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Номер 857, страница 286 - гдз по алгебре 8 класс учебник Дорофеев, Суворова
Авторы: Дорофеев Г. В., Суворова С. Б., Бунимович Е. А., Кузнецова Л. В., Минаева С. С., Рослова Л. О.
Тип: Учебник
Издательство: Просвещение
Год издания: 2019 - 2022
Цвет обложки: белый, бирюзовый, оранжевый
Допущено Министерством просвещения Российской Федерации
Популярные ГДЗ в 8 классе
Глава 6. Вероятность и статистика. 6.1. Статистические характеристики. Упражнения - номер 857, страница 286.
App\Models\Task {#1024 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 210137 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "286" "field_page_end" => null "field_url" => "/8-klass/algebra/dorofeev-uchebnik/857" "field_display_title" => "857" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 208997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Вероятность и статистика" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "282" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 80 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Term {#1039 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:6 [ 0 => App\Models\Term {#1041 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дорофеев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Георгий" "field_patronymic" => "Владимирович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1042 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5879 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Суворова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Светлана" "field_patronymic" => "Борисовна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1043 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3941 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бунимович" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1044 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Людмила" "field_patronymic" => "Викторовна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кузнецова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null …4 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Term {#1045 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Term {#1046 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ 0 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => "7" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1059 #items: array:1 [ 0 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => "2022" "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для общеобразовательных организаций" "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1206" "field_priority" => "14" "field_default_folder" => "/algebra_08/dorofeev/" "field_isbn" => null "field_cover" => array:1 [ 0 => "/media/algebra_08/dorofeev/covers/cover1.webp?ts=1734213765" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_08/dorofeev/covers/cover1.webp?ts=1734213765" "alt" => "" "width" => "1919" "height" => "2577" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/algebra/dorofeev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:3 [ 0 => App\Models\Term {#1066 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1068 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2> Почему ученикам нужен решебник? </h2> <p> Многое из того, что изучается в школе, в дальнейшем не пригодится. Так, по крайней мере думают подростки. Однако на практике все получается совершенно по-другому. Поэтому как бы сложен не был предмет (например, алгебра), его необходимо как следует изучить. Чтобы процесс восприятия материала проходил легко и без заминок, следует использовать «<strong>ГДЗ по Алгебре 8 класс Учебник Дорофеев, Суворова, Бунимович, Кузнецова, Минаева, Рослова (Просвещение)</strong>». </p> <p> В справочнике нашли отражение следующие темы: <ol> <li>Алгебраическая дробь, ее свойства, действия с ней.</li> <li>Как преобразовать степень?</li> <li>Теорема Пифагора.</li> <li>График зависимости y=√х.</li> <li>Квадратный и кубический корни.</li> <li>Двойные радикалы, и т.д.</li> </ol> <p> В восьмом классе по предмету проходят спаренные уроки, что с одной стороны должно помочь учителю более подробно объяснить каждую тему. Но на деле и этого времени все равно не хватает, так как программа стала еще обширнее. В итоге, как и раньше, ребятам придется многое разбирать самостоятельно и закреплять полученные в классе навыки практическим путем, но уже дома. Такая задача весьма сложна не только для сильно отстающих учеников, но и для отличников, так что дополнительная помощь никогда не помешает. В этом случае на выручку всегда может прийти решебник. </p> <h2> Делать д/з лучше с ГДЗ к учебнику Дорофеева </h2> <p> Количество домашних заданий в этом году значительно возрастает, так что порой ребята проводят над тетрадями не один час. Но даже это не гарантирует, что все упражнения будут сделаны правильно. Поэтому необходимо сразу же проверять написанное, чтобы не схлопотать плохую оценку. Так как самостоятельно подростки такого мониторинга не проводят, то им поможет в этом <strong>сборник ответов по алгебре 8 класс к учебнику Дорофеева</strong>. </p> <p> Благодаря изданию учащиеся смогут: <ol> <li>улучшить качество письменных работ;</li> <li>избавиться от любых недочетов;</li> <li>приобрести хорошую успеваемость;</li> <li>устранять трудности по мере их возникновения.</li> </ol> <p> Систематически занимаясь с решебником, восьмиклассники научатся не только разбираться в самых непростых темах, но и будут активно применять свои навыки на практике. Это позволит им выбиться в отличники и успешно справляться со всеми поставленными учителем задачами. Кроме того, они могут не переживать о результатах многочисленных проверочных работ, так как будут знать весь материал «на зубок». </p> <h2> Как часто можно использовать онлайн-справочник? </h2> <p> В скором времени учащимся предстоит сдавать первые экзамены, после чего многие из них навсегда покинут школьные стены. Из-за этого на первое место встают успеваемость и качество полученных знаний. Родители стараются всячески помочь детям преодолеть все трудности и нередко записывают их к репетитору. Но намного действеннее могут оказаться занятия с <strong>гдз по алгебре за 8 класс Учебник Дорофеев</strong>. </p> <p> Сборник позволит ученикам: <ul> <li>самостоятельно разобрать все проблемные моменты;</li> <li>дополнительно потренироваться перед контрольными;</li> <li>работать в удобном для себя темпе;</li> <li>не зависеть от помощи взрослых.</li> </ul> <p> Опытные методисты, которые составили решебник, предоставили много полезной информации, благодаря чему никакие дополнительные действия для освоения дисциплины не понадобятся. Но, конечно, если подростки хотят добиться хороших результатов, им стоит забыть о списывании. Необходимо тщательно изучать все сведения, проводить анализ задач и уравнений, чтобы понять принцип их выполнения. 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Статистические характеристики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_page_start" => "282" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1122 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123 …2} ] #original: array:24 [ "id" => 208998 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "6.1. Статистические характеристики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_page_start" => "282" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1122 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 209000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117} "field_page_start" => "286" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1118} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1119} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:5 [ 0 => App\Models\Element {#1125 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 233768 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Edition {#1127 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_content_source" => null ] #original: array:21 [ "id" => 729 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "tolik" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "210137" "type" => "task" ] "text" => "<p><strong>857 АНАЛИЗИРУЕМ</strong> В таблице приведены расходы студента за шесть учебных дней недели.</p><table> <thead> <tr> <th>День недели</th> <th>Понедельник</th> <th>Вторник</th> <th>Среда</th> <th>Четверг</th> <th>Пятница</th> <th>Суббота</th> </tr> </thead> <tbody> <tr> <td>Расходы, р.</td> <td>38</td> <td>40</td> <td>35</td> <td>40</td> <td>27</td> <td>24</td> </tr> </tbody></table><p>Определите, какая статистическая характеристика находится в каждом случае:</p><p><strong>а)</strong> $38 + 40 + 35 + 40 + 27 + 24 = 204,$<br>$204 : 6 = 34, \Box = 34 \text{ р.;}$</p><p><strong>б)</strong> $24, 27, 35, 38, 40, 40,$<br>$(35 + 38) : 2 = 36,5, \Box = 36,5 \text{ р.;}$</p><p><strong>в)</strong> $38, 40, 35, 40, 27, 24, \Box = 40 \text{ р.;}$</p><p><strong>г)</strong> $40 - 24 = 16, \Box = 16 \text{ р.}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "857-1.jpg" "alt" => null "width" => "1632" "height" => 847 "path" => "/media/algebra_08/dorofeev/0-00/857-1.webp?ts=1734264706" ] ] ] #original: array:7 [ "id" => 233768 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1126} "task" => array:2 [ "refs" => "210137" "type" => "task" ] "text" => "<p><strong>857 АНАЛИЗИРУЕМ</strong> В таблице приведены расходы студента за шесть учебных дней недели.</p><table> <thead> <tr> <th>День недели</th> <th>Понедельник</th> <th>Вторник</th> <th>Среда</th> <th>Четверг</th> <th>Пятница</th> <th>Суббота</th> </tr> </thead> <tbody> <tr> <td>Расходы, р.</td> <td>38</td> <td>40</td> <td>35</td> <td>40</td> <td>27</td> <td>24</td> </tr> </tbody></table><p>Определите, какая статистическая характеристика находится в каждом случае:</p><p><strong>а)</strong> $38 + 40 + 35 + 40 + 27 + 24 = 204,$<br>$204 : 6 = 34, \Box = 34 \text{ р.;}$</p><p><strong>б)</strong> $24, 27, 35, 38, 40, 40,$<br>$(35 + 38) : 2 = 36,5, \Box = 36,5 \text{ р.;}$</p><p><strong>в)</strong> $38, 40, 35, 40, 27, 24, \Box = 40 \text{ р.;}$</p><p><strong>г)</strong> $40 - 24 = 16, \Box = 16 \text{ р.}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "857-1.jpg" "alt" => null "width" => "1632" "height" => 847 "path" => "/media/algebra_08/dorofeev/0-00/857-1.webp?ts=1734264706" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1133 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 237259 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Edition {#1135 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_content_source" => null ] #original: array:21 [ "id" => 730 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "210137" "type" => "task" ] "img" => array:4 [ 0 => array:5 [ "name" => "857-1.png" "alt" => null "width" => "705" "height" => 1502 "path" => "/media/algebra_08/dorofeev/1-00/857-1.webp?ts=1734266521" ] 1 => array:5 [ "name" => "857-2.png" "alt" => null "width" => "705" "height" => 1538 "path" => "/media/algebra_08/dorofeev/1-00/857-2.webp?ts=1734266521" ] 2 => array:5 [ "name" => "857-3.png" "alt" => null "width" => "705" "height" => 1502 "path" => "/media/algebra_08/dorofeev/1-00/857-3.webp?ts=1734266521" ] 3 => array:5 [ "name" => "857-4.png" "alt" => null "width" => "705" "height" => 1457 "path" => "/media/algebra_08/dorofeev/1-00/857-4.webp?ts=1734266521" ] ] ] #original: array:6 [ "id" => 237259 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134} "task" => array:2 [ "refs" => "210137" "type" => "task" ] "img" => array:4 [ 0 => array:5 [ "name" => "857-1.png" "alt" => null "width" => "705" "height" => 1502 "path" => "/media/algebra_08/dorofeev/1-00/857-1.webp?ts=1734266521" ] 1 => array:5 [ "name" => "857-2.png" "alt" => null "width" => "705" "height" => 1538 "path" => "/media/algebra_08/dorofeev/1-00/857-2.webp?ts=1734266521" ] 2 => array:5 [ "name" => "857-3.png" "alt" => null "width" => "705" "height" => 1502 "path" => "/media/algebra_08/dorofeev/1-00/857-3.webp?ts=1734266521" ] 3 => array:5 [ "name" => "857-4.png" "alt" => null "width" => "705" "height" => 1457 "path" => "/media/algebra_08/dorofeev/1-00/857-4.webp?ts=1734266521" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1141 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 236131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Edition {#1143 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1147 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_content_source" => null ] #original: array:21 [ "id" => 731 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1147 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "210137" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "857-1.png" "alt" => null "width" => "397" "height" => 224 "path" => "/media/algebra_08/dorofeev/2-00/857-1.webp?ts=1734264970" ] ] ] #original: array:6 [ "id" => 236131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142} "task" => array:2 [ "refs" => "210137" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "857-1.png" "alt" => null "width" => "397" "height" => 224 "path" => "/media/algebra_08/dorofeev/2-00/857-1.webp?ts=1734264970" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Element {#1149 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 236320 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Edition {#1151 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_content_source" => null ] #original: array:21 [ "id" => 732 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "210137" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "857-1.jpg" "alt" => null "width" => "322" "height" => 161 "path" => "/media/algebra_08/dorofeev/3-00/857-1.webp?ts=1734265033" ] ] ] #original: array:6 [ "id" => 236320 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1150} "task" => array:2 [ "refs" => "210137" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "857-1.jpg" "alt" => null "width" => "322" "height" => 161 "path" => "/media/algebra_08/dorofeev/3-00/857-1.webp?ts=1734265033" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Element {#1157 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1374025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1158 #items: array:1 [ 0 => App\Models\Edition {#1159 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1160 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1162 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1160 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1162 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "210137" "type" => "task" ] "text" => "<p>В этой задаче требуется определить, какая статистическая характеристика вычисляется в каждом из четырех случаев на основе данных о расходах студента за шесть дней: 38, 40, 35, 40, 27, 24.</p><p><strong>а)</strong> В данном случае вычисляется сумма всех расходов за шесть дней, а затем результат делится на количество дней (6). Формула расчета: $ (38 + 40 + 35 + 40 + 27 + 24) \div 6 = 204 \div 6 = 34 $. Это определение <strong>среднего арифметического</strong>, которое показывает средний расход студента в день за этот период.<br>Ответ: среднее арифметическое.</p><p><strong>б)</strong> Здесь ряд данных сначала упорядочивается по возрастанию: 24, 27, 35, 38, 40, 40. Так как количество элементов в ряду четное (6), для нахождения центрального значения берутся два средних элемента (35 и 38) и вычисляется их среднее арифметическое: $ (35 + 38) \div 2 = 36.5 $. Это является определением <strong>медианы</strong> для ряда с четным количеством членов. Медиана делит упорядоченный ряд данных на две равные части.<br>Ответ: медиана.</p><p><strong>в)</strong> В исходном ряду данных (38, 40, 35, 40, 27, 24) значение 40 встречается дважды, чаще любого другого значения. Статистическая характеристика, которая представляет собой наиболее часто встречающееся значение в ряду данных, называется <strong>модой</strong>.<br>Ответ: мода.</p><p><strong>г)</strong> В этом вычислении находится разность между наибольшим и наименьшим значениями в ряду данных. Наибольший расход составляет 40 р., а наименьший — 24 р. Их разность: $ 40 - 24 = 16 $. Эта величина называется <strong>размахом</strong> ряда и показывает, насколько велик разброс значений в данных.<br>Ответ: размах.</p>" ] #original: array:6 [ "id" => 1374025 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1158} "task" => array:2 [ "refs" => "210137" "type" => "task" ] "text" => "<p>В этой задаче требуется определить, какая статистическая характеристика вычисляется в каждом из четырех случаев на основе данных о расходах студента за шесть дней: 38, 40, 35, 40, 27, 24.</p><p><strong>а)</strong> В данном случае вычисляется сумма всех расходов за шесть дней, а затем результат делится на количество дней (6). Формула расчета: $ (38 + 40 + 35 + 40 + 27 + 24) \div 6 = 204 \div 6 = 34 $. Это определение <strong>среднего арифметического</strong>, которое показывает средний расход студента в день за этот период.<br>Ответ: среднее арифметическое.</p><p><strong>б)</strong> Здесь ряд данных сначала упорядочивается по возрастанию: 24, 27, 35, 38, 40, 40. Так как количество элементов в ряду четное (6), для нахождения центрального значения берутся два средних элемента (35 и 38) и вычисляется их среднее арифметическое: $ (35 + 38) \div 2 = 36.5 $. Это является определением <strong>медианы</strong> для ряда с четным количеством членов. Медиана делит упорядоченный ряд данных на две равные части.<br>Ответ: медиана.</p><p><strong>в)</strong> В исходном ряду данных (38, 40, 35, 40, 27, 24) значение 40 встречается дважды, чаще любого другого значения. Статистическая характеристика, которая представляет собой наиболее часто встречающееся значение в ряду данных, называется <strong>модой</strong>.<br>Ответ: мода.</p><p><strong>г)</strong> В этом вычислении находится разность между наибольшим и наименьшим значениями в ряду данных. Наибольший расход составляет 40 р., а наименьший — 24 р. Их разность: $ 40 - 24 = 16 $. Эта величина называется <strong>размахом</strong> ряда и показывает, насколько велик разброс значений в данных.<br>Ответ: размах.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "210138" "type" => "task" ] "previous" => array:2 [ "refs" => "210136" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1165 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:1 [ 0 => App\Models\BookPage {#1179 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 930057 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "286" "field_url" => "/8-klass/algebra/dorofeev-uchebnik/page-286" "field_display_title" => "286" "field_folder" => "1" "field_image_name" => "286" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1181 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:1 [ 0 => App\Models\Book {#1182 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1218 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1229 #items: array:1 [ 0 => App\Models\Element {#1228 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "930058" "type" => "book_page" ] "previous" => array:2 [ "refs" => "930056" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1658 #items: array:6 [ 0 => App\Models\Task {#1670 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1757 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Task {#1801 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1812 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#2113 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#2160 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 930057 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "286" "field_url" => "/8-klass/algebra/dorofeev-uchebnik/page-286" "field_display_title" => "286" "field_folder" => "1" "field_image_name" => "286" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1181} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1220} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1218} "content" => Illuminate\Database\Eloquent\Collection {#1229} "next" => array:2 [ "refs" => "930058" "type" => "book_page" ] "previous" => array:2 [ "refs" => "930056" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1658} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 210137 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "286" "field_page_end" => null "field_url" => "/8-klass/algebra/dorofeev-uchebnik/857" "field_display_title" => "857" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1070} "content" => Illuminate\Database\Eloquent\Collection {#1124} "next" 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№857 (с. 286)
Условие. №857 (с. 286)
скриншот условия
857 АНАЛИЗИРУЕМ В таблице приведены расходы студента за шесть учебных дней недели.
| День недели | Понедельник | Вторник | Среда | Четверг | Пятница | Суббота |
|---|---|---|---|---|---|---|
| Расходы, р. | 38 | 40 | 35 | 40 | 27 | 24 |
Определите, какая статистическая характеристика находится в каждом случае:
а) $38 + 40 + 35 + 40 + 27 + 24 = 204,$
$204 : 6 = 34, \Box = 34 \text{ р.;}$
б) $24, 27, 35, 38, 40, 40,$
$(35 + 38) : 2 = 36,5, \Box = 36,5 \text{ р.;}$
в) $38, 40, 35, 40, 27, 24, \Box = 40 \text{ р.;}$
г) $40 - 24 = 16, \Box = 16 \text{ р.}$
Решение 1. №857 (с. 286)
Решение 2. №857 (с. 286)
Решение 3. №857 (с. 286)
Решение 4. №857 (с. 286)
В этой задаче требуется определить, какая статистическая характеристика вычисляется в каждом из четырех случаев на основе данных о расходах студента за шесть дней: 38, 40, 35, 40, 27, 24.
а) В данном случае вычисляется сумма всех расходов за шесть дней, а затем результат делится на количество дней (6). Формула расчета: $ (38 + 40 + 35 + 40 + 27 + 24) \div 6 = 204 \div 6 = 34 $. Это определение среднего арифметического, которое показывает средний расход студента в день за этот период.
Ответ: среднее арифметическое.
б) Здесь ряд данных сначала упорядочивается по возрастанию: 24, 27, 35, 38, 40, 40. Так как количество элементов в ряду четное (6), для нахождения центрального значения берутся два средних элемента (35 и 38) и вычисляется их среднее арифметическое: $ (35 + 38) \div 2 = 36.5 $. Это является определением медианы для ряда с четным количеством членов. Медиана делит упорядоченный ряд данных на две равные части.
Ответ: медиана.
в) В исходном ряду данных (38, 40, 35, 40, 27, 24) значение 40 встречается дважды, чаще любого другого значения. Статистическая характеристика, которая представляет собой наиболее часто встречающееся значение в ряду данных, называется модой.
Ответ: мода.
г) В этом вычислении находится разность между наибольшим и наименьшим значениями в ряду данных. Наибольший расход составляет 40 р., а наименьший — 24 р. Их разность: $ 40 - 24 = 16 $. Эта величина называется размахом ряда и показывает, насколько велик разброс значений в данных.
Ответ: размах.
Другие задания:
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