Peluang pert 2
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1) Permutasi refers to the number of arrangements or orderings of all or some elements. It can refer to arrangements of different elements, arrangements of r elements from n different elements, arrangements that include duplicate elements, or cyclic arrangements where order matters. 2) Examples are provided to calculate permutations in different situations such as arranging letters, numbers, arranging r objects from n total objects, and arrangements with duplicate elements. Formulas are provided for each case. 3) Permutations with duplicates involves counting arrangements while accounting for duplicate elements and their frequencies. Cyclic permutations refer to arrangements on a circular setting where position matters. Repeated permutations allow duplicates and use the formula nr.
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There are several key concepts around permutations discussed in the document:
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Tugas latihan menghitung nilai ekspresi matematika dan menentukan jumlah kombinasi yang mungkin terjadi dari angka, huruf, dan objek berbeda yang disusun, termasuk menghitung jumlah kata dari string huruf dan menentukan susunan mutiara dan huruf dalam batasan yang diberikan.
Bentuk akar
1. The document defines root forms as the roots of rational numbers that result in irrational numbers. The general form is √an/m = a1/nm.
2. It provides examples of simplifying root forms, such as √32 = 4√2, and describes addition, subtraction, multiplication, and distribution rules for operating on root forms.
3. Examples are given of simplifying expressions involving addition, subtraction, multiplication, and distribution of root forms according to the defined rules.
Bentuk akar
1. The document defines root forms as the roots of rational numbers that result in irrational numbers. The general form is √an/m = a1/nm.
2. It provides examples of simplifying root forms, such as √32 = 4√2, and describes addition, subtraction, multiplication, and distribution rules for operating on root forms.
3. Examples are given of simplifying expressions involving addition, subtraction, multiplication, and distribution of root forms according to the defined rules.
Wulangan 1
Teks tersebut membahas tentang tiga wara-wara (informasi singkat) yang berisi informasi promosi produk kalender, informasi acara ruwatan sukerta, dan informasi mengenai meninggalnya seseorang.
Bahan ajar Program Linear
This document provides teaching materials on linear programming. It begins with an introduction to linear programming and its applications. It then covers various topics related to linear programming, including feasible regions, linear inequalities, graphical solutions, and determining optimal values. Examples of solving linear programming problems are provided, such as finding the maximum value of an objective function given a feasible region. The materials are intended to help students learn concepts and techniques for solving problems involving two-variable linear programs.
Lks 2 dikonversi
The document provides examples and exercises for students to determine systems of linear inequalities from given regions. In the examples, students are shown how to: 1) identify the intersection points with the x- and y-axes to write the equations of lines, 2) test points to write inequalities, and 3) determine the region bounded based on the axes. Students are then given graphs and asked to determine the corresponding systems of inequalities. The goal is for students to understand how to precisely determine systems of linear inequalities from given solution regions by discussing examples in groups.
Turunan fungsi (1)
Bab 4 membahas turunan fungsi. Turunan fungsi adalah batas dari turunan pertama fungsi ketika h mendekati nol. Turunan fungsi konstan sama dengan nol, sedangkan turunan fungsi yang berbentuk x^n sama dengan n kali x^(n-1). Jika fungsi berbentuk ax^n, maka turunan fungsi tersebut sama dengan a kali n kali x^(n-1).
Ppt 1
Dokumen ini membahas tentang program linear satu dan dua variabel. Tujuan pembelajaran antara lain menumbuhkan sikap disiplin dan kerjasama serta mampu menentukan daerah penyelesaian pertidaksamaan dan sistem pertidaksamaan linear satu dan dua variabel dengan benar. Diberikan pula contoh soal dan penyelesaiannya untuk memahami cara menentukan daerah penyelesaian tersebut dengan menggambar grafik pada bidang koordinat.
Soal limit evaluasi
Ini soal yang kemarin ada di menu tes
silakan kerjakan beserta langkah-langkahnya
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Peluang pert 2
- 1. 3. Permutasi Permutasi adalah banyaknya susunan (cara pengurutan) dari semua atau sebagian unsur. a. Permutasi n unsur yang berbeda Contoh: 1) Tentukan banyaknya cara untuk menyusun huruf-huruf H, A, T, I. Penyelesaian n = 4 4 P 4 = 4! = 4 . 3. 2. 1 = 24 cara 2) Tentukan banyaknya bilangan yang dapat dibentuk dari angka 5, 7, dan 9 jika tidak boleh ada angka yang sama. Penyelesaian n = 3 3 P 3 = 3! = 3. 2. 1 = 6 cara b. Permutasi r unsur dari n unsur yang berbeda Keterangan n : banyaknya unsur yang berbeda r : unsur yang diambil Contoh: 1) Hitunglah nilai dari 5 P 3 ! Penyelesaian 5 P 3 = 5! (5−3)! = 5! 2! = 5.4.3.2! 2! = 5. 4. 3 = 60 2) Tentukan banyak susunan 3 huruf dari huruf-huruf A, B, C, D, E, dan F. Penyelesaian n = 6 r = 3 6 P 3 = 6! (6−3)! = 6! 3! = 6.5.4.3! 3! = 6. 5. 4 = 120 susunan n P n = n . (n – 1) . (n – 2) . ... 3. 2. 1 = n! n P r = 𝑛! (𝑛−𝑟)! , 𝑟 ≤ 𝑛
- 2. c. Permutasi yang memuat unsur yang sama Contoh: Berapa kata dapat disusun dengan semua huruf pada kata “MATEMATIKA” ! Penyelesaian n = 10 k1 = M = 2, k2 = A = 3, k3 = T = 2 10 P 2,3,2 = 10! 2!3!2! = 10.9.8.7.6.5.4.3! 2!3!2! = 10.9.8.7.6.5.4 4 = 151.200 d. Permutasi Siklis Permutasi siklis adalah permutasi yang memperhatikan tempat kedudukan unsur di lingkaran (ditempatkan secara melingkar). Contoh: 1. Hitung banyak permutasi siklis yang terdiri atas 7 unsur yang berlainan. Penyelesaian 7 P (siklis) = (7 − 1)! = 6! = 6.5.4.3.2.1 = 720 2. Dalam suatu pertemuan, ada 8 peserta akan menempati 8 kursi yang mengelilingi meja bundar. Berapa banyak susunan yang mungkin terjadi? Penyelesaian 8 P (siklis) = (8 − 1)! = 7! = 7.6.5.4.3.2.1 = 5.040 susunan e. Permutasi Berulang Contoh: 1. Berapa banyak susunan 3 huruf yang diambil dari huruf-huruf “K, A, M, I, dan S” , jika unsur-unsur yang tersedia itu boleh ditulis berulang? Penyelesaian n = 5, r = 3 P (berulang) = 53 = 125 susunan 2. Berapa banyak bilangan terdiri 2 angka yang dapat disusun dari angka-angka 3, 4, 6, 7, 8, dan 9, jika angka-angka yang tersedia boleh ditulis berulang? Penyelesaian n = 6, r = 2 P (berulang) = 62 = 36 susunan n P (k1, k2, ...., kn) = 𝑛! 𝑘1! 𝑘2! 𝑘3 !… 𝑘𝑛! n P (siklis) = (𝑛 − 1)! P (berulang) = 𝑛𝑟