The figure numbers are 1,2,3,4 and the corresponding areas are 2,4,7,11, respectively.  Write an equation for the pattern using n for the figure number.
119077
(the corresponding area for n) = (n(n+1)/2) +1.\n\nnote that the corresponding number is one plus the sum of all the numbers 1 to n.  that sum can be represented as\nn(n+1)/2.
608940
The pattern is +11, +5, +8, +11, +11\nThe next number could be 76 (+11) or the +5, +8 could begin to repeat meaning the next number could be 70 followed by 78
516125
1) We know from the formula for the area of a rectangle that A = B * H.\nWe know from the problem that B= H+3.  Substituting, we get A = H * H * 3, or 3H^2.\n\nHowever, we're not using the area of the painting, but the area of the border.  So this means\n100 = (B+2)(H+2) or BH + 2B + 2H + 4.  Substituting for B we get\n100 = H(H+3) + 2(H+3) + 2H + 4, or\n100 = H^2 + 3H + 2H + 6 + 2H + 4 = H^2 + 8H + 10.  \nI don't see a simple factoring for this, use the Quadratic Equation.\n\n2) 12X = 1.5Y and Y = 5X + 120.  Substitute for Y\n12X = 7.5X + 180\n4.5X = 180\nX = 40\nY = 320\nChecking, 12(40) = 1.5(320) = 480
571514
1) 120 words\n\n2)12345 (these represent teh letters) first make all the words with 1 at teh beginning then 2 then 3 and so on
324513
p=pennies, n=nickels, d=dimes\n3p= 3,  2p+1n=7,  2p+1d=12\n\n3n=15,  2n+1p=11,  2n+1d=20\n\n3d=30,  2d+1p=21,  2d+1n=25\n\n1p+1n+1d=16\nSorry, I could only come up with 10.  :)
377999
Regroup and add.  You got the 5n, so you should be able to get the other part!\n\nn + n - 1 + n - 2 + n + 7 + n - 11 = \nn + n + n + n + n - 1 - 2 + 7 - 11 =\n5n - 7\n\nNotice that -1 -2 - 11 = -14, add 7 to it and you get -7\n\nNRT
241988
1 1 1 2\n1 1 2 1\n1 2 1 1\n2 1 1 1\n\nNo other case is possible, So n(A)=4\n\n\n1 1 1 3\n1 1 3 1\n1 3 1 1\n3 1 1 1\n\n1 1 2 2\n1 2 1 2\n1 2 2 1\n\n2 1 1 2\n2 1 2 1\n2 2 1 1\n\nNo other possibility\nn(B)=10
531057
it is from a logic work sheet.  directions are find the next item in the pattern.  examples:  12321, 23432, 34543, 45654\na, z, b, y, c, x, d\ntam, tan, rib, rid, rat, raw, hip
567552
1.  (0,y)\n2.  (x,x) or (y,,y)\n3.  they are three whole numbers that will satisfy the pythagorean equation, a^2+b^2=c^2. ("^2" means raising the number to 2).  an example would be 3,4,5.\n4. 12\n\nFOrmulas\n\n1.volume:sphere= (4/3)*pi*r*r*r\n\ncone = (1/3)*pi*r*r*h\n\n2.circumference is 2*pi*r
179043
you count the number of times each figure appears (this has been asked many other times):\nfirst row: 1\nsecond row: one 1: 11\nthird row: two 1: 21\nfourth row: one 2 one 1: 1211\nfifth row: one 1 one 2 two 1: 111221\nsixth row: three 1 two 2 one 1: 312211\n\n... and so on ...
481172
Please double check the output because there is no pattern.  Also add the level of Math this is
546155
D)6\n\nNote the pattern:\nIf f(1) = a, f(2) = b, then\nf(3) = b-a\nf(4) = -a\nf(5) = -b\nf(6) = -b+a\nf(7) = a\nf(8) = b\n\nAt f(7), the pattern starts repeating.  Therefore, the six values are f(1) through f(6) above.\nThis really isn't a permutation/combination problem, but you can often find good answers here on Yahoo Answers!  If you have specific problems with which you have difficulty, why dont you post a few related ones in one question here?  I'm sure I or others should be able to help.\n\nYOUR FOLLOW-UP:\nThis is two small problems in one.\nFirst, find the # of ways to choose the order of the backgrounds.  We have 3 choices for the first one, then 2 choices for the second, then 1 left for the third.  Therefore, there are 3*2*1=6 ways to choose the order of the backgrounds.\n{ (b, e, r), (b, r, e), (e, b, r), (e, r, b), (r, b, e), ( r, e, b) }\nSecond, there would be 3*2*1 = 6 ways to interview the business people.  There would be 2*1 = 2 ways to interview the education people, and just 1 way to interview the recreation person.  So that would make 6*2*1 = 12 ways to interview the people after the background order is set.\n\nThe total number of ways is then 6*12=72 ways to interview all 6.
14470
Let No of square is N\nPerimeter = 2xN + 2 \n\nAssumptions:\nThey are arranged in a row.\nThey are of same size.\nThey are of UNIT size.
156601
2, 9, 16, 23, 30\n\nU(n+1) = Un + 7\n\nMoving through weeks on a calendar.\n\n\n\n50, 100, 200, 400\n\nU(n+1) = 2Un\n\nDoubling ingredients in a recipe.
617631
It's as simple as plugging in numbers.  The number 15 becomes the letter "a", the number 7 is "b", and the number 55 is "c".  Just substitute the number for the letter in the formula and solve.
307771
I'm assuming you mean an equation like the following where A,B,C,D,E,F,G,H and I are in the set {1-9} without any duplication.\n\nABC\nDEF +\n------\nGHI\n\nI used a site to solve this equation but it included 0 and came up with 1088 answers.  I then used Excel to remove all the answers that had 0 in them.  That resulted in the following 336 answers.  I'm therefore unsure of the differences in the counts between 140, 280 and 336... There is obviously something else unstated in your problem domain.\n\nHere are the 336 solutions to ABC+DEF=GHI\n173+286=459\n176+283=459\n183+276=459\n186+273=459\n273+186=459\n276+183=459\n283+176=459\n286+173=459\n173+295=468\n175+293=468\n193+275=468\n195+273=468\n273+195=468\n275+193=468\n293+175=468\n295+173=468\n127+359=486\n129+357=486\n157+329=486\n159+327=486\n327+159=486\n329+157=486\n357+129=486\n359+127=486\n127+368=495\n128+367=495\n167+328=495\n168+327=495\n327+168=495\n328+167=495\n367+128=495\n368+127=495\n162+387=549\n167+382=549\n182+367=549\n187+362=549\n362+187=549\n367+182=549\n382+167=549\n387+162=549\n128+439=567\n129+438=567\n138+429=567\n139+428=567\n218+349=567\n219+348=567\n248+319=567\n249+318=567\n318+249=567\n319+248=567\n348+219=567\n349+218=567\n428+139=567\n429+138=567\n438+129=567\n439+128=567\n182+394=576\n184+392=576\n192+384=576\n194+382=576\n382+194=576\n384+192=576\n392+184=576\n394+182=576\n216+378=594\n218+376=594\n276+318=594\n278+316=594\n316+278=594\n318+276=594\n376+218=594\n378+216=594\n152+487=639\n157+482=639\n182+457=639\n187+452=639\n452+187=639\n457+182=639\n482+157=639\n487+152=639\n251+397=648\n257+391=648\n291+357=648\n297+351=648\n351+297=648\n357+291=648\n391+257=648\n397+251=648\n218+439=657\n219+438=657\n238+419=657\n239+418=657\n418+239=657\n419+238=657\n438+219=657\n439+218=657\n182+493=675\n183+492=675\n192+483=675\n193+482=675\n281+394=675\n284+391=675\n291+384=675\n294+381=675\n381+294=675\n384+291=675\n391+284=675\n394+281=675\n482+193=675\n483+192=675\n492+183=675\n493+182=675\n215+478=693\n218+475=693\n275+418=693\n278+415=693\n415+278=693\n418+275=693\n475+218=693\n478+215=693\n143+586=729\n146+583=729\n183+546=729\n186+543=729\n543+186=729\n546+183=729\n583+146=729\n586+143=729\n142+596=738\n146+592=738\n192+546=738\n196+542=738\n542+196=738\n546+192=738\n592+146=738\n596+142=738\n124+659=783\n129+654=783\n154+629=783\n159+624=783\n214+569=783\n219+564=783\n264+519=783\n269+514=783\n514+269=783\n519+264=783\n564+219=783\n569+214=783\n624+159=783\n629+154=783\n654+129=783\n659+124=783\n134+658=792\n138+654=792\n154+638=792\n158+634=792\n634+158=792\n638+154=792\n654+138=792\n658+134=792\n243+576=819\n246+573=819\n273+546=819\n276+543=819\n352+467=819\n357+462=819\n362+457=819\n367+452=819\n452+367=819\n457+362=819\n462+357=819\n467+352=819\n543+276=819\n546+273=819\n573+246=819\n576+243=819\n142+695=837\n145+692=837\n192+645=837\n195+642=837\n241+596=837\n246+591=837\n291+546=837\n296+541=837\n541+296=837\n546+291=837\n591+246=837\n596+241=837\n642+195=837\n645+192=837\n692+145=837\n695+142=837\n317+529=846\n319+527=846\n327+519=846\n329+517=846\n517+329=846\n519+327=846\n527+319=846\n529+317=846\n125+739=864\n129+735=864\n135+729=864\n139+725=864\n271+593=864\n273+591=864\n291+573=864\n293+571=864\n571+293=864\n573+291=864\n591+273=864\n593+271=864\n725+139=864\n729+135=864\n735+129=864\n739+125=864\n214+659=873\n219+654=873\n254+619=873\n259+614=873\n614+259=873\n619+254=873\n654+219=873\n659+214=873\n234+657=891\n237+654=891\n254+637=891\n257+634=891\n324+567=891\n327+564=891\n364+527=891\n367+524=891\n524+367=891\n527+364=891\n564+327=891\n567+324=891\n634+257=891\n637+254=891\n654+237=891\n657+234=891\n243+675=918\n245+673=918\n273+645=918\n275+643=918\n342+576=918\n346+572=918\n372+546=918\n376+542=918\n542+376=918\n546+372=918\n572+346=918\n576+342=918\n643+275=918\n645+273=918\n673+245=918\n675+243=918\n341+586=927\n346+581=927\n381+546=927\n386+541=927\n541+386=927\n546+381=927\n581+346=927\n586+341=927\n152+784=936
650821
draw a picture of the graph over the specified interval.  divide the graph into vertical rectangles.  the area under the curve will be the sum of the areas of the rectangles.  saying that youve made "n" rectangles, the only way to get the exact area is to find the sum for the limit as n approaches infinity.  work from that concept.  if you already knew that, or need more help or something, email me and i can give you more steps and a much more detailed description.  that would take a really long time though so im gonna see if this helps first.