...Binary Numbers Overview Binary is a number system used by digital devices like computers, cd players, etc. Binary is Base 2, unlike our counting system decimal which is Base 10 (denary). In other words, Binary has only 2 different numerals (0 and 1) to denote a value, unlikeDecimal which has 10 numerals (0,1,2,3,4,5,6,7,8 and 9). Here is an example of a binary number: 10011100 As you can see it is simply a bunch of zeroes and ones, there are 8 numerals in all which make this an 8 bit binary number. Bit is short for Binary Digit, and each numeral is classed as a bit. The bit on the far right, in this case a 0, is known as the Least significant bit (LSB). The bit on the far left, in this case a 1, is known as the Most significant bit (MSB) notations used in digital systems: 4 bits = Nibble 8 bits = Byte 16 bits = Word 32 bits = Double word 64 bits = Quad Word (or paragraph) When writing binary numbers you will need to signify that the number is binary (base 2), for example, let's take the value 101. As it is written, it would be hard to work out whether it is a binary or decimal (denary) value. To get around this problem it is common to denote the base to which the number belongs, by writing the base value with the number, for example: 1012 is a binary number and 10110 is a decimal (denary) value. Once we know the base then it is easy to work out the value, for example: 1012 = 1*22 + 0*21 + 1*20 = 5 (five) 10110 = 1*102 + 0*101 +...
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...The Importance of Number Sense in the Elementary Classroom Robyn Thomas EDU Instructor: Dr. Silvernail November 2, 2011 Abstract In today’s elementary classrooms, students are expected to think and speak on high levels of intelligence. Teachers are encouraged to set high expectations, to question and probe and to ask students to explain what they are thinking. This paper will focus on the importance of understanding numbers or possessing number sense at the elementary level. The idea that students should already have some number sense is controversial. Struggling students in today’s classroom in the area of math seem to lack a major concept, which is a basic math skill or understanding numbers. What is number sense? Number sense refers to a person's general understanding of number and operations along with the ability to use this understanding in flexible ways to make mathematical judgments and to develop useful strategies for solving complex problems. Number sense develops gradually, and varies as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms. Most children acquire this conceptual structure informally through interactions with parents and siblings before they enter kindergarten (Marshall 2010) . Other children who have not acquired it require formal instruction to do so. For example, one child may enter school knowing that...
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...THE NUMBER LINE BY George L Williams III Contents * THE NUMBER LINE * Extended real number line * Drawing the number line * Line segmentation * Comparing numbers * Arithmetic Operations * Arithmetic Operations (cont.) * Algebraic properties * Cartesian Plane/Cartesian Coordinate System * An Overview * My words * Applications of the number line * Resources * THE NUMBER LINE Mathematics is one of the most useful and fascinating divisions of human knowledge. In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer – 5 and the fraction 4/3, and all the irrational numbers such as positive square root of 2,√2. Real numbers can be thought of as points on an infinitely long number line. In basic mathematics, a number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point. Often the integers are shown as specially-marked points evenly spaced on the line. Although this image only shows the integers from −9 to 9, the line includes all real numbers, continuing forever in each direction, as shown by the arrows and also numbers not marked that are between the integers. It is often used as an aid in teaching simple addition and subtraction, especially involving negative numbers. On the number line, numbers located...
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...complex number. Since a complex number z = x + iy is comprised of two real numbers it is natural to consider a plane in which to place a complex number. We shall see that there is a close connection between complex numbers and two-dimensional vectors. In the second part of this Block we introduce an alternative form, called the polar form, for representing complex numbers. We shall see that the polar form is particularly advantageous when multiplying and dividing complex numbers. 9 6 x know what a complex number is Prerequisites Before starting this Block you should . . . 8 y understand how to use trigonometric functions cos θ, sin θ and tan θ z understand what a polynomial function is { possess a knowledge of vectors 7 Learning Outcomes Learning Style After completing this Block you should be able To achieve what is expected of you . . . to . . . represent complex numbers on an Argand diagram obtain the polar form of a complex number multiply and divide complex numbers in polar form allocate sufficient study time briefly revise the prerequisite material attempt every guided exercise and most of the other exercises 1. The Argand diagram In Block 10.1 we met a complex number z = x + iy in which x, y are real numbers and √ i = −1. We learned how to combine complex numbers together using the usual operations of addition, subtraction, multiplication and division. In this block we examine a useful geometrical description of complex numbers. Since a complex number is...
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...Fibonacci Numbers In the 13th century a man named Leonardo of Pisa or Fibonacci founded Fibonacci Numbers. Fibonacci Numbers are “a series of numbers in which each number is the sum of the two preceding numbers” (Burger 57). His book “Liber Abaci” written in 1202 introduced this sequence to Western European mathematics, although they had been described earlier in Indian mathematics. He proved that through spiral counts there is a sequence of numbers with a definite pattern. The simplest series is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…and so on. When looking at this series the pattern proves that adding the previous number to the next will give you the following number in the series. For example, (1+1=2), (2+3=5), and etc. In order to ensure accuracy when using Fibonacci Numbers a formula was created. The formula or rule that follows the Fibonacci sequence is Fn = Fn-1 + Fn-2. By plugging in any numbers in a problem to this equation a student can find the right answer. This gives students the ability to calculate any Fibonacci Number. In modern times society uses these numbers to calculate numerous things. For instance, like the sizes of our arms relative to our torso and even the structure of hurricanes. On another note, Fibonacci Numbers can also be found in patterns in nature. It is truly astonishing to think about how relations in Fibonacci Numbers may possibly be represented in our lives. Works Cited Burger, Edward B., and Michael P. Starbird....
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...Number 40 The feeling of forgetting a phone, a name, and an address is simply frustrating and can mess with your head. It can make you quite uneasy and ruin the rest of the day. Some part of you is not really there, when you forget you’re most valuable belongings. The feeling of forgetting and delirious is exactly what we see in the short “Number 40” by Sarah Butler, from the anthology The Picador Book of 40, 2012. In the short story Number 40 we meet the anxious and unbalanced Melissa. Melissa is feeling anxious because she forgets a lot of things, and this time it is her phone. The short story is told through a third person limited narrator, where the narrator follows the forgetful Melissa throughout the story, and the reader is only able to read only her thoughts and feelings (s. 1, ll. 1-2) Melissa is living with her fiancé Simon: “Now they were living together”. “The ring Simon has given her two weeks ago” – “Three neat diamonds caught in three gold claws”. Simon has proposed to her, just two weeks ago. Melissa felt sick at the time, Simon proposed to her (s.3, ll. 84-85) she either felt vile because of the food or maybe she had a bad hunch towards the relationship. Moreover the relationship did not always seem to go as smooth (s.1, ll. 1-7) She feels like he is ignoring her, like she is not even there. The narrator uses flash back (s. 1, ll. 14-27) where Melissa and Simon was on vacation, where everything seemed wonderful and happy. But as soon as they came home...
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...MMLS NOTE: Spanish Level 1 ➢ Numbers Un and Uno (one) Uno and un are synonyms. Both of them refer to the number one, but “un” must be used before masculine words. Observe that “un” means “one” and “a” (the indefinite article). Study the examples below: Examples: • un coche – one car / a car • un hombre – one man / a man • un niño – one boy / a boy Una Una means “one” and a” (the indefinite article) and must be used along with feminine words. Study the examples: Examples: • una casa – one house / a house • una mujer – one woman / a woman • una niña – one girl / a girl Continue: Cardinal Numbers from 0 to 30 Numbers from 0 to 30 are written as one word. 0. cero 1. uno 2. dos 3. tres 4. cuatro 5. cinco 6. seis 7. siete 8. ocho 9. nueve 10. diez 11. once 12. doce 13. trece 14. catorce 15. quince 16. dieciséis 17. diecisiete 18. dieciocho 19. diecinueve 20. veinte 21. veintiuno 22. veintidós 23. veintitrés 24. veinticuatro 25. veinticinco 26. veintiséis 27. veintisiete 28. veintiocho 29. veintinueve 30. treinta Cardinal Numbers from 31 to 99 From 31 to 99 you have to add “y” (which means "and") between the tens and the unities. Examples: • 31. treinta y uno • 32. treinta y dos ...
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...Weekdays AM 4, 11, 18, 25 Aug09 Mon 8-11 am 3,10,17,24 Aug09 Tues 8-11am 6, 13, 20, 27Aug 09 Wed 8-11am 5, 12 19, 26 Aug09 Thurs 8-11am 7, 14, 21,28Aug09 Fri 8-11am Weekdays PM 7, 14, 21, 28Aug09 Fri 8 12-3pm & 4-7pm 6, 13, 20, 27Aug09 Thurs 12-3pm & 4-7pm 5, 12, 19, 26 Aug 09 Wed 12-3pm & 4-7pm 4, 11, 18, 25Aug09 Tues 12-3pm & 4-7pm 3,10,17,24, 31Aug09 Mon 12-3pm & 4-7pm Here are your random numbers: Days 23 25 24 4 22 2 23 28 7 30 27 26 8 17 5 30 12 17 7 15 8 29 30 6 18 25 6 17 29 24 3 7 9 20 26 5 31 3 22 27 13 18 8 28 19 10 16 13 1 10 27 12 13 27 Timestamp: 2014-01-17 23:49:38 UTC Here are your random numbers: AM Hours 4 3 3 2 1 4 2 1 2 1 2 3 2 1 1 4 4 1 1 4 3 Here are your random numbers: PM hours 3 6 8 6 7 2 7 2 1 4 4 5 8 2 3 6 6 8 7 7 8 Timestamp: 2014-01-18 00:08:43 UTC Weekend AM 2, 9, 16, 23, 30Aug09 Sat 8-11am 1, 8, 15, 22, 29Aug09 Sun 8-11am Weekends PM 1, 8, 15, 22, 29Aug09 Sat 12-3pm & 4-7pm 2, 9, 16, 23,30Aug09 Sun 12-3pm &...
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...Random numbers in C++ and The Pythagorean Theorem Name Course Date Random numbers in C++ and The Pythagorean Theorem Introduction Computer programs in light of the technological advances that have been made, arguably make up for the most important concepts in such developments. A set of instructions designed to assist a computer to prefer a given task is referred to as a computer program. There are numerous languages used to create/design computer for instance Java Script, Java, C++, SQL and Sage (Laine, 2013). Computer programming is defined as a process of developing a working set of computer instructions meant to aid the computer in the performance of a given task. Computer programming starts with the formulation of a valid computer problem. This process is then followed by the development of an executable computer program, for instance Firefox Web Brower (Laine 2013). It is worth noting that there are other programs in the same realm. Computer programming is a diverse field that is of utmost importance in the modern world, especially with the continuous expansion of the internet. Perhaps the relevance of this can be underlined by the fact that computer programming has carved out as a course on itself. Computer programming is offered under several courses studied in colleges and universities (Laine, 2013). Computer programming is not only for computer students but for all who use computers on a day to day basis. This is by extension everyone since the...
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...Let's make something clear from the outset. You are not just represented by one number. When I hear someone say "I am a Numerology number 1", I say "and... what else?". Upon further discussion it turns out the person is usually referring to their Numerology Life Path being calculated as being 1. This is an important number to know, but it is just the beginning. This article looks at the meaning of the number 1 as it relates to Life Path as well as the Soul Urge and the Expression. Numerology Life Path Number 1 The Life Path number is also known as the Birth Path number or Birth Force number. It is calculated from the numbers in your birth date, one of the few things in your life that will never change. The Life Path number gives insight into...
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...OK…So your tired of your current service provider. You’re tired of their sloppy customer service. Tired of having to speak to their discourteous customer representatives. Tired of receiving calls from unknown numbers in the middle of an important meeting only to hear “Kabhi Kabhi Aditi … ” being played and a mechanical female voice saying “Press 1 to set it as your callertune”. So…What would u want to do?? Change your service provider of course! Ah…but wait..you’re attached to your number! All of us are! Why change the number and put up with the trouble of having to remember a completely new one?? The solution to this seemingly never ending problem arrives in India, early next year in the form of Mobile Number Portability. Wondering what this is all about? Simple..you can switch between service providers without having to change your number and you can do this irrespective of the technology that you use. In other words, if you have a CDMA mobile and want to switch to GSM network, you can go ahead and do it with glee Of course, everything comes with a cost. But luckily in this case, the cost isn’t much high!! According to TRAI (Telecom Regulatory Authority of India), subscribers should not be charged more than Rs.19/- for changing their service provider. Mobile services will be disrupted for a few hours when the transfer is in process but this is again a minor hiccup. This service will initially be available only in metros and selected cities by early 2010. And thus...
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...Mathematical Operations of Numbers and Simplifying Algebraic Expressions Section A.: Mathematical Operations of Numbers 1.) 8+((12+5) x 4)/2= 8+(17x4)/2= 8+68/2= 8+34= 42 2.) ((3+4)²+4)-2= (7²+4)-2= (49+4)-2= 53-2= 51 3.) ((12+7)+(8/4)²) (19)+(2)² 19+4 23 4.) ½ + ¼ - ⅓= 6/12+3/12-4/12= 9/12-4/12= 5/12 5.) 2/3 x 3/5 = Multiply straight across 2/3 x 3/5 = 6/15 Find common denominator Reduce to lowest term 6/15 ÷ 3/3 = 2/5 6.) ⅓ ÷ ½ = Multiply by reciprocal ⅓ x 2/1= 2/3 7.) 3/2 ÷ ( 1/5 + 6/10) = 3/2 ÷ (2/10 + 6/10) = 3/2 ÷ 8/10 = Multiply by reciprocal 3/2 x 10/8 = 30/16 = 15/8 = 1 7/8 Section B.: Simplifying Algebraic Expressions 1.) 2x + 3x - 5x + x = 5x - 5x + x = 0 + x = x 2.) 2(6x + 5) = 2(6x) + (2x5) = 12x + 10 = 3.) (14x - 7) /7 = 14x - 7 ÷ 7 = 14x ÷ 7 = 2x -7 ÷ 7 = -1 2x - 1 4.) -(-15x) - 3x = 15x - 3x = 12x 5.) 5(3x+4) - 4 = 15x + 20 - 4 = 15x + 16 = 6.) 5(3x-2)+12x = 15x -10+12x = 27x - 10 = 7.) 4(2y-6)+3(5y+10) = 8y-24+15y+30 = 23y-24+30 = 23y+6= 8.) (x+1) (x-2) = Multiply the first 2, outside 2, inside 2, last 2 xx - 2x + 1x - 2 = xx - 2x + x - 2...
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...If an entire world can be expressed in ones and zero, then why not our living world? In seeing a random sequence of numbers such as 413270, it brings a slew of thoughts to mind. 314 are the first three digits of pi. 4, 3, 2, 1 speaks to me of the applied math and cause of history. 2.71 is my favorite number though an outdated concept for a mature individual. A random sequence of numbers can provide many memories. One of the saddest things lost in childhood is the interest in a favorite number. Nobody over the age of 10 asks another what their favorite number is. Perhaps as we mature we become less attached to certain digit sequences and closer to the meanings of such digits. A favorite number may end up being any numeral that represents a large sum of money. Favorite colors, shapes, and numbers lose importance as we grow and become more aware of our own wants and needs. My favorite number when I was 12 years old was the number 7. I had no particular love of 6 or 8 or any even number for that matter. My birth month, July, is the seventh month and 7 seemed to me to be a significant piece of my personality. It may seem absurd that a number may be of note for someone, but to a 12 year old girl or to a regular lottery ticket purchaser a number is the difference between happiness and misery. As I aged, my favorite number...
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...7.1 2. Fill in the blank If cosθ=-.65, cos-θ= -.65 8. Find sin. θ in quadrant IV cotθ=-13 1+cot2θ=csc2θ 1+-132=csc2θ 1+19=csc2θ 103=cscθ sinθ=1cscθ=1103=-310=-31010 26. Find the five remaining trig functions. cosθ=15, θ in quadrant I sin2θ=1-cos2θ=1-152=1-125=2425=265 secθ=1cosθ=115=5 tanθ= sinθcosθ=26515=26 cotθ=cosθsinθ=15265=126=612 cscθ=1sinθ=12612=526=5612 34.Choose the expression that completes the identity. tanx=sinxcosx , (D.) 38. –tanxcosx=-sinxcosxcosx=-sinx=sin-x, (C.) 56. Write expression in terms of sin and cos, simplify so that no quotients appear in the final expression. cot2θ(1+tan2θ) cos2θsin2θ1cos2θ 1sin2θ=csc2θ 7.2 2. Secxcscx+cscxsecx 1cosx1sinx+1sinx1cosx sinxcosx+cosxsinx sin2x+cos2xcosxsinx 1cosxsinx=secx 18. 4tan2β+tanβ-3=(tanβ+1)(4tanβ-3) 26. cott+tant=1tant(tant)=1 36. tanαsecα=sinα * working w/ left side tanαsecα=sinαcosα1cosα=sinα 46. cosθsinθcotθ=1 *working w/ left side cosθsinθcotθ=cosθsinθ1cotθ=1tanθtanθ=1 68. sinθ+cosθ=sinθ1-cosθsinθ+cosθ1-sinθcosθ 84. 1+cot2x=sec2xsec2x 7.3 6. cos-15° cos30°-45° cos30°cos45°+sin30°sin45° 3222+1222 5+24 72. tanπ4+x=tanπ4+tanx1-tanπ4tanx=1+tanx1-tanx 106. sins+tcosscost=tans+tant * working w/left side sinscost+cosssintcosscost sinscostcosscost+cosssintcosscost sinscoss+sintcost=tans+tant 7.4 20. 1-2sin2221°2=cos[1(221°2)]=cos45°=22 30. cos3x cos2x+x cos2xcosx-sin2xsinx 56. 8sin7xsin9x 8×12[cos7x-9x-cos(7x+9)] 4cos-2x-cos16x 4cos2x-cos16x 58....
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...Connecting to the Real World Brandy Whited Everest University Online Professor Wolf August 23, 2013 Since I started online school sometimes it’s hard to get the correct answer from somebody especially in the financial aid department. Every time I called them regular my financial aid I always get a different answers then I was told. I think the reasons why I get so many different answers they are getting the proper training on how to do their job better. There is one thing that affects me when it comes to my financial aid department. They never give me the correct answer when it comes to the paper work they need from me. It gets me, so frustrated why couldn’t they give me the correct answer in the first place. During that process it makes me feel why I even chose this university. I remember I get challenge from the professor at this university which that is they thing I really like. I feel if they got the proper training they could make students feel more comfortable when it comes to the financial aid process. The financial aid process is long process you need to make sure you have the patience through the whole process. I feel my journey at Everest was long process, because financial aid never gave me the correct what I was...
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