New!
Get regular updates about newly solved problems
via algebra.com's RSS system.
Recent problems solved by 'stanbon'
stanbon answered: 57135 problems
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 , 4740..4769 , 4770..4799 , 4800..4829 , 4830..4859 , 4860..4889 , 4890..4919 , 4920..4949 , 4950..4979 , 4980..5009 , 5010..5039 , 5040..5069 , 5070..5099 , 5100..5129 , 5130..5159 , 5160..5189 , 5190..5219 , 5220..5249 , 5250..5279 , 5280..5309 , 5310..5339 , 5340..5369 , 5370..5399 , 5400..5429 , 5430..5459 , 5460..5489 , 5490..5519 , 5520..5549 , 5550..5579 , 5580..5609 , 5610..5639 , 5640..5669 , 5670..5699 , 5700..5729 , 5730..5759 , 5760..5789 , 5790..5819 , 5820..5849 , 5850..5879 , 5880..5909 , 5910..5939 , 5940..5969 , 5970..5999 , 6000..6029 , 6030..6059 , 6060..6089 , 6090..6119 , 6120..6149 , 6150..6179 , 6180..6209 , 6210..6239 , 6240..6269 , 6270..6299 , 6300..6329 , 6330..6359 , 6360..6389 , 6390..6419 , 6420..6449 , 6450..6479 , 6480..6509 , 6510..6539 , 6540..6569 , 6570..6599 , 6600..6629 , 6630..6659 , 6660..6689 , 6690..6719 , 6720..6749 , 6750..6779 , 6780..6809 , 6810..6839 , 6840..6869 , 6870..6899 , 6900..6929 , 6930..6959 , 6960..6989 , 6990..7019 , 7020..7049 , 7050..7079 , 7080..7109 , 7110..7139 , 7140..7169 , 7170..7199 , 7200..7229 , 7230..7259 , 7260..7289 , 7290..7319 , 7320..7349 , 7350..7379 , 7380..7409 , 7410..7439 , 7440..7469 , 7470..7499 , 7500..7529 , 7530..7559 , 7560..7589 , 7590..7619 , 7620..7649 , 7650..7679 , 7680..7709 , 7710..7739 , 7740..7769 , 7770..7799 , 7800..7829 , 7830..7859 , 7860..7889 , 7890..7919 , 7920..7949 , 7950..7979 , 7980..8009 , 8010..8039 , 8040..8069 , 8070..8099 , 8100..8129 , 8130..8159 , 8160..8189 , 8190..8219 , 8220..8249 , 8250..8279 , 8280..8309 , 8310..8339 , 8340..8369 , 8370..8399 , 8400..8429 , 8430..8459 , 8460..8489 , 8490..8519 , 8520..8549 , 8550..8579 , 8580..8609 , 8610..8639 , 8640..8669 , 8670..8699 , 8700..8729 , 8730..8759 , 8760..8789 , 8790..8819 , 8820..8849 , 8850..8879 , 8880..8909 , 8910..8939 , 8940..8969 , 8970..8999 , 9000..9029 , 9030..9059 , 9060..9089 , 9090..9119 , 9120..9149 , 9150..9179 , 9180..9209 , 9210..9239 , 9240..9269 , 9270..9299 , 9300..9329 , 9330..9359 , 9360..9389 , 9390..9419 , 9420..9449 , 9450..9479 , 9480..9509 , 9510..9539 , 9540..9569 , 9570..9599 , 9600..9629 , 9630..9659 , 9660..9689 , 9690..9719 , 9720..9749 , 9750..9779 , 9780..9809 , 9810..9839 , 9840..9869 , 9870..9899 , 9900..9929 , 9930..9959 , 9960..9989 , 9990..10019 , 10020..10049 , 10050..10079 , 10080..10109 , 10110..10139 , 10140..10169 , 10170..10199 , 10200..10229 , 10230..10259 , 10260..10289 , 10290..10319 , 10320..10349 , 10350..10379 , 10380..10409 , 10410..10439 , 10440..10469 , 10470..10499 , 10500..10529 , 10530..10559 , 10560..10589 , 10590..10619 , 10620..10649 , 10650..10679 , 10680..10709 , 10710..10739 , 10740..10769 , 10770..10799 , 10800..10829 , 10830..10859 , 10860..10889 , 10890..10919 , 10920..10949 , 10950..10979 , 10980..11009 , 11010..11039 , 11040..11069 , 11070..11099 , 11100..11129 , 11130..11159 , 11160..11189 , 11190..11219 , 11220..11249 , 11250..11279 , 11280..11309 , 11310..11339 , 11340..11369 , 11370..11399 , 11400..11429 , 11430..11459 , 11460..11489 , 11490..11519 , 11520..11549 , 11550..11579 , 11580..11609 , 11610..11639 , 11640..11669 , 11670..11699 , 11700..11729 , 11730..11759 , 11760..11789 , 11790..11819 , 11820..11849 , 11850..11879 , 11880..11909 , 11910..11939 , 11940..11969 , 11970..11999 , 12000..12029 , 12030..12059 , 12060..12089 , 12090..12119 , 12120..12149 , 12150..12179 , 12180..12209 , 12210..12239 , 12240..12269 , 12270..12299 , 12300..12329 , 12330..12359 , 12360..12389 , 12390..12419 , 12420..12449 , 12450..12479 , 12480..12509 , 12510..12539 , 12540..12569 , 12570..12599 , 12600..12629 , 12630..12659 , 12660..12689 , 12690..12719 , 12720..12749 , 12750..12779 , 12780..12809 , 12810..12839 , 12840..12869 , 12870..12899 , 12900..12929 , 12930..12959 , 12960..12989 , 12990..13019 , 13020..13049 , 13050..13079 , 13080..13109 , 13110..13139 , 13140..13169 , 13170..13199 , 13200..13229 , 13230..13259 , 13260..13289 , 13290..13319 , 13320..13349 , 13350..13379 , 13380..13409 , 13410..13439 , 13440..13469 , 13470..13499 , 13500..13529 , 13530..13559 , 13560..13589 , 13590..13619 , 13620..13649 , 13650..13679 , 13680..13709 , 13710..13739 , 13740..13769 , 13770..13799 , 13800..13829 , 13830..13859 , 13860..13889 , 13890..13919 , 13920..13949 , 13950..13979 , 13980..14009 , 14010..14039 , 14040..14069 , 14070..14099 , 14100..14129 , 14130..14159 , 14160..14189 , 14190..14219 , 14220..14249 , 14250..14279 , 14280..14309 , 14310..14339 , 14340..14369 , 14370..14399 , 14400..14429 , 14430..14459 , 14460..14489 , 14490..14519 , 14520..14549 , 14550..14579 , 14580..14609 , 14610..14639 , 14640..14669 , 14670..14699 , 14700..14729 , 14730..14759 , 14760..14789 , 14790..14819 , 14820..14849 , 14850..14879 , 14880..14909 , 14910..14939 , 14940..14969 , 14970..14999 , 15000..15029 , 15030..15059 , 15060..15089 , 15090..15119 , 15120..15149 , 15150..15179 , 15180..15209 , 15210..15239 , 15240..15269 , 15270..15299 , 15300..15329 , 15330..15359 , 15360..15389 , 15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659 , 15660..15689 , 15690..15719 , 15720..15749 , 15750..15779 , 15780..15809 , 15810..15839 , 15840..15869 , 15870..15899 , 15900..15929 , 15930..15959 , 15960..15989 , 15990..16019 , 16020..16049 , 16050..16079 , 16080..16109 , 16110..16139 , 16140..16169 , 16170..16199 , 16200..16229 , 16230..16259 , 16260..16289 , 16290..16319 , 16320..16349 , 16350..16379 , 16380..16409 , 16410..16439 , 16440..16469 , 16470..16499 , 16500..16529 , 16530..16559 , 16560..16589 , 16590..16619 , 16620..16649 , 16650..16679 , 16680..16709 , 16710..16739 , 16740..16769 , 16770..16799 , 16800..16829 , 16830..16859 , 16860..16889 , 16890..16919 , 16920..16949 , 16950..16979 , 16980..17009 , 17010..17039 , 17040..17069 , 17070..17099 , 17100..17129 , 17130..17159 , 17160..17189 , 17190..17219 , 17220..17249 , 17250..17279 , 17280..17309 , 17310..17339 , 17340..17369 , 17370..17399 , 17400..17429 , 17430..17459 , 17460..17489 , 17490..17519 , 17520..17549 , 17550..17579 , 17580..17609 , 17610..17639 , 17640..17669 , 17670..17699 , 17700..17729 , 17730..17759 , 17760..17789 , 17790..17819 , 17820..17849 , 17850..17879 , 17880..17909 , 17910..17939 , 17940..17969 , 17970..17999 , 18000..18029 , 18030..18059 , 18060..18089 , 18090..18119 , 18120..18149 , 18150..18179 , 18180..18209 , 18210..18239 , 18240..18269 , 18270..18299 , 18300..18329 , 18330..18359 , 18360..18389 , 18390..18419 , 18420..18449 , 18450..18479 , 18480..18509 , 18510..18539 , 18540..18569 , 18570..18599 , 18600..18629 , 18630..18659 , 18660..18689 , 18690..18719 , 18720..18749 , 18750..18779 , 18780..18809 , 18810..18839 , 18840..18869 , 18870..18899 , 18900..18929 , 18930..18959 , 18960..18989 , 18990..19019 , 19020..19049 , 19050..19079 , 19080..19109 , 19110..19139 , 19140..19169 , 19170..19199 , 19200..19229 , 19230..19259 , 19260..19289 , 19290..19319 , 19320..19349 , 19350..19379 , 19380..19409 , 19410..19439 , 19440..19469 , 19470..19499 , 19500..19529 , 19530..19559 , 19560..19589 , 19590..19619 , 19620..19649 , 19650..19679 , 19680..19709 , 19710..19739 , 19740..19769 , 19770..19799 , 19800..19829 , 19830..19859 , 19860..19889 , 19890..19919 , 19920..19949 , 19950..19979 , 19980..20009 , 20010..20039 , 20040..20069 , 20070..20099 , 20100..20129 , 20130..20159 , 20160..20189 , 20190..20219 , 20220..20249 , 20250..20279 , 20280..20309 , 20310..20339 , 20340..20369 , 20370..20399 , 20400..20429 , 20430..20459 , 20460..20489 , 20490..20519 , 20520..20549 , 20550..20579 , 20580..20609 , 20610..20639 , 20640..20669 , 20670..20699 , 20700..20729 , 20730..20759 , 20760..20789 , 20790..20819 , 20820..20849 , 20850..20879 , 20880..20909 , 20910..20939 , 20940..20969 , 20970..20999 , 21000..21029 , 21030..21059 , 21060..21089 , 21090..21119 , 21120..21149 , 21150..21179 , 21180..21209 , 21210..21239 , 21240..21269 , 21270..21299 , 21300..21329 , 21330..21359 , 21360..21389 , 21390..21419 , 21420..21449 , 21450..21479 , 21480..21509 , 21510..21539 , 21540..21569 , 21570..21599 , 21600..21629 , 21630..21659 , 21660..21689 , 21690..21719 , 21720..21749 , 21750..21779 , 21780..21809 , 21810..21839 , 21840..21869 , 21870..21899 , 21900..21929 , 21930..21959 , 21960..21989 , 21990..22019 , 22020..22049 , 22050..22079 , 22080..22109 , 22110..22139 , 22140..22169 , 22170..22199 , 22200..22229 , 22230..22259 , 22260..22289 , 22290..22319 , 22320..22349 , 22350..22379 , 22380..22409 , 22410..22439 , 22440..22469 , 22470..22499 , 22500..22529 , 22530..22559 , 22560..22589 , 22590..22619 , 22620..22649 , 22650..22679 , 22680..22709 , 22710..22739 , 22740..22769 , 22770..22799 , 22800..22829 , 22830..22859 , 22860..22889 , 22890..22919 , 22920..22949 , 22950..22979 , 22980..23009 , 23010..23039 , 23040..23069 , 23070..23099 , 23100..23129 , 23130..23159 , 23160..23189 , 23190..23219 , 23220..23249 , 23250..23279 , 23280..23309 , 23310..23339 , 23340..23369 , 23370..23399 , 23400..23429 , 23430..23459 , 23460..23489 , 23490..23519 , 23520..23549 , 23550..23579 , 23580..23609 , 23610..23639 , 23640..23669 , 23670..23699 , 23700..23729 , 23730..23759 , 23760..23789 , 23790..23819 , 23820..23849 , 23850..23879 , 23880..23909 , 23910..23939 , 23940..23969 , 23970..23999 , 24000..24029 , 24030..24059 , 24060..24089 , 24090..24119 , 24120..24149 , 24150..24179 , 24180..24209 , 24210..24239 , 24240..24269 , 24270..24299 , 24300..24329 , 24330..24359 , 24360..24389 , 24390..24419 , 24420..24449 , 24450..24479 , 24480..24509 , 24510..24539 , 24540..24569 , 24570..24599 , 24600..24629 , 24630..24659 , 24660..24689 , 24690..24719 , 24720..24749 , 24750..24779 , 24780..24809 , 24810..24839 , 24840..24869 , 24870..24899 , 24900..24929 , 24930..24959 , 24960..24989 , 24990..25019 , 25020..25049 , 25050..25079 , 25080..25109 , 25110..25139 , 25140..25169 , 25170..25199 , 25200..25229 , 25230..25259 , 25260..25289 , 25290..25319 , 25320..25349 , 25350..25379 , 25380..25409 , 25410..25439 , 25440..25469 , 25470..25499 , 25500..25529 , 25530..25559 , 25560..25589 , 25590..25619 , 25620..25649 , 25650..25679 , 25680..25709 , 25710..25739 , 25740..25769 , 25770..25799 , 25800..25829 , 25830..25859 , 25860..25889 , 25890..25919 , 25920..25949 , 25950..25979 , 25980..26009 , 26010..26039 , 26040..26069 , 26070..26099 , 26100..26129 , 26130..26159 , 26160..26189 , 26190..26219 , 26220..26249 , 26250..26279 , 26280..26309 , 26310..26339 , 26340..26369 , 26370..26399 , 26400..26429 , 26430..26459 , 26460..26489 , 26490..26519 , 26520..26549 , 26550..26579 , 26580..26609 , 26610..26639 , 26640..26669 , 26670..26699 , 26700..26729 , 26730..26759 , 26760..26789 , 26790..26819 , 26820..26849 , 26850..26879 , 26880..26909 , 26910..26939 , 26940..26969 , 26970..26999 , 27000..27029 , 27030..27059 , 27060..27089 , 27090..27119 , 27120..27149 , 27150..27179 , 27180..27209 , 27210..27239 , 27240..27269 , 27270..27299 , 27300..27329 , 27330..27359 , 27360..27389 , 27390..27419 , 27420..27449 , 27450..27479 , 27480..27509 , 27510..27539 , 27540..27569 , 27570..27599 , 27600..27629 , 27630..27659 , 27660..27689 , 27690..27719 , 27720..27749 , 27750..27779 , 27780..27809 , 27810..27839 , 27840..27869 , 27870..27899 , 27900..27929 , 27930..27959 , 27960..27989 , 27990..28019 , 28020..28049 , 28050..28079 , 28080..28109 , 28110..28139 , 28140..28169 , 28170..28199 , 28200..28229 , 28230..28259 , 28260..28289 , 28290..28319 , 28320..28349 , 28350..28379 , 28380..28409 , 28410..28439 , 28440..28469 , 28470..28499 , 28500..28529 , 28530..28559 , 28560..28589 , 28590..28619 , 28620..28649 , 28650..28679 , 28680..28709 , 28710..28739 , 28740..28769 , 28770..28799 , 28800..28829 , 28830..28859 , 28860..28889 , 28890..28919 , 28920..28949 , 28950..28979 , 28980..29009 , 29010..29039 , 29040..29069 , 29070..29099 , 29100..29129 , 29130..29159 , 29160..29189 , 29190..29219 , 29220..29249 , 29250..29279 , 29280..29309 , 29310..29339 , 29340..29369 , 29370..29399 , 29400..29429 , 29430..29459 , 29460..29489 , 29490..29519 , 29520..29549 , 29550..29579 , 29580..29609 , 29610..29639 , 29640..29669 , 29670..29699 , 29700..29729 , 29730..29759 , 29760..29789 , 29790..29819 , 29820..29849 , 29850..29879 , 29880..29909 , 29910..29939 , 29940..29969 , 29970..29999 , 30000..30029 , 30030..30059 , 30060..30089 , 30090..30119 , 30120..30149 , 30150..30179 , 30180..30209 , 30210..30239 , 30240..30269 , 30270..30299 , 30300..30329 , 30330..30359 , 30360..30389 , 30390..30419 , 30420..30449 , 30450..30479 , 30480..30509 , 30510..30539 , 30540..30569 , 30570..30599 , 30600..30629 , 30630..30659 , 30660..30689 , 30690..30719 , 30720..30749 , 30750..30779 , 30780..30809 , 30810..30839 , 30840..30869 , 30870..30899 , 30900..30929 , 30930..30959 , 30960..30989 , 30990..31019 , 31020..31049 , 31050..31079 , 31080..31109 , 31110..31139 , 31140..31169 , 31170..31199 , 31200..31229 , 31230..31259 , 31260..31289 , 31290..31319 , 31320..31349 , 31350..31379 , 31380..31409 , 31410..31439 , 31440..31469 , 31470..31499 , 31500..31529 , 31530..31559 , 31560..31589 , 31590..31619 , 31620..31649 , 31650..31679 , 31680..31709 , 31710..31739 , 31740..31769 , 31770..31799 , 31800..31829 , 31830..31859 , 31860..31889 , 31890..31919 , 31920..31949 , 31950..31979 , 31980..32009 , 32010..32039 , 32040..32069 , 32070..32099 , 32100..32129 , 32130..32159 , 32160..32189 , 32190..32219 , 32220..32249 , 32250..32279 , 32280..32309 , 32310..32339 , 32340..32369 , 32370..32399 , 32400..32429 , 32430..32459 , 32460..32489 , 32490..32519 , 32520..32549 , 32550..32579 , 32580..32609 , 32610..32639 , 32640..32669 , 32670..32699 , 32700..32729 , 32730..32759 , 32760..32789 , 32790..32819 , 32820..32849 , 32850..32879 , 32880..32909 , 32910..32939 , 32940..32969 , 32970..32999 , 33000..33029 , 33030..33059 , 33060..33089 , 33090..33119 , 33120..33149 , 33150..33179 , 33180..33209 , 33210..33239 , 33240..33269 , 33270..33299 , 33300..33329 , 33330..33359 , 33360..33389 , 33390..33419 , 33420..33449 , 33450..33479 , 33480..33509 , 33510..33539 , 33540..33569 , 33570..33599 , 33600..33629 , 33630..33659 , 33660..33689 , 33690..33719 , 33720..33749 , 33750..33779 , 33780..33809 , 33810..33839 , 33840..33869 , 33870..33899 , 33900..33929 , 33930..33959 , 33960..33989 , 33990..34019 , 34020..34049 , 34050..34079 , 34080..34109 , 34110..34139 , 34140..34169 , 34170..34199 , 34200..34229 , 34230..34259 , 34260..34289 , 34290..34319 , 34320..34349 , 34350..34379 , 34380..34409 , 34410..34439 , 34440..34469 , 34470..34499 , 34500..34529 , 34530..34559 , 34560..34589 , 34590..34619 , 34620..34649 , 34650..34679 , 34680..34709 , 34710..34739 , 34740..34769 , 34770..34799 , 34800..34829 , 34830..34859 , 34860..34889 , 34890..34919 , 34920..34949 , 34950..34979 , 34980..35009 , 35010..35039 , 35040..35069 , 35070..35099 , 35100..35129 , 35130..35159 , 35160..35189 , 35190..35219 , 35220..35249 , 35250..35279 , 35280..35309 , 35310..35339 , 35340..35369 , 35370..35399 , 35400..35429 , 35430..35459 , 35460..35489 , 35490..35519 , 35520..35549 , 35550..35579 , 35580..35609 , 35610..35639 , 35640..35669 , 35670..35699 , 35700..35729 , 35730..35759 , 35760..35789 , 35790..35819 , 35820..35849 , 35850..35879 , 35880..35909 , 35910..35939 , 35940..35969 , 35970..35999 , 36000..36029 , 36030..36059 , 36060..36089 , 36090..36119 , 36120..36149 , 36150..36179 , 36180..36209 , 36210..36239 , 36240..36269 , 36270..36299 , 36300..36329 , 36330..36359 , 36360..36389 , 36390..36419 , 36420..36449 , 36450..36479 , 36480..36509 , 36510..36539 , 36540..36569 , 36570..36599 , 36600..36629 , 36630..36659 , 36660..36689 , 36690..36719 , 36720..36749 , 36750..36779 , 36780..36809 , 36810..36839 , 36840..36869 , 36870..36899 , 36900..36929 , 36930..36959 , 36960..36989 , 36990..37019 , 37020..37049 , 37050..37079 , 37080..37109 , 37110..37139 , 37140..37169 , 37170..37199 , 37200..37229 , 37230..37259 , 37260..37289 , 37290..37319 , 37320..37349 , 37350..37379 , 37380..37409 , 37410..37439 , 37440..37469 , 37470..37499 , 37500..37529 , 37530..37559 , 37560..37589 , 37590..37619 , 37620..37649 , 37650..37679 , 37680..37709 , 37710..37739 , 37740..37769 , 37770..37799 , 37800..37829 , 37830..37859 , 37860..37889 , 37890..37919 , 37920..37949 , 37950..37979 , 37980..38009 , 38010..38039 , 38040..38069 , 38070..38099 , 38100..38129 , 38130..38159 , 38160..38189 , 38190..38219 , 38220..38249 , 38250..38279 , 38280..38309 , 38310..38339 , 38340..38369 , 38370..38399 , 38400..38429 , 38430..38459 , 38460..38489 , 38490..38519 , 38520..38549 , 38550..38579 , 38580..38609 , 38610..38639 , 38640..38669 , 38670..38699 , 38700..38729 , 38730..38759 , 38760..38789 , 38790..38819 , 38820..38849 , 38850..38879 , 38880..38909 , 38910..38939 , 38940..38969 , 38970..38999 , 39000..39029 , 39030..39059 , 39060..39089 , 39090..39119 , 39120..39149 , 39150..39179 , 39180..39209 , 39210..39239 , 39240..39269 , 39270..39299 , 39300..39329 , 39330..39359 , 39360..39389 , 39390..39419 , 39420..39449 , 39450..39479 , 39480..39509 , 39510..39539 , 39540..39569 , 39570..39599 , 39600..39629 , 39630..39659 , 39660..39689 , 39690..39719 , 39720..39749 , 39750..39779 , 39780..39809 , 39810..39839 , 39840..39869 , 39870..39899 , 39900..39929 , 39930..39959 , 39960..39989 , 39990..40019 , 40020..40049 , 40050..40079 , 40080..40109 , 40110..40139 , 40140..40169 , 40170..40199 , 40200..40229 , 40230..40259 , 40260..40289 , 40290..40319 , 40320..40349 , 40350..40379 , 40380..40409 , 40410..40439 , 40440..40469 , 40470..40499 , 40500..40529 , 40530..40559 , 40560..40589 , 40590..40619 , 40620..40649 , 40650..40679 , 40680..40709 , 40710..40739 , 40740..40769 , 40770..40799 , 40800..40829 , 40830..40859 , 40860..40889 , 40890..40919 , 40920..40949 , 40950..40979 , 40980..41009 , 41010..41039 , 41040..41069 , 41070..41099 , 41100..41129 , 41130..41159 , 41160..41189 , 41190..41219 , 41220..41249 , 41250..41279 , 41280..41309 , 41310..41339 , 41340..41369 , 41370..41399 , 41400..41429 , 41430..41459 , 41460..41489 , 41490..41519 , 41520..41549 , 41550..41579 , 41580..41609 , 41610..41639 , 41640..41669 , 41670..41699 , 41700..41729 , 41730..41759 , 41760..41789 , 41790..41819 , 41820..41849 , 41850..41879 , 41880..41909 , 41910..41939 , 41940..41969 , 41970..41999 , 42000..42029 , 42030..42059 , 42060..42089 , 42090..42119 , 42120..42149 , 42150..42179 , 42180..42209 , 42210..42239 , 42240..42269 , 42270..42299 , 42300..42329 , 42330..42359 , 42360..42389 , 42390..42419 , 42420..42449 , 42450..42479 , 42480..42509 , 42510..42539 , 42540..42569 , 42570..42599 , 42600..42629 , 42630..42659 , 42660..42689 , 42690..42719 , 42720..42749 , 42750..42779 , 42780..42809 , 42810..42839 , 42840..42869 , 42870..42899 , 42900..42929 , 42930..42959 , 42960..42989 , 42990..43019 , 43020..43049 , 43050..43079 , 43080..43109 , 43110..43139 , 43140..43169 , 43170..43199 , 43200..43229 , 43230..43259 , 43260..43289 , 43290..43319 , 43320..43349 , 43350..43379 , 43380..43409 , 43410..43439 , 43440..43469 , 43470..43499 , 43500..43529 , 43530..43559 , 43560..43589 , 43590..43619 , 43620..43649 , 43650..43679 , 43680..43709 , 43710..43739 , 43740..43769 , 43770..43799 , 43800..43829 , 43830..43859 , 43860..43889 , 43890..43919 , 43920..43949 , 43950..43979 , 43980..44009 , 44010..44039 , 44040..44069 , 44070..44099 , 44100..44129 , 44130..44159 , 44160..44189 , 44190..44219 , 44220..44249 , 44250..44279 , 44280..44309 , 44310..44339 , 44340..44369 , 44370..44399 , 44400..44429 , 44430..44459 , 44460..44489 , 44490..44519 , 44520..44549 , 44550..44579 , 44580..44609 , 44610..44639 , 44640..44669 , 44670..44699 , 44700..44729 , 44730..44759 , 44760..44789 , 44790..44819 , 44820..44849 , 44850..44879 , 44880..44909 , 44910..44939 , 44940..44969 , 44970..44999 , 45000..45029 , 45030..45059 , 45060..45089 , 45090..45119 , 45120..45149 , 45150..45179 , 45180..45209 , 45210..45239 , 45240..45269 , 45270..45299 , 45300..45329 , 45330..45359 , 45360..45389 , 45390..45419 , 45420..45449 , 45450..45479 , 45480..45509 , 45510..45539 , 45540..45569 , 45570..45599 , 45600..45629 , 45630..45659 , 45660..45689 , 45690..45719 , 45720..45749 , 45750..45779 , 45780..45809 , 45810..45839 , 45840..45869 , 45870..45899 , 45900..45929 , 45930..45959 , 45960..45989 , 45990..46019 , 46020..46049 , 46050..46079 , 46080..46109 , 46110..46139 , 46140..46169 , 46170..46199 , 46200..46229 , 46230..46259 , 46260..46289 , 46290..46319 , 46320..46349 , 46350..46379 , 46380..46409 , 46410..46439 , 46440..46469 , 46470..46499 , 46500..46529 , 46530..46559 , 46560..46589 , 46590..46619 , 46620..46649 , 46650..46679 , 46680..46709 , 46710..46739 , 46740..46769 , 46770..46799 , 46800..46829 , 46830..46859 , 46860..46889 , 46890..46919 , 46920..46949 , 46950..46979 , 46980..47009 , 47010..47039 , 47040..47069 , 47070..47099 , 47100..47129 , 47130..47159 , 47160..47189 , 47190..47219 , 47220..47249 , 47250..47279 , 47280..47309 , 47310..47339 , 47340..47369 , 47370..47399 , 47400..47429 , 47430..47459 , 47460..47489 , 47490..47519 , 47520..47549 , 47550..47579 , 47580..47609 , 47610..47639 , 47640..47669 , 47670..47699 , 47700..47729 , 47730..47759 , 47760..47789 , 47790..47819 , 47820..47849 , 47850..47879 , 47880..47909 , 47910..47939 , 47940..47969 , 47970..47999 , 48000..48029 , 48030..48059 , 48060..48089 , 48090..48119 , 48120..48149 , 48150..48179 , 48180..48209 , 48210..48239 , 48240..48269 , 48270..48299 , 48300..48329 , 48330..48359 , 48360..48389 , 48390..48419 , 48420..48449 , 48450..48479 , 48480..48509 , 48510..48539 , 48540..48569 , 48570..48599 , 48600..48629 , 48630..48659 , 48660..48689 , 48690..48719 , 48720..48749 , 48750..48779 , 48780..48809 , 48810..48839 , 48840..48869 , 48870..48899 , 48900..48929 , 48930..48959 , 48960..48989 , 48990..49019 , 49020..49049 , 49050..49079 , 49080..49109 , 49110..49139 , 49140..49169 , 49170..49199 , 49200..49229 , 49230..49259 , 49260..49289 , 49290..49319 , 49320..49349 , 49350..49379 , 49380..49409 , 49410..49439 , 49440..49469 , 49470..49499 , 49500..49529 , 49530..49559 , 49560..49589 , 49590..49619 , 49620..49649 , 49650..49679 , 49680..49709 , 49710..49739 , 49740..49769 , 49770..49799 , 49800..49829 , 49830..49859 , 49860..49889 , 49890..49919 , 49920..49949 , 49950..49979 , 49980..50009 , 50010..50039 , 50040..50069 , 50070..50099 , 50100..50129 , 50130..50159 , 50160..50189 , 50190..50219 , 50220..50249 , 50250..50279 , 50280..50309 , 50310..50339 , 50340..50369 , 50370..50399 , 50400..50429 , 50430..50459 , 50460..50489 , 50490..50519 , 50520..50549 , 50550..50579 , 50580..50609 , 50610..50639 , 50640..50669 , 50670..50699 , 50700..50729 , 50730..50759 , 50760..50789 , 50790..50819 , 50820..50849 , 50850..50879 , 50880..50909 , 50910..50939 , 50940..50969 , 50970..50999 , 51000..51029 , 51030..51059 , 51060..51089 , 51090..51119 , 51120..51149 , 51150..51179 , 51180..51209 , 51210..51239 , 51240..51269 , 51270..51299 , 51300..51329 , 51330..51359 , 51360..51389 , 51390..51419 , 51420..51449 , 51450..51479 , 51480..51509 , 51510..51539 , 51540..51569 , 51570..51599 , 51600..51629 , 51630..51659 , 51660..51689 , 51690..51719 , 51720..51749 , 51750..51779 , 51780..51809 , 51810..51839 , 51840..51869 , 51870..51899 , 51900..51929 , 51930..51959 , 51960..51989 , 51990..52019 , 52020..52049 , 52050..52079 , 52080..52109 , 52110..52139 , 52140..52169 , 52170..52199 , 52200..52229 , 52230..52259 , 52260..52289 , 52290..52319 , 52320..52349 , 52350..52379 , 52380..52409 , 52410..52439 , 52440..52469 , 52470..52499 , 52500..52529 , 52530..52559 , 52560..52589 , 52590..52619 , 52620..52649 , 52650..52679 , 52680..52709 , 52710..52739 , 52740..52769 , 52770..52799 , 52800..52829 , 52830..52859 , 52860..52889 , 52890..52919 , 52920..52949 , 52950..52979 , 52980..53009 , 53010..53039 , 53040..53069 , 53070..53099 , 53100..53129 , 53130..53159 , 53160..53189 , 53190..53219 , 53220..53249 , 53250..53279 , 53280..53309 , 53310..53339 , 53340..53369 , 53370..53399 , 53400..53429 , 53430..53459 , 53460..53489 , 53490..53519 , 53520..53549 , 53550..53579 , 53580..53609 , 53610..53639 , 53640..53669 , 53670..53699 , 53700..53729 , 53730..53759 , 53760..53789 , 53790..53819 , 53820..53849 , 53850..53879 , 53880..53909 , 53910..53939 , 53940..53969 , 53970..53999 , 54000..54029 , 54030..54059 , 54060..54089 , 54090..54119 , 54120..54149 , 54150..54179 , 54180..54209 , 54210..54239 , 54240..54269 , 54270..54299 , 54300..54329 , 54330..54359 , 54360..54389 , 54390..54419 , 54420..54449 , 54450..54479 , 54480..54509 , 54510..54539 , 54540..54569 , 54570..54599 , 54600..54629 , 54630..54659 , 54660..54689 , 54690..54719 , 54720..54749 , 54750..54779 , 54780..54809 , 54810..54839 , 54840..54869 , 54870..54899 , 54900..54929 , 54930..54959 , 54960..54989 , 54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>Next
Exponential-and-logarithmic-functions/170020: Please help me with this problem:
If (-10,10) is on the graph y=f(x), what point do you know is on the graph of
f(1/2(x))?
Thank you.
1 solutions
Answer 125631 by stanbon(57203)   on 2008-11-29 21:02:24 (Show Source):
You can put this solution on YOUR website!If (-10,10) is on the graph y=f(x), what point do you know is on the graph of
f((1/2)(x))?
--------------------
f(-10) = 10
f((1/2)(-20)) = 10
---------------
The point (-20,10) is on the graph of f((1/2)x)
================================================
Cheers,
Stan H.
|
percentage/170174: In 1992 the cost of stamps went up $.15 to $.18. What is the percent increase?
1 solutions
Answer 125615 by stanbon(57203) on 2008-11-29 20:10:00 (Show Source):
You can put this solution on YOUR website!In 1992 the cost of stamps went up $.15 to $.18. What is the percent increase?
-----------------------------------------
Quantity Increase: 0.18 - 0.15 = 3 cents
Percent increase: 3/15 = 1/5 = 20%
-----------------------------
Cheers,
Stan H.
|
Mixture_Word_Problems/170153: A GROCER MIXES 6 POUNDS OF COFFEE THAT IS 60% COLUMBIAN WITH ONE THAT 80% COLUMBIAN HOW MANY POUNDS OF THE SECOND TYPE SHOULD BE USED TO OBTAIN A MIXTURE THAT IS 78% COLUMBIAN?
1 solutions
Answer 125601 by stanbon(57203) on 2008-11-29 18:34:01 (Show Source):
You can put this solution on YOUR website!A GROCER MIXES 6 POUNDS OF COFFEE THAT IS 60% COLUMBIAN WITH ONE THAT 80% COLUMBIAN HOW MANY POUNDS OF THE SECOND TYPE SHOULD BE USED TO OBTAIN A MIXTURE THAT IS 78% COLUMBIAN?
--------------------
Columbian Equation: 0.60*6 + 0.80x = 0.78(6+x)
Multiply thru by 100 to get:
60*6 + 80(x) = 78*6 + 78x
2x = 18*6
x = 9*6 = 54 lbs. (amt. of 80% coffee in the mixture)
===========================
Cheers,
Stan H.
|
Linear-equations/170157: using AX =BY+C
solve and graph:
3x+y=3
1 solutions
Answer 125600 by stanbon(57203) on 2008-11-29 18:21:21 (Show Source):
You can put this solution on YOUR website!solve and graph:
3x+y=3
3x = -y + 3
---------------
x-intercept: let y = 0, then x = 1: (1,0)
------------
y-intercept: let x = 0, then y = 3: (0,3)
----------------------------------------------
===============================================
Cheers,
Stan H.
|
Money_Word_Problems/170155: a sum of $3600 together with the interest earned is left for 3 years in a bank that pays an interest rate of 6% compounded annually. How much interest is earned (to the nearest cent)?
1 solutions
Answer 125599 by stanbon(57203) on 2008-11-29 18:16:53 (Show Source):
You can put this solution on YOUR website!a sum of $3600 together with the interest earned is left for 3 years in a bank that pays an interest rate of 6% compounded annually. How much interest is earned (to the nearest cent)?
-------------------------------
A(3) = 3600**(1.06)^3 = $4287.6576
Inerest = 4287.6576-3600 = $687.66
=================================
Cheers,
Stan H.
|
Parallelograms/170143: i need help to understand and solve these 5 problems, thank u
1.the quadrilateral whose consecutive sides have measures 2, 3, 2, 3 is a(n)________.
2.the quad. whose cons. sides have meas. 2 , 3, 2, 3, is a(n)__________.
3.the quad. with two distinct pairs of NON-opposite angles congruent is a(n)________.
4.if cons. midpoints of a rectangle are joined, a(n)__________is formed.
5. if at leaset one pair of opposite angles of a quad. are congruent and the other pair of angles are each bisected by a diagonal, the figure formed is a(n)__________.
1 solutions
Answer 125597 by stanbon(57203) on 2008-11-29 17:03:39 (Show Source):
You can put this solution on YOUR website!i need help to understand and solve these 5 problems, thank u
1.the quadrilateral whose consecutive sides have measures 2, 3, 2, 3 is a(n)----parallelogram
=====================================
2.the quad. whose cons. sides have meas. 2 , 3, 2, 3, is a(n)__________.
parallelogram
======================================
3.the quad. with two distinct pairs of NON-opposite angles congruent is a(n)trapezoid.
=======================================
4.if cons. midpoints of a rectangle are joined, a(n)parallelogram is formed.
========================================
5. if at leaset one pair of opposite angles of a quad. are congruent and the other pair of angles are each bisected by a diagonal, the figure formed is a(n)mystery.
=========================================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/170131: my problem reads, write the standard equation of each vertex, and these are the problems they give me
1. y^2-8y-8x+64=0
2. 36x^2-288x+25y^2-150y=99
1 solutions
Answer 125596 by stanbon(57203) on 2008-11-29 16:57:16 (Show Source):
You can put this solution on YOUR website!write the standard equation of each vertex, and these are the problems they give me
1. y^2-8y-8x+64=0
Complete the square on the y-terms:
y^2-8y+16 =8x-64+16
(y-4)^2 = 8x-48
(y-4)^2 = 8(x-6)
The vertex is (6,4)
---------------------------
2. 36x^2-288x+25y^2-150y=99
Complete the square on the x and on the y-terms:
36x^2-288x+? + 25y^2-150y+? = -99+?
36(x^2- 8x + 16) + 25(y^2 - 6y + 9) = -99 + 36*16 + 25*9
36(x-4)^2 + 25(y-3)^2 = 702
Divide thru by 702 to get:
(x-4)^2/19.5 + (y-3)^2/28.08 = 1
------------------------------
center at (4,3)
vertices at (4,3+sqrt(28.08)) and (4(3-sqrt(28.08))
=========================================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/170145: The question states, write the standard equation for each conic given the following info.
Parabola with a focus (-2,3) and a directrix x=2
how do i write the standard equation with this given information?
1 solutions
Answer 125589 by stanbon(57203) on 2008-11-29 16:05:17 (Show Source):
You can put this solution on YOUR website!write the standard equation for each conic given the following info.
Parabola with a focus (-2,3) and a directrix x=2
---------------
Plot the information you have so you can see what is happening.
The vertex is equidistanc from the directrix and the focus
so it must be at (0,3)
--------------------
p is the distance from the vertex to the focus; so p=-2.
Then 4p = -8
-------------------
Equation Form:
(y-k)^2 = 4p(x-h) where (h,k) is the vertex.
Your Equation:
(y-3)^2 = -8(x)
===========
Cheers,
Stan H.
|
Trigonometry-basics/170144: I'm attempting to do corrections on a test, but these three questions are giving me trouble! I've tried several different things, and I keep coming up with the same (wrong!) answer!
1) If  is an angle in quadrant 4 and  , find the value of   .
2) What is the solution set of the equation
 =  in the interval  ?
3) Find the solution set of  over the domain  °.
1 solutions
Answer 125583 by stanbon(57203) on 2008-11-29 15:55:46 (Show Source):
You can put this solution on YOUR website!1) If x is an angle in quadrant 4 and cotx= -7/24, find the value of
sin[(1/2)x].
If cotx = -7/24, x = 7 and y = -24
Then r = sqrt(7^2 + 24^2) = 25
------------
sin[(1/2)x] = sqrt[(1-cos(x))/2]
So, sin[(1/2)x] = sqrt[(1-(7/25))/2] = sqrt[9/25] = 3/5
=============================================================
2) What is the solution set of the equation sin(2x)-cos^2(x+1) = sin^2(x)+sinx in the interval 0
Comment: That is a mess to analyze. Graph the left side and the right side
separagely and see where they intersect under the condition the 0
=============================================================
3) Find the solution set of 6sinx + 11= 2cscx over the domain 0
Multiply thru by sin(x) to get:
6sin^2(x) + 11sin(x) - 2 = 0
---
Let w = sin(x)
Substitute to get:
6w^2 + 11w - 2 = 0
6w^2 +12w - w -2= 0
6w(w+2) -(w+2) = 0
(w+2)(6w-1) = 0
w = -2 or w = 1/6
-----
Solve for x:
sin(x) = -2 or sin(x)= 1/6
sin(x) cannot be -2.
If sin(x) = 1/6, x = 9.594.. degrees or 170.41 degrees
========================================================
Cheers,
Stan H.
|
Subset/170139: This question is from textbook intermediate algebra
90) 3^2x -8 . 3^x +15=0
94) If x= (log125 5)^log5 125
Please help me to solve this two. Thank You
1 solutions
Answer 125575 by stanbon(57203) on 2008-11-29 15:24:11 (Show Source):
You can put this solution on YOUR website!90) 3^2x -8(3^x) +15=0
Let w = 3^x
----
Rewrite the quadratic equation:
w^2 - 8w + 15 = 0
(w-5)(w-3) = 0
w = 3 or w = 5
-----------
Solve for x:
3^x = 3 or 3^x = 5
x = 1 or x = [log5/log3] = 1.4649735...
-----------------------------------------
94) If x= (log125 5)^log5 125
log125 5 = log(5)/log(125) = 1/3
log5 125 = 3
-------------------
Therefore x = (1/3)3 = 1
============================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/170141: im having trouble graphing out an finding the focus eccentricity,directrix an axis of symetry of this standard equation.
(y-4)^2=8(x-6)
1 solutions
Answer 125571 by stanbon(57203) on 2008-11-29 15:11:14 (Show Source):
You can put this solution on YOUR website!finding the focus eccentricity,directrix an axis of symetry of this standard equation.
(y-4)^2=8(x-6)
--------------
Vertex: (6,8)
4p = 8, so p = 2
The parabola opens to the right so focus at (8,8)
Axis of symmetry: y = 8
e = 1 for any parabola.
The directrix is perpendicular to the axis of symmetry and is "p"
to the left of the vertex. Its equation is x = 4
=========================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/170123: A plumber needs four sections of pipe 2 7/8 feet long. Can this be cut from a 12-foot section? If so, how much pipe will be left over? If not, why not?
1 solutions
Answer 125566 by stanbon(57203) on 2008-11-29 13:40:02 (Show Source):
You can put this solution on YOUR website! A plumber needs four sections of pipe 2 7/8 feet long. Can this be cut from a 12-foot section? If so, how much pipe will be left over? If not, why not?
-----------------
12 ft - 4(2 7/8) ft.
= 12 - 4(23/8)
= 12 - 92/8
= 96/8 - 92/8 = 4/8= 1/2 ft.
--------------------
There will be 1/2 ft left over.
==========================
Cheers,
Stan H.
|
Rational-functions/170124: Let the function f be defined by f(x)=x+1. If 2f(p)=20, what is the value of f(3p)?
1 solutions
Answer 125565 by stanbon(57203) on 2008-11-29 13:35:27 (Show Source):
You can put this solution on YOUR website!Let the function f be defined by f(x)=x+1. If 2f(p)=20, what is the value of f(3p)?
--------------------------
f(3p) = 3p + 1
---------------
If 2f(p) = 20, then f(p) = 10
But f(p) = p+1
So, p+1 = 10
Therefore p = 9
-----------------
Final Answer: f(3p) = 3p+1 = 3*9+1 = 28
==========================================
Cheers,
Stan H.
|
Matrices-and-determiminant/170126: 3. A company’s employees are working to create a new energy bar. They would like the two key ingredients to be peanut butter and oats, and they want to make sure they have enough carbohydrates and protein in the bar to supply the athlete. They want a total of 22 carbohydrates and 14 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work to receive full credit.
Carbohydrates Protein
Peanut Butter 2 4
Oats 8 1
A. Write an equation for the total amount of carbohydrates.
B. Write an equation for the total amount of protein.
C. Determine the augmented matrix that represents the previous two equations.
D. Solve for the previous matrix. Show all work to receive full credit.
E. How many tablespoons of each will there need to be for the new energy bar?
4. A total of 700 tickets were sold for a musical. Senior citizen tickets sold for $15, children tickets sold for $20, and adult tickets sold for $25; the total earnings from ticket sales was $15,750. Five times more children tickets were sold than senior citizen tickets. How many tickets of each type were sold? Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.
A. What are the three unknowns?
B. Write a separate equation representing each of the first three sentences of the word problem.
C. Determine the augmented matrix that represents the three equations.
D. Solve for the matrix. Show all work to receive full credit.
E. How many of each type of ticket were sold?
1 solutions
Answer 125564 by stanbon(57203) on 2008-11-29 13:29:23 (Show Source):
You can put this solution on YOUR website!They want a total of 22 carbohydrates and 14 grams of protein to make the bar sufficient. Using the following table, create a system of two equations and two unknowns to find how many tablespoons of each ingredient the bar will need. Solve the system of equations using matrices. Show all work to receive full credit.
------------
Carbohydrates Protein
Peanut Butter 2 4
Oats 8 1
A. Write an equation for the total amount of carbohydrates.
2P + 8O = 22
----------------
B. Write an equation for the total amount of protein.
4P + O = 14
-------------------
C. Determine the augmented matrix that represents the previous two equations.
2...8..|22
4...1..|14
--------------------
D. Solve for the previous matrix. Show all work to receive full credit.
----------
Subtract twice the 1st row from the 2nd to get:
2.....8..|22
0...-15..|-30
----------
Divide thru the 2nd equation by -15 to get:
2.....8..|22
0.....1..|2
--------------------
Subtract 8 times the 2nd from from the 1st to get:
2.....0..|18
0.....1..|2
------
Divide thru the 1st equation by 2 to get:
1.....0..|9
0.....1..|2
======================
P = 9
O = 2
========
E. How many tablespoons of each will there need to be for the new energy bar?
9 of peanut butter; 2 of oats
===================================
4. A total of 700 tickets were sold for a musical. Senior citizen tickets sold for $15, children tickets sold for $20, and adult tickets sold for $25; the total earnings from ticket sales was $15,750. Five times more children tickets were sold than senior citizen tickets. How many tickets of each type were sold? Set up a system of three equations and three unknowns, use an augmented matrix to solve, and show all work to receive full credit.
A. What are the three unknowns?
# of senior; # of children; # of adult
----------------------------------------
B. Write a separate equation representing each of the first three sentences of the word problem.
s + c + a = 700
15s + 20c + 25a = 15750
s - 5c + 0 = 0
-----------------
Comment: To be realistic the answer should be whole numbers. It is not.
Use your method to find:
s = 159.090909...
c = 31.818181...
a = 509.090909...
===================
Cheers,
Stan H.
C. Determine the augmented matrix that represents the three equations.
D. Solve for the matrix. Show all work to receive full credit.
E. How many of each type of ticket were sold?
|
Quadratic-relations-and-conic-sections/170128: im familar with writing conic sections in there standard equation but there are 2 questions that have me stumped in peticular.here is one of them.
y^2-8y-8x+64=0
and im suppose to write this in standard form
1 solutions
Answer 125560 by stanbon(57203) on 2008-11-29 13:04:31 (Show Source):
You can put this solution on YOUR website!y^2-8y-8x+64=0
and I'm supposed to write this in standard form
-----------------
Complete the square of the y terms, as follows:
y^2 - 8y + 16 = 8x -64 + 16
(y-4)^2 = 8x - 48
(y-4)^2 = 8(x-6)
--------------------
This form shows you the vertex is at (6,4) and the
focus of the parabola is 8/4 = 2 units above the vertex.
-------------------------------
Cheers,
Stan H.
|
Proportions/170098: Ratio and Proportion
3. An administrator of a popular web site is told that a new server can handle 41,000 "hits" (users accessing the site) per second. The web site currently experiences a peak demand of about 105,000 hits per second; but every month, the peak demand increases by 2800 hits per second. Use a proportion equation to determine how many new servers the administrator should buy to address expected traffic for the next 24 months.
Again, I am stumped on word problems. I had 24 questions and the last three are word problems that totally gets me confused because I don't know where to begin and what information I need to get started. Can someone please help me with this? It would be greatly appreciated!
1 solutions
Answer 125543 by stanbon(57203) on 2008-11-29 10:31:00 (Show Source):
You can put this solution on YOUR website!An administrator of a popular web site is told that a new server can handle 41,000 "hits" (users accessing the site) per second. The web site currently experiences a peak demand of about 105,000 hits per second; but every month, the peak demand increases by 2800 hits per second. Use a proportion equation to determine how many new servers the administrator should buy to address expected traffic for the next 24 months.
--------------
[# of servers/hits per sec] = [# of servers/hits per sec]
1/41000 = x/[105,000+24*2800]
x = [105,000+24*2800]/41000
-------
x = 172200/41000
x = 4.2
Rounding up they will need 5 servers to handle the peak demandin 24 mths.
-------------
How many servers do they have NOW?
105000/41000 = 2.56
So, they must have 3 servers NOW.
----------
Ans: they will need 2 new servers in 24 months.
=================================
Cheers,
Stan H.
|
Proportions/170097: Ratio and Proportion
1. A lawyer bills her clients $200 per hour of service. If a client's case requires 39 hours to complete, use proportion to calculate how much the client will owe the lawyer (excluding tax).
I am having a really hard time figuring out this word problem. I have always had trouble figuring them out because I never know where to begin. I figured it I multiply 39*200=7,800.00, but I know this is totally wrong. Can you please help me! I have two more word problems to do that are similar to this. Thank you so much for assisting.
1 solutions
Answer 125542 by stanbon(57203) on 2008-11-29 10:18:08 (Show Source):
You can put this solution on YOUR website!A lawyer bills her clients $200 per hour of service. If a client's case requires 39 hours to complete, use proportion to calculate how much the client will owe the lawyer (excluding tax).
------------------------
hrs/charge = hrs/charge
--------------------------
1/200 = 39/x
Cross-multiply to get:
x = 39*200
x = $7800
---
You are totally right.
===============
Cheers,
Stan H.
|
Proportions/170096: Ratio and Proportion
2. A new virus is released on the internet; the administrator of a department's Local Area Network ( LAN) is given five minutes by a manager to estimate the impact. The administrator samples 15 of the PCs connected to the LAN, and finds that 9 are infected; use proportion to estimate the number of infected PCs if there are a total of 202 PCs connected to the LAN.
This problem has me totally confused! Again, I am not good a word problems. I never know where to start, I have been trying to work out the problem, but I don't know where to begin. Please help me!
1 solutions
Answer 125541 by stanbon(57203) on 2008-11-29 10:14:00 (Show Source):
You can put this solution on YOUR website!A new virus is released on the internet; the administrator of a department's Local Area Network ( LAN) is given five minutes by a manager to estimate the impact. The administrator samples 15 of the PCs connected to the LAN, and finds that 9 are infected; use proportion to estimate the number of infected PCs if there are a total of 202 PCs connected to the LAN.
------------------
Use a proportion:
[9 infected/15 sampled] = [x infected/all the PCs]
(9/15) = (x/202)
x = 202(9/15)
x = 202(3/5)
x = 121.2
Round down to get x = 121 infected PC's out of 202
-------------------
Cheers,
Stan H.
|
Graphs/170094: Please help me, I don't understand!
Find the equation for each of the following items below:
a. A line that passes through (6,2) and has a slope of 2.
b. A line that passes though the points (2,4) and (8,16)
c. A line that passes through (7,3) and has a slope of -1.
d. A line that passes through (1, 1) and is perpendicular to the line 3x+4Y=12.
e. A circle with a radius of 9 and a midpoint at (3,3)
1 solutions
Answer 125538 by stanbon(57203) on 2008-11-29 10:09:14 (Show Source):
You can put this solution on YOUR website!Find the equation for each of the following items below:
a. A line that passes through (6,2) and has a slope of 2.
Line equation y = mx + b; find m and b.
m = 2
b: 2 = 2*6 + b
b = -10
Equation: y = 2x - 10
--------------------------------------
b. A line that passes though the points (2,4) and (8,16)
Line equation y = mx + b; find m and b
m = [16-4]/[8-2] = 2
b: 4 = 2*2 + b
b = 0
Equation: y = 2x
=======================
c. A line that passes through (7,3) and has a slope of -1.
same procudure as above
-----------------------------
d. A line that passes through (1, 1) and is perpendicular to the line 3x+4Y=12.
Find slope of give line: 4y = -3x + 12; y = (-3/4)x + 3
Its slope is -3/4 so the perpendicular line has m = 4/3
b: 1= (4/3)*1 + b
b = -1/3
Equation: y = (4/3)x - (1/3)
-----------------------------
e. A circle with a radius of 9 and a midpoint at (3,3)
(x-3)^2 + (y-3)^2 = 9^2
================================
Cheers,
Stan H.
|
Square-cubic-other-roots/170089: This question is from textbook
A small garden measures 8 feet by 10 feet. A uniform border around the garden increases the total area to 143 square feet. What is the width of the border?
1 solutions
Answer 125536 by stanbon(57203) on 2008-11-29 10:02:06 (Show Source):
You can put this solution on YOUR website!A small garden measures 8 feet by 10 feet. A uniform border around the garden increases the total area to 143 square feet. What is the width of the border?
-------------------
Draw the picture of the garden with its border.
Original area of the garden = 80 sq. ft.
-------------
Let the width of the border be "x".
-------------
New area = (8+2x)(10+2x) = 80 +143
80 + 36x + 4x^2 = 80 + 143
4x^2 + 36x - 143 = 0
x = [-36 +- sqrt(36^2 - 4*4*-143]/8
x = [-36 +- sqrt(3584)]/8
x = [-36 +- 59.87]/8
Positive solution:
x = 2.98 ft. (width of the border)
========================================
Cheers,
Stan H.
|
Square-cubic-other-roots/170091: This question is from textbook
Geometry:
The lengths of two sides of a square are extended 5 inch. The area of the resulting square 64 square inch. Find the length of a side of the orginal square?
1 solutions
Answer 125535 by stanbon(57203) on 2008-11-29 09:52:25 (Show Source):
You can put this solution on YOUR website!The lengths of two sides of a square are extended 5 inch. The area of the resulting square 64 square inch. Find the length of a side of the orginal square?
------------------
Let original side be "x".
Original area = x^2.
------------------
New side is x+5.
New area = (x+5)^2
-------------------
EQUATION:
(x+5)^2 = 64
x+5 = 8
x = 3 inches (original side length)
===================================
Cheers,
Stan H.
|
Quadratic-relations-and-conic-sections/170037: I have such a hard time doing this problem:
Write Standard Equation of Ellipse, Given Foci: (-2,0) and (2,0) and Vertices: (-6,0) and (6,0).
1 solutions
Answer 125534 by stanbon(57203) on 2008-11-29 09:48:36 (Show Source):
You can put this solution on YOUR website!I have such a hard time doing this problem:
Write Standard Equation of Ellipse, Given Foci: (-2,0) and (2,0) and Vertices: (-6,0) and (6,0).
-----------------------
Draw the picture.
Do you see that a = 6 and c = 2.
For an ellipse, a^2 + b^2 = c^2, so b = sqrt[6^2-2^2] = sqrt(32) = 4sqrt(2)
----------------------------
EQUATION:
x^2/36 + y^2/32 = 1
=========================
Cheers,
Stan H.
=========================
|
Polynomials-and-rational-expressions/170073: perform the indicated operation
5/x-5 - 8/x+8
1 solutions
Answer 125531 by stanbon(57203) on 2008-11-29 09:07:06 (Show Source):
You can put this solution on YOUR website!perform the indicated operation
5/x-5 - 8/x+8
---------------
lcd = (x-5)(x+8)
---
Rewrite each fraction with the lcd as its denominator:
5(x+8)/lcd - 8(x-5)/lcd
-------
Combine the numerators over the lcd:
[5x+40-8x+40]/lcd
-----
Simplify:
[-3x+80]/[(x-5)(x+8]
====================
Cheers,
Stan H.
|
logarithm/170088: The questions are rewrite the following expression using one or more properties of logarithims and evaluate without a calculator.
1. log 5 (25 2/5 -)=
Plese check and see if this is correct. log5 25 2 - log5 5, 2 log5 25- log5 5, 2x2-1= 4-1=3
2. log5 125 + log5 5=
I was able to figure out a portion of the problem but then got lost. Please check and help me with the rest. log5 (125x5)= log5 625 ( this is where I got lost)
3. log9 3 - log9 243=
I think I figured out a portion of this problem as well, but then got lost. Please check and help me with the rest. log9 3/243 reduced to log9 1/81,
log9 81 ( this is where I got lost)
1 solutions
Answer 125530 by stanbon(57203) on 2008-11-29 09:02:59 (Show Source):
You can put this solution on YOUR website!The questions are rewrite the following expression using one or more properties of logarithims and evaluate without a calculator.
1. log 5 (25^2/5)= Log5(25^2) - log5(5) = 2log(5^2) - 1 = 4-1 = 3
----------------------------
Note the "-" to the right of the 5 has no meaning is nothing
follows it.
------------------------------
============================================================
2. log5 (125) + log5 (5) = 2 + 1 = 3
=================================================================
I was able to figure out a portion of the problem but then got lost. Please check and help me with the rest. log5 (125x5)= log5 625 ( this is where I got lost)
--
Correct answer: log5(125*5) = log5(125) + log5(5) = 3+1 = 4
============================================================
3. log9 3 - log9 243=
Correct answer:
[log3/log9] - [log243]/log9]
Using base 3 to would get:
[1/2] - [5/2] = -2
==========================
Cheers,
Stan H.
|
Human-and-algebraic-language/170086: 2. A student writes down the following as part of her response:
a ) 3^2 x 3^3 = 729. and b) 3^-2 = -9.
Are her answers correct? If not, explain why you think her answers are incorrect.
Include in your explanation what she did wrong, if any.
What would you advise her to do instead?
1 solutions
Answer 125529 by stanbon(57203) on 2008-11-29 08:53:44 (Show Source):
You can put this solution on YOUR website!2. A student writes down the following as part of her response:
a ) 3^2 x 3^3 = 729
Correct answer:::: 9*27 = 243
-------------------
b) 3^-2 = -9.
Correct answer:::: 3^-2 = 1/3^2 = 1/9
==========================================
Cheers,
Stan H.
==========================================
Are her answers correct? If not, explain why you think her answers are incorrect.
Include in your explanation what she did wrong, if any.
|
|
