4.5a Box Whiskers
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This document provides instructions for building a box and whiskers plot. It explains that you should line up and find the median of the numbers, note the minimum and maximum values, and build the plot with a box covering the middle three quartiles and whiskers extending from the box. An example number line is given that could be used as a pattern for the box and whiskers plot, along with instructions to find the minimum, maximum, median, and first and third quartiles.
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This document provides an introduction to box plots, including their anatomy, parts, and applications. It discusses the five number summary used to construct box plots, which includes the minimum, first quartile, median, third quartile, and maximum. Examples are given to demonstrate how to construct a box plot from a data set by ordering the values, finding the five number summary, and plotting the box and whiskers on a number line. Box plots can show the distribution, outliers, and skew of a data set.
Sudoku
This document describes an approach for solving Sudoku puzzles through a step-by-step process of improving an initial brute force solver. It begins with a simple representation of Sudoku grids and validity checking, then introduces techniques to prune invalid choices, collapse partial grids, and expand single choices to iteratively reduce the search space. The final solver uses these techniques to efficiently solve any newspaper Sudoku puzzle instantly by avoiding blocked states that cannot lead to a solution.
Math chapter 6
Here are the key steps to add fractions with like denominators using the properties of addition:
1. Write the fractions with a common denominator. This is necessary so the fractions have the "same unit" to add.
2. Use the commutative property of addition to rearrange the terms in any order.
3. Group the terms using parentheses according to the associative property. This allows you to add the numerators inside the parentheses first before combining groups.
4. Simplify if possible by cancelling out common factors in the numerator and denominator.
5. The sum is a fraction with the common denominator and the total of the numerators as the new numerator.
So in summary - identify a common
Section 5.1
Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors.
5.1 updated
Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors.
Sec. 5.1
Prime numbers are only divisible by 1 and themselves, while composite numbers are divisible by more than two numbers. The first six prime numbers are 2, 3, 5, 7, 11, 13. Prime factorization is writing a composite number as a product of prime factors, using tools like factor trees or ladders. Students will learn how to find factors and write numbers as products of prime factors through examples and reviewing rules for divisibility.
L2 calc stats 08feb12
The document provides instruction on calculating and displaying various statistical measures including the mean, median, mode, range, quartiles, and interquartile range. It includes examples of finding these measures for different data sets and discusses box plots and histograms as good graph types for visualizing the data. Learners are asked to use a graphics calculator to calculate these statistical measures and display them in a box plot graph.
Box And Whisker Plots
This document provides instruction on calculating measures of variability such as range, quartiles, and creating box-and-whisker plots. It includes examples of finding the range and quartiles for data sets. Additional examples demonstrate how to make box-and-whisker plots from data and compare plots to analyze differences between data sets. Practice problems are provided to have students calculate range, quartiles, and create box-and-whisker plots.
Math trick
The document provides step-by-step instructions for performing lattice multiplication with decimals. It demonstrates multiplying 3.42 by 6.9 using a lattice method. The steps include drawing a grid, placing the numbers in the grid with decimals aligned, multiplying the numbers and placing results in the grid, adding the diagonals while carrying numbers, and finally placing the decimal point to get the final answer of 23.598.
Math trick
The document provides step-by-step instructions for performing lattice multiplication with decimals. It demonstrates multiplying 3.42 by 6.9 using a lattice method. The steps include drawing a grid, placing the numbers in the grid with decimals aligned, multiplying the numbers and placing results in the grid, adding the diagonals while carrying numbers, and finally placing the decimal point to get the final answer of 23.598.
Math Trick
The document provides step-by-step instructions for performing lattice multiplication with decimals. It demonstrates multiplying 3.42 by 6.9 using a lattice method. The steps include drawing a grid, placing the numbers in the grid with decimals aligned, multiplying the numbers and placing results in the grid, adding the diagonals while carrying numbers, and finally placing the decimal point to get the final answer of 23.598.
Y5 t2u8d1 4
This document contains a mathematics lesson plan for Year 5 students. It includes two learning objectives - one focused on whole numbers and fractions, and the other on interpreting data in bar charts and line graphs. The lesson consists of exercises to order numbers, identify equivalent fractions, collect and analyze data from dice rolling experiments, and plot temperature and light intensity measurements on line graphs. Students are asked questions throughout to check their understanding of key concepts.
MATHEMATICS WORKBOOK FOR THE UNIT "REAL NUMBERS"
This document contains 6 worksheets with math problems focused on real numbers and number lines for 9th grade students. The worksheets include problems like calculating the length of a diagonal of a square, finding the perimeter of a circle, marking points and positions on number lines, identifying number ranges that satisfy conditions, calculating distances between numbers on a number line, and solving absolute value equations. The goal is to help students practice key concepts involving real numbers.
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Lesson 8 8 A Just Started
This document discusses properties of two special right triangles: 45/45/90 triangles and 30/60/90 triangles. For 45/45/90 triangles, the hypotenuse is √2 times the length of either leg. For 30/60/90 triangles, the longer leg is twice the length of the shorter leg. Examples are given to illustrate these properties and how to find missing side lengths.
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8 3 Similar Triangles
The document discusses similar triangles and how to determine if two triangles are similar. It explains that two triangles are similar if corresponding angles are congruent. It provides examples of using the Angle-Angle similarity criterion to show triangles are similar and using proportions to find missing sides of similar triangles. The lesson covered congruent triangles, similar triangles, determining similarity using corresponding angles, and applying similarity to find unknown lengths.
8 3similar Triangles
The document discusses similar triangles and how to determine if triangles are similar. It explains that similar triangles have congruent angles, while congruent triangles have both congruent angles and sides. It provides examples of using the Angle-Angle similarity criterion to determine if triangles are similar and setting up ratio proportions to calculate missing sides of similar triangles. The lesson objectives are to apply properties of similar triangles and prove that triangles are similar.
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The document discusses several geometry theorems including:
1. The Triangle Sum Theorem which states that the sum of the interior angles of any triangle is 180 degrees.
2. The theorem that the sum of the interior angles of any quadrilateral is 360 degrees.
3. The Exterior Angle Theorem which states that an exterior angle of a triangle is equal to the sum of the two remote interior angles.
The document provides examples of using these theorems to prove other statements and find missing angle measures in geometric figures. It also assigns practice problems for students.
9 2power Of Power
The document discusses exponents and properties related to exponents. It introduces the power of powers property, which states that when a number is raised to a power that is then raised to another power, you multiply the exponents. For example, (3^3)^4 = 3^(3×4) = 3^12. It also discusses how to simplify expressions with negative exponents by writing them as fractions with positive exponents.
4 6 Probablitiy
This document reviews probability and statistics concepts from Algebra I Chapter 4.3. It discusses experimental versus theoretical probability and provides examples of calculating probability using fractions, decimals, and percentages. Sample spaces and probability trees are presented for coin flips, rolling dice, and drawing colored buttons from a bag. Calculating theoretical probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
4 5b Histograms
The document discusses histograms and how they are used to organize and summarize data. Histograms divide a continuous range of data into bins of equal size to display the frequency distribution. They show the frequency of data values within each discrete interval. The document provides an example of students measuring the density of an unknown liquid and creating a histogram to analyze the results. It outlines the steps to organize the density data values, determine the appropriate bin ranges, count the data into groups, and interpret the frequency table and histogram created.
4 1 Proportions
The document provides examples of using proportions to solve various math problems involving ratios, fractions, rates, and geometric similarities. It includes word problems about book sales, fertilizer amounts, heights and shadows, and finding missing values in proportions. The examples demonstrate setting up and solving proportions to find unknown quantities.
4[1].4central Tendencies
The document discusses employee absences and how statistics can be used to analyze absence data. It notes that 40% of illness-related absences occur on Mondays and Fridays, potentially reducing workplace effectiveness. It asks how a boss would feel about this statistic and notes that only 2/5 of absences occur at the start and end of the work week. The document also provides an overview of measures of central tendency, including mean, median, mode, and range.
4.4central Tendencies
The document discusses employee absences and productivity. It notes that 40% of illness-related absences occur on Mondays and Fridays, reducing workplace effectiveness. It asks how a boss would feel about this statistic and notes that only 2/5 of absences occur at the start and end of the work week. The document also provides an overview of measures of central tendency, including mean, median, mode, and range.
3 3two Step Equations
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2 5math Laws
The document discusses various mathematical properties including:
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- Identity properties which show that adding or multiplying a number by its identity (0 for addition, 1 for multiplication) does not change the number.
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- Properties of equality including reflexive, symmetric, transitive, and substitution properties which define when expressions can be said to be equal.
2 3 Subtract Integers
1) Subtracting real numbers is the same as adding the opposite (negative) number.
2) To subtract, change the operation to addition and change the sign of the number being subtracted.
3) For example, 4 - 5 would become 4 + (-5), where -5 is the opposite (negative) of 5.
2 4mult Pos By Neg
The document discusses multiplication and division of integers. It explains that:
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- Division of integers can be performed by rewriting it as multiplication using the reciprocal of the second factor.
- Fractions and their reciprocals are also discussed as ways to rewrite division of fractions as multiplication.
2 2bpos Neg Fractionss
This document discusses adding and subtracting positive and negative integers without calculators. It provides warm up problems asking students to add opposites and lists problems from the textbook for students to work on, including problems subtracting odd integers from pages 47 and 71 of the textbook.
2 2 Pos Neg Numbers
This document discusses adding positive and negative numbers. It begins with warm up questions asking students to find sums and differences without calculators. It then reviews homework answers from the previous day. The document explains how to add positive and negative numbers using colored buttons as an example. It shows -7 + 4 equals 3 negatives. In 3 sentences or less.
1 5 Stem Leaf Plot
A stem and leaf plot is a way to organize and display numerical data. It involves separating each data point into a stem and a leaf. The stems are placed in order and the leaves attached to form a plot. This organized format makes it easier to find values like the median and mode from the data set. To create the plot, the data is first listed, then each value is broken into stem and leaf. The stems are listed in order with the leaves attached to form the plot.
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Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
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Chapter 6
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2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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4.5a Box Whiskers
- 1. Build a Box and Whiskers Plot Box and Whisker plots are related to median averages
- 2. First: Line up your numbers 2 5 3 6 12 9 1 4 2 4