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 Travel_Word_Problems/670601: Two pipes can together fill a tank in 40/13 mins. If one pipe takes 3 mins more than the other to fill it, find the timein which each pipe can fill the tank.1 solutions Answer 417125 by ankor@dixie-net.com(15638)   on 2012-10-23 17:37:16 (Show Source): You can put this solution on YOUR website! Two pipes can together fill a tank in 40/13 mins. If one pipe takes 3 mins more than the other to fill it, find the time in which each pipe can fill the tank. : let x = time for the other pipe to fill it then (x+3) = time for one pipe to fill it : Let the completed job = 1 (a full tank) : + = 1 multiply by x(x+3), resulting in (x+3) + x = x(x+3) multiply each term by 13, to get rid of those annoying denominators at last 40(x+3) + 40x = 13x(x+3) : 40x + 120 + 40x = 13x^2 + 39x Combine as a quadratic equation on the right 0 = 13x^2 + 39x - 80x - 120 13x^2 - 41x - 120 - 0 you can use the quadratic formula here, but this will factor to: (13x+24)(x-5) = 0 the positive solution x = 5 min for the other pipe and 5 + 3 = 8 min for one pipe. : : We can check this using the decimal equiv of 40/13; 3.077. 3.077/5 + 3.077/8 = .6154 + .384625 = 1.000
 Problems-with-consecutive-odd-even-integers/670305: I don't understand how to set up the equation for this problem. Find two consecutive integers such that 3 times the larger exceeds twice the smaller by 34 1 solutions Answer 416879 by ankor@dixie-net.com(15638)   on 2012-10-22 19:11:22 (Show Source): You can put this solution on YOUR website! Find two consecutive integers such that 3 times the larger exceeds twice the smaller by 34 : let n = the 1st integer then (n+1) = the next consecutive integer : Write an equation for what it says: : "3 times the larger exceeds twice the smaller by 34" 3(n+1) = 2n + 34 3n + 3 = 2n + 34 3n - 2n = 34 - 3 n = 31, 32; are the two integers, (pretty easy, right?)
 Rational-functions/669998: One hour after a truck has left on an overnight haul, a messenger on a motorcycle leaves from the same starting point to overtake the truck. If the messenger travels at an average rate of 65 mi/hr and overtakes the truck in 4 hr, what is the average rate of the truck?1 solutions Answer 416850 by ankor@dixie-net.com(15638)   on 2012-10-22 17:56:20 (Show Source): You can put this solution on YOUR website!One hour after a truck has left on an overnight haul, a messenger on a motorcycle leaves from the same starting point to overtake the truck. If the messenger travels at an average rate of 65 mi/hr and overtakes the truck in 4 hr, what is the average rate of the truck? : Let t = av rate of the truck (truck's travel time = 5 hrs) : When the bike overtakes the truck, they will have traveled the same distance Write a distance equation; dist = rate * time : Truck dist = bike dist 5t = 4*65 5t = 260 t = t = 52 mph is the truck speed : : Confirm this by finding the actual distance each traveled Truck: 5(52) = 260 mi Bike: 4(65) = 260 mi
 Numbers_Word_Problems/670237: The product of some negative number and 11 less than three times that number is 20. Find the number. 1 solutions Answer 416834 by ankor@dixie-net.com(15638)   on 2012-10-22 16:38:21 (Show Source): You can put this solution on YOUR website! The product of some negative number and 11 less than three times that number is 20. Find the number. n(3n-11) = 20 3n^2 - 11n - 20 = 0 Factors to (3n + 4)(n - 5) the negative solution is what they want here 3n = -4 n = -4/3 n = -1 : : See if that works, use n = -1.33 -1.33(3(-1.33)-11) = 20 -1.33(-4-11) = 20 -1.33*-15 ~ 20
 Mixture_Word_Problems/670216: A chemist needs 150 milliliters of a 44% solution but has only 24% and 99% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.1 solutions Answer 416832 by ankor@dixie-net.com(15638)   on 2012-10-22 16:18:23 (Show Source): You can put this solution on YOUR website!A chemist needs 150 milliliters of a 44% solution but has only 24% and 99% solutions available. Find how many milliliters of each that should be mixed to get the desired solution. : Let x = amt of 99% solution required the resulting amt is to be 150 ml, therefore: (150-x) = amt of 24% solution : A typical mixture equation : .99x + .24(150-x) = .44(150) .99x + 36 - .24x = 66 .99x - .24x = 66 - 36 .75x = 20 x = 30/.75 x = 40 ml of the 99% solution then 150 - 40 = 110 ml of the 24% solution : : You should check this in the original mixture equation .99(40) + .24(110) = .44(150)
 Travel_Word_Problems/669835: A car went 175 mph in 3 hours one way and 4.5 hours on the way back. What is the average miles?1 solutions Answer 416830 by ankor@dixie-net.com(15638)   on 2012-10-22 16:10:17 (Show Source): You can put this solution on YOUR website!A car went 175 mph in 3 hours one way and 4.5 hours on the way back. What is the average speed? : let a = the average speed for the round trip; speed = dist/time : a = = = 46 mph
 Miscellaneous_Word_Problems/670008: Janet goes shopping. In the first store, she spends three fourths of her money. In the next store, she spends two thirds of what is left. She then has \$13. How much did she have before she went shopping?1 solutions Answer 416811 by ankor@dixie-net.com(15638)   on 2012-10-22 14:59:05 (Show Source): You can put this solution on YOUR website!Janet goes shopping. In the first store, she spends three fourths of her money. In the next store, she spends two thirds of what is left. She then has \$13. How much did she have before she went shopping? : Let x = the original amt : x - x = x, amt when she enters the 2nd store then x - x = 13 x - x = 13 Find the common denominator x - x = 13 x = 13 x = 12 * 13 x = \$156 original amt
 Triangles/669934: its says a SMALL JAR cyrindical glass has radius 3 cm and height 7 sm , the larger jar is similar to the shape the glass is 216 times of the small jar. Work out the radius and height of the jar1 solutions Answer 416770 by ankor@dixie-net.com(15638)   on 2012-10-22 12:49:25 (Show Source): You can put this solution on YOUR website!a SMALL JAR; cylindrical glass has radius 3 cm and height 7 cm, the larger jar is similar to the shape the glass is 216 times of the small jar. Work out the radius and height of the jar : let r = the radius of the big jar then r = the height of the big jar : The equation = ": = divide both sides by pi 13608 = r^3 : = *13608 : = 5832 find the cube root of both sides r = r = 18 cm is the radius of the big jar and *18 = 42 cm is the height
 Travel_Word_Problems/669925: Carol has 8 hours to spend on a hike up a mountain and back again. She can walk up the trail at an average of 2 mph and can walk down at an average of 3 mph. How long should she plan to spend on the uphill part of the hike? 1 solutions Answer 416714 by ankor@dixie-net.com(15638)   on 2012-10-22 10:38:26 (Show Source): You can put this solution on YOUR website!Carol has 8 hours to spend on a hike up a mountain and back again. She can walk up the trail at an average of 2 mph and can walk down at an average of 3 mph. How long should she plan to spend on the uphill part of the hike? : let t = time spent walking up-hill then (8-t) = time walking down ; Write a distance equation; dist = speed * time. (distance up and down are equal) 2t = 3(8-t) 2t = 24 - 3t 2t + 3t = 24 5t = 24 t = 24/5 t = 4.8 hrs walking up : : Confirm this by finding the distances 2(4.8) = 9.6 mi 3(8-4.8) = 9.6 mi
 Travel_Word_Problems/669964: A lady drove to a city 30 miles away to shop and returned home in the evening. She spent15 minutes longer driving the return trip than in the going, and she drover three-fourths as fast when returning as she did when going to the city. How long did it take her to drive to the city?1 solutions Answer 416712 by ankor@dixie-net.com(15638)   on 2012-10-22 09:56:53 (Show Source): You can put this solution on YOUR website!A lady drove to a city 30 miles away to shop and returned home in the evening. She spent15 minutes longer driving the return trip than in the going, and she drover three-fourths as fast when returning as she did when going to the city. How long did it take her to drive to the city? : Find the speed first let s = speed to the city then .75s = return speed : Change 15 min to .25 hr : Write a time equation; time = dist/speed + .25 = multiply by 3s, to clear the denominators, results 3(30) + 3s(.25) = 4(30) 90 + .75s = 120 .75s = 120 - 90 .75s = 30 s = 30/.75 s = 40 mph to the city : Find the time 30/40 = .75 hrs or 45 min to drive to the city
 Quadratic_Equations/669972: A number is added to one-half of its reciprocal and the sum is again added to one-third of the original number's reciprocal. If the sum is equal to number added to 4, find the number.1 solutions Answer 416694 by ankor@dixie-net.com(15638)   on 2012-10-22 08:43:37 (Show Source): You can put this solution on YOUR website!A number is added to one-half of its reciprocal and the sum is again added to one-third of the original number's reciprocal. If the sum is equal to number added to 4, find the number. : n + + = n + 4 Subtract n from both side + = 4 multiply by 6n 3 + 2 = 6n(4) 5 = 24n n = is the number :
 Rate-of-work-word-problems/669609: It takes 8 hours to fill a pool with the inlet pipe. It can be emptied in 12 hours with the outlet pipe. If the pool is 1/2 full to begin with, how long will it take to fill it from there if both pipes are open?1 solutions Answer 416595 by ankor@dixie-net.com(15638)   on 2012-10-21 21:51:11 (Show Source): You can put this solution on YOUR website!It takes 8 hours to fill a pool with the inlet pipe. It can be emptied in 12 hours with the outlet pipe. If the pool is 1/2 full to begin with, how long will it take to fill it from there if both pipes are open? : let t = time when both valves are left open : let the completed job = 1 (full pool) : - = multiply by 24, resulting in 3t - 2t = 12 t = 12 hrs to complete filling the pool
 Linear-systems/669557: The tens digit of a two-digit number is 3 more than 5 times the units digit. If the digits are reversed, the new number is 2 more than twice the tens digit of the original number. Find the original number.1 solutions Answer 416593 by ankor@dixie-net.com(15638)   on 2012-10-21 21:43:25 (Show Source): You can put this solution on YOUR website!let a = the 10's digit let b = the units: Write an equation for each statemennt : " The tens digit of a two-digit number is 3 more than 5 times the units digit." a = 5b + 3 right here you know that b has to = 1 and then a = 8 81 is the number : You can confirm this using the 2nd statement : " If the digits are reversed, the new number is 2 more than twice the tens digit of the original number." Find the original number.
 Quadratic_Equations/669596: I need help with this problem of algebra 2: The general form of an equation for a parabola is y=ax^2+bx+c, where (x,y) is a point on the parabola. If three points on a parabola were (2,-10)(-5,-101)and (6,-90) determine the values of a, b and c write the general form of the equation.1 solutions Answer 416569 by ankor@dixie-net.com(15638)   on 2012-10-21 20:00:16 (Show Source): You can put this solution on YOUR website!The general form of an equation for a parabola is y=ax^2+bx+c, where (x,y) is a point on the parabola. If three points on a parabola were (2,-10)(-5,-101)and (6,-90) determine the values of a, b and c write the general form of the equation. ; Use elimination or substitution to find a, b, c, write an equation for each pair : 2,-10 (2^2)a + 2b + c = -10 4a + 2b + c = -10 : -5,-101 25a - 5b + c = -101 : 6,-90 36a + 6b + c = -90 : Eliminate c, subtract the 1st equation from the 2nd equation 25a - 5b + c = -101 4a + 2b + c = -10 -------------------Subtracting eliminates c 21a - 7b = -91 : subtract the 1st eq from the 3rd eq 36a + 6b + c = -90 4a + 2b + c = -10 --------------------- 32a + 4b = -80 4b = -32a - 80 simplify divide by 4 b = -8a - 20 : Replace b with (-8a-20) in eq: 21a - 7b = -91 21a - 7(-8a-20) = -91 21a + 56a + 140 = -91 77a = -91 - 140 77a = -231 a = -3 : Find b, replace a b = -8(-3) - 20 b = +24 - 20 b = 4 : Find c using the 1st equation 4(-3) + 2(4) + c = -10 -12 + 8 + c = -10 -4 + c = -10 c = -10 + 4 c = -6 : The equation: y = -3x^2 + 4x - 6 : I checked this on my Ti83, to ensure the given pairs are on the graph you should do the same
 Age_Word_Problems/669410: the age of father exeeds to the square of the age his son by 4 years.the sum of the age of father and four times the age of his son is 64 years.find their ages. 1 solutions Answer 416516 by ankor@dixie-net.com(15638)   on 2012-10-21 17:30:40 (Show Source): You can put this solution on YOUR website!let d = Dad's age let s = don's age : Write an equation for each statement: : the age of father exeeds to the square of the age his son by 4 years. d = s^2 + 4 : the sum of the age of father and four times the age of his son is 64 years. d + 4s = 64 Replace d with (s^2+4) s^2 + 4 + 4s = 64 A quadratic equation s^2 + 4s - 60 = 0 Factors to (s+10)(s-6) = 0 the positive solution s = 6 yrs is the son's age : Find Dad's age 6^2 + 4 = 40 yrs : : check solutions in the 2nd statement 40 + 4(6) = 64
 Money_Word_Problems/669497: mary wants to make 200 pounds of blended coffee selling for \$5.50 per pound. How many pounds of \$6.00 coffee must she mix with how many pounds of \$4.00?1 solutions Answer 416511 by ankor@dixie-net.com(15638)   on 2012-10-21 17:21:55 (Show Source): You can put this solution on YOUR website!mary wants to make 200 pounds of blended coffee selling for \$5.50 per pound. How many pounds of \$6.00 coffee must she mix with how many pounds of \$4.00? : Let x = amt of \$6 coffee required the total is given as 200 lb, therefore: (200-x) = amt of \$4 coffee : A typical mixture equation: 6x + 4(200-x) = 5.50(200) : : You should be able to do it now. If not, let me know in the comments.
 Linear-equations/669455: twice a number exceeds 24 by as much as twice a second number is less than 80.thrice the first number divided by 5 is equal to the second number divided by 4. find the numbers 1 solutions Answer 416508 by ankor@dixie-net.com(15638)   on 2012-10-21 17:15:30 (Show Source): You can put this solution on YOUR website!Two numbers, a & a ; twice a number exceeds 24 by as much as twice a second number is less than 80. 2a - 24 = 80 - 2b 2a + 2b = 80 + 24 2a + 2b = 104 Simplify, divide by 2 a + b = 52 : thrice the first number divided by 5 is equal to the second number divided by 4. = cross multiply 4(3a) = 5b 12a = 5b 12a - 5b = 0 5a + 5b = 260 multiplied the 1st equation by 5 -------------- addition eliminates b, find a 17a = 260 a ~ 15.294, I would have expected integers here, anyway : a + b = 52 15.294 + b = 52 b = 52 - 15.294 b = 36.706 : : See if that satisfies the 2nd statement, using a calc: = 9.1764 ~ 9.1765, close anyway
 Travel_Word_Problems/669535: the hiking club hiked to a state park at 4mph. they got aride back to town in a truck that wnt 20mph. If the round trip took 18 houers, how tar was it from town to the park. My question is how to write the equetions to solve this problem?1 solutions Answer 416497 by ankor@dixie-net.com(15638)   on 2012-10-21 16:40:03 (Show Source): You can put this solution on YOUR website! the hiking club hiked to a state park at 4 mph. they got a ride back to town in a truck that went 20 mph. If the round trip took 18 hrs, how far was it from town to the park. : Let d = distance to the park and distance back to town : Write a time equation; time = dist/speed : Walk time + ride time = 18 hrs + = 18 multiply by 20, cancel the denominators and you have: 5d + d = 20(18) 6d = 360 d = 360/6 d = 60 mi : : See if that checks out, find the times 60/4 = 15 hrs 60/20 = 3 hrs --------------- tot time 18 hrs
 Quadratic_Equations/669481: a man travels a total distance of 166km/hr. his average speed for the first 130km is xkm/hr and for the remaining journey , (x-25)km/hr. if the whole journey takes 3 hours and 15 minutes , form an equation in terms of x. solve this equation and hence find the time he would have saved if he maintains an average speed of xkm/hr throughout ? 1 solutions Answer 416490 by ankor@dixie-net.com(15638)   on 2012-10-21 16:16:32 (Show Source): You can put this solution on YOUR website! a man travels a total distance of 166km/hr. his average speed for the first 130km is xkm/hr and for the remaining journey, (x-25)km/hr. if the whole journey takes 3 hours and 15 minutes, form an equation in terms of x. : Change 3 hrs 15 min to 3.25 hrs : Write a time equation; time = dist/speed + = 3.25 Multiply by x(x-25), results 130(x-25) + 36x = 3.25x(x-25) : 130x - 3250 + 36x = 3.25x^2 - 81.25x : 166x - 3250 = 3.25x^2 - 81.25x A quadratic equation 3.25x^2 - 81.25x - 166x + 3250 = 0 : 3.25x^2 - 247.25x + 3250 = 0 : solve this equation Use the quadratic formula to find x; a=3.25, b=-247.25, c=3250 Do this rather tedious math, the reasonable solution x ~ 59.18 km/h ; find the time he would have saved if he maintains an average speed of xkm/hr throughout ? : = 2.8 hrs 3.25 - 2.8 = .45 hrs saved (.45*60 = 27 min)
 Quadratic_Equations/669267: word problem involving quadratic equation working together, kim and dominic can paint their apartment in 2 days.working alone,kim can complete the job in 3 days less than dominic, working alone.how long would it take each person working alone? 1 solutions Answer 416297 by ankor@dixie-net.com(15638)   on 2012-10-20 18:06:09 (Show Source): You can put this solution on YOUR website! kim and dominic can paint their apartment in 2 days. working alone,kim can complete the job in 3 days less than dominic, working alone. how long would it take each person working alone? : let t = time required by Kim to do the job then (t+3) = time required by Dom : Let the completed job = 1; (a painted room) : A typical shared work equation + = 1 Multiply by t(t+3), cancel the denominators: 2(t+3) + 2t = t(t+3) 2t + 6 + 2t = t^2 + 3t Combine as a quadratic on the right 0 = t^2 + 3t - 4t - 6 t^2 - t - 6 = 0 factors to (t-3)(t+2) = 0 the positive solution t = 3 days, Kim working alone then 3 + 3 = 6 days, Dome working alone : : Check this 2/3 + 2/6 = 1
 Mixture_Word_Problems/669159: have 5 gallons of glacial acetic acid . need to make a total of 3 gallons of a 30% solution. how many milliliters of distilled wate and how many milliliters of glacial acetic acid are needed to make 3 gallons of 30% solution? please reply to jr8565@ bellsouth.net1 solutions Answer 416241 by ankor@dixie-net.com(15638)   on 2012-10-20 13:46:27 (Show Source): You can put this solution on YOUR website! have 5 gallons of glacial acetic acid . need to make a total of 3 gallons of a 30% solution. how many milliliters of distilled water and how many milliliters of glacial acetic acid are needed to make 3 gallons of 30% solution? : let x = amt of acid required (in gal) the resulting amt is to be 3 gal, therefore (3-x) = amt of water required : x = .3(3) x = .9 gal of acid required then 3 -.9 = 2.1 gal of water : But for some obscure reason, they want the amts to be in milliliters : 1 gal = 3.785 liters which is 3785 milliliter : Acid: .9(3785) = 3406.5 milliliters water: 2.1(3785) = 7948.5 milliliters
 Linear-equations/669185: the sum of the reciprocals of two number is 5/8. four times the reciprocal of the first is twice as much as eight times the reciprocal of the second. find the numbers.1 solutions Answer 416210 by ankor@dixie-net.com(15638)   on 2012-10-20 11:39:41 (Show Source): You can put this solution on YOUR website!Write an equation for each statement; the two numbers are a & B : the sum of the reciprocals of two number is 5/8. + = four times the reciprocal of the first is twice as much as eight times the reciprocal of the second. = which is = cross multiply 4b = 16a divide both sides by 4 b = 4a : find the numbers. Back to the 1st equation, replace b with 4a + = multiply by 8a, results: 8 + 2 = 5a 10 = 5a a = 2 then b = 4*2 b = 8 : : See if that checks out + = + =
 Surface-area/669144: The question is: The measurements given are rounded to the nearest foot. ( width: 6 feet height: 10 feet). Use these measurements to find the approximate area of the trapezoid. Describe your method. I have no idea how to do this otherwise i would've tried. 1 solutions Answer 416207 by ankor@dixie-net.com(15638)   on 2012-10-20 11:26:29 (Show Source): You can put this solution on YOUR website!Check out this website: http://www.mathopenref.com/trapezoidarea.html
 Travel_Word_Problems/668969: I rode my bike for 15 minutes. For 10 minutes I rode for 15 mph, for 5 minutes I rode for 20 mph. what is my average speed for the entire trip.1 solutions Answer 416183 by ankor@dixie-net.com(15638)   on 2012-10-20 10:04:37 (Show Source): You can put this solution on YOUR website! I rode my bike for 15 minutes. For 10 minutes I rode for 15 mph, for 5 minutes I rode for 20 mph. what is my average speed for the entire trip. : Convert 15 min to or .25 hr : Convert 10 min to hr Find the distance at 15 mph; *15 = 2.5 mi : Convert 5 min to hr Find the distance at 20 mph; *20 = 1.67 mi : then total distance: 2.5 + 1.67 = 4.17 mi : Average for the trip (total dist/total time): 4.17/.25 ~ 16.8 mph
 Travel_Word_Problems/669083: Lindsey went on a 6-mile bicycle ride that took her 4.4 hours to complete. What was Lindsey's average speed in feet per second? 1 solutions Answer 416181 by ankor@dixie-net.com(15638)   on 2012-10-20 09:40:52 (Show Source): You can put this solution on YOUR website! Lindsey went on a 6-mile bicycle ride that took her 4.4 hours to complete. What was Lindsey's average speed in feet per second? : Find the speed in mph, convert to ft per second * = 2 ft per second, that's slower than walking!
 Travel_Word_Problems/669082: In a 100-meter race, Todd crosses the finish line 5 meters ahead of Scott. To even things up, Todd suggests to Scott that they race again, this time with Todd lining up 5 meters behind the start. (a) Assuming that Todd and Scott run at the same pace as before, does the second race end in a tie? (b) If not, who wins? (c) By how many meters does he win? (d) How far back should Todd start so that the race ends in a tie? After running the race a second time, Scott, to even things up, suggests to Todd that he (Scott) line up 5 meters in front of the start. (e) Assuming again that they run at the same pace as in the first race, does the third race result in a tie? (f) If not, who wins? (g) By how many meters? (h) How far ahead should Scott start so that the race ends in a tie? I understand that Scott is running at 0.95 times the speed of Todd but that's all I understand. I think that I could do the second half after seeing and understand how the first half is done. Thanks so much!1 solutions Answer 416105 by ankor@dixie-net.com(15638)   on 2012-10-19 22:09:06 (Show Source): You can put this solution on YOUR website!In a 100-meter race, Todd crosses the finish line 5 meters ahead of Scott. To even things up, Todd suggests to Scott that they race again, this time with Todd lining up 5 meters behind the start. : Assume that Todd runs it in 10 sec 100/10 = 10 m/sec is Todd's running speed then 95/10 = 9.5 m/sec is Scott's speed : (a) Assuming that Todd and Scott run at the same pace as before, does the second race end in a tie? Find Todd's time to run 105 meters: 105/10 = 10.5 sec Find Scott's time to run 100 meters: 100/9.5 = 10.5263 sec : (b) If not, who wins? Todd still wins, but Scott is only .0263 sec behind him : (c) By how many meters does he win? .0263 * 9.5 ~ .25 meters (d) How far back should Todd start so that the race ends in a tie? let a = distance back for Todd so it end's in a tie, write a time equation = cross multiply 9.5(a+100) = 10*100 9.5a + 950 = 1000 9.5a = 1000 - 950 9.5a = 50 a = 50/9.5 a = 5.263 meters behind : After running the race a second time, Scott, to even things up, suggests to Todd that he (Scott) line up 5 meters in front of the start. (e) Assuming again that they run at the same pace as in the first race, does the third race result in a tie? We know Todds time to run 100 m = 10 sec Find Scotts time to run 95 m: 95/9.5 = 10 sec : (f) If not, who wins? A tie : (g) By how many meters? (h) How far ahead should Scott start so that the race ends in a tie? I understand that Scott is running at 0.95 times the speed of Todd but that's all I understand. I think that I could do the second half after seeing and understand how the first half is done. Thanks so much! 0 solutions
 Linear_Equations_And_Systems_Word_Problems/668817: The annual consumption of frozen yogurt has decayed approximately exponentially from 2.6 pounds per person in 1995 to 1.0 pound per person in 2006. Predict when the consumption will be 0.5 pounds per person. Show steps. 1 solutions Answer 416090 by ankor@dixie-net.com(15638)   on 2012-10-19 20:28:12 (Show Source): You can put this solution on YOUR website!The annual consumption of frozen yogurt has decayed approximately exponentially from 2.6 pounds per person in 1995 to 1.0 pound per person in 2006. : Use the exponential decay formula using e Ao*e^(-t/k} = A, where Ao = initial amt A = resulting amt after t time t = time in yrs k = constant of decay of substance : t = 11 yrs (1995 to 2006) 2.6*e^(-11/k) = 1 Divide both sides by 2.6 e^(-11/k) = .3846 nat log of both sides (ln of e = 1) = ln(.3846) = -.9555 k = k = +11.512 is the constant of decay : Predict when the consumption will be 0.5 pounds per person. k = 11.512, find t 2.6*e^(-t/11.512) = .5 Divide both sides by 2.6 e^(-t/11.512) = .1923 Nat logs of both sides = -1.6487 t = -1.6487 * -11.512 t ~ 19 yrs from 1995; 2014, the year when consumption is only .5 lb
 Length-and-distance/669079: Two candles are lit at the same time. One is 12 inches tall and burns 1/2 inch per hour. The other candle is 6 inches tall and burns 1/4 inch per hour. Which candle will burn down first? Thank your for your help.1 solutions Answer 416074 by ankor@dixie-net.com(15638)   on 2012-10-19 19:42:45 (Show Source): You can put this solution on YOUR website!Two candles are lit at the same time. One is 12 inches tall and burns 1/2 inch per hour. The other candle is 6 inches tall and burns 1/4 inch per hour. Which candle will burn down first? : let t = time in hrs each candle burns : 1st candle: .5t = 12 t = 24 hrs : 2nd candle .25t = 6 t = 24 hrs : They're the same
 Mixture_Word_Problems/669021: one solar heating panel can raise the temperature of water 1° in 16 min . a second solar heating panel can raise the temperature 1° in 24min. how lond will it take to raise the temperature of the water 1° if both panels are operating? 1 solutions Answer 416062 by ankor@dixie-net.com(15638)   on 2012-10-19 19:16:31 (Show Source): You can put this solution on YOUR website!one solar heating panel can raise the temperature of water 1° in 16 min. a second solar heating panel can raise the temperature 1° in 24 min. how long will it take to raise the temperature of the water 1° if both panels are operating? : let b = time required when both panels are operating let the completed job = 1 (raising the temp 1 degree) : A shared work equation : + = 1 multiply by 48 to clear the denominators, results: 3b + 2b = 48 5b = 48 b = 48/5 b = 9.6 minutes working together : : check this 9.6/16 + 9.6/24 = .6 + .4 = 1
 Age_Word_Problems/669028: Amy is 4 years older than Anna.Anna is 8 years older than Alice,Alice is 9 years older than Angela, How much older than Angela is Amy?1 solutions Answer 416045 by ankor@dixie-net.com(15638)   on 2012-10-19 18:10:51 (Show Source): You can put this solution on YOUR website!let a = Amy's age let b = Anne's age let c = Alice's age let d = Angela's age : Write an equation for each statement : Amy is 4 years older than Anna. a = b + 4 : Anna is 8 years older than Alice, b = c + 8 : Alice is 9 years older than Angela, c = d + 9 : How much older than Angela is Amy? 21 yrs older (4+8+9)
 Linear_Equations_And_Systems_Word_Problems/668898: I need to figure out how to get the amount from a phone bill sent to Boston on June 16. The Rate for First Minute is .4698, the Rate for Additional Minutes is .3740, and the Total Minutes are 17. How do I get the amount?1 solutions Answer 416026 by ankor@dixie-net.com(15638)   on 2012-10-19 16:29:39 (Show Source): You can put this solution on YOUR website!The Rate for First Minute is .4698, the Rate for Additional Minutes is .3740, and the Total Minutes are 17. How do I get the amount? Cost = 16(.3740) + .4698 Cost = 6.45 cents