to increase the side of the square by one soldier. How many soldiers are there in the regiment?1 solutions Answer 166101 by ankor@dixie-net.com(15652)   on 2009-10-04 16:54:00 (Show Source): You can put this solution on YOUR website!A colonel, on attempting to draw up his regiment in the form of a solid square, finds that he has 30 men left over, and that he would require 25 solders in his regiment to increase the side of the square by one soldier. How many soldiers are there in the regiment? ; Let (x^2 + 30) = no. of soldiers in the regiment : It says that 25 more would give him one more in each side: We can write that (x + 1)^2 = x^2 + 30 + 25 : x^2 + 2x + 1 = x^2 + 55 ; x^2 - x^2 + 2x = 55 - 1 : 2x = 54 x = x = 27 therefore 27^2 + 30 = 759 soldiers : Is this true? 28^2 - 759 = 25
 test/221116: Rus and dufus each took some money froma piggy bank to buy an ice cream cone but rufus was 24 cent short and dufus was 2 cent short of the price of cone. they decided to pool their resources, but found they still could not afford to buy the cone. how many cents did the ice cream cost?1 solutions Answer 166086 by ankor@dixie-net.com(15652)   on 2009-10-04 16:20:47 (Show Source): You can put this solution on YOUR website!Rus and dufus each took some money from a piggy bank to buy an ice cream cone but rufus was 24 cent short and dufus was 2 cent short of the price of cone. they decided to pool their resources, but found they still could not afford to buy the cone. how many cents did the ice cream cost? : Let the cost of the cone = x then x - 24 = R's amt and x - 2 = D's amt : The total amt of both: (x-24) + (x-2) = (2x - 26) : Total amt was not enough to buy a cone, write an inequality 2x - 26 < x 2x - x < 26 x < 26 cents Let x = 25 cents be the price of a cone ; Is this true? 25 - 24 = 1 cents for R and 25 - 2 = 23 cents for D : Together they had 24 cents, not enough for a 25 cent cone
 Geometry_Word_Problems/221381: A red ball and a green ball are simultaneously tossed in to the air. The red bass is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is -16^2+96tfeet. The green ball is given an initial velocity of 80 feet persecond, and its height t seconds after it is tossed is -16t^2+80t feet. Find a polynomial d(t) that represents the fiddference in the heights of the two balls, how much higher is the reball 2 seconds after the balls are tossed. In reality, when does the difference in the deights stop increasing? 1 solutions Answer 166075 by ankor@dixie-net.com(15652)   on 2009-10-04 15:30:07 (Show Source): You can put this solution on YOUR website!A red ball and a green ball are tossed into the air. The red ball is given an initial velocity of 96 feet per second and its height "t" seconds after it is tossed is -16t^2 + 96t feet. The green ball is given an initial velocity of 80 feet per second and its height "t" seconds after being tossed is -16t^2 +80t feet. : Find a polynomial D(t) that represents the difference in the heights of the two balls. D(t) = (-16t^2 + 96t) - (-16t^2 +80t) : Remove brackets D(t) = -16t^2 + 96t + 16t^2 - 80t : combine like terms: D(t) = 16t : How much higher is the red ball 2 seconds after the balls are tossed? D(t) = 16(2) D(t) = 32 ft difference after 2 seconds : When does the difference in the heights stop increasing? : Obviously, when one of the balls hits the ground : Find when the lowest ball hits the ground (h=0) -16t^2 + 80t = 0 Factor out -16t -16t(t - 5) = 0 t = 5 seconds when the difference stops increasing; : A graph illustrates this well
 Linear-equations/221070: What would the answer be if i need to write an equation for the line in slope intercept-form when it passes throught (5,-2) and is parallel to y=-9x+6?1 solutions Answer 166035 by ankor@dixie-net.com(15652)   on 2009-10-04 11:41:44 (Show Source): You can put this solution on YOUR website!What would the answer be if i need to write an equation for the line in slope intercept-form when it passes through (5,-2) and is parallel to y=-9x+6? ; remember that parallel lines have the same slope, here it is -9. : Use point/slope formula; y - y1 = m(x - x1) our equation: y - (-2) = -9(x - 5) y + 2 = -9x + 45 y = -9x + 45 - 2 y = -9x + 43, is the equation in the slope/intercept form
 Circles/221262: I have four circles each with a 10 foot radius, they are put togeather to form a squire of circles what I need to know is the squire foot of the waste in the very middle1 solutions Answer 166027 by ankor@dixie-net.com(15652)   on 2009-10-04 11:29:38 (Show Source): You can put this solution on YOUR website!I have four circles each with a 10 foot radius, they are put together to form a square of circles. What I need to know is the square foot of the waste in the very middle. : Picture a single circle a radius of 10, inscribed in a single square, a side of 20 Find the area of the square, subtract the area of the circle : (20^2) - (pi*10^2) = 400 - 314.159 = 85.84 sq/ft; the total wasted in a all 4 corners : This is also the total of the 4 corners from the 4 circles described therefore 85.84 sq/ft wasted ; Did this make sense to you?
 Numbers_Word_Problems/221245: i am less than 500. i am divisible 11 and 5. i have three digits. the sum of my digits is 14?1 solutions Answer 166002 by ankor@dixie-net.com(15652)   on 2009-10-04 09:53:35 (Show Source): You can put this solution on YOUR website!i am less than 500. i am divisible 11 and 5. i have three digits. the sum of my digits is 14? : with a calc: multiply 55 * 9 = 495 subtract 55 until the digits add up to 14 440 385 330 275 digits add up to 14
 Travel_Word_Problems/220972: plane flies 420 mph in still air. With wind, a trip from a to b takes 10 minutes less than the return trip flying against wind from b to a. Distance between a to b is 360 miles. Find speed of wind.1 solutions Answer 165933 by ankor@dixie-net.com(15652)   on 2009-10-03 21:10:46 (Show Source): You can put this solution on YOUR website!plane flies 420 mph in still air. With wind, a trip from a to b takes 10 minutes less than the return trip flying against wind from b to a. Distance between a to b is 360 miles. Find speed of wind. : Let w = speed of the wind then (420+w) = speed with the wind and (420-w) = speed against the wind : Convert 10 min to hr : Time b-a - Time a-b = 10 min - = Multiply equation by 6(420-w)(420+w) : 6(420-w)(420+w)* - 6(420-w)(420+w)* = 6(420-w)(420+w)* : Cancel the denominators and you have 6(420+w)*360 - 6(420-w)*360 = (420+w)(420-w) ; 2160(420+w) - 2160(420-w) = 176400 - w^2 : 1327200 + 2160w - 1327200 + 2150w = 176400 - w^2 : Combine on the left to form a quadratic equation: w^2 + 4320w - 176400 = 0 You have to use the quadratic formula to find w : I got a positive solution of w = 40.4545 mph ; : Check this with a calc - = .9485 - .7818 = .1667 .1667 = .1667
 Probability-and-statistics/221123: Suppose that the mean score of a class of 28 students was 74. The 18 male students in the class had a mean score of 66. What was the mean score for the 10 female students? I don't understand how to find this answer.1 solutions Answer 165912 by ankor@dixie-net.com(15652)   on 2009-10-03 19:11:58 (Show Source): You can put this solution on YOUR website!Suppose that the mean score of a class of 28 students was 74. The 18 male students in the class had a mean score of 66. What was the mean score for the 10 female students? : Let x = mean score of the girls : write a total score equation boys + girls = total 18*66 + 10x = 28*74 : 1188 + 10x = 2072 : 10x = 2072 - 1188 : 10x = 884 x = x = 88.4 girls mean score
 Exponents/221139: A 2000L tank containing 550L of water is being filled with water at the rate of 75L per minute from a full 1600L tank. How long will it be before the two tanks have the same amount of water?1 solutions Answer 165910 by ankor@dixie-net.com(15652)   on 2009-10-03 18:57:59 (Show Source): You can put this solution on YOUR website!A 2000L tank containing 550L of water is being filled with water at the rate of 75L per minute from a full 1600L tank. How long will it be before the two tanks have the same amount of water? : Let t = time required for the two levels to be equal : 2k tank amt = 1600 tank amt 75t + 550 = 1600 - 75t : 75t + 75t = 1600 - 550 : 150t = 1050 t = t = 7 hrs ; : Check solution by finding the amt in each 75(7) + 550 = 1600 - 75(7) 525 + 550 = 1600 - 525 1075 = 1075
 Inequalities/221007: How would you out this in inequality form Five times a number decreased by eight is at the most ten more than twice the number. 1 solutions Answer 165909 by ankor@dixie-net.com(15652)   on 2009-10-03 18:42:46 (Show Source): You can put this solution on YOUR website!Five times a number decreased by eight is at the most ten more than twice the number. 5x - 8 =< 2x + 10 : 5x - 2x =< 10 + 8 : 3x =< 18 : x =< 6
 test/221084: if the nine-digit integer 3365097 ab is divisible by 72. find the possible ordered pairs of digits (a,b)1 solutions Answer 165871 by ankor@dixie-net.com(15652)   on 2009-10-03 16:34:26 (Show Source): You can put this solution on YOUR website!if the nine-digit integer 3365097 ab is divisible by 72. find the possible ordered pairs of digits (a,b) : try a=9, b=9 Using a calc 336509799/72 = 4673747.208 : .208 * 72 ~ 15 : Subtract 15 from 99 = 84 a=8, b=4 336509784/72 = 4673747 : Subtract 72: a=1, b=2 336509712/72 = 4673746 ; Possible a, b values 8, 4 and 1, 2
 Equations/221017: I really cannot figure this out! Please help!!! A disk jockey must play 12 commercial spots during one hour of a radio show. Each comercial is either 30 seconds or 60 seconds long. If the total commercial time during one hour is 8 minutes, how many 30-sec commercials were played that hour? How many 60-sec commercials?1 solutions Answer 165863 by ankor@dixie-net.com(15652)   on 2009-10-03 16:13:43 (Show Source): You can put this solution on YOUR website!A disk jockey must play 12 commercial spots during one hour of a radio show. Each comercial is either 30 seconds or 60 seconds long. If the total commercial time during one hour is 8 minutes, how many 30-sec commercials were played that hour? How many 60-sec commercials? : Let x = no. of 30 sec let y = no. of 60 sec : Convert 8 min to 480 second : Two equations: x + y = 12 arrange for substitution x = 12-y : 30x + 60y = 480 simplify, divide by 30 x + 2y = 16 ; Replace x with (12 - y) 12 - y + 2y = 16 -y + 2y = 16 - 12 y = 4 ea 60 sec commercials and x = 12 - 4 x = 8 ea 30 sec commercials ; Check solution in 2nd original equation 30(8) + 60(4) = 240 + 240 = 480 sec = 8 min
 Miscellaneous_Word_Problems/220981: While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field? I understand x^2 , x+1, x+3, however, when I write the equation to separate I cannot get to area of each field if total is 38. Thank you, Brett 1 solutions Answer 165851 by ankor@dixie-net.com(15652)   on 2009-10-03 15:47:45 (Show Source): You can put this solution on YOUR website!While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field? : I understand x^2 , x+1, x+3, however, when I write the equation to separate I cannot get to area of each field if total is 38. : I think it should be: x^2 + (x+1)^2 + (x+3)^2 = 38 FOIL x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38 Combine like terms 3x^2 + 8x + 10 = 38 : 3x^2 + 8x + 10 - 38 = 0 : 3x^2 + 8x - 28 = 0 Factors to (3x + 14)(x - 2) = 0 Positive solution x = 2 km ; The three field sides, 2, 3, 5 ; Check: 2^2 + 3^2 + 5^2 = 38
 Linear-equations/220888: Write an equation for the perpendicular bisector of the line segment connecting A(-1, 4) and B(3, 5). The perpendicular bisector of a line segment AB is the line that is perpendicular to AB and cuts AB into two equal pieces1 solutions Answer 165843 by ankor@dixie-net.com(15652)   on 2009-10-03 15:33:49 (Show Source): You can put this solution on YOUR website! an equation for the perpendicular bisector of the line segment connecting A(-1, 4) and B(3, 5). The perpendicular bisector of a line segment AB is the line that is perpendicular to AB and cuts AB into two equal pieces : Find the slope (m1) of the given line segment x1 = -1; y1 = 4 x2 = 3; y2 = 5 : m1 = = = : Find the midpoint of the line: m.p. = , m.p. = , m.p. = x=1, y=4.5; is the mid-point : Find the slope of the perpendicular line *m2 = -1 m2 = 4(-1) m2 = -4 : Find equation of the bisecting line using this slope and the midpoint y - 4.5 = -4(x - 1) y - 4.5 = -4x + 4 y = -4x + 4 + 4.5 y = -4x + 8.5; is the bisecting perpendicular line
 Linear_Equations_And_Systems_Word_Problems/221030: Write a system of the form ax+by=c dx+ey=f where a,b,c,d,e, and f are consecutive integers. Solve the system and make a conjecture. Please help! this is taken fron the textbook Beginning Algebra By Addison WEsley1 solutions Answer 165827 by ankor@dixie-net.com(15652)   on 2009-10-03 13:54:36 (Show Source): You can put this solution on YOUR website!Write a system of the form ax+by=c dx+ey=f where a,b,c,d,e, and f are consecutive integers. Solve the system and make a conjecture. : 1x + 2y = 3 4x + 5y = 6 : Multiply the 1st equation by 4, subtract the 2nd equation from it: 4x + 8y = 12 4x + 5y = 6 --------------eliminate x 3y = 6 y = 2 then use the 1st equation to find x x + 2(2) = 3 x = 3 - 4 x = -1 ; : Check solutions in the 2nd equation 4(-1) + 5(2) = 6 -4 + 10 = 6 : : Can we conjecture that any system like this will have solutions x = -1 and y = 2
 Square-cubic-other-roots/220830: Write each product of primes factors, thin simplify. Give answers in simplifiied radical form. 3root of 1351 solutions Answer 165817 by ankor@dixie-net.com(15652)   on 2009-10-03 13:22:35 (Show Source): You can put this solution on YOUR website!3root of 135 : Factor Extract the square of 3
 Miscellaneous_Word_Problems/220813: Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 5 miles per hour and Dave bikes at 9 miles per hour. How long will it be until they ar 28 miles apart from each other?1 solutions Answer 165812 by ankor@dixie-net.com(15652)   on 2009-10-03 12:57:07 (Show Source): You can put this solution on YOUR website!Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 5 miles per hour and Dave bikes at 9 miles per hour. How long will it be until they ar 28 miles apart from each other? ; You can do this in your head, their relative speed: 9 + 5 = 14 mph How long to cover 28 at 14 mph, obviously, it's 2 hrs