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Номер 7, страница 139 - гдз по алгебре 10 класс учебник Абылкасымова, Жумагулова
Авторы: Абылкасымова А. Е., Жумагулова З. А.
Тип: Учебник
Издательство: Мектеп
Год издания: 2019 - 2026
ISBN: 978-601-07-1142-6
Утверждено Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 10 классе
Глава 7. Случайные величины и их числовые характеристики. Проверь себя! - номер 7, страница 139.
App\Models\Task {#1030 // 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" => 1114033 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #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 {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 1113586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Случайные величины и их числовые характеристики" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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" => "126" "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 {#1078 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 4293 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "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 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "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 {#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 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "mektep" ] #original: array:6 [ "id" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "mektep" ] #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 {#1056 #items: array:2 [ 0 => App\Models\Term {#1057 #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" => 6997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Абылкасымова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алма" "field_patronymic" => "Есимбековна" "field_surname_rp" => null ] #original: array:12 [ "id" => 6997 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Абылкасымова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алма" "field_patronymic" => "Есимбековна" "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 {#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:12 [ "id" => 6999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумагулова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Зауре" "field_patronymic" => "Абдыкеновна" "field_surname_rp" => null ] #original: array:12 [ "id" => 6999 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумагулова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Зауре" "field_patronymic" => "Абдыкеновна" "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 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #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_country" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #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_city" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #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_series" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 10 класса общественно-гуманитарного направления общеобразовательных школ" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "514" "field_priority" => "2" "field_default_folder" => "/algebra_10/Abylkasymova-u/" "field_isbn" => "978-601-07-1142-6" "field_cover" => array:1 [ 0 => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/algebra/abylkasymova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 542 "class_subject" => 387 ] ] #original: array:50 [ "id" => 4293 "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060} "field_country" => Illuminate\Database\Eloquent\Collection {#1062} "field_city" => Illuminate\Database\Eloquent\Collection {#1064} "field_series" => Illuminate\Database\Eloquent\Collection {#1066} "field_umk" => Illuminate\Database\Eloquent\Collection {#1067} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1071} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 10 класса общественно-гуманитарного направления общеобразовательных школ" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "514" "field_priority" => "2" "field_default_folder" => "/algebra_10/Abylkasymova-u/" "field_isbn" => "978-601-07-1142-6" "field_cover" => array:1 [ 0 => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_10/Abylkasymova-u/covers/cover1.webp?ts=1752146622" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1072} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1073} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1074} "field_url" => "/10-klass/algebra/abylkasymova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1075} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 542 "class_subject" => 387 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1113586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Случайные величины и их числовые характеристики" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "126" "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 {#1078} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1076} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:2 [ 0 => App\Models\Branch {#1113 #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" => 1113586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Случайные величины и их числовые характеристики" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "126" "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 {#1115 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1113586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Случайные величины и их числовые характеристики" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1114} "field_page_start" => "126" "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 {#1115} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1116} ] #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\Branch {#1117 #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" => 1113589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Проверь себя!" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "138" "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 {#1119 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1113589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Проверь себя!" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118} "field_page_start" => "138" "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 {#1119} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120} ] #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 {#1102 #items: array:3 [ 0 => App\Models\Element {#1095 #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" => 1291134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Edition {#1094 #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" => 4958 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Term {#1093 #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_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" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4958 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092} "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" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088} "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" => "1114033" "type" => "task" ] "text" => "<p><strong>7.</strong> Законы распределения случайных величин X и Y заданы соответственно таблицами 57, 58:</p><p>Таблица 57</p><svg width="240" height="50"><rect x="0" y="0" width="40" height="25" stroke="black" fill="none"/><text x="20" y="17" text-anchor="middle" dominant-baseline="middle">X</text><rect x="40" y="0" width="40" height="25" stroke="black" fill="none"/><text x="60" y="17" text-anchor="middle" dominant-baseline="middle">1</text><rect x="80" y="0" width="40" height="25" stroke="black" fill="none"/><text x="100" y="17" text-anchor="middle" dominant-baseline="middle">3</text><rect x="120" y="0" width="40" height="25" stroke="black" fill="none"/><text x="140" y="17" text-anchor="middle" dominant-baseline="middle">5</text><rect x="160" y="0" width="40" height="25" stroke="black" fill="none"/><text x="180" y="17" text-anchor="middle" dominant-baseline="middle">7</text><rect x="200" y="0" width="40" height="25" stroke="black" fill="none"/><text x="220" y="17" text-anchor="middle" dominant-baseline="middle">9</text><rect x="0" y="25" width="40" height="25" stroke="black" fill="none"/><text x="20" y="42" text-anchor="middle" dominant-baseline="middle">P</text><rect x="40" y="25" width="40" height="25" stroke="black" fill="none"/><text x="60" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text><rect x="80" y="25" width="40" height="25" stroke="black" fill="none"/><text x="100" y="42" text-anchor="middle" dominant-baseline="middle">0,2</text><rect x="120" y="25" width="40" height="25" stroke="black" fill="none"/><text x="140" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="160" y="25" width="40" height="25" stroke="black" fill="none"/><text x="180" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="200" y="25" width="40" height="25" stroke="black" fill="none"/><text x="220" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text></svg><p>Таблица 58</p><svg width="240" height="50"><rect x="0" y="0" width="40" height="25" stroke="black" fill="none"/><text x="20" y="17" text-anchor="middle" dominant-baseline="middle">Y</text><rect x="40" y="0" width="40" height="25" stroke="black" fill="none"/><text x="60" y="17" text-anchor="middle" dominant-baseline="middle">3</text><rect x="80" y="0" width="40" height="25" stroke="black" fill="none"/><text x="100" y="17" text-anchor="middle" dominant-baseline="middle">5</text><rect x="120" y="0" width="40" height="25" stroke="black" fill="none"/><text x="140" y="17" text-anchor="middle" dominant-baseline="middle">8</text><rect x="160" y="0" width="40" height="25" stroke="black" fill="none"/><text x="180" y="17" text-anchor="middle" dominant-baseline="middle">12</text><rect x="200" y="0" width="40" height="25" stroke="black" fill="none"/><text x="220" y="17" text-anchor="middle" dominant-baseline="middle">15</text><rect x="0" y="25" width="40" height="25" stroke="black" fill="none"/><text x="20" y="42" text-anchor="middle" dominant-baseline="middle">P</text><rect x="40" y="25" width="40" height="25" stroke="black" fill="none"/><text x="60" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text><rect x="80" y="25" width="40" height="25" stroke="black" fill="none"/><text x="100" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="120" y="25" width="40" height="25" stroke="black" fill="none"/><text x="140" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="160" y="25" width="40" height="25" stroke="black" fill="none"/><text x="180" y="42" text-anchor="middle" dominant-baseline="middle">0,2</text><rect x="200" y="25" width="40" height="25" stroke="black" fill="none"/><text x="220" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text></svg><p>Вычислите:</p><p><strong>1)</strong> $M(3X - 4Y)$;</p><p><strong>A)</strong> 7,5; 60,59;</p><p><strong>C)</strong> 7,5; 139,33;</p><p><strong>2)</strong> $D(2X + 3Y)$;</p><p><strong>B)</strong> 2,3; 60,59;</p><p><strong>D)</strong> 2,3; 139,33.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "2796" "height" => 1012 "path" => "/media/algebra_10/Abylkasymova-u/0-prceb138/7-1.webp?ts=1753263295" ] ] ] #original: array:7 [ "id" => 1291134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087} "task" => array:2 [ "refs" => "1114033" "type" => "task" ] "text" => "<p><strong>7.</strong> Законы распределения случайных величин X и Y заданы соответственно таблицами 57, 58:</p><p>Таблица 57</p><svg width="240" height="50"><rect x="0" y="0" width="40" height="25" stroke="black" fill="none"/><text x="20" y="17" text-anchor="middle" dominant-baseline="middle">X</text><rect x="40" y="0" width="40" height="25" stroke="black" fill="none"/><text x="60" y="17" text-anchor="middle" dominant-baseline="middle">1</text><rect x="80" y="0" width="40" height="25" stroke="black" fill="none"/><text x="100" y="17" text-anchor="middle" dominant-baseline="middle">3</text><rect x="120" y="0" width="40" height="25" stroke="black" fill="none"/><text x="140" y="17" text-anchor="middle" dominant-baseline="middle">5</text><rect x="160" y="0" width="40" height="25" stroke="black" fill="none"/><text x="180" y="17" text-anchor="middle" dominant-baseline="middle">7</text><rect x="200" y="0" width="40" height="25" stroke="black" fill="none"/><text x="220" y="17" text-anchor="middle" dominant-baseline="middle">9</text><rect x="0" y="25" width="40" height="25" stroke="black" fill="none"/><text x="20" y="42" text-anchor="middle" dominant-baseline="middle">P</text><rect x="40" y="25" width="40" height="25" stroke="black" fill="none"/><text x="60" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text><rect x="80" y="25" width="40" height="25" stroke="black" fill="none"/><text x="100" y="42" text-anchor="middle" dominant-baseline="middle">0,2</text><rect x="120" y="25" width="40" height="25" stroke="black" fill="none"/><text x="140" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="160" y="25" width="40" height="25" stroke="black" fill="none"/><text x="180" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="200" y="25" width="40" height="25" stroke="black" fill="none"/><text x="220" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text></svg><p>Таблица 58</p><svg width="240" height="50"><rect x="0" y="0" width="40" height="25" stroke="black" fill="none"/><text x="20" y="17" text-anchor="middle" dominant-baseline="middle">Y</text><rect x="40" y="0" width="40" height="25" stroke="black" fill="none"/><text x="60" y="17" text-anchor="middle" dominant-baseline="middle">3</text><rect x="80" y="0" width="40" height="25" stroke="black" fill="none"/><text x="100" y="17" text-anchor="middle" dominant-baseline="middle">5</text><rect x="120" y="0" width="40" height="25" stroke="black" fill="none"/><text x="140" y="17" text-anchor="middle" dominant-baseline="middle">8</text><rect x="160" y="0" width="40" height="25" stroke="black" fill="none"/><text x="180" y="17" text-anchor="middle" dominant-baseline="middle">12</text><rect x="200" y="0" width="40" height="25" stroke="black" fill="none"/><text x="220" y="17" text-anchor="middle" dominant-baseline="middle">15</text><rect x="0" y="25" width="40" height="25" stroke="black" fill="none"/><text x="20" y="42" text-anchor="middle" dominant-baseline="middle">P</text><rect x="40" y="25" width="40" height="25" stroke="black" fill="none"/><text x="60" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text><rect x="80" y="25" width="40" height="25" stroke="black" fill="none"/><text x="100" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="120" y="25" width="40" height="25" stroke="black" fill="none"/><text x="140" y="42" text-anchor="middle" dominant-baseline="middle">0,3</text><rect x="160" y="25" width="40" height="25" stroke="black" fill="none"/><text x="180" y="42" text-anchor="middle" dominant-baseline="middle">0,2</text><rect x="200" y="25" width="40" height="25" stroke="black" fill="none"/><text x="220" y="42" text-anchor="middle" dominant-baseline="middle">0,1</text></svg><p>Вычислите:</p><p><strong>1)</strong> $M(3X - 4Y)$;</p><p><strong>A)</strong> 7,5; 60,59;</p><p><strong>C)</strong> 7,5; 139,33;</p><p><strong>2)</strong> $D(2X + 3Y)$;</p><p><strong>B)</strong> 2,3; 60,59;</p><p><strong>D)</strong> 2,3; 139,33.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "2796" "height" => 1012 "path" => "/media/algebra_10/Abylkasymova-u/0-prceb138/7-1.webp?ts=1753263295" ] ] ] #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 {#1089 #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" => 1291648 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Edition {#1086 #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" => 4959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Term {#1085 #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_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" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1082} "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" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1084} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1083} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080} "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" => "1114033" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1948" "height" => 1603 "path" => "/media/algebra_10/Abylkasymova-u/1-prceb138/7-1.webp?ts=1753263526" ] ] ] #original: array:6 [ "id" => 1291648 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1079} "task" => array:2 [ "refs" => "1114033" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1948" "height" => 1603 "path" => "/media/algebra_10/Abylkasymova-u/1-prceb138/7-1.webp?ts=1753263526" ] ] ] #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 {#1081 #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" => 1549702 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Edition {#1077 #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" => 5655 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => 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: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_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" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1034 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5655 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1041} "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" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1034} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1039} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1104} "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" => "1114033" "type" => "task" ] "text" => "<p>Для решения задачи необходимо вычислить математическое ожидание (M) и дисперсию (D) для каждой случайной величины, а затем использовать свойства этих характеристик.</p><p><strong>Шаг 1: Вычисление M(X) и D(X) для случайной величины X.</strong></p><p>Закон распределения X:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center;">X</td><td style="text-align: center;">1</td><td style="text-align: center;">3</td><td style="text-align: center;">5</td><td style="text-align: center;">7</td><td style="text-align: center;">9</td></tr><tr><td style="text-align: center;">P</td><td style="text-align: center;">0,1</td><td style="text-align: center;">0,2</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,1</td></tr></tbody></table><p>Математическое ожидание M(X) вычисляется по формуле $M(X) = \sum x_i p_i$:</p><p>$M(X) = 1 \cdot 0,1 + 3 \cdot 0,2 + 5 \cdot 0,3 + 7 \cdot 0,3 + 9 \cdot 0,1 = 0,1 + 0,6 + 1,5 + 2,1 + 0,9 = 5,2$.</p><p>Для вычисления дисперсии $D(X) = M(X^2) - [M(X)]^2$ сначала найдем $M(X^2)$:</p><p>$M(X^2) = \sum x_i^2 p_i = 1^2 \cdot 0,1 + 3^2 \cdot 0,2 + 5^2 \cdot 0,3 + 7^2 \cdot 0,3 + 9^2 \cdot 0,1$</p><p>$M(X^2) = 1 \cdot 0,1 + 9 \cdot 0,2 + 25 \cdot 0,3 + 49 \cdot 0,3 + 81 \cdot 0,1 = 0,1 + 1,8 + 7,5 + 14,7 + 8,1 = 32,2$.</p><p>Теперь вычислим дисперсию D(X):</p><p>$D(X) = 32,2 - (5,2)^2 = 32,2 - 27,04 = 5,16$.</p><p><strong>Шаг 2: Вычисление M(Y) и D(Y) для случайной величины Y.</strong></p><p>Закон распределения Y:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center;">Y</td><td style="text-align: center;">3</td><td style="text-align: center;">5</td><td style="text-align: center;">8</td><td style="text-align: center;">12</td><td style="text-align: center;">15</td></tr><tr><td style="text-align: center;">P</td><td style="text-align: center;">0,1</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,2</td><td style="text-align: center;">0,1</td></tr></tbody></table><p>Математическое ожидание M(Y) вычисляется по формуле $M(Y) = \sum y_i p_i$:</p><p>$M(Y) = 3 \cdot 0,1 + 5 \cdot 0,3 + 8 \cdot 0,3 + 12 \cdot 0,2 + 15 \cdot 0,1 = 0,3 + 1,5 + 2,4 + 2,4 + 1,5 = 8,1$.</p><p>Для вычисления дисперсии $D(Y) = M(Y^2) - [M(Y)]^2$ сначала найдем $M(Y^2)$:</p><p>$M(Y^2) = \sum y_i^2 p_i = 3^2 \cdot 0,1 + 5^2 \cdot 0,3 + 8^2 \cdot 0,3 + 12^2 \cdot 0,2 + 15^2 \cdot 0,1$</p><p>$M(Y^2) = 9 \cdot 0,1 + 25 \cdot 0,3 + 64 \cdot 0,3 + 144 \cdot 0,2 + 225 \cdot 0,1 = 0,9 + 7,5 + 19,2 + 28,8 + 22,5 = 78,9$.</p><p>Теперь вычислим дисперсию D(Y):</p><p>$D(Y) = 78,9 - (8,1)^2 = 78,9 - 65,61 = 13,29$.</p><p><strong>1)</strong> M(3X – 4Y);</p><p>Используем свойство линейности математического ожидания: $M(aX + bY) = aM(X) + bM(Y)$.</p><p>$M(3X - 4Y) = 3M(X) - 4M(Y)$.</p><p>Подставляем ранее вычисленные значения $M(X)=5,2$ и $M(Y)=8,1$:</p><p>$M(3X - 4Y) = 3 \cdot 5,2 - 4 \cdot 8,1 = 15,6 - 32,4 = -16,8$.</p><p><em>(Примечание: полученный результат не совпадает ни с одним из предложенных вариантов ответа, что указывает на возможную опечатку в условии задачи или в вариантах ответов.)</em></p><p><strong>Ответ:</strong> -16,8</p><p><strong>2)</strong> D(2X + 3Y):</p><p>Для независимых случайных величин используется свойство дисперсии: $D(aX + bY) = a^2D(X) + b^2D(Y)$. Предполагая, что X и Y независимы, получаем:</p><p>$D(2X + 3Y) = 2^2 D(X) + 3^2 D(Y) = 4D(X) + 9D(Y)$.</p><p>Подставляем ранее вычисленные значения $D(X)=5,16$ и $D(Y)=13,29$:</p><p>$D(2X + 3Y) = 4 \cdot 5,16 + 9 \cdot 13,29 = 20,64 + 119,61 = 140,25$.</p><p><em>(Примечание: полученный результат 140,25 близок к варианту ответа 139,33, разница может быть вызвана опечаткой в исходных данных.)</em></p><p><strong>Ответ:</strong> 140,25</p>" ] #original: array:6 [ "id" => 1549702 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108} "task" => array:2 [ "refs" => "1114033" "type" => "task" ] "text" => "<p>Для решения задачи необходимо вычислить математическое ожидание (M) и дисперсию (D) для каждой случайной величины, а затем использовать свойства этих характеристик.</p><p><strong>Шаг 1: Вычисление M(X) и D(X) для случайной величины X.</strong></p><p>Закон распределения X:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center;">X</td><td style="text-align: center;">1</td><td style="text-align: center;">3</td><td style="text-align: center;">5</td><td style="text-align: center;">7</td><td style="text-align: center;">9</td></tr><tr><td style="text-align: center;">P</td><td style="text-align: center;">0,1</td><td style="text-align: center;">0,2</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,1</td></tr></tbody></table><p>Математическое ожидание M(X) вычисляется по формуле $M(X) = \sum x_i p_i$:</p><p>$M(X) = 1 \cdot 0,1 + 3 \cdot 0,2 + 5 \cdot 0,3 + 7 \cdot 0,3 + 9 \cdot 0,1 = 0,1 + 0,6 + 1,5 + 2,1 + 0,9 = 5,2$.</p><p>Для вычисления дисперсии $D(X) = M(X^2) - [M(X)]^2$ сначала найдем $M(X^2)$:</p><p>$M(X^2) = \sum x_i^2 p_i = 1^2 \cdot 0,1 + 3^2 \cdot 0,2 + 5^2 \cdot 0,3 + 7^2 \cdot 0,3 + 9^2 \cdot 0,1$</p><p>$M(X^2) = 1 \cdot 0,1 + 9 \cdot 0,2 + 25 \cdot 0,3 + 49 \cdot 0,3 + 81 \cdot 0,1 = 0,1 + 1,8 + 7,5 + 14,7 + 8,1 = 32,2$.</p><p>Теперь вычислим дисперсию D(X):</p><p>$D(X) = 32,2 - (5,2)^2 = 32,2 - 27,04 = 5,16$.</p><p><strong>Шаг 2: Вычисление M(Y) и D(Y) для случайной величины Y.</strong></p><p>Закон распределения Y:</p><table border="1" style="border-collapse: collapse; width: 100%;"><tbody><tr><td style="text-align: center;">Y</td><td style="text-align: center;">3</td><td style="text-align: center;">5</td><td style="text-align: center;">8</td><td style="text-align: center;">12</td><td style="text-align: center;">15</td></tr><tr><td style="text-align: center;">P</td><td style="text-align: center;">0,1</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,3</td><td style="text-align: center;">0,2</td><td style="text-align: center;">0,1</td></tr></tbody></table><p>Математическое ожидание M(Y) вычисляется по формуле $M(Y) = \sum y_i p_i$:</p><p>$M(Y) = 3 \cdot 0,1 + 5 \cdot 0,3 + 8 \cdot 0,3 + 12 \cdot 0,2 + 15 \cdot 0,1 = 0,3 + 1,5 + 2,4 + 2,4 + 1,5 = 8,1$.</p><p>Для вычисления дисперсии $D(Y) = M(Y^2) - [M(Y)]^2$ сначала найдем $M(Y^2)$:</p><p>$M(Y^2) = \sum y_i^2 p_i = 3^2 \cdot 0,1 + 5^2 \cdot 0,3 + 8^2 \cdot 0,3 + 12^2 \cdot 0,2 + 15^2 \cdot 0,1$</p><p>$M(Y^2) = 9 \cdot 0,1 + 25 \cdot 0,3 + 64 \cdot 0,3 + 144 \cdot 0,2 + 225 \cdot 0,1 = 0,9 + 7,5 + 19,2 + 28,8 + 22,5 = 78,9$.</p><p>Теперь вычислим дисперсию D(Y):</p><p>$D(Y) = 78,9 - (8,1)^2 = 78,9 - 65,61 = 13,29$.</p><p><strong>1)</strong> M(3X – 4Y);</p><p>Используем свойство линейности математического ожидания: $M(aX + bY) = aM(X) + bM(Y)$.</p><p>$M(3X - 4Y) = 3M(X) - 4M(Y)$.</p><p>Подставляем ранее вычисленные значения $M(X)=5,2$ и $M(Y)=8,1$:</p><p>$M(3X - 4Y) = 3 \cdot 5,2 - 4 \cdot 8,1 = 15,6 - 32,4 = -16,8$.</p><p><em>(Примечание: полученный результат не совпадает ни с одним из предложенных вариантов ответа, что указывает на возможную опечатку в условии задачи или в вариантах ответов.)</em></p><p><strong>Ответ:</strong> -16,8</p><p><strong>2)</strong> D(2X + 3Y):</p><p>Для независимых случайных величин используется свойство дисперсии: $D(aX + bY) = a^2D(X) + b^2D(Y)$. Предполагая, что X и Y независимы, получаем:</p><p>$D(2X + 3Y) = 2^2 D(X) + 3^2 D(Y) = 4D(X) + 9D(Y)$.</p><p>Подставляем ранее вычисленные значения $D(X)=5,16$ и $D(Y)=13,29$:</p><p>$D(2X + 3Y) = 4 \cdot 5,16 + 9 \cdot 13,29 = 20,64 + 119,61 = 140,25$.</p><p><em>(Примечание: полученный результат 140,25 близок к варианту ответа 139,33, разница может быть вызвана опечаткой в исходных данных.)</em></p><p><strong>Ответ:</strong> 140,25</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" => "1114034" "type" => "task" ] "previous" => array:2 [ "refs" => "1114032" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\BookPage {#1042 #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" => 1098476 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/page-139" "field_display_title" => "139" "field_folder" => "1" "field_image_name" => "139" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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 {#1112 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Element {#1126 #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" => 1261901 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Edition {#1094} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "139-1.jpg" "alt" => null "width" => "3196" "height" => 4602 "path" => "/media/algebra_10/Abylkasymova-u/0-1/139-1.webp?ts=1752147543" ] ] ] #original: array:6 [ "id" => 1261901 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128} "book_page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "139-1.jpg" "alt" => null "width" => "3196" "height" => 4602 "path" => "/media/algebra_10/Abylkasymova-u/0-1/139-1.webp?ts=1752147543" ] ] ] #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" => "1098477" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1098475" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:5 [ 0 => App\Models\Task {#1207 #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" => 1114030 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1209 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1210 #items: array:1 [ 0 => App\Models\Branch {#1113} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:2 [ 0 => App\Models\Branch {#1113} 1 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:3 [ 0 => App\Models\Element {#1223 #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 [ …7] #original: array:7 [ …7] #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\Element {#1225 #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] } 2 => App\Models\Element {#1227 #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" => "1114031" "type" => "task" ] "previous" => array:2 [ "refs" => "1114029" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #original: array:24 [ "id" => 1114030 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1208} "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 {#1209} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1210} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1211} "content" => Illuminate\Database\Eloquent\Collection {#1214} "next" => array:2 [ "refs" => "1114031" "type" => "task" ] "previous" => array:2 [ "refs" => "1114029" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1220} "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #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\Task {#1213 #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" => 1114031 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1212 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1219 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Branch {#1113} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:2 [ 0 => App\Models\Branch {#1113} 1 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:3 [ 0 => App\Models\Element {#1237 #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 [ …7] #original: array:7 [ …7] #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\Element {#1239 #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] } 2 => App\Models\Element {#1241 #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: [] …13 } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1114032" "type" => "task" ] "previous" => array:2 [ "refs" => "1114030" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #original: array:24 [ "id" => 1114031 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1212} "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 {#1219} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217} "content" => Illuminate\Database\Eloquent\Collection {#1216} "next" => array:2 [ "refs" => "1114032" "type" => "task" ] "previous" => array:2 [ "refs" => "1114030" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1234} "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #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\Task {#1218 #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" => 1114032 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1215 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1233 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1235 #items: array:1 [ 0 => App\Models\Branch {#1113} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:2 [ 0 => App\Models\Branch {#1113} 1 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:3 [ 0 => App\Models\Element {#1251 …30} 1 => App\Models\Element {#1253 …30} 2 => App\Models\Element {#1255 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1114033" "type" => "task" ] "previous" => array:2 [ "refs" => "1114031" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #original: array:24 [ "id" => 1114032 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1215} "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 {#1233} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1235} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231} "content" => Illuminate\Database\Eloquent\Collection {#1230} "next" => array:2 [ "refs" => "1114033" "type" => "task" ] "previous" => array:2 [ "refs" => "1114031" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1248} "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #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\Task {#1232 #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" => 1114033 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1229 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1247 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ 0 => App\Models\Branch {#1113} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:2 [ 0 => App\Models\Branch {#1113} 1 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:3 [ 0 => App\Models\Element {#1095} 1 => App\Models\Element {#1089} 2 => App\Models\Element {#1081} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1114034" "type" => "task" ] "previous" => array:2 [ "refs" => "1114032" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #original: array:24 [ "id" => 1114033 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => null "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1229} "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 {#1247} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1249} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245} "content" => Illuminate\Database\Eloquent\Collection {#1243} "next" => array:2 [ "refs" => "1114034" "type" => "task" ] "previous" => array:2 [ "refs" => "1114032" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1246} "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #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\Task {#1244 #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" => 1114034 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => "140" "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-8" "field_display_title" => "8" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1257 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1258 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:1 [ 0 => App\Models\Branch {#1113} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:2 [ 0 => App\Models\Branch {#1113} 1 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:3 [ 0 => App\Models\Element {#1272 …30} 1 => App\Models\Element {#1274 …30} 2 => App\Models\Element {#1276 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1114035" "type" => "task" ] "previous" => array:2 [ "refs" => "1114033" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #original: array:24 [ "id" => 1114034 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_page_end" => "140" "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/prceb138-8" "field_display_title" => "8" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1257} "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 {#1258} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1259} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1260} "content" => Illuminate\Database\Eloquent\Collection {#1263} "next" => array:2 [ "refs" => "1114035" "type" => "task" ] "previous" => array:2 [ "refs" => "1114033" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1269} "page" => array:2 [ "refs" => "1098476" "type" => "book_page" ] ] #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:21 [ "id" => 1098476 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "139" "field_url" => "/10-klass/algebra/abylkasymova-uchebnik/page-139" "field_display_title" => "139" "field_folder" => "1" "field_image_name" => "139" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1040} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1103} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => 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№7 (с. 139)
Условие. №7 (с. 139)
скриншот условия
7. Законы распределения случайных величин X и Y заданы соответственно таблицами 57, 58:
Таблица 57
Таблица 58
Вычислите:
1) $M(3X - 4Y)$;
A) 7,5; 60,59;
C) 7,5; 139,33;
2) $D(2X + 3Y)$;
B) 2,3; 60,59;
D) 2,3; 139,33.
Решение. №7 (с. 139)
Решение 2. №7 (с. 139)
Для решения задачи необходимо вычислить математическое ожидание (M) и дисперсию (D) для каждой случайной величины, а затем использовать свойства этих характеристик.
Шаг 1: Вычисление M(X) и D(X) для случайной величины X.
Закон распределения X:
| X | 1 | 3 | 5 | 7 | 9 |
| P | 0,1 | 0,2 | 0,3 | 0,3 | 0,1 |
Математическое ожидание M(X) вычисляется по формуле $M(X) = \sum x_i p_i$:
$M(X) = 1 \cdot 0,1 + 3 \cdot 0,2 + 5 \cdot 0,3 + 7 \cdot 0,3 + 9 \cdot 0,1 = 0,1 + 0,6 + 1,5 + 2,1 + 0,9 = 5,2$.
Для вычисления дисперсии $D(X) = M(X^2) - [M(X)]^2$ сначала найдем $M(X^2)$:
$M(X^2) = \sum x_i^2 p_i = 1^2 \cdot 0,1 + 3^2 \cdot 0,2 + 5^2 \cdot 0,3 + 7^2 \cdot 0,3 + 9^2 \cdot 0,1$
$M(X^2) = 1 \cdot 0,1 + 9 \cdot 0,2 + 25 \cdot 0,3 + 49 \cdot 0,3 + 81 \cdot 0,1 = 0,1 + 1,8 + 7,5 + 14,7 + 8,1 = 32,2$.
Теперь вычислим дисперсию D(X):
$D(X) = 32,2 - (5,2)^2 = 32,2 - 27,04 = 5,16$.
Шаг 2: Вычисление M(Y) и D(Y) для случайной величины Y.
Закон распределения Y:
| Y | 3 | 5 | 8 | 12 | 15 |
| P | 0,1 | 0,3 | 0,3 | 0,2 | 0,1 |
Математическое ожидание M(Y) вычисляется по формуле $M(Y) = \sum y_i p_i$:
$M(Y) = 3 \cdot 0,1 + 5 \cdot 0,3 + 8 \cdot 0,3 + 12 \cdot 0,2 + 15 \cdot 0,1 = 0,3 + 1,5 + 2,4 + 2,4 + 1,5 = 8,1$.
Для вычисления дисперсии $D(Y) = M(Y^2) - [M(Y)]^2$ сначала найдем $M(Y^2)$:
$M(Y^2) = \sum y_i^2 p_i = 3^2 \cdot 0,1 + 5^2 \cdot 0,3 + 8^2 \cdot 0,3 + 12^2 \cdot 0,2 + 15^2 \cdot 0,1$
$M(Y^2) = 9 \cdot 0,1 + 25 \cdot 0,3 + 64 \cdot 0,3 + 144 \cdot 0,2 + 225 \cdot 0,1 = 0,9 + 7,5 + 19,2 + 28,8 + 22,5 = 78,9$.
Теперь вычислим дисперсию D(Y):
$D(Y) = 78,9 - (8,1)^2 = 78,9 - 65,61 = 13,29$.
1) M(3X – 4Y);
Используем свойство линейности математического ожидания: $M(aX + bY) = aM(X) + bM(Y)$.
$M(3X - 4Y) = 3M(X) - 4M(Y)$.
Подставляем ранее вычисленные значения $M(X)=5,2$ и $M(Y)=8,1$:
$M(3X - 4Y) = 3 \cdot 5,2 - 4 \cdot 8,1 = 15,6 - 32,4 = -16,8$.
(Примечание: полученный результат не совпадает ни с одним из предложенных вариантов ответа, что указывает на возможную опечатку в условии задачи или в вариантах ответов.)
Ответ: -16,8
2) D(2X + 3Y):
Для независимых случайных величин используется свойство дисперсии: $D(aX + bY) = a^2D(X) + b^2D(Y)$. Предполагая, что X и Y независимы, получаем:
$D(2X + 3Y) = 2^2 D(X) + 3^2 D(Y) = 4D(X) + 9D(Y)$.
Подставляем ранее вычисленные значения $D(X)=5,16$ и $D(Y)=13,29$:
$D(2X + 3Y) = 4 \cdot 5,16 + 9 \cdot 13,29 = 20,64 + 119,61 = 140,25$.
(Примечание: полученный результат 140,25 близок к варианту ответа 139,33, разница может быть вызвана опечаткой в исходных данных.)
Ответ: 140,25
Другие задания:
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