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Question 1161182: Please help me solve this equation:
The quadratic equation has a repeated real solution. Prove that .
Click here to see answer by math_helper(2461)

Question 1161158: 1) Find the future value of a simple interest loan of $4,000 at 5.5% interest for 7 months?
2) Find the present value of $26,500 in 9 months at 5.8% interest.
3) Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Click here to see answer by Theo(13342)

Question 1161183: Please help me solve this:
(last time i typed wrong)
The quadratic equation {{ (b-c)x^2+(c-a)x+(a-b)=0 }}} has a repeated real solution. Prove that
Thanks!

Click here to see answer by ikleyn(52776)

Question 1161177: In 1893, Pittsburgh bridge builder George Ferris designed and built a gigantic revolving steel wheel whose height was 264 feet and diameter was 250 feet. This Ferris wheel opened at the 1893 exposition in Chicago. It had 36 wooden cars, each capable of holding 60 passengers.
a) What is the radius of the Ferris Wheel?
b) How close is the wheel to the ground?
c) How high is the center of the wheel from the ground?
d) Using the axes in the drawing, what are the coordinates of the center of the wheel?
e) Write the equation that represents the wheel.
Click here to see answer by greenestamps(13198)

Question 1161206: A salesman sold $400 more than the rest of the sales staff. If the sales total for the day was $1600,how much did the rest of the sales staff sell?
Click here to see answer by Boreal(15235)

Question 1161270: Solve by elimination method.
An airplane travels 400 miles against the wind in 5 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

Click here to see answer by Alan3354(69443)

Question 1161294: If evaluate
Click here to see answer by ikleyn(52776)

Question 1161271: Solve by elimination method.
Jill is 27.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 3 kilometers per hour. They meet in 5 hours. How fast is Joe walking?

Click here to see answer by ankor@dixie-net.com(22740)

Question 1161269: Solve by elimination method.
A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower than the power boat. Find the speed of each boat
Click here to see answer by josgarithmetic(39616)

Question 1161267: solve by elimination method.
A salesman sold $400 more than the rest of the sales staff. If the sales total for the day was $1600,how much did the rest of the sales staff sell?
Click here to see answer by ikleyn(52776)

Question 1161357: A rectangle’s length is 3 yards less than 5 times of its width. If the rectangle’s perimeter must be between 18 and 90 yards, what is the range of its width? Use an inequality to solve this problem.
Click here to see answer by solver91311(24713)

Question 1161268: Solve by elimination method.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $120 for 3 days and 300 miles, while Mary was charged $210 for 5 days and 600 miles. What does Best Rental charge per day and per mile?

Click here to see answer by KMST(5328)

Question 1161406: Hank's winning margin in a board game was 806 points. The total points scored by Hank and his opponent was 1736. What was Hank's score?
Click here to see answer by josgarithmetic(39616)

Question 1161435: A rectangular room is
1.2
1.2
times as long as it is wide, and its perimeter is
30
30
meters. Find the dimension of the room.
Click here to see answer by ikleyn(52776)

Question 1161436: A rectangular room is 1.2 times as long as it is wide, and its perimeter is
30 meters. Find the dimension of the room.
Click here to see answer by ikleyn(52776)

Question 1161448: I came across this question and they solved it by using the bar model.
How do I solve this algebraically? Why do you add 6+10 to get 16?
Mr. Lee wants to buy 5 shirts. If he buys 3 shirts, he will have $6 left. If he gets all of them, he will be $10 short. How much money does Mr. Lee have?
2 units: 6+10=16
1 unit: 16/2=8
Mr. Lee has $30
Mr. Lee has money for 3 shirts and $6 extra
To buy two more shirts, Mr. Lee has to use $6 leftover and find another $10 he is short of.
Thanks in advance.

Click here to see answer by ikleyn(52776)

Question 1161475: Find an equation of the line containing the points (-0.8, -2) and (3, -0.6) what is the slope and equation of the line, find x and y intercept
Click here to see answer by josgarithmetic(39616)

Question 1161500: The cost of publishing a poster is $2000 for setting up the printing equipment, plus $3 per
poster printed. What is the total cost to produce 2000 posters?
Click here to see answer by Boreal(15235)

Question 1161540: Population of a particular bacterial colony; i.e. the number of cells at time t (hours) is given by the function (N(t)=N0^e^kt) where k is the growth constant
When this bacterium is grown under ideal laboratory conditions, the number of
cells in a culture doubles every 30 minutes. Find the value of k to 2 decimal
places
How Do I find K value for this question?
Click here to see answer by ikleyn(52776)

Question 1161566: Find and simplify f(x)=x2- 3x+ 4, given f(a+ h)- f(a).
Click here to see answer by MathLover1(20849)

Question 1161565: Find the perimeter of the geometric figure.
Rectangle: length3x2 + 6x + 16 width 6x2 - 2x+ 19
Click here to see answer by josgarithmetic(39616)

Question 1161564: Solve:
A lamp shade has the geometric form as shown. The total surface area of a lamp shade with a slant height s and top and bottom base radii of r2 and r1 is given byΔr12 + Δr22 + Δr1s + Δr2s. Find an equivalent expression for the total surface area by factoring out a common factor.
Click here to see answer by greenestamps(13198)

Question 1161563: Solve:
An automobile is traveling at61 ft/sec. The driver applies the brakes in such a way that the velocity decreases to zero according to the relationv(t) =61- 0.61t2, where t= time. Find an equivalent expression for v(t) by factoring out a factor with a negative coefficient.
Click here to see answer by KMST(5328)

Question 1161709: Help! Im stuck on this equation:

(note that these two equations are in the same question)
Please help!
Click here to see answer by josgarithmetic(39616)

Question 1161709: Help! Im stuck on this equation:

(note that these two equations are in the same question)
Please help!
Click here to see answer by ikleyn(52776)

Question 1161902: An automobile is traveling at61 ft/sec. The driver applies the brakes in such a way that the velocitydecreases to zero according to the relationv(t)=61-0.61t2, where t= time. Find an equivalentexpression for v(t) by factoring out a factor with a negative coefficient.
Click here to see answer by jim_thompson5910(35256)

Question 1161924: If the equation √(2x^2 )-√3x+k=0 with k a constant has two solutions sin θ and cos θ (0 ≤ θ ≤ π/2 ) then k = ?
Click here to see answer by solver91311(24713)

Question 1162000: Use a system of two equations in two variables to solve the problem.
At a store, ice cream cones cost $1.80 and sundaes cost $3.30. One day a total of 158 cones and sundaes were sold, and the receipts totaled $389.40. How many cones were sold?

Click here to see answer by ankor@dixie-net.com(22740)

Question 1162001: Use two equations in two variables to solve the problem.
The perimeter of the rectangular garden shown below is 80 meters. The width of the garden is two-thirds its length, find its area A.
Click here to see answer by ikleyn(52776)

Question 1162004: A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 40 kilograms of the 40% silver alloy?
50% alloy :
25% alloy :
Click here to see answer by ikleyn(52776)

Question 1162027: Hello:
How would I go about setting up an equation for this problem?
Ryan and Juan had $500 altogether. After Ryan spent $80, he had 3/5 as money as Juan.
How much money did Juan have
How much money did Ryan have at first?
Thanks in advance for your help.

Click here to see answer by solver91311(24713)

Question 1162045: 3(x-5)-2=6-(5-x)
Click here to see answer by josgarithmetic(39616)

Question 1162052: In a certain year, the number of Americans who died from heart disease was about 5 times the number who died from accidents. If the total number of deaths from these two causes was 960,000, how many Americans died from each cause in that year?
Click here to see answer by ikleyn(52776)

Question 1162071: How much money should a young married couple invest now at a 6% annual rate if they want to have $100,000 in the bank when they reach retirement age in 40 years? (See the present value formula below. Round your answer to the nearest dollar.)
Click here to see answer by ikleyn(52776)

Question 1162070: Use the illustration to find the volume of the bowling ball and the cardboard box it is packaged in when a = 6. You may leave π in your answer.
(unsure if you'll be able to see the picture that I will link, but it's basically a bowling ball in a box)
https://www.webassign.net/tgintroalgp4/5-1-144-alt.gif
Click here to see answer by Boreal(15235)

Question 1162089: To determine the number of fish in a lake, a park ranger catches 220 fish, tags them, and returns them to the lake. Later, 72 fish are caught, and it is found that 20 of them are tagged. Estimate the number of fish in the lake.
Click here to see answer by ikleyn(52776)

Question 1162088: Mara can type 39 words per minute. How many words would she type in 1/4 hour (15 minutes)?
Click here to see answer by Alan3354(69443)

Question 1162087: The current in a stream moves at a rate of 4 mph. If a boat travels 56 miles downstream in the same time that it takes to travel 28 miles upstream, what is the speed of the boat in still water?
Click here to see answer by ikleyn(52776)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580