2 n-1 c 0 + (2 n-1 -1)c 1
... Example • What’s the minimum number of students, each of whom comes from one of the 50 states must be enrolled in a university to guarantee that there are at least 100 who come from the same state? ...
... Example • What’s the minimum number of students, each of whom comes from one of the 50 states must be enrolled in a university to guarantee that there are at least 100 who come from the same state? ...
Basic Math: Functions Name: ____TEACHER COPY CCSS.Math
... Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Lesson Plan: 1. Hook (adapted from: jokes4us.com): Mom/Dad: Did you work on your algebra homework at the family reunion? Kid: Yep, it was a function ...
... Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Lesson Plan: 1. Hook (adapted from: jokes4us.com): Mom/Dad: Did you work on your algebra homework at the family reunion? Kid: Yep, it was a function ...
Review sheet
... Also look over homework, old exams and the exercises at the end of each chapter. The most important thing is for you to identify any areas in which you feel weak and get help if you need it. 1. The negation of x P(x) is _______________________ 2.. State the inverse, converse and contrapositive of t ...
... Also look over homework, old exams and the exercises at the end of each chapter. The most important thing is for you to identify any areas in which you feel weak and get help if you need it. 1. The negation of x P(x) is _______________________ 2.. State the inverse, converse and contrapositive of t ...
Daily tests 2 reg 8 relations and functions G
... S = {x | x prime factor of 25} Which can correspond one-one is .... A. P and R C. Q and R B. P and S D. Q and 15. Many one-to-one correspondence that may be from the set L = {i, s, l, a, m} to the set M = [i, h, s, a, n} is ... A. 8 ways C. 24 ways B. 16 ways D. 120 ways 16. The number of handshakes ...
... S = {x | x prime factor of 25} Which can correspond one-one is .... A. P and R C. Q and R B. P and S D. Q and 15. Many one-to-one correspondence that may be from the set L = {i, s, l, a, m} to the set M = [i, h, s, a, n} is ... A. 8 ways C. 24 ways B. 16 ways D. 120 ways 16. The number of handshakes ...
Document
... Combinations Imagine a set S containing n elements and a set T containing (n + 1) elements, namely all elements in S plus a new element a. Calculating C(n + 1, k) is equivalent to answering the question: How many subsets of T containing k items are there? Case I: The subset contains (k – 1) element ...
... Combinations Imagine a set S containing n elements and a set T containing (n + 1) elements, namely all elements in S plus a new element a. Calculating C(n + 1, k) is equivalent to answering the question: How many subsets of T containing k items are there? Case I: The subset contains (k – 1) element ...
Math 308: Defining the rationals and the reals
... The real numbers R are a set that (strictly) contains the rational numbers Q. Addition and multiplication of real numbers extends (agrees with the previous definition of) addition and multiplication of rational numbers (still satisfying field axioms) The relation extends from Q to R (still s ...
... The real numbers R are a set that (strictly) contains the rational numbers Q. Addition and multiplication of real numbers extends (agrees with the previous definition of) addition and multiplication of rational numbers (still satisfying field axioms) The relation extends from Q to R (still s ...
Lecture 4: Combinations, Subsets and Multisets
... Change the problem into counting solutions to an equation Let a1 , a2 , . . . , ak be the k different elements of S, each appearing infinitely many times in S. We want to know how many ways there are to choose a1 some number n1 of times, with n1 ≥ 0 a2 some number n2 of times, with n2 ≥ 0 . . . ak s ...
... Change the problem into counting solutions to an equation Let a1 , a2 , . . . , ak be the k different elements of S, each appearing infinitely many times in S. We want to know how many ways there are to choose a1 some number n1 of times, with n1 ≥ 0 a2 some number n2 of times, with n2 ≥ 0 . . . ak s ...