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x---12-rightarrow-x--frac127--verify--x--1--to-ensure-validity-85780722026-04-21T02:07:52+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-factor--z4--z2--1--z2--z--1z2---z--1--0--solving--z2--z--1--0--gives-roots--z--frac-1-pm-isqrt32--with-imaginary-parts--pm-fracsqrt32--solving--z2---z--1--0--gives--z--frac1-pm-isqrt32--with-imaginary-parts--pm-fracsqrt32--the-maximum-imaginary-part-is--fracsqrt32--sin-60circ--11049422026-04-21T02:07:52+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-compute--mathbfa--mathbfb--mathbfc2--3--2mathbfa-cdot-mathbfb--mathbfb-cdot-mathbfc--mathbfc-cdot-mathbfa--3--2leftfrac12--frac12--frac12right--3--3--6--thus-the-norm-is--sqrt6--53479002026-04-21T02:07:52+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-choose-2-sorbets-from-8-inom82--rac8-cdot-72--28-72099932026-04-21T02:27:47+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-each-of-the-4-volcanoes-independently-exhibits-one-of-3-eruption-intensities-low-medium-or-high-since-the-volcanoes-are-distinguishable-due-to-different-locations-but-the-eruption-profile-ie-the-multiset-of-intensities-only-considers-counts-of-each-type-and-the-volcanoes-are-distinguishable-we-are-counting-the-number-of-4-tuples-where-each-element-is-from-a-3-element-set-low-medium-high-and-the-order-does-not-matter-in-terms-of-labelingwait-correction-since-each-volcano-is-a-distinct-entity-eg-monitored-individually-the-classification-is-based-on-assigning-an-intensity-to-each-volcano-and-even-though-eruptive-profiles-are-unordered-in-reporting-the-underlying-assignment-to-specific-volcanoes-is-tracked-therefore-we-are-counting-functional-mappings-from-4-distinguishable-volcanoes-to-3-intensity-categories-with-repetition-allowed-and-order-of-assignment-does-not-affect-group-countsbut-since-volcanoes-are-distinguishable-each-different-assignment-is-unique-unless-specified-otherwise-79009042026-02-23T15:18:01+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-factor-the-polynomial-as-fracz8---1z2---1--0-excluding-roots-of-z2--1-the-roots-are-the-8th-roots-of-unity-except-pm-1-the-roots-with-maximum-imaginary-part-are-eipi4-and-ei3pi4-with-imaginary-part-fracsqrt22--cospi4-52336302026-04-21T02:34:31+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-apply-de-moivres-theorem-cos-15circ--i-sin-15circ12--cos180circ--i-sin180circ---1--0i-36823692026-04-21T02:34:36+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/sofias-journey-the-confident-fit-of-a-fat-black-guy-that-shocked-the-internet-4180212026-04-21T02:39:34+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-a-four-digit-number-ranges-from-1000-to-9999-a-number-is-divisible-by-5-if-its-last-digit-is-0-or-5-the-smallest-four-digit-number-divisible-by-5-is-1000-and-the-largest-is-9995-these-form-an-arithmetic-sequence-with-first-term-1000-common-difference-5-and-last-term-9995-the-number-of-terms-is-given-by-frac9995---10005--1--frac89955--1--1799--1--1800-therefore-there-are-boxed1800-four-digit-numbers-divisible-by-5-90461752026-04-21T02:53:38+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-divide--frac34--by-5-29637202026-04-21T03:10:40+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-find-a-common-denominator--x---1x--2--63228422026-04-21T03:39:52+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-compute--b2--f2--2---rac244--2---rac164--2---4---2--then--b3--f-2---2---rac-244---2---rac164---2---4---6--thus--b3--oxed-6--75881042026-02-23T17:21:16+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-assume--hx--ax2--bx--c--substitute-into-the-equation-24498592026-04-21T04:20:31+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-apply-the-formula--a---b2--a2---2ab--b2--here--2x2---2-cdot-2x-cdot-3y--3y2--4x2---12xy--9y2--oxed4x2---12xy--9y2-70563422026-04-21T04:33:10+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/soit-la-largeur--w-alors-la-longueur--2w-16760602026-04-21T04:55:22+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solde--1-000---1--0053--1-000---1157625--1-15763--62094002026-04-21T04:55:22+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/soldiers-steal-this-haircutget-the-stylish-military-cut-today-1950962026-04-21T05:18:38+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solucin-para-encontrar-la-probabilidad-de-extraer-una-ficha-amarilla-o-verde-primero-determinamos-el-nmero-total-de-fichas-y-el-nmero-de-resultados-favorables-54948992026-04-21T05:28:54+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solucin-utilizamos-el-concepto-de-combinaciones-para-calcular-la-probabilidad-77101602026-04-21T05:28:54+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solucin-calcula-la-probabilidad-paso-a-paso-99025262026-04-21T05:28:54+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solucin-calcula-la-probabilidad-complementaria-ninguna-negra-y-rstala-de-1-17191862026-04-21T05:29:01+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solucin-el-problema-es-una-permutacin-de-un-multiconjunto-61834352026-04-21T05:29:01+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-consider-the-polynomial-59473432026-04-21T05:46:32+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-find-the-least-common-multiple-lcm-of-6-and-10-94392622026-04-21T05:46:46+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-first-find-the-number-of-damaged-leaves-8271672026-04-21T05:46:56+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-compute-the-average-22046502026-04-21T05:46:56+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-first-choose-4-distinct-layers-from-7-which-is--binom74--35--then-select-2-of-these-4-layers-to-apply-the-pump-water-operation-which-can-be-done-in--binom42--6--ways-the-remaining-2-layers-are-analyzed-without-the-operation-and-the-sequence-of-4-layers-is-ordered-giving--4--24--permutations-however-since-the-operation-affects-only-the-selection-not-the-order-of-non-pump-layers-the-total-is-46937412026-04-21T06:01:48+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-assume--vt--at2--bt--c--from--v1--a--b--c--120---v2--4a--2b--c--200---v3--9a--3b--c--300--subtract-first-equation-from-the-second--3a--b--80--subtract-second-from-the-third--5a--b--100--subtract-these--2a--20----a--10--then--310--b--80----b--50--from--a--b--c--120---10--50--c--120----c--60--thus--vt--10t2--50t--60--for--t--4---v4--1016--504--60--160--200--60--420--final-answer--oxed420--2293952026-04-21T06:53:54+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution--dt--pt3--qt2--rt--s--compute--dt--3pt2--2qt--r--from--d1--p--q--r--s--10---d1--3p--2q--r--12---d2--8p--4q--2r--s--28---d2--12p--4q--r--30--subtract-first-equation-from-third--7p--3q--r--18--subtract--d1--from-this--7p--3q--r---3p--2q--r--4p--q--6--from--d2---12p--4q--r--30--and--d1---3p--2q--r--12--subtract--9p--2q--18--now-solve--4p--q--6--and--9p--2q--18--multiply-first-by-2--8p--2q--12--subtract--p--6--then--46--q--6----q---18--from--d1---36--2-18--r--12----18---36--r--12----r--30--from--d1---6---18--30--s--10----s---8--thus--d0--s---8--final-answer--oxed-8--99410042026-02-23T20:10:30+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/soft-brown-sugar-like-maple-syrup-heres-howfast--simple-67705702026-04-21T06:56:41+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-a-regular-hexagon-inscribed-in-a-circle-has-side-length-equal-to-the-radius-thus-each-side-is-6-units-the-area-of-a-regular-hexagon-is-frac3sqrt32-s2--frac3sqrt32-times-36--54sqrt3-boxed54sqrt3-41238992026-04-21T06:57:25+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-8-88575882026-04-24T12:39:11+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-9-84451792026-04-24T12:39:09+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-10-13102372026-04-24T12:39:13+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-11-15675462026-04-21T07:14:25+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-12-89122772026-04-21T07:14:25+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-13-39852662026-04-21T07:14:28+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-14-94454662026-04-21T07:14:38+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-15-19241642026-04-21T07:14:38+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-first-compute--f4--34---7--12---7--5--then-substitute-into--gx---g5--52--25--25--10--35--the-value-of--gf4--is--boxed35--67308452026-04-21T07:16:52+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-cross-multiply--23y---1--4y--7--expand--6y---2--4y--28--subtract--4y---2y---2--28--add-2--2y--30--divide-by-2--y--15--final-answer--boxed15--80945692026-04-21T07:21:57+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solar-generation-3600--8--360082880028800-kwh-84649502026-04-21T07:26:15+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/soit-x-le-montant-en-dollars-reu-par-la-premire-startup-72694512026-04-21T07:28:02+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-first-choose-2-phonemes-from-5--binom52--10--for-each-pair-the-number-of-4-phoneme-words-using-both-phonemes-but-not-just-one-is--24---2--14--subtracting-the-two-monochromatic-words-total-favorable-outcomes--10-cdot-14--140--total-possible-words--54--625--probability-30116832026-04-21T07:29:05+00:00daily0.8https://internal-admin.roadrunner.travel/highlights/solution-co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