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-zones-and-at-least-1-wetland-21945392026-04-24T15:08:58+00:00daily0.8https://dev.imagemakers.co.za/guides/we-want-exactly-1-non-volatile-and-at-least-2-volatile-32788552026-04-22T15:00:33+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-also-told-that-there-are-12-more-parrots-than-toucans-66746192026-04-22T15:03:37+00:00daily0.8https://dev.imagemakers.co.za/guides/webstation-alerts-fidelity-plan-sponsors-are-cutting-feesdont-miss-this-game-changer-98691982026-04-22T15:06:27+00:00daily0.8https://dev.imagemakers.co.za/guides/we-want-to-count-how-many-numbers-in-this-range-are-divisible-by-11-73496772026-04-22T15:07:14+00:00daily0.8https://dev.imagemakers.co.za/guides/we-seek-the-probability-that-at-least-one-strain-infects-a-cell-which-is-given-by-the-formula-for-the-union-of-two-events-65592192026-04-22T15:22:14+00:00daily0.8https://dev.imagemakers.co.za/guides/we-use-the-given-values-to-form-a-system-of-equations-7172026-04-22T15:22:14+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-rolling-four-6-sided-dice-and-want-the-probability-that-exactly-two-dice-show-a-number-greater-than-4-ie-a-5-or-a-6-61527002026-04-22T15:24:54+00:00daily0.8https://dev.imagemakers.co.za/guides/we-want-exactly-2-out-of-4-dice-to-show-a-number--4-this-is-a-binomial-probability-91538912026-04-24T15:15:54+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-arranging-6-people-in-a-circle-such-that-dr-lee-and-dr-kim-sit-directly-opposite-each-other-96084642026-04-24T15:15:54+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-selecting-4-applications-out-of-7-3-ml-m-2-qc-q-2-bc-b-37348672026-04-22T15:24:55+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-10-distinguishable-river-sites-each-to-be-assigned-one-of-3-pollution-levels-high-moderate-or-low-since-the-order-of-classification-does-not-matter-we-are-distributing-10-distinguishable-objects-into-3-distinguishable-categories-levels-where-each-object-belongs-to-exactly-one-category-47281812026-03-14T23:00:17+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-coloring-a-linear-sequence-of-7-distinct-fish-species-with-3-colors-red-blue-green-such-that-no-two-adjacent-species-receive-the-same-color-65565192026-03-14T23:00:36+00:00daily0.8https://dev.imagemakers.co.za/guides/we-seek-the-largest-integer-that-must-divide--p--since-this-is-always-true-for-any-such-sequence-of-49-multiples-of-6-in-this-form-the-minimal-such-divisor-common-to-all-such-products-but-specifically-for-this-one-is-determined-by-the-prime-factorization-of--p--98099152026-04-24T15:21:24+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-to-find-the-largest-integer-that-divides-this-number-but-every-product-of-these-numbers-is-a-multiple-of-this-number-only-if-permuted-but-here-the-set-is-fixed-so-the-number-is-fixed-40029972026-04-24T15:21:25+00:00daily0.8https://dev.imagemakers.co.za/guides/we-calculate-the-number-of-ways-to-choose-2-gene-sequences-from-8-and-3-vectors-from-5-since-the-choices-are-independent-we-multiply-the-combinations-89983622026-04-22T16:02:21+00:00daily0.8https://dev.imagemakers.co.za/guides/we-use-the-hypergeometric-distribution-total-dishes-9-3-radiation-exposed-6-normal-select-4-dishes-want-exactly-1-radiation-exposed-81293472026-04-22T16:02:21+00:00daily0.8https://dev.imagemakers.co.za/guides/we-find-the-smallest-4-digit-number-divisible-by-11-52311722026-04-24T15:26:25+00:00daily0.8https://dev.imagemakers.co.za/guides/we-find-the-largest-4-digit-number-divisible-by-11-65152692026-04-24T15:26:25+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-count-the-number-of-5-digit-numbers-divisible-by--36--5463272026-04-22T16:03:12+00:00daily0.8https://dev.imagemakers.co.za/guides/we-solve-the-absolute-value-inequality-95973702026-04-22T16:07:10+00:00daily0.8https://dev.imagemakers.co.za/guides/we-calculate-the-number-of-ways-to-choose-4-workshops-from-12-and-3-activities-from-7-53130822026-04-24T15:27:45+00:00daily0.8https://dev.imagemakers.co.za/guides/we-compute-the-number-of-ways-to-choose-3-beam-types-from-9-and-2-reinforcement-strategies-from-4-73982012026-04-24T15:27:45+00:00daily0.8https://dev.imagemakers.co.za/guides/we-aim-to-find-the-range-of--pt--for-all-real--t--29042042026-04-24T15:27:58+00:00daily0.8https://dev.imagemakers.co.za/guides/we-seek-the-number-of-three-digit-multiples-of-30-59662122026-04-22T16:10:24+00:00daily0.8https://dev.imagemakers.co.za/guides/we-begin-by-solving-the-quadratic-equation-993522026-04-22T16:16:09+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-distributing--n--10--identical-items-sunlight-units-into--k--4--distinct-groups-zones-where-each-group-can-receive-zero-or-more-57741532026-04-22T16:16:07+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-to-distribute-6-identical-solar-trackers-indistinguishable-into-4-distinguishable-sites-labels-with-the-constraint-that-no-site-receives-more-than-2-trackers-15489352026-04-22T16:16:11+00:00daily0.8https://dev.imagemakers.co.za/guides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e-are-given--a--b--6---ab--4--compute-80442042026-03-15T12:10:04+00:00daily0.8https://dev.imagemakers.co.za/guides/we-must-find-the-least-common-multiple-lcm-of-8-14-and-22-79304322026-03-15T12:23:29+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-search-for-integer-solutions--x-y--satisfying-this-diophantine-equation-rearranging-28007112026-04-24T17:00:59+00:00daily0.8https://dev.imagemakers.co.za/guides/we-want-the-smallest-four-digit--n--so-71578062026-04-24T17:00:59+00:00daily0.8https://dev.imagemakers.co.za/guides/we-have-four-rolls-two-of-one-value-say-78331632026-04-24T17:02:12+00:00daily0.8https://dev.imagemakers.co.za/guides/we-know-t-1--5-the-difference-t0---t-1-is-63863792026-03-15T12:49:18+00:00daily0.8https://dev.imagemakers.co.za/guides/we-total-number-of-distinct-linear-sequences-is-70258912026-03-15T12:49:40+00:00daily0.8https://dev.imagemakers.co.za/guides/we-shift-to-a-probabilistic-interpretation-inspired-by-uniform-random-tiling-90871832026-04-22T23:21:30+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-that-request-times-are-uniformly-distributed-between-100-ms-and-200-ms-inclusive-in-range-the-total-range-of-possible-values-is-17942082026-04-22T23:22:15+00:00daily0.8https://dev.imagemakers.co.za/guides/webview2-secrets-how-microsofts-tiny-tool-is-changing-web-development-forever-71316102026-04-22T23:23:14+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given--r--4--and-need-to-find--s--let-the-legs-be--a--and--b--and-hypotenuse--c--20--62521772026-04-22T23:27:32+00:00daily0.8https://dev.imagemakers.co.za/guides/we-can-write-it-with-common-denominator-54254622026-04-22T23:29:09+00:00daily0.8https://dev.imagemakers.co.za/guides/we-factor-105-into-its-prime-factors-87708062026-04-22T23:41:12+00:00daily0.8https://dev.imagemakers.co.za/guides/we-need-the-least-common-multiple-of-12-and-16-62235122026-04-22T23:41:12+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-choosing-3-tools-from-12-for-the-first-kit-and-we-want-the-probability-that-a-specific-tool-fire-starter-is-included-58935442026-04-22T23:43:14+00:00daily0.8https://dev.imagemakers.co.za/guides/we-treat-the-group-of-3-students-as-a-single-block-reducing-the-number-of-entities-to-arrange-from-7-to-5-the-4-educators-and-1-student-block-45979242026-04-22T23:43:13+00:00daily0.8https://dev.imagemakers.co.za/guides/we-compute-the-probability-that-a-specific-sensor-is-among-the-3-chosen-from-8-72901112026-04-22T23:43:14+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-that--j--s--and-we-are-to-compute-44776292026-04-22T23:46:58+00:00daily0.8https://dev.imagemakers.co.za/guides/we-can-test-integers-systematically-by-calculating-their-fourth-powers-modulo-10000-10563802026-04-22T23:51:34+00:00daily0.8https://dev.imagemakers.co.za/guides/we-will-solve-this-quadratic-equation-using-the-quadratic-formula-95296942026-04-22T23:54:05+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-solve-this-system-of-linear-equations-5906192026-03-15T13:31:20+00:00daily0.8https://dev.imagemakers.co.za/guides/we-use-the-tangent-addition-formula-84504932026-04-23T00:00:34+00:00daily0.8https://dev.imagemakers.co.za/guides/we-seek-the-least-common-multiple-lcm-of-18-and-30-96144442026-04-24T17:18:43+00:00daily0.8https://dev.imagemakers.co.za/guides/weekly-increase--25-growth-factor--125-7218912026-04-23T00:04:59+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-looking-for-the-number-of-integers-between-1000-and-9999-inclusive-that-are-divisible-by-4-72930572026-04-23T00:08:38+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-also-told-the-product-of-the-two-smallest-numbers-is-48-31308722026-04-23T00:14:19+00:00daily0.8https://dev.imagemakers.co.za/guides/we-expand-the-product-using-the-distributive-property-52825592026-04-23T00:14:20+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-the-quadratic-equation-51353572026-04-23T00:32:19+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-interested-in-the-conditional-ordering-of-a-b-and-c-within-the-sequence-among-all-permutations-the-relative-order-of-a-b-and-c-ignoring-the-others-can-be-any-of-the-3--6-possible-orderings-since-the-bee-visits-flowers-randomly-and-no-preference-is-indicated-each-of-these-6-orderings-is-equally-likely-87983372026-04-24T17:27:39+00:00daily0.8https://dev.imagemakers.co.za/guides/we-want-the-specific-order-a-before-b-before-c-only-one-of-the-six-possible-relative-orderings-satisfies-this-54167512026-04-24T17:27:39+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-count-how-many-of-these-satisfy-57855682026-04-24T17:27:38+00:00daily0.8https://dev.imagemakers.co.za/guides/we-list-all-such-triplets-and-count-how-many-satisfy--2b--a--c--90467532026-03-15T14:11:04+00:00daily0.8https://dev.imagemakers.co.za/guides/we-can-fix--b--then--a--b---c--b--and-search-68188852026-03-15T14:11:06+00:00daily0.8https://dev.imagemakers.co.za/guides/we-fix--b--and-for-each--d1--1--to--b---1---d2--d1--1--to--8---b--count-valid--d1-d2--then-sum-65746422026-04-24T17:27:39+00:00daily0.8https://dev.imagemakers.co.za/guides/we-need--f63--with-no-two-reds-adjacent-41435002026-04-24T17:27:39+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-told-that-the-10th-grant-is-issued-in-month-84-substituting--n--10--93466882026-04-23T00:35:49+00:00daily0.8https://dev.imagemakers.co.za/guides/we-have-the-following-system-based-on-the-properties-of-an-ellipse-16885542026-04-23T00:39:17+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-solve-the-four-combinations-using-the-chinese-remainder-theorem-44201212026-04-23T01:04:57+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-told-this-equals--6x--4--comparing-coefficients-23292222026-04-23T01:05:44+00:00daily0.8https://dev.imagemakers.co.za/guides/week-1--week-2-4--5--9-instruments-38490542026-04-23T01:18:47+00:00daily0.8https://dev.imagemakers.co.za/guides/we-approximate-using-the-normal-distribution-due-to-large-n-but-for-accuracy-use-poisson-approximation-or-direct-computation-alternatively-use-known-binomial-formula-or-calculator-55649202026-04-23T01:19:22+00:00daily0.8https://dev.imagemakers.co.za/guides/we-analyze-the-spherical-coordinate-equation-89581782026-04-24T17:40:43+00:00daily0.8https://dev.imagemakers.co.za/guides/we-seek-integer-solutions--x-y--such-that-both--x---y--and--x--y--are-integers-and-their-product-is--144--since--x--83810762026-04-23T01:22:52+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-compute-the-number-of-favorable-outcomesthose-with-at-least-2-high-resilience-districts-this-includes-the-cases-of-exactly-2-3-or-4-high-resilience-districts-59253162026-04-24T17:42:30+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-asked-to-compute-the-number-of-distinct-permutations-of-a-multiset-the-total-number-of-bees-is-98189262026-04-23T01:25:44+00:00daily0.8https://dev.imagemakers.co.za/guides/we-have-3-beetles-b-and-2-flies-f-total-5-insects-number-of-distinct-arrangements-46622222026-04-23T01:25:44+00:00daily0.8https://dev.imagemakers.co.za/guides/we-must-choose-2-distinct-gaps-such-that-they-are-not-adjacent--but-since-were-placing-one-moth-per-gap-any-two-distinct-gaps-ensure-non-adjacency-so-number-of-ways-to-choose-2-non-adjacent-positions-from-6-gaps-is-34682812026-04-23T01:25:44+00:00daily0.8https://dev.imagemakers.co.za/guides/we-choose-2-positions-for-moths-such-that-they-are-not-adjacent-24213072026-04-23T01:25:44+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-that-each-daily-temperature-anomaly-is-an-integer-from--3-to-3-inclusive-there-are-7-independent-days-and-we-want-the-probability-that-the-sum-of-the-7-anomalies-equals-zero-92768972026-04-24T17:42:46+00:00daily0.8https://dev.imagemakers.co.za/guides/we-use-generating-functions-the-generating-function-for-one-day-is-49971742026-04-24T17:42:47+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-to-compute-the-probability-that-in-10-independent-trials-simulations-exactly-3-distinct-alleles-among-6-are-observed-where-at-each-step-an-allele-is-selected-with-probability-proportional-to-its-frequency-ie-multinomial-sampling-without-replacement--but-since-no-actual-frequencies-are-given-assume-uniform-distribution-over-alleles-for-symmetry-however-the-problem-states-selected-uniformly-based-on-relative-frequency-but-without-specific-weights-and-to-make-it-solvable-we-interpret-that-each-allele-has-equal-chance--or-more-naturally-that-the-selection-is-uniform-over-the-6-alleles-at-each-step-ie-discrete-uniform-75514912026-04-24T17:42:46+00:00daily0.8https://dev.imagemakers.co.za/guides/we-count-the-number-of-sequences-of-length-10-with-exactly-3-distinct-alleles-35402662026-04-24T17:42:47+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-to-count-the-number-of-permutations-of-the-6-distinct-artifacts-such-that-no-two-axes-are-adjacent-no-two-bowls-are-adjacent-and-no-two-pectorals-are-adjacent-72076502026-04-23T01:27:59+00:00daily0.8https://dev.imagemakers.co.za/guides/we-use-inclusion-exclusion-over-the-three-forbidden-adjacencies-20511272026-04-23T01:28:00+00:00daily0.8https://dev.imagemakers.co.za/guides/we-begin-by-observing-that-the-equation-is-a-perfect-square-trinomial-17687812026-03-15T15:17:49+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-the-symmetric-equation-of-a-line-61275822026-04-23T01:41:12+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-find-how-many-4-digit-numbers-are-divisible-by-12-16101352026-04-23T01:43:38+00:00daily0.8https://dev.imagemakers.co.za/guides/we-now-find-the-gcd-of-these-numbers-6-15-28-45-and-66-78598392026-04-24T17:47:34+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-choosing-3-distinct-energy-sources-from-12-of-which-4-are-fusion-based-and-8-are-non-fusion-59182182026-04-23T01:45:18+00:00daily0.8https://dev.imagemakers.co.za/guides/we-must-count-the-number-of-4-digit-numbers-using-exactly-two-distinct-digits-with-no-leading-zero-53718042026-04-23T01:48:13+00:00daily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-need-to-choose-3-of-these-6-gaps-to-place-exactly-one-1-in-each-to-avoid-adjacency-19340692026-04-24T17:59:33+00:00daily0.8https://dev.imagemakers.co.za/guides/we-seek-the-area-of-intersection-between-the-two-diamonds-73289892026-03-15T16:07:13+00:00daily0.8https://dev.imagemakers.co.za/guides/we-can-verify-by-checking-vertices-of-intersection-94854242026-03-15T16:07:15+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-three-independent-events-with-probabilities-of-success-accurate-recording-92282392026-04-24T18:02:05+00:00daily0.8https://dev.imagemakers.co.za/guides/we-want-the-probability-that-exactly-two-of-the-three-texts-are-accurate-there-are-three-mutually-exclusive-cases-92652452026-04-24T18:02:13+00:00daily0.8https://dev.imagemakers.co.za/guides/we-analyze-the-systems-stability-by-examining-the-fixed-points-and-eigenvalues-of-the-jacobian-85872842026-03-15T16:12:29+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given--x-y-z--0--with--x--y--z--1--and-we-are-to-minimize-1966542026-04-24T18:03:53+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-a-linear-homogeneous-recurrence-relation-6500522026-04-24T18:03:53+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-pairing-6-distinct-primates-into-3-unordered-pairs-the-total-number-of-ways-to-partition-6-primates-into-3-unordered-pairs-is-65331482026-04-24T18:06:49+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-choosing-5-artifacts-from-12-of-which-4-are-fragile-and-8-are-not-we-want-exactly-2-fragile-artifacts-among-the-5-selected-97551642026-04-23T02:51:09+00:00daily0.8https://dev.imagemakers.co.za/guides/we-want-the-largest-possible-such--x--79297182026-04-23T02:51:35+00:00daily0.8https://dev.imagemakers.co.za/guides/wear-ozempatch-every-day-and-watch-the-weight-melt-awayclinically-proven-magic-79646242026-04-24T18:06:50+00:00daily0.8https://dev.imagemakers.co.za/guides/we-have-the-following-system-of-equations-based-on-the-given-conditions-15782282026-04-23T02:52:42+00:00daily0.8https://dev.imagemakers.co.za/guides/wear-a-pedometer-and-witness-rapid-weight-lossheres-how-it-works-5179912026-04-24T18:12:46+00:00daily0.8https://dev.imagemakers.co.za/guides/we-have-2-ns-to-place-in-these-4-gaps-this-is-equivalent-to-solving-the-problem-of-placing-2-indistinguishable-ns-into-4-distinguishable-gaps-where-gaps-can-hold-zero-or-more-ns-30237642026-04-23T03:13:34+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-to-count-the-number-of-binary-like-sequences-of-length-6-using-symbols-l-and-m-where-no-two-ms-are-adjacent-97303482026-04-23T03:13:35+00:00daily0.8https://dev.imagemakers.co.za/guides/we-break-this-into-two-mutually-exclusive-cases-7157612026-04-23T03:22:51+00:00daily0.8https://dev.imagemakers.co.za/guides/we-compute-the-sequence--cn--iteratively-87818902026-04-23T03:36:04+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-a-finite-difference-equation-53443552026-04-23T03:36:04+00:00daily0.8https://dev.imagemakers.co.za/guides/we-compute-the-binomial-coefficients-5930162026-04-24T18:22:48+00:00daily0.8https://dev.imagemakers.co.za/guides/we-find-the-number-of-integers-divisible-by-9-in-this-range-81441762026-04-24T18:26:40+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-given-that--px--is-a-cubic-polynomial-satisfying-82640012026-04-24T18:27:13+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-looking-for-whole-numbers-between-707-and-1414-which-are-8-9-10-11-12-13-and-14-61548062026-04-23T03:59:04+00:00daily0.8https://dev.imagemakers.co.za/guides/we-use-herons-formula-the-semi-perimeter--s--is-6800162026-04-24T18:27:51+00:00daily0.8https://dev.imagemakers.co.za/guides/we-first-calculate-the-area-using-herons-formula-the-semi-perimeter--s--is-70574922026-04-24T18:27:52+00:00daily0.8https://dev.imagemakers.co.za/guides/we-have-two-equations-based-on-the-information-58151882026-04-24T18:30:14+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-to-count-the-number-of-circular-arrangements-where-all-5-assistants-sit-together-and-8-researchers-are-distinct-individuals-36164402026-04-23T04:08:10+00:00daily0.8https://dev.imagemakers.co.za/guides/we-use-generating-functions-and-roots-of-unity-filter-80721512026-04-23T04:08:10+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-summing-the-signal-strength-from-n--1-to-n--10-20632302026-04-24T18:31:16+00:00daily0.8https://dev.imagemakers.co.za/guides/we-are-told-that--f3--g3--evaluate-both-functions-at--x--3--57052722026-04-23T04:13:45+00:00daily0.8https://dev.imagemakers.co.za/guides/we-search-for-the-smallest-three-digit-number-ending-in-3-that-satisfies-both-divisibility-conditions-77240142026-04-23T04:17:29+00:00daily0.8https://dev.imagemakers.co.za/guides/we-compute-the-number-of-favorable-outcomes-selections-with-at-least-one-from-each-group-use-complementary-counting-subtract-cases-missing-at-least-one-group-64258122026-04-23T04:24:28+00:00daily0.8https://dev.imagemakers.co.za/guides/we-categorize-the-number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