1 Numbers 2 Inequalities
... and go to b is at least as much distance from 0 to a + b. Theorem 4 (Triangle Inequality). For every x, y real numbers, we have |x + y| ≤ |x| + |y| Remark 1. Notice, what I said the theorem said is not at all like it’s written about. It’s important to be able to think about the meaning of a theorem ...
... and go to b is at least as much distance from 0 to a + b. Theorem 4 (Triangle Inequality). For every x, y real numbers, we have |x + y| ≤ |x| + |y| Remark 1. Notice, what I said the theorem said is not at all like it’s written about. It’s important to be able to think about the meaning of a theorem ...
Chapter 4
... Signed Integers Positive numbers and zero can be represented by unsigned n-digit, radix r numbers. We need a representation for negative numbers. To represent a sign (+ or –) we need exactly one more bit of information (1 binary digit gives 21 = 2 elements which is exactly what is needed). Si ...
... Signed Integers Positive numbers and zero can be represented by unsigned n-digit, radix r numbers. We need a representation for negative numbers. To represent a sign (+ or –) we need exactly one more bit of information (1 binary digit gives 21 = 2 elements which is exactly what is needed). Si ...
MCC7.EE.1 Apply properties of operations as strategies to add
... MCC7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. MCC7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole number ...
... MCC7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. MCC7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole number ...
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the
... Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: r = 1/3 Show work in this space. Each term is the previous term divided by 3 or times 1/3 b) Using the formula for the sum of the first n terms of a geometric ...
... Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following: a) What is r, the ratio between 2 consecutive terms? Answer: r = 1/3 Show work in this space. Each term is the previous term divided by 3 or times 1/3 b) Using the formula for the sum of the first n terms of a geometric ...
Week #24
... Caroline is making oatmeal cookies and needs to add 8/12 cup of sugar. Her measuring cup does not have 8/12 cup marked. What is an equivalent measure she could use that would be marked? Which sentence is true about decimal fractions? A. 0.7 < 0.07 B. 0.07 > 0.17 ...
... Caroline is making oatmeal cookies and needs to add 8/12 cup of sugar. Her measuring cup does not have 8/12 cup marked. What is an equivalent measure she could use that would be marked? Which sentence is true about decimal fractions? A. 0.7 < 0.07 B. 0.07 > 0.17 ...
Exam 2
... 6. You take 80% of a number, then take 70% of the result. Will you get the same answer if you first take 70% of the number, then 80% of the result? If the answer is yes, prove it. If it is no, give a counterexample. 80% of 70% of x equals .80(.70)x 70% of 80% of x equals .70(.80)x. Therefore these t ...
... 6. You take 80% of a number, then take 70% of the result. Will you get the same answer if you first take 70% of the number, then 80% of the result? If the answer is yes, prove it. If it is no, give a counterexample. 80% of 70% of x equals .80(.70)x 70% of 80% of x equals .70(.80)x. Therefore these t ...
We are given a set of n lectures (in no particular order) that are
... When the initial automaton is reduced to a two-state automaton, the transition on the arc gives us the desired regular expression. Thus, L(M) = a*b(aUba*b)* 4. Suppose that L={an : n is prime} is regular. Then, according to pumping lemma, there must be an integer n≥1 such that any string w L with ...
... When the initial automaton is reduced to a two-state automaton, the transition on the arc gives us the desired regular expression. Thus, L(M) = a*b(aUba*b)* 4. Suppose that L={an : n is prime} is regular. Then, according to pumping lemma, there must be an integer n≥1 such that any string w L with ...
Integers Foldable
... 1. Pre-cut manila folders to create a strip that is approximately 5.5 inches wide and 20 cm long on each side of the center fold. ...
... 1. Pre-cut manila folders to create a strip that is approximately 5.5 inches wide and 20 cm long on each side of the center fold. ...
Chapter 2 sec 1
... denoted by n(A). A set is finite if its cardinal number is a whole number. An infinite set is one that is not finite. ...
... denoted by n(A). A set is finite if its cardinal number is a whole number. An infinite set is one that is not finite. ...
Project 2
... Let bound be an integer. Let x be an integer between 0 and bound. Let hits=0. Generate a sequence of n integers using a random number generator where the numbers of the sequence are between 0 and bound. Save this new sequence in an array Sequence. If x is equal to any of the numbers generated in the ...
... Let bound be an integer. Let x be an integer between 0 and bound. Let hits=0. Generate a sequence of n integers using a random number generator where the numbers of the sequence are between 0 and bound. Save this new sequence in an array Sequence. If x is equal to any of the numbers generated in the ...
ppt
... “… there is no such thing as a random number – there are only methods to produce random numbers, and an arithmetical procedure is of course not such a method…” “..... a problem we suspect of being solvable by random methods may be solvable by some rigorously defined sequence….” ...
... “… there is no such thing as a random number – there are only methods to produce random numbers, and an arithmetical procedure is of course not such a method…” “..... a problem we suspect of being solvable by random methods may be solvable by some rigorously defined sequence….” ...
Prime Factorization - Math with Mr. Hunt
... • Factors are the numbers you multiply together to get a product. • For example, the product 24 has several factors. • 24 = 1 x 24 • 24 = 2 x 12 • 24 = 3 x 8 • 24 = 4 x 6 • SO, the factors are 1, 2, 3, 4, 6, 8, 12, 24 ...
... • Factors are the numbers you multiply together to get a product. • For example, the product 24 has several factors. • 24 = 1 x 24 • 24 = 2 x 12 • 24 = 3 x 8 • 24 = 4 x 6 • SO, the factors are 1, 2, 3, 4, 6, 8, 12, 24 ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.