Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'jim_thompson5910'

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, >>Next

 Functions/214736: I have to find the composition of functions! Can't figure this one out either! g(x)=3/(x-1) f(x)=(x-1)/(x-3) find (fog)(x) Again, thanks!!!!!1 solutions Answer 162174 by jim_thompson5910(28598)   on 2009-09-18 18:07:38 (Show Source): You can put this solution on YOUR website!Remember that is another way of saying . Start with the given function. Plug in Note: this involves replacing 'x' on the left side with and replacing each 'x' on the right side with . Multiply EVERY term by the inner LCD to clear out the inner fractions. Simplify Distribute Combine like terms. So
 Linear_Equations_And_Systems_Word_Problems/214725: This question is from textbook Practicing to Take the GRE General Test I am having problems with this word problem: A group can charter a particular aircraft at a total fixed cost. If 36 people charter the aircraft rather than 40 people, then the cost per person is greater by $12. What is the cost per person if 40 people charter the aircraft? I have defined the cost if 40 people charter as x and the cost if 36 people charter as y. The only equation I can come up with so far is 36y=40(x+12), but I know I need some other equation if I want to solve for either variable. The back of the book states the answer as 108, but I cannot figure out how to get there. Thanks in advance for your help!1 solutions Answer 162168 by jim_thompson5910(28598) on 2009-09-18 17:38:19 (Show Source): You can put this solution on YOUR website!Let x=cost per person (for 40 people) in dollars y=total cost in dollars If 40 people attend, then the cost per person 'x' is simply the total cost 'y' divided by the number of people going (40). In other words, (eg: if the total cost is$80, then the cost per person is dollars). This is your first equation. Now if 36 people attend instead of 40, the cost per person will increase by $12. So this means that the new cost per person is if 36 people go. This is equal to (since the total cost is now divided among 36 people). So . This is the second equation. Start with the second equation. Plug in Multiply EVERY term by the LCD to clear out the fractions. Multiply and simplify. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. Since 'y' is the total cost, this means that the total cost is$4,320 Move back to the first equation. Plug in Divide Since 'x' is the cost per person when 40 people were going, this means that the cost per person for 40 people is $108. Linear-systems/214712: use the intercepts to graph the equation 4x-2y=8 please help me solve and graph 1 solutions Answer 162150 by jim_thompson5910(28598) on 2009-09-18 16:38:34 (Show Source): You can put this solution on YOUR website! #### x-intercept To find the x-intercept, plug in and solve for x Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. Divide both sides by to isolate . Reduce. So the x-intercept is . ------------------------------------------ #### y-intercept To find the y-intercept, plug in and solve for y Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. Divide both sides by to isolate . Reduce. So the y-intercept is . Now plot the points and draw a straight line through them to graph the equation Graph of  Inequalities/214692: Solve the inequality, and express the solutions in terms of intervals whenever possible: 3x - 2 > 18 1 solutions Answer 162126 by jim_thompson5910(28598) on 2009-09-18 14:00:27 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add 2 to both sides. Add Divide both sides by 3 to isolate 'x' So the solution is which in interval notation is  Graphs/214690: Give the center and radius of the circle: x^2+y^2-10x+6y+25 I first completed the square: (x^2-10x+25)+(y^2+6y+9)=-25 (x-5)^2+(y-3)^2=-25+25+9 (x-5)+(x-3)=9 (-5,-3) with a radius of 9 but I am not sure if I did that right?!?!1 solutions Answer 162125 by jim_thompson5910(28598) on 2009-09-18 13:55:32 (Show Source): You can put this solution on YOUR website!The last equation should be , since factors to . We can take this equation and then rewrite as and to to get Recall that the general equation of a circle is where (h,k) is the center and 'r' is the radius. Looking at (which is in the circle form described above), we see that , and (I'm just matching the two forms). So the center is (5,-3) and the radius is 3 units. So you just had some minor errors (such as the sign differences and forgetting to take the square root of 9)  Exponents/214688: write each expression using positive exponets. 7^-21 solutions Answer 162124 by jim_thompson5910(28598) on 2009-09-18 13:51:27 (Show Source): You can put this solution on YOUR website!Recall that . In other words, if you have a negative exponent, you can rewrite the expression with a positive exponent by flipping the fraction. In this problem, or simply  Expressions-with-variables/214209: Write an algebraic expression for, "four times the sum of 2a and (b) increased by twice the sum of 6a and 2b." Then simplify, indicating the properties used.1 solutions Answer 162123 by jim_thompson5910(28598) on 2009-09-18 13:34:10 (Show Source): You can put this solution on YOUR website!"four times the sum of 2a and (b)" translates to "twice the sum of 6a and 2b" means that and altogether, "four times the sum of 2a and (b) increased by twice the sum of 6a and 2b." tells us Start with the given expression Distribute Combine like terms. So  Linear-equations/214676: media services charges$20 for a phone and $30/month for its economy plan. What is the total cost of C (t) of operating a media service phone for t months? C(t)= what is the total cost for 7 months of service? C(t)=1 solutions Answer 162122 by jim_thompson5910(28598) on 2009-09-18 13:27:08 (Show Source): You can put this solution on YOUR website!Any linear function can be written in the form where 'm' is the slope and represents the change of the function and 'b' is the initial value of the function. In our case, the change is$30 (since the total cost goes up $30 a month) while the initial fee is$20. So this means and giving us the function If you're unsure of the answer, simply plug in values of 't' Examples: When , the number of months is zero. So this represents the start of the plan. Plug this into C(t) to get . So no matter what, you're going to pay $20 up front (which is exactly what the problem states). Now one month later, the value of 't' is now . If you simply add$30 to the down payment of $20, you get$50. In other words, you've paid $50 for the first month. If we plug in t=1, we get which is exactly what we just got. So you may be asking why we're going through all the trouble of using functions when we could just add. Using functions will save us time for larger values of 't'. For instance, let's say you want to know what the total cost will be 20 months from now. Are you going to add 20 sets of$30 to 20 to find the answer? You could, but why do that when you can simply use the function. Also, you can also answer other questions that the previous technique would have a hard time doing so. --------------------------------------------------------------------- To find the cost of 7 months of service, just plug in t=7: Start with the given function. Plug in Multiply Add So 7 months of service will cost \$230
 Probability-and-statistics/214683: if a jar contains 23 red marbles and 4 green marbles, the probability that a marble selectted from the jar at random will be green is? If the above green is not replaced, what is the probability that the next pulled marbles is red? if you reached into the jar 4 times, what is the probability that you would never choose a green marble (after each pullout you do not replace the chosen marble?1 solutions Answer 162121 by jim_thompson5910(28598)   on 2009-09-18 13:18:02 (Show Source): You can put this solution on YOUR website!a) Total number of marbles = 23 + 4 = 27 marbles P(Green Marble) = (# of green marbles)/(# of marbles total) = 4/27 = 0.148 So the probability is 4/27 which is about a 14.8% chance ------------------------------------ b) Since the selected marble from part a) is not replaced, the total number of marbles is now 27-1=26 P(Red Marble) = (# of red marbles)/(# of marbles total) = 23/26 = 0.885 So the probability is 23/27 which is about a 88.5% chance ------------------------------------ c) To find the probability of NOT choosing green after four selections, you simply calculate the probability of choosing red 4 times in a row (without replacement). This works because there are only two choices in marble selection. So the basic outline is P(4 red) = P(red)*P(red with 1 less from total)*P(red with 2 less from total)*P(red with 3 less from total) I'll let you take it from here. Let me know if you still need help.
 Probability-and-statistics/214681: if a jar contains 23 red marbles and 4 green marbles, the probability that a marble selected from the jar at random will be green is?1 solutions Answer 162119 by jim_thompson5910(28598)   on 2009-09-18 13:10:46 (Show Source): You can put this solution on YOUR website!Total number of marbles = 23 + 4 = 27 marbles P(Green Marble) = (# of green marbles)/(# of marbles total) = 4/27 = 0.148 So the probability is 4/27 which is about a 14.8% chance
 Polynomials-and-rational-expressions/214677: please help me solve this questionfind all numbers for which the rational expression is undefined 8/w-11 solutions Answer 162118 by jim_thompson5910(28598)   on 2009-09-18 13:08:31 (Show Source): You can put this solution on YOUR website!Is the expression or is it ??? is undefined when the denominator is zero. So set the denominator equal to zero and solve for 'w' to get ----> So is undefined when -------------------------------- is undefined when the denominator is zero. So set the denominator equal to zero to get So is undefined when
 Equations/214537: Please help me solve the following question 5/2t - t = 3 + 3/2t1 solutions Answer 162043 by jim_thompson5910(28598)   on 2009-09-17 19:55:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Subtract from both sides. Combine like terms on the left side. Simplify. Since this equation is NEVER true for any 't' value, this means that there are no solutions.
Polynomials-and-rational-expressions/214534: This question is from textbook blitzer college algebra essential
factor x^2+2x-3
1 solutions

Answer 162042 by jim_thompson5910(28598)   on 2009-09-17 19:45:25 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,3
-1,-3

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-3) = -3
(-1)*(3) = -3

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-31+(-3)=-2
-13-1+3=2

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

===============================================================

So factors to .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

 Equations/214498: What is the charge of an ion with 38 electrons, 38 neutrons, and 35 protons?1 solutions Answer 162021 by jim_thompson5910(28598)   on 2009-09-17 18:58:11 (Show Source): You can put this solution on YOUR website!This is more a chemistry question, but I happen to know a little bit about it. Remember that an ion is simply "an atom or molecule where the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge." (from Wikipedia). Recall that the charge of an electron is -1 while the charge of a single proton is +1. If there are more protons than electrons, then the atom/molecule is positively charged which makes it a cation. If there are more electrons than protons, then the atom/molecule is negatively charged which makes it an anion. To find the net charge, simply subtract the number of electrons from the number of protons to get: 35-38 = -3 Note: this is the same as saying: 38(1)+35(-1) = -3 So the net charge of this ion is -3 which means that it's negatively charged and that it's an anion.
 Rational-functions/214421: Evaluate the following piecewise defined function at f(0), f(2), and f(3) f(x)= 5 if x<2 2x-3 if x>=21 solutions Answer 161959 by jim_thompson5910(28598)   on 2009-09-17 13:47:58 (Show Source): You can put this solution on YOUR website!Take note that x=0 satisfies the inequality . So to find , plug x=0 into the first function . The values x=2 and x=3 are both greater than or equal to 2. So they satisfy . This means to find f(2) and f(3), just plug in x=2 and x=3 respectively into .
 absolute-value/214420: |-2| 1 solutions Answer 161957 by jim_thompson5910(28598)   on 2009-09-17 13:33:20 (Show Source): You can put this solution on YOUR website! Remember, the absolute value of ANY number is ALWAYS positive.
 Polynomials-and-rational-expressions/214414: how to factor 16x^4-11 solutions Answer 161954 by jim_thompson5910(28598)   on 2009-09-17 13:21:58 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as Take note that we have a difference of squares in which and . We can factor this difference of squares using the formula Start with the difference of squares formula Plug in and So factors to We can keep going and factor further. Rewrite as . Rewrite as Notice that we again have a difference of squares in which and . We can factor this difference of squares using the formula Start with the difference of squares formula Plug in and So factors to --------------------------------------------- Answer: Putting all of this together tells us that completely factors to
 Equations/214415: 6x+7=25 solve for x1 solutions Answer 161952 by jim_thompson5910(28598)   on 2009-09-17 13:15:52 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 7 from both sides. Combine like terms. Divide both sides by 6 to isolate 'x' Reduce So the solution is
 Divisibility_and_Prime_Numbers/214411: This question is from textbook algebra 1 an integrated approach if a is an integer, which of the following is always an odd integer? (a)4a+2 (b)10a (c)8a+1 (d).83 please help!!!!!!1 solutions Answer 161951 by jim_thompson5910(28598)   on 2009-09-17 13:09:51 (Show Source): You can put this solution on YOUR website!Recall that if 'k' is an integer, then is ALWAYS odd. Why? The number is ALWAYS even (because all even integers are a multiple of 2). If you add 1 to an even integer, you will get an odd integer. So this shows us that is ALWAYS odd where 'k' is an integer. So the goal is to try to transform each choice into either the form (even form) or (odd form). a) Start with the given expression Factor out the GCF 2 Replace 'a+1' with 'k' (which is an integer) So is ALWAYS even (try plugging in some integers for 'a' to test this). ----------------------------- b) We can rewrite as which can come to (where . So is ALWAYS even. ----------------------------- c) We can rewrite as and then let . Now replace '4a' with 'k' to get . So (where ) This shows us that is ALWAYS odd. ----------------------------- d) The value 0.83 is neither even nor odd. Why is this? A number can only be even or odd when it is a whole number or integer. Since 0.83 is NOT a whole number, it is neither even nor odd. So to recap, the only odd integer of the group is
 Polynomials-and-rational-expressions/214181: Need help in this problem? Is (-2,-2) a solution of the system x-3y=4 3x+y=-81 solutions Answer 161766 by jim_thompson5910(28598)   on 2009-09-16 15:36:06 (Show Source): You can put this solution on YOUR website!Simply plug in x=-2 and y=-2 into both equations and simplify. If you get two identities, then (-2,-2) is the solution. If one is not (or both aren't) an identity, then (-2,-2) is NOT the solution. Note: an identity is an equation that is ALWAYS true. A simple identity is 0=0.
Polynomials-and-rational-expressions/214178: How is this algebra problem done?
factor p^2+12p+36
1 solutions

Answer 161764 by jim_thompson5910(28598)   on 2009-09-16 15:33:54 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,4,6,9,12,18,36
-1,-2,-3,-4,-6,-9,-12,-18,-36

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*36
2*18
3*12
4*9
6*6
(-1)*(-36)
(-2)*(-18)
(-3)*(-12)
(-4)*(-9)
(-6)*(-6)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1361+36=37
2182+18=20
3123+12=15
494+9=13
666+6=12
-1-36-1+(-36)=-37
-2-18-2+(-18)=-20
-3-12-3+(-12)=-15
-4-9-4+(-9)=-13
-6-6-6+(-6)=-12

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

Condense

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).