The document discusses different types of topological spaces, including Hausdorff and non-Hausdorff spaces. It defines separation axioms like T0, T1, T2, etc. and explains that metric spaces and the real number line are Hausdorff. Non-Hausdorff spaces are exemplified using an equivalence relation on the space [0,1]∪[2,3]. Regular, normal and compact Hausdorff spaces are also discussed.
The document provides information about PricewaterhouseCoopers (PwC), one of the largest professional services firms. It details that PwC brings in $25 billion annually, employs 146,000 people across 150 countries, and specializes in accounting, audit, consulting, financial advisory, and tax services. The internship involves comprehensive training through case studies, exercises, and modules to familiarize interns with the firm and technology. PwC looks for poise, communication skills, maturity, integrity, stability, self-reliance, adaptability, initiative, enthusiasm, and aptitude in intern candidates.
This document discusses Cauchy's integral formula and its derivation from Taylor series. It shows that the derivative of an analytic function f(z) can be written as the limit of the Taylor series coefficients divided by (z-z0). Taking the integral of both sides yields Cauchy's integral formula, which expresses f(z) as an integral involving its value at z0 over a contour enclosing z0.
The document discusses homework assignments involving using experiments and simulations to determine probabilities. The first assignment involves simulating a 6 question multiple choice test by guessing answers. The second asks to simulate a 10 question true/false test using coins to find the probability of scoring at least 70% by guessing. The third asks to find the probability of flipping 3 pennies and getting at least 1 head. Guidance is provided on using the calculator's randBin function and the Random.org website to perform the simulations.
The document discusses volumes of revolution and provides formulas to calculate volumes. It mentions volumes can be found by rotating a function about the x-axis and using a function that represents the changing cross-sectional areas. The document also references homework problems and calculating the volume of a cone but provides minimal details or explanations.
The document contains several math and probability word problems and examples presented as homework assignments. It provides the questions, working, and answers for problems involving Pascal's triangle, counting paths, probability, coin flipping, and spinners. The document is a collection of homework questions and solutions on topics of combinatorics, probability, and experimental vs theoretical probability.
This document provides instructions for calculating the volumes of various 3D shapes using integrals. It discusses finding the volume of a revolving cube, calculating the area between curves, and using a function for the changing radii to determine the volume of a cone.
The document discusses different types of topological spaces, including Hausdorff and non-Hausdorff spaces. It defines separation axioms like T0, T1, T2, etc. and explains that metric spaces and the real number line are Hausdorff. Non-Hausdorff spaces are exemplified using an equivalence relation on the space [0,1]∪[2,3]. Regular, normal and compact Hausdorff spaces are also discussed.
The document provides information about PricewaterhouseCoopers (PwC), one of the largest professional services firms. It details that PwC brings in $25 billion annually, employs 146,000 people across 150 countries, and specializes in accounting, audit, consulting, financial advisory, and tax services. The internship involves comprehensive training through case studies, exercises, and modules to familiarize interns with the firm and technology. PwC looks for poise, communication skills, maturity, integrity, stability, self-reliance, adaptability, initiative, enthusiasm, and aptitude in intern candidates.
This document discusses Cauchy's integral formula and its derivation from Taylor series. It shows that the derivative of an analytic function f(z) can be written as the limit of the Taylor series coefficients divided by (z-z0). Taking the integral of both sides yields Cauchy's integral formula, which expresses f(z) as an integral involving its value at z0 over a contour enclosing z0.
The document discusses homework assignments involving using experiments and simulations to determine probabilities. The first assignment involves simulating a 6 question multiple choice test by guessing answers. The second asks to simulate a 10 question true/false test using coins to find the probability of scoring at least 70% by guessing. The third asks to find the probability of flipping 3 pennies and getting at least 1 head. Guidance is provided on using the calculator's randBin function and the Random.org website to perform the simulations.
The document discusses volumes of revolution and provides formulas to calculate volumes. It mentions volumes can be found by rotating a function about the x-axis and using a function that represents the changing cross-sectional areas. The document also references homework problems and calculating the volume of a cone but provides minimal details or explanations.
The document contains several math and probability word problems and examples presented as homework assignments. It provides the questions, working, and answers for problems involving Pascal's triangle, counting paths, probability, coin flipping, and spinners. The document is a collection of homework questions and solutions on topics of combinatorics, probability, and experimental vs theoretical probability.
This document provides instructions for calculating the volumes of various 3D shapes using integrals. It discusses finding the volume of a revolving cube, calculating the area between curves, and using a function for the changing radii to determine the volume of a cone.
The document discusses translations and stretches of graphs, with sections on the role of parameters a and b in shifting graphs right or left (parameter a) and up or down (parameter b). It also covers stretches and compressions along the x and y axes depending on whether parameters a or b are greater than, less than, or between 0 and 1.
A car leaves Winnipeg traveling east or west on a highway at 35 miles per hour. The document discusses using integrals to calculate how far the car is from Winnipeg after 4 hours, taking into account the car's average speed and time traveled. It provides some examples of potential velocity functions that could model the car's motion and notes the driver's poor driving abilities may impact the results.
The document discusses translations of graphs and functions. It provides examples of translating graphs by sliding them along the x-axis. It asks the reader to write equations representing translations of sine graphs based on given functions. It also asks the reader to write one function in terms of another after a translation. Homework assigned is to complete exercise 7 and encourages studying.
The document discusses experimental and theoretical probability. Experimental probability is determined by repeated testing and observing results, calculated as the number of times an event occurred divided by the total number of tests. Theoretical probability is calculated under ideal circumstances based on possible outcomes. For a family with 3 children, the theoretical probability of having 2 girls can be calculated as the number of ways to have 2 girls (3 combinations) divided by the total possible outcomes (8 combinations). An example is also given of simulating a binomial experiment using a calculator to determine the probability of getting exactly 2 heads when flipping 3 coins 40 times.
In a family with 3 children, the probability that 2 of the children will be girls can be calculated as follows:
There are 3 children and each child can be either a boy or a girl. So there are 2 possible outcomes for each child. Using the fundamental principle of counting, there are 2 * 2 * 2 = 8 possible combinations of boys and girls. Out of these 8 combinations, 3 combinations will have exactly 2 girls. Therefore, the probability that 2 of the 3 children will be girls is 3/8.
This document contains answers to a pre-test, including: the time in minutes taken to complete a task; an equation for height h in terms of meters m; the values for variables A, B, and C; the lengths of sides of triangles ABC and BCD; and ratios of sides for triangles ABC and BCD.
This document contains 10 multiple choice questions testing math skills. The questions cover topics like fractions, square roots, averages, profit calculations, and repeating decimals. The document is assessing understanding of basic mathematical operations and concepts.
The document discusses that if the discriminant of a quadratic function is negative, then the roots of the quadratic function are imaginary numbers rather than real numbers.
The document contains 5 math problems involving geometry, calculating distances, finding equations of lines, and writing equations in slope-intercept form. It gives the questions and worked out solutions. The problems cover topics like finding coordinates of a point given other information, calculating distances between points, finding the equation of a line passing through two points, writing an equation in slope-intercept form, and finding the equation of a line perpendicular to another line with a given x-intercept.
The document contains math word problems asking to find equations of lines from points and slopes, find intercepts of lines, and homework assignments for the week including exercises due today and Thursday, a pre-test on Friday, and a unit test on Monday.
This document discusses Riemann sums, which are used to approximate the definite integral of a function over an interval. A Riemann sum takes the area under a curve and approximates it using rectangles. It does this by dividing the interval into subintervals and using the values of the function at the left or right endpoint of each subinterval to determine the height of each rectangle. The closer the subintervals, the more accurate the Riemann sum approximation will be to the true value of the integral.
The document discusses the definite integral and how to estimate distances traveled from a velocity-time graph. It includes a table of velocity values and asks the reader to (1) sketch the velocity-time graph, (2) estimate the lower and upper distances traveled in 5 seconds, (3) estimate the actual distance traveled, and (4) represent the lower estimate as a shaded region on the graph. The document also asks why we began by looking at the picture of rectangles.
The document discusses translations and stretches of graphs, with sections on the role of parameters a and b in shifting graphs right or left (parameter a) and up or down (parameter b). It also covers stretches and compressions along the x and y axes depending on whether parameters a or b are greater than, less than, or between 0 and 1.
A car leaves Winnipeg traveling east or west on a highway at 35 miles per hour. The document discusses using integrals to calculate how far the car is from Winnipeg after 4 hours, taking into account the car's average speed and time traveled. It provides some examples of potential velocity functions that could model the car's motion and notes the driver's poor driving abilities may impact the results.
The document discusses translations of graphs and functions. It provides examples of translating graphs by sliding them along the x-axis. It asks the reader to write equations representing translations of sine graphs based on given functions. It also asks the reader to write one function in terms of another after a translation. Homework assigned is to complete exercise 7 and encourages studying.
The document discusses experimental and theoretical probability. Experimental probability is determined by repeated testing and observing results, calculated as the number of times an event occurred divided by the total number of tests. Theoretical probability is calculated under ideal circumstances based on possible outcomes. For a family with 3 children, the theoretical probability of having 2 girls can be calculated as the number of ways to have 2 girls (3 combinations) divided by the total possible outcomes (8 combinations). An example is also given of simulating a binomial experiment using a calculator to determine the probability of getting exactly 2 heads when flipping 3 coins 40 times.
In a family with 3 children, the probability that 2 of the children will be girls can be calculated as follows:
There are 3 children and each child can be either a boy or a girl. So there are 2 possible outcomes for each child. Using the fundamental principle of counting, there are 2 * 2 * 2 = 8 possible combinations of boys and girls. Out of these 8 combinations, 3 combinations will have exactly 2 girls. Therefore, the probability that 2 of the 3 children will be girls is 3/8.
This document contains answers to a pre-test, including: the time in minutes taken to complete a task; an equation for height h in terms of meters m; the values for variables A, B, and C; the lengths of sides of triangles ABC and BCD; and ratios of sides for triangles ABC and BCD.
This document contains 10 multiple choice questions testing math skills. The questions cover topics like fractions, square roots, averages, profit calculations, and repeating decimals. The document is assessing understanding of basic mathematical operations and concepts.
The document discusses that if the discriminant of a quadratic function is negative, then the roots of the quadratic function are imaginary numbers rather than real numbers.
The document contains 5 math problems involving geometry, calculating distances, finding equations of lines, and writing equations in slope-intercept form. It gives the questions and worked out solutions. The problems cover topics like finding coordinates of a point given other information, calculating distances between points, finding the equation of a line passing through two points, writing an equation in slope-intercept form, and finding the equation of a line perpendicular to another line with a given x-intercept.
The document contains math word problems asking to find equations of lines from points and slopes, find intercepts of lines, and homework assignments for the week including exercises due today and Thursday, a pre-test on Friday, and a unit test on Monday.
This document discusses Riemann sums, which are used to approximate the definite integral of a function over an interval. A Riemann sum takes the area under a curve and approximates it using rectangles. It does this by dividing the interval into subintervals and using the values of the function at the left or right endpoint of each subinterval to determine the height of each rectangle. The closer the subintervals, the more accurate the Riemann sum approximation will be to the true value of the integral.
The document discusses the definite integral and how to estimate distances traveled from a velocity-time graph. It includes a table of velocity values and asks the reader to (1) sketch the velocity-time graph, (2) estimate the lower and upper distances traveled in 5 seconds, (3) estimate the actual distance traveled, and (4) represent the lower estimate as a shaded region on the graph. The document also asks why we began by looking at the picture of rectangles.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,