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http://nrich.maths.org/public/leg.php?code=31&cl=2&cldcmpid=1181 | 1,505,874,041,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818686117.24/warc/CC-MAIN-20170920014637-20170920034637-00250.warc.gz | 246,905,318 | 10,005 | # Search by Topic
#### Resources tagged with Addition & subtraction similar to Traffic Lights:
Filter by: Content type:
Stage:
Challenge level:
### First Connect Three for Two
##### Stage: 2 and 3 Challenge Level:
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
### Domino Numbers
##### Stage: 2 Challenge Level:
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
### First Connect Three
##### Stage: 2 and 3 Challenge Level:
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
### Number Differences
##### Stage: 2 Challenge Level:
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
### Connect Three
##### Stage: 3 and 4 Challenge Level:
Can you be the first to complete a row of three?
##### Stage: 2 Challenge Level:
If you have only four weights, where could you place them in order to balance this equaliser?
### A Square of Numbers
##### Stage: 2 Challenge Level:
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
### One Million to Seven
##### Stage: 2 Challenge Level:
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
### Have You Got It?
##### Stage: 3 Challenge Level:
Can you explain the strategy for winning this game with any target?
##### Stage: 1 and 2 Challenge Level:
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
### Difference
##### Stage: 2 Challenge Level:
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
### Cunning Card Trick
##### Stage: 3 Challenge Level:
Delight your friends with this cunning trick! Can you explain how it works?
### Making Maths: Double-sided Magic Square
##### Stage: 2 and 3 Challenge Level:
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
### A Dotty Problem
##### Stage: 2 Challenge Level:
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
### Which Symbol?
##### Stage: 2 Challenge Level:
Choose a symbol to put into the number sentence.
### Countdown
##### Stage: 2 and 3 Challenge Level:
Here is a chance to play a version of the classic Countdown Game.
### Got it Article
##### Stage: 2 and 3
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
### Number Pyramids
##### Stage: 3 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
### Cayley
##### Stage: 3 Challenge Level:
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
### Weights
##### Stage: 3 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
### Cycling Squares
##### Stage: 2 Challenge Level:
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
### Cubes Within Cubes
##### Stage: 2 and 3 Challenge Level:
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
### More Plant Spaces
##### Stage: 2 and 3 Challenge Level:
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
### Got It
##### Stage: 2 and 3 Challenge Level:
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
### More Children and Plants
##### Stage: 2 and 3 Challenge Level:
This challenge extends the Plants investigation so now four or more children are involved.
### Number Daisy
##### Stage: 3 Challenge Level:
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
### Dodecamagic
##### Stage: 2 Challenge Level:
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
### Two and Two
##### Stage: 3 Challenge Level:
How many solutions can you find to this sum? Each of the different letters stands for a different number.
### Rod Measures
##### Stage: 2 Challenge Level:
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
### On Target
##### Stage: 2 Challenge Level:
You have 5 darts and your target score is 44. How many different ways could you score 44?
### Clocked
##### Stage: 3 Challenge Level:
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
### Sort Them Out (2)
##### Stage: 2 Challenge Level:
Can you each work out the number on your card? What do you notice? How could you sort the cards?
### A-magical Number Maze
##### Stage: 2 Challenge Level:
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
### Strike it Out
##### Stage: 1 and 2 Challenge Level:
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
### Painting Possibilities
##### Stage: 2 Challenge Level:
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
### Wild Jack
##### Stage: 2 Challenge Level:
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
##### Stage: 2 Challenge Level:
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
### Code Breaker
##### Stage: 2 Challenge Level:
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
### Criss Cross Quiz
##### Stage: 2 Challenge Level:
A game for 2 players. Practises subtraction or other maths operations knowledge.
##### Stage: 3 Challenge Level:
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
### Pouring the Punch Drink
##### Stage: 2 Challenge Level:
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
### Bean Bags for Bernard's Bag
##### Stage: 2 Challenge Level:
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
### Sitting Round the Party Tables
##### Stage: 1 and 2 Challenge Level:
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
### Neighbours
##### Stage: 2 Challenge Level:
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
### Consecutive Negative Numbers
##### Stage: 3 Challenge Level:
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
### Magic Triangle
##### Stage: 2 Challenge Level:
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
### Arranging the Tables
##### Stage: 2 Challenge Level:
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
### Prison Cells
##### Stage: 2 Challenge Level:
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
### Hubble, Bubble
##### Stage: 2 Challenge Level:
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
### Build it up More
##### Stage: 2 Challenge Level:
This task follows on from Build it Up and takes the ideas into three dimensions! | 2,203 | 9,436 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2017-39 | latest | en | 0.905293 |
https://howmany.cc/convert/convert-15-74-cm-to-inches/ | 1,675,221,577,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499899.9/warc/CC-MAIN-20230201013650-20230201043650-00459.warc.gz | 296,400,160 | 15,888 | # Convert 15.74 cm to inches
## How many inches is in a centimeter?
When you want to convert 15.74 cm to a number in inches, first you need to determine how many inches one centimeter is equal to.
Here’s what I can be specific: one cm equals 0.3937 inches.
## Definition:Centimeter
The centimeter unit is a base unit of length.
It equals to 10 millimeters.
This unit is used in CGS system, maps, home repaire and all areas in our life.
A single centimeter is roughly equivalent to 39.37 inches.
## Definition of Inch
The inch is a unit of length in the UK and the US customary systems of measurement. An inch is equal to 1/12 of a foot or 1/36 yard.
## How can you convert 1 cm into inches?
To convert 1 centimeter into inches, simply multiply 1cm by the conversion factor of 0.3937.
This makes it much easier to convert 15.74 cm to inches.
So, 1 cm into inches = 1 times 0.3937 = 0.3937 inches, exactly.
• What is one centimeter to inches?
• What is conversion rate cm to inches?
• How many inches is equal to 1 cm?
• What is 1 cm in inches equal?
### How do u convert 15.74 cm to inches?
From the above, you have a good grasp of cm to inches.
Here is the exact algorithm:
Value in inches = value in cm × 0.3937
So, 15.74 cm to inches = 15.74 cm × 0.3937 = 6.196838 inches
This formula can also be used to answer similar questions:
• What is the formula to convert 15.74 cm to inches?
• How do I convert cm to inches?
• How to translate cm to inches?
• How to measure cm into inches?
• What size are 15.74 cm into inches?
cm inches 15.34 cm 6.039358 inches 15.39 cm 6.059043 inches 15.44 cm 6.078728 inches 15.49 cm 6.098413 inches 15.54 cm 6.118098 inches 15.59 cm 6.137783 inches 15.64 cm 6.157468 inches 15.69 cm 6.177153 inches 15.74 cm 6.196838 inches 15.79 cm 6.216523 inches 15.84 cm 6.236208 inches 15.89 cm 6.255893 inches 15.94 cm 6.275578 inches 15.99 cm 6.295263 inches 16.04 cm 6.314948 inches 16.09 cm 6.334633 inches | 605 | 1,953 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.71875 | 4 | CC-MAIN-2023-06 | longest | en | 0.815029 |
https://www.sawaal.com/quantitative-aptitude-arithmetic-ability-questions-and-answers/if-160y2-x1x-160then-160what-160is-160the-160value-160of-1601y1-160-1602y1y2-1-160_21584 | 1,656,793,288,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104204514.62/warc/CC-MAIN-20220702192528-20220702222528-00292.warc.gz | 1,025,681,225 | 14,577 | 0
Q:
A) (1+x)(2-x)2x-1 B) (1-x)(2+x)x-1 C) (1+x)(2-x)1-2x D) (1+x)(1-2x)2-x
Explanation:
Q:
The given Bar Graph presents the Imports and Exports of an item (in tonnes) manufactured by a company for the five financial years, 2013-2014 to 2017-2018.
What is the average of Export (in tonnes) during the five financial years ?
A) 1279.5 B) 1552.4 C) 1025.9 D) 1279.6
Explanation:
0 26
Q:
There was 25% off on bags. A lady bought a bag and got additional 20% discount for paying in cash. She paid ₹480. What was the price tag (in ₹) on the bag?
A) 950 B) 825 C) 800 D) 750
Explanation:
1 162
Q:
What is the area of a rhombus(in cm ) whose side is 20 cm and one of the diagonals is 24 cm ?
A) 396 B) 392 C) 350 D) 384
Explanation:
0 97
Q:
The simplified value of is A circle is inscribed in a triangle ABC.It touches sides AB, BC and AC at points P, Q and R respectively. If BP = 9 cm, CQ = 10 cm and AR = 11 cm, then the perimeter (in cm)of the triangle ABC is:
A) 72.5 B) 57.5 C) 60 D) 75
Explanation:
1 106
Q:
The given Bar Graph presents the Imports and Exports of an item (in tonnes) manufactured by a company for the five financial years, 2013-2014 to 2017-2018.
What is the average of total Import and Export (in tonnes) during the five financial year ?
A) 2508.8 B) 2279.5 C) 2552.4 D) 2325.9
Explanation:
0 171
Q:
The given Bar Graph presents the Imports and Exports of an item (in tonnes) manufactured by a company for the five financial years, 2013-2014 to 2017-2018.
What is the ratio of total Imports to total Exports during 2013-2014, 2015-2016 and 2017-2018?
A) 4175 : 4011 B) 4011 : 4175 C) 3619 : 3604 D) 3604 : 3073
Answer & Explanation Answer: C) 3619 : 3604
Explanation:
0 118
Q:
In which financial year the total of the Exports and Imports is the lowest ?
A) 2013-2014 B) 2017-2018 C) 2015-2016 D) 2014-2015
Explanation:
0 156
Q:
The given Bar Graph presents the Imports and Exports of an item (in tonnes) manufactured by a company for the five financial years, 2013-2014 to 2017-2018.
The given Bar Graph presents the Imports and Exports of an item (in tonnes) manufactured by a company for the five financial years, 2013-2014 to 2017-2018.
A) 2016-2017 B) 2014-2015 C) 2015-2016 D) 2017-2018 | 779 | 2,254 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2022-27 | latest | en | 0.753029 |
https://notesread.com/theorem/ | 1,653,329,612,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662560022.71/warc/CC-MAIN-20220523163515-20220523193515-00680.warc.gz | 483,430,035 | 23,394 | Theorem
Theorem . It is a statement that must be demonstrated within a formal system. Proving theorems is a central issue in deductive mathematics . However, how the theorems arise is the task of intuitive mathematics [1]
Summary
[ hide ]
• 1 Terminology
• 2 Definitions of theorem
• 3 Theorems in mathematical logic
• 4 Theorems in other sciences
• 5 Examples of theorems
• 6 Utterances
• 1 Usual form
• 2 Implicative form
• 3 Disjunctive form
• 7 Sources
• 8 References
Terminology
From the Latin word theorēma , a theorem is a proposition that must be proved logically from its hypothesis, resorting to axioms or other theorems previously demonstrated. This demonstration process is done using certain rules of inference.
The theorem is, therefore, a statement of importance. There are lower-level statements, such as the lemma (a statement linked to a longer theorem and guides the proof of this), the corollary ‘ (the statement that immediately follows the theorem) or the proposition (a result that is not found associated with no specific theorem); finally, scholium which is an important propositional observation.
It should be noted that, until the statement is proven, it is called either an unproven conjecture or proposition.
A theorem generally has a number of premises that must be listed or clarified beforehand. Then there is a conclusion, a mathematical statement, which is true under the given conditions. The informative content of the theorem is the relationship between the hypothesis and the thesis or conclusion.
Corollary . A logical statement that is an immediate consequence of a theorem, and can be proved using the properties of the theorem previously demonstrated.
Definitions of theorem
• A theorem is a statement that can be proved to be true within a logical framework.
• Theorem is a Propositionthat needs to be proved to be evident. For example: The sum of the angles of a triangle equals two right angles.
• Proposition that affirms a demonstrable truth.
• For every set, there is a set that does not belong to it. Proof. Let A be any set. Let D be the set of y that belong to set A, such that they fulfill the property “and does not belong to y”. …
• It is a truth not evident, but demonstrable.
Theorems in mathematical logic
A theorem requires a logical framework; This framework will consist of a set of Axioms Axiomatic System and an Inference process, which allows to derive theorems from the axioms and theorems that have been previously derived.
In Mathematical Logic and Propositional Logic , any proved statement is called a theorem. More specifically in mathematical logic a finite sequence of well-formed Formulas (well-formed logical formulas) F1, …, Fn is called proof , such that each Fi is either an axiom or a theorem that follows from two previous formulas Fj and Fk (such that j <i and k <i) using a deduction rule.
Given a proof like the one above if the final element Fn is not an axiom then it is a theorem. Summing up, the above can be formally said, a theorem is a well-formed formula, which is not an axiom, and which may be the final element of some proof, that is, a theorem is a well-formed logical formula for which there is a proof .
Theorems in other sciences
Frequently in Physics or Economics some important statements that can be deduced or justified from other basic statements or hypotheses are commonly called theorems. However, frequently the areas of knowledge where these statements appear have often not been properly formalized in the form of an axiomatic system, so the term theorem should strictly be used with caution to refer to these demonstrable or deductible statements of “more basic” assumptions.
Examples of theorems
Dual theorem. The principle of duality affirms that from any theorem or construction of projective geometry we can obtain another, known as the Dual Theorem, only the words point and line can be interchanged, also modifying the relationships between the points and the lines. So, by this principle:
• A point becomes a line.
• Aligned points become lines that pass through a point.
• Tangent lines become the point of tangency.
• A circumscribed circle becomes an inscribed circle.
The dual theorem the theorem Pascal is the theorem Brianchon , Theorem Feuerbach . The Circumference Euler or 9 points, is tangent to the inscribed circumferences and exinscrita to the triangle.
• Gauss theorem. The midpoints of the diagonals of an entire quadrilateral are in a straight line.
• Euler’s theorem. In any convex polyhedron , the number of faces plus the number of vertices is equal to the number of edges plus two. (faces + vertices = edges + 2).
One of the best known theorems is Thales’ Theorem , which indicates that, by drawing a Line parallel to any of its sides in a triangle, two similar triangles are obtained (that is, they have equal angles and their sides are proportional).
Another very popular theorem is the Pythagorean Theorem , which states that, in a right triangle, the square of the Hypotenuse (the side with the longest length and opposite to the right angle), is equal to the sum of the squares of the legs ( the two minor sides of the right triangle).
Statements
Usual way
when the hypothesis and the thesis are not properly distinguished;
as an example “an exterior angle of a triangle is equal to the sum of the nonadjacent triangle angles” [2]
Implicative form
they are stated in the form if p , then q , being p the hypothesis and q , the conclusion or thesis.
as an example: if the natural number p is a multiple of 8, then p is a multiple of 4
Disjunctive form
is stated as p or not q , p being the hypothesis and q the conclusion.
For example: the triangle ACB is a rectangle with the right angle at C or the sum of the squares of the legs is not equal to the square of the hypotenuse.
byAbdullah Sam
I’m a teacher, researcher and writer. I write about study subjects to improve the learning of college and university students. I write top Quality study notes Mostly, Tech, Games, Education, And Solutions/Tips and Tricks. I am a person who helps students to acquire knowledge, competence or virtue. | 1,460 | 6,165 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2022-21 | latest | en | 0.859529 |
http://mathhelpforum.com/advanced-statistics/99393-find-mean-variance-standard-deviation-print.html | 1,511,220,644,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806258.88/warc/CC-MAIN-20171120223020-20171121003020-00246.warc.gz | 172,762,421 | 3,030 | # Find the mean, variance, and standard deviation
Printable View
• Aug 27th 2009, 02:21 AM
extrem3
Find the mean, variance, and standard deviation
Q.7
In an assembly line production of industrial robots, gearbox assemblies can be installed in
two minute each if holes have been properly drilled in the boxes and in nice minutes if
the holes must be be redrilled. Twenty gearboxes are in stock, 2 with improperly drilled
holes. Five gearboxes must be selected from the 20 that are available for installation in the next five robots.
i) Find the probability that all 5 gearbox will fit properly. (2 marks)
ii) Find the mean, variance, and standard deviation of the time to install these 5 gearbox
I have no problem with Question 7(i), but i dont know how to solve 7(ii),
the following is my solution but somehow it seems to be incorrect, someone please help me.
http://img143.imageshack.us/img143/4549/7ii.jpg
• Aug 27th 2009, 04:56 AM
HallsofIvy
Quote:
Originally Posted by extrem3
Q.7
In an assembly line production of industrial robots, gearbox assemblies can be installed in
two minute each if holes have been properly drilled in the boxes and in nice minutes if
the holes must be be redrilled. Twenty gearboxes are in stock, 2 with improperly drilled
holes. Five gearboxes must be selected from the 20 that are available for installation in the next five robots.
i) Find the probability that all 5 gearbox will fit properly. (2 marks)
ii) Find the mean, variance, and standard deviation of the time to install these 5 gearbox
I have no problem with Question 7(i), but i dont know how to solve 7(ii),
the following is my solution but somehow it seems to be incorrect, someone please help me.
http://img143.imageshack.us/img143/4549/7ii.jpg
Well, that's not the mean of the time since you haven't use the fact that the values are 2 minutes and 9 minutes.
• Aug 27th 2009, 07:24 AM
extrem3 | 477 | 1,899 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2017-47 | longest | en | 0.91529 |
https://oeis.org/A081118 | 1,611,251,476,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703527224.75/warc/CC-MAIN-20210121163356-20210121193356-00071.warc.gz | 486,063,763 | 4,548 | The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A081118 Triangle of first n numbers per row having exactly n 1's in binary representation. 9
1, 3, 5, 7, 11, 13, 15, 23, 27, 29, 31, 47, 55, 59, 61, 63, 95, 111, 119, 123, 125, 127, 191, 223, 239, 247, 251, 253, 255, 383, 447, 479, 495, 503, 507, 509, 511, 767, 895, 959, 991, 1007, 1015, 1019, 1021, 1023, 1535, 1791, 1919, 1983, 2015, 2031, 2039, 2043 (list; table; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS T(n,n) = A036563(n+1) = 2^(n+1) - 3. Numbers of the form 2^t - 2^k - 1, 1 <= k < t. LINKS Reinhard Zumkeller, Rows n=1..150 of triangle, flattened FORMULA T(n, k) = 2^(n+1) - 2^(n-k+1) - 1, 1<=k<=n. a(n) = (2^A002260(n)-1)*2^A004736(n)-1; a(n)=(2^i-1)*2^j-1, where i=n-t*(t+1)/2, j=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Apr 04 2013 EXAMPLE Triangle begins: .......... 1 ......... ................ 1 ........ 3...5 ....... .............. 11 101 ...... 7..11..13 ..... .......... 111 1011 1101 ... 15..23..27..29 ... ...... 1111 10111 11011 11101 . 31..47..55..59..61 . . 11111 101111 110111 111011 111101. MATHEMATICA Table[2^(n+1)-2^(n-k+1)-1, {n, 10}, {k, n}]//Flatten (* Harvey P. Dale, Apr 09 2020 *) PROG (Haskell) a081118 n k = a081118_tabl !! (n-1) !! (k-1) a081118_row n = a081118_tabl !! (n-1) a081118_tabl = iterate (\row -> (map ((+ 1) . (* 2)) row) ++ [4 * (head row) + 1]) [1] a081118_list = concat a081118_tabl -- Reinhard Zumkeller, Feb 23 2012 CROSSREFS Cf. A000079, A018900, A014311, A014312, A014313, A023688, A023689, A023690, A023691, A038461, A038462, A038463. Cf. A181741 (primes), A208083, subsequence of A089633. Cf. A131094. Sequence in context: A153183 A247648 A117203 * A003255 A263321 A244365 Adjacent sequences: A081115 A081116 A081117 * A081119 A081120 A081121 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Mar 06 2003 STATUS approved
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Last modified January 21 12:45 EST 2021. Contains 340350 sequences. (Running on oeis4.) | 943 | 2,356 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2021-04 | latest | en | 0.384347 |
https://earthspot.org/geo/?search=Center_of_population | 1,660,271,172,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571538.36/warc/CC-MAIN-20220812014923-20220812044923-00764.warc.gz | 233,630,754 | 20,691 | # Center of population
For representational purposes only: The point on earth closest to everyone in the world on average was in calculated to be in Central Asia, with a mean distance of 5,000 kilometers (3,000 mi). Its antipodal point is correspondingly the farthest point from everyone on earth, and is located in the South Pacific near Easter Island, with a mean distance of 15,000 kilometers (9,300 mi). The data used by this figure is lumped at the country level, and is therefore precise only to country-scale distances, larger nations heavily skewed. Far more granular data -- kilometer level, is now available -- compares with this old "textbook" example.
In demographics, the center of population (or population center) of a region is a geographical point that describes a centerpoint of the region's population. There are several ways of defining such a "center point", leading to different geographical locations; these are often confused. [1]
## Definitions
Three commonly used (but different) center points are:
1. the mean center, also known as the centroid or center of gravity;
2. the median center, which is the intersection of the median longitude and median latitude;
3. the geometric median, also known as Weber point, Fermat–Weber point, or point of minimum aggregate travel.
A further complication is caused by the curved shape of the Earth. Different center points are obtained depending on whether the center is computed in three-dimensional space, or restricted to the curved surface, or computed using a flat map projection.
### Mean center
The mean center, or centroid, is the point on which a rigid, weightless map would balance perfectly, if the population members are represented as points of equal mass.
Mathematically, the centroid is the point to which the population has the smallest possible sum of squared distances. It is easily found by taking the arithmetic mean of each coordinate. If defined in the three-dimensional space, the centroid of points on the Earth's surface is actually inside the Earth. This point could then be projected back to the surface. Alternatively, one could define the centroid directly on a flat map projection; this is, for example, the definition that the US Census Bureau uses.
Contrary to a common misconception, the centroid does not minimize the average distance to the population. That property belongs to the geometric median.
### Median center
The median center is the intersection of two perpendicular lines, each of which divides the population into two equal halves. [2] Typically these two lines are chosen to be a parallel (a line of latitude) and a meridian (a line of longitude). In that case, this center is easily found by taking separately the medians of the population's latitude and longitude coordinates. John Tukey called this the cross median. [3]
### Geometric median
The geometric median is the point to which the population has the smallest possible sum of distances (or equivalently, the smallest average distance). Because of this property, it is also known as the point of minimum aggregate travel. Unfortunately, there is no direct closed-form expression for the geometric median; it is typically computed using iterative methods.[ citation needed]
## Determination
In practical computation, decisions are also made on the granularity (coarseness) of the population data, depending on population density patterns or other factors. For instance, the center of population of all the cities in a country may be different from the center of population of all the states (or provinces, or other subdivisions) in the same country. Different methods may yield different results.
Practical uses for finding the center of population include locating possible sites for forward capitals, such as Brasília, Nur-Sultan or Austin, and, along the same lines, to make tax collection easier. Practical selection of a new site for a capital is a complex problem that depends also on population density patterns and transportation networks.
## World
It is important to use a method that does not depend on a two-dimensional projection when dealing with the entire world. In a study from the Institut national d'études démographiques, [4] the solution methodology deals only with the globe. As a result, the answer is independent of which map projection is used or where it is centered. As described above, the exact location of the center of population will depend on both the granularity of the population data used, and the distance metric. With geodesic distances as the metric, and a granularity of 1,000 kilometers (600 mi), meaning that two population centers within 1000 km of each other are treated as part of a larger common population center of intermediate location, the world's center of population is found to lie where South Asia meets Central Asia [5] with an average distance of 5,200 kilometers (3,200 mi) to all humans. [4] The data used in the reference support this result to a precision of only a few hundred kilometers, hence the exact location is not known. Another analysis utilising city level population data found that the world's center of population is located close to Almaty, Kazakhstan. [6]
## By country
### Australia
Australia's population centroid is in central New South Wales. By 1996 it had moved only a little to the north-west since 1911. [7]
In Canada, a 1986 study placed the point of minimum aggregate travel just north of Toronto in the city of Richmond Hill, and moving westward at a rate of approximately 2 metres per day. [8]
### China
China's population centroid has wandered within southern Henan from 1952 to 2005. Incidentally, the two end point dates are remarkably close to each other. [9] China also plots its economic centroid or center of economy/GDP, which has also wandered, and is generally located at the eastern Henan borders.
### Estonia
European Countries median center of population in 2011
The center of population of Estonia was on the northwestern shore of Lake Võrtsjärv in 1913 and moved an average of 6 km northwest with every decade until the 1970s. The higher immigration rates during the late Soviet occupation to mostly Tallinn and Northeastern Estonia resulted the center of population moving faster towards north and continuing urbanization has seen it move northwest towards Tallinn since the 1990s. The center of population according to the 2011 census was in Jüri, just 6 km southeast from the border of Tallinn. [10]
### Finland
In Finland, the point of minimum aggregate travel is located in the former municipality of Hauho. [11] It is moving slightly to the south-west-west every year because people are moving out of the peripheral areas of northern and eastern Finland.
### Germany
In Germany, the centroid of the population is located in Spangenberg, Hesse, close to Kassel. [12]
### Great Britain
The centre of population in Great Britain did not move significantly in the 20th century. In 1901, it was in Rodsley, Derbyshire and in 1911 in Longford. In 1971 it was at Newhall, Swadlincote, South Derbyshire and in 2000, it was in Appleby Parva, Leicestershire. [13] [14] Using the 2011 census the population center can be calculated at Snarestone, Swadlincote. [15]
### Ireland
The center of population of the entire island of Ireland is located near Kilcock, County Kildare. This is significantly further east than the Geographical centre of Ireland, reflecting the disproportionately large cities of the east of the island ( Belfast and Dublin). [16] The center of population of the Republic of Ireland is located southwest of Edenderry, County Offaly. [17]
### Japan
The centroid of population of Japan is in Gifu Prefecture, almost directly north of Nagoya city, and has been moving east-southeast for the past few decades. [18] More recently,[ when?] the only large regions in Japan with significant population growth have been in Greater Nagoya and Greater Tokyo.
### New Zealand
New Zealand's median center of population over time
In June 2008, New Zealand's median center of population was located near Taharoa, around 100 km (65 mi) southwest of Hamilton on the North Island's west coast. [19] In 1900 it was near Nelson and has been moving steadily north (towards the Equator) ever since. [20]
### Sweden
The demographical center of Sweden (using the median center definition) is Hjortkvarn in Hallsberg Municipality, Örebro county. Between the 1989 and 2007 census the point moved a few kilometres to the south, due to a decreasing population in northern Sweden and immigration to the south. [21]
### Russia
The center of population in the Russian Federation is calculated by A. K. Gogolev to be at , 42 km (26 mi) south of Izhevsk. [22]
### United States
The mean center of the United States population (using the centroid definition) has been calculated for each U.S. Census since 1790. Over the last two centuries, it has progressed westward and, since 1930, southwesterly, reflecting population drift. For example, in 2010, the mean center was located near Plato, Missouri, in the south-central part of the state, whereas, in 1790, it was in Kent County, Maryland, 47 miles (76 km) east-northeast of the future federal capital, Washington, D.C.
## Sources
• Bellone F. and Cunningham R. (1993). "All Roads Lead to... Laxton, Digby and Longford." Statistics Canada 1991 Census Short Articles Series.
## References
1. ^ Kumler, Mark P.; Goodchild, Michael F. (1992). "The population center of Canada – Just north of Toronto?!?". In Janelle, Donald G. (ed.). Geographical snapshots of North America: commemorating the 27th Congress of the International Geographical Union and Assembly. pp. 275–279.
2. ^ "Centers of Population Computation for the United States, 1950-2010" (PDF). Washington, DC: Geography Division, U.S. Census Bureau. March 2011.
3. ^ Tukey, John (1977). . Addison-Wesley. p. 668. ISBN 9780201076165.
4. ^ a b Claude Grasland and Malika Madelin (May 2001). "The unequal distribution of population and wealth in the world" (PDF). Population et SociétéS. Institut national d'études démographiques. 368: 1–4. ISSN 0184-7783.
5. ^ exact phrase in the paper is "at the crossroads between China, India, Pakistan and Tajikistan"
6. ^ "Center of World Population". City Extremes. 2017. Retrieved 21 August 2017.
7. ^ "Figure 15: Shifts in the Australian Population Centroid*, 1911–1996". Parliament of Australia Parliamentary Library. Archived from the original on 19 August 2000. Retrieved 7 January 2009.
8. ^ "The Population Center of Canada – Just North of Toronto?!?" (PDF). Retrieved 21 April 2012.
9. ^
10. ^ Haav, Mihkel (2010) - "Eesti dünaamika 1913-1999"
11. ^ Uusirauma.fi Kaupunkilehti Uusi Rauma 03.08.2009 Päivän kysymys? Missä Rauman keskipiste? (in Finnish)
12. ^ Dradio.de Archived 24 October 2007 at the Wayback Machine (in German)
13. ^ "News Item". University of Leeds. Archived from the original on 3 October 2006. Retrieved 25 November 2007.
14. ^ "Population Centre". Appleby Magna & Appleby Parva. Archived from the original on 23 November 2007. Retrieved 25 November 2007.
15. ^ "Archived copy" (PDF). Archived from the original (PDF) on 23 July 2021. Retrieved 15 March 2020.```{{ cite web}}```: CS1 maint: archived copy as title ( link)
16. ^
17. ^
18. ^ "Our Country's Center of Population (我が国の人口重心)". Stat.go.jp. Retrieved 21 April 2012.
19. ^ "Subnational Population Estimates: At 30 June 2008 -- Commentary". Statistics New Zealand. Retrieved 11 November 2014.
20. ^
21. ^ "Sweden's demographic centre, SCB.se, 2008-03-18". Scb.se. 18 March 2008. Archived from the original on 29 March 2012. Retrieved 21 April 2012.
22. ^
23. ^ | 2,730 | 11,703 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2022-33 | longest | en | 0.935278 |
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# Findings from several studies on corporate mergers
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Findings from several studies on corporate mergers [#permalink]
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12 Oct 2013, 10:50
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Findings from several studies on corporate mergers and acquisitions during the 1970s and 1980s raise questions about why firms initiate and consummate such transactions. One study showed, for example, that acquiring firms were on average unable to maintain acquired firms’ pre-merger levels of profitability. A second study concluded that postacquisition gains to most acquiring firms were not adequate to cover the premiums paid to obtain acquired firms. A third demonstrated that, following the announcement of a prospective merger, the stock of the prospective acquiring fi rm tends to increase in value much less than does that of the firm for which it bids. Yet mergers and acquisitions remain common, and bidders continue to assert that their objectives are economic ones.
Acquisitions may well have the desirable effect of channeling a nation’s resources efficiently from less to more efficient sectors of its economy, but the individual acquisitions executives arranging these deals must see them as advancing either their own or their companies’ private economic interests. It seems that factors having little to do with corporate economic interests explain acquisitions. These factors may include the incentive compensation of executives, lack of monitoring by boards of directors, and managerial error in estimating the value of firms targeted for acquisition. Alternatively, the acquisition acts of bidders may derive from
modeling: a manager does what other managers do.
Questions 64–70 refer to the passage above.
64. The primary purpose of the passage is to
(A) review research demonstrating the benefi ts of corporate mergers and acquisitions and examine some of the drawbacks that acquisition behavior entails
(B) contrast the effects of corporate mergers and acquisitions on acquiring firms and on firms that are acquired
(C) report findings that raise questions about a reason for corporate mergers and acquisitions and suggest possible alternative reasons
(D) explain changes in attitude on the part of acquiring firms toward corporate mergers and acquisitions
(E) account for a recent decline in the rate of corporate mergers and acquisitions
OA &OE
[Reveal] Spoiler:
64. A The research cited in the passage calls into question whether mergers and acquisitions are beneficial to firms.
B Th e passage is not concerned with comparing the relative effects of mergers and acquisitions on the acquired and acquiring firms.
C Correct. Th e passage surveys reports that question the reasons given by firms when they acquire other firms and suggests other reasons for these acquisitions.
D Th e passage does not indicate that there has been a change in the attitude of acquiring firms toward mergers and acquisitions.
E The passage does not indicate that there has been a decline in the rate of mergers and acquisitions.
65. The findings cited in the passage suggest which of the following about the outcomes of corporate mergers and acquisitions with respect to acquiring firms?
(A) They include a decrease in value of many acquiring firms’ stocks.
(B) They tend to be more benefi cial for small firms than for large firms.
(C) They do not fulfill the professed goals of most acquiring firms.
(D) They tend to be beneficial to such firms in the long term even though apparently detrimental in the short term.
(E) They discourage many such firms from attempting to make subsequent bids and acquisitions.
OA & OE
[Reveal] Spoiler:
65 A The passage suggests that the stock of acquiring firms tends to increase in value (lines 12–13), albeit less than the firm it acquires.
B The three studies cited in the passage do contrast the effects of corporate mergers on acquiring firms and on acquired firms, but the effects in question are signifi cant only insofar as they contribute to the wider investigation into why mergers take place at all.
C Correct. The passage indicates that even while acquiring firms cite economic goals, the results of the studies indicate that these goals are not being met.
D The passage makes no comparison between the long-term and short-term gains of acquiring firms.
E The passage does not indicate that firms have been affected by the results of the studies cited.
66. It can be inferred from the passage that the author would be most likely to agree with which of the following statements about corporate acquisitions?
(A) Their known benefi ts to national economies explain their appeal to individual firms during the 1970s and 1980s.
(B) Despite their adverse impact on some firms,they are the best way to channel resources from less to more productive sectors of a nation’s economy.
(C) They are as likely to occur because of poor monitoring by boards of directors as to be caused by incentive compensation for managers.
(D) They will be less prevalent in the future, since their actual effects will gain wider recognition.
(E) Factors other than economic benefit to the acquiring fi rm help to explain the frequency with which they occur.
OA & OE
[Reveal] Spoiler:
66. A The passage indicates that while mergers and acquisitions may benefit the national economy, the appeal of mergers and
acquisitions must be tied to companies’ private economic interests (lines 19–22).
B The passage makes no judgment as to the best way for firms to help channel resources from less to more effi cient economic sectors.
C The passage makes no comparison between the influence of poor monitoring by boards and that of executive incentives.
D The passage makes no prediction as to future trends in the market for mergers and acquisitions.
E Correct. The passage states that factors other than economic interests drive mergers and acquisitions.
67. The author of the passage mentions the effect of acquisitions on national economies most probably in order to
(A) provide an explanation for the mergers and acquisitions of the 1970s and 1980s overlooked by the fi ndings discussed in the passage
(B) suggest that national economic interests played an important role in the mergers and acquisitions of the 1970s and 1980s
(C) support a noneconomic explanation for the mergers and acquisitions of the 1970s and 1980s that was cited earlier in the passage
(D) cite and point out the inadequacy of one possible explanation for the prevalence of mergers and acquisitions during the 1970s and 1980s
(E) explain how modeling affected the decisions made by managers involved in mergers and acquisitions during the 1970s and 1980s
OA &OE
[Reveal] Spoiler:
67 A The passage does not mention national economies as part of an explanation for the occurrence of mergers and acquisitions.
B The passage suggests that the effect of acquisitions on national economies is not tied to any explanations for why acquisitions occur.
C The eff ect of acquisitions on national economies is not mentioned in the passage as an explanation for why acquisitions occur.
D Correct. Th e passage uses the mention of national economies as part of a larger point questioning the stated motivations behind firms’ efforts to acquire other firms.
E In the passage, modeling is unrelated to the idea that acquisitions may have a desirable effect on national economies.
68. According to the passage, during the 1970s and 1980s bidding firms differed from the firms for which they bid in that bidding firms
(A) tended to be more profi table before a merger than after a merger
(B) were more often concerned about the impact of acquisitions on national economies
(C) were run by managers whose actions were modeled on those of other managers
(D) anticipated greater economic advantages from prospective mergers
(E) experienced less of an increase in stock value when a prospective merger was announced
OA OE
[Reveal] Spoiler:
68. A The passage does not indicate whether the profitability of acquiring firms tended to be greater or less after a merger.
B The passage does not indicate that acquiring firms were concerned about the impact of their actions on national economies.
C The passage does not mention the actions of managers at firms that are being acquired.
D The passage does not discuss whether acquiring firms tended to expect greater overall economic gains than actually occurred.
E Correct. The passage indicates that the stock value of acquiring firms grew less than that of the firms they were attempting to acquire.
69. According to the passage, which of the following was true of corporate acquisitions that occurred during the
1970s and 1980s?
(A) Few of the acquisitions that f rms made were subsequently divested.
(B) Most such acquisitions produced only small increases in acquired firms’ levels of profitability.
(C) Most such acquisitions were based on an overestimation of the value of target firms.
(D) The gains realized by most acquiring firms did not equal the amounts expended in acquiring target firms.
(E) About half of such acquisitions led to long-term increases in the value of acquiring firms’ stocks.
OA &OE
[Reveal] Spoiler:
69 A The passage does not discuss post - acquisition divesting.
B The passage indicates that on average, the profitability of acquired firms fell after being acquired (lines 5–7).
C The passage does not indicate whether most acquiring firms overestimated the value of the firms they acquired.
D Correct. The passage states that for most acquiring firms the costs of buying the acquired fi rm were greater than the gains derived from acquiring it.
E The passage does not indicate what percentage of acquiring firms, if any, experienced long-term gains in their stock value.
70. The author of the passage implies that which of the following is a possible partial explanation for acquisition behavior during the 1970s and 1980s?
(A) Managers wished to imitate other managers primarily because they saw how financially beneficial other firms’ acquisitions were.
(B) Managers miscalculated the value of firms that were to be acquired.
(C) Lack of consensus within boards of directors resulted in their imposing conflicting goals on managers.
(D) Total compensation packages for managers increased during that period.
(E) The value of bidding firms’ stock increased significantly when prospective mergers were announced.
OA &OE
[Reveal] Spoiler:
70 A While the passage indicates that managers may have modeled their behavior on other managers, it does not provide a reason for why this would be so.
B Correct. The author states that one explanation for acquisition behavior may be that managers erred when they estimated the value of firms being acquired.
C The author discusses a lack of monitoring by boards of directors but makes no mention of consensus within these boards.
D The author does not discuss compensation packages for managers.
E The passage does not state how significantly the value of the bidding firm’s stock increased upon announcing a merger but only that it increased less in value than did the stock of the prospective firm being acquired.
.
[Reveal] Spoiler: Question #1 OA
[Reveal] Spoiler: Question #2 OA
[Reveal] Spoiler: Question #3 OA
[Reveal] Spoiler: Question #4 OA
[Reveal] Spoiler: Question #5 OA
[Reveal] Spoiler: Question #6 OA
[Reveal] Spoiler: Question #7 OA
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Re: Findings from several studies on corporate mergers [#permalink]
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13 Oct 2013, 21:43
Can anyone explain 67? I did not find any of them right
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Re: Findings from several studies on corporate mergers [#permalink]
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17 Oct 2013, 23:13
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roopika2990 wrote:
Can anyone explain 67? I did not find any of them right
D would be the correct answer choice here. First, locate the sentence you need to read to answer this question. The impact on national economies is mentioned in the first line of the second paragraph, so we need go no farther then here to find the answer. What does this sentence say about the effect on national companies? That although there may be a positive effect, this is not why such deals were arranged. This implies that some people have considered the positive effect on national economies to be an explanation of all those mergers and acquisitions. Now, notice the bare logical structure of this sentence: X may well be..., but....Y. In other words, Although X, Y. What is X - Acquisitions' impact on national economies. What is Y? The company or personal interest of executives. So what this sentence telling us? That X is not an adequate explanation of mergers and acquisitions, but Y is. This is precisely what answer choice D is telling us: cite and point out the inadequacy of one possible explanation, etc.
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Re: Findings from several studies on corporate mergers [#permalink]
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25 Nov 2013, 06:04
daagh could you plz post the official answers?
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Re: Findings from several studies on corporate mergers [#permalink]
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28 Mar 2014, 11:26
Question 69
Also is this a 700+ RC..because I got only 3 right in like 12 mins
Or I will just accept that I have to work hard on RCs.
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Re: Findings from several studies on corporate mergers [#permalink]
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01 Sep 2014, 20:45
What's considered an acceptable time frame for this passage + set of questions? Should it ideally be completed within 9 minutes? I completed it in 10:06 because I had to stop and think for a few of them. Felt like I was taking longer than I should have. Input would be great. Thanks!
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Re: Findings from several studies on corporate mergers [#permalink]
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02 Sep 2014, 05:14
1
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Can anyone explain Q66
I am not getting how to infer the bold part in option E
Factors other than economic benefit to the acquiring firm help to explain the frequency with which they occur
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Re: Findings from several studies on corporate mergers [#permalink]
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03 Sep 2014, 07:56
2
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dream21 wrote:
Can anyone explain Q66
I am not getting how to infer the bold part in option E
Factors other than economic benefit to the acquiring firm help to explain the frequency with which they occur
Hey there,
If you look at the last line of para 1 it says "Yet mergers and acquisitions remain common, and bidders continue to assert that their objectives are economic ones" where "common" more or less means "frequent".
Hope this helps!
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Re: Findings from several studies on corporate mergers [#permalink]
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01 Nov 2014, 05:12
maggie27 wrote:
dream21 wrote:
Can anyone explain Q66
I am not getting how to infer the bold part in option E
Factors other than economic benefit to the acquiring firm help to explain the frequency with which they occur
Hey there,
If you look at the last line of para 1 it says "Yet mergers and acquisitions remain common, and bidders continue to assert that their objectives are economic ones" where "common" more or less means "frequent".
Hope this helps!
I had also problems with this question. The statement about the frequency is wrong, because it was not mentioned in the passage, it's just an assumption. But E seems to be the only wright answer compared with other answer choices. As I see, sometimes right answers can be only derived by excluding more wrong answers.
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Re: Findings from several studies on corporate mergers [#permalink]
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01 Nov 2014, 22:20
In the second paragraph, the author explicitly says "It seems that factors having little to do with corporate economic interests explain acquisitions."
This statement tells you that factors other than economic interests help explain acquisitions -- a logical inference is that if you know why the acquisitions occur, you can explain the frequency with which they occur with a high degree of accuracy. Hence E.
The first paragraph provides examples of firms initiating acquisitions even when they don't derive economic benefit from them, and says that acquisitions remain common. "Common" in this context seems to mean "frequent", but even this inference is not required; the inference in the above paragraph should suffice.
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Re: Findings from several studies on corporate mergers [#permalink]
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04 May 2015, 08:43
282552 wrote:
Question 69
Also is this a 700+ RC..because I got only 3 right in like 12 mins
Or I will just accept that I have to work hard on RCs.
D says that most such acquisitions were based on an overestimation of the value of target firms.
Actually this piece of information about overestimation of the value of target firms appears in the second para.
However, the information that we need to look for this question, is limited to the first para, since that is where it is specifically covered what the scenario was in the 70s and 80s.
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Re: Findings from several studies on corporate mergers [#permalink]
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05 May 2015, 21:08
IlanaEconomistGMAT wrote:
roopika2990 wrote:
Can anyone explain 67? I did not find any of them right
D would be the correct answer choice here. First, locate the sentence you need to read to answer this question. The impact on national economies is mentioned in the first line of the second paragraph, so we need go no farther then here to find the answer. What does this sentence say about the effect on national companies? That although there may be a positive effect, this is not why such deals were arranged. This implies that some people have considered the positive effect on national economies to be an explanation of all those mergers and acquisitions. Now, notice the bare logical structure of this sentence: X may well be..., but....Y. In other words, Although X, Y. What is X - Acquisitions' impact on national economies. What is Y? The company or personal interest of executives. So what this sentence telling us? That X is not an adequate explanation of mergers and acquisitions, but Y is. This is precisely what answer choice D is telling us: cite and point out the inadequacy of one possible explanation, etc.
this passage is easy but the questions are harder. reading skill is never taught and discussed in rc forum though it is fatally important.
thank you expert, sir
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Re: Findings from several studies on corporate mergers [#permalink]
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18 Aug 2015, 14:53
Hello everyone ....
I have a doubt in question 70, its pretty simple but my concern is the question's phrasing . The questions says" The author of the passage implies..... ?"
Now as far as I know if we have a imply question the answer to that question will not be explicitly mentioned in the passage and that is not case here. Answer choice B is clearly stated.Its like restating the given.
So is my thumb rule for imply questions incorrect ?? or this a strange case.
Thanks and kudos for solutions !
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Re: Findings from several studies on corporate mergers [#permalink]
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20 Aug 2015, 21:54
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Expert's post
Hi Anurag,
The word IMPLIES (in this question) - is towards the word "Partial Explanation" as the answer choice B (explicitly mentioned in the passage) is only one of the three factors mentioned in the second paragraph.
Since, the choice only referes to one factor that is why "implies that ..possible partial explanation".
Hope it helps!
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Re: Findings from several studies on corporate mergers [#permalink] 21 Oct 2016, 00:27
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Concepts Lectures on Real Numbers and Divisibility
## Concept Lectures
Session # 1 What are Real Numbers?
Session # 2 What is meant by divisibility?
Session # 3 Properties of divisibility : Part 1
Session # 4 Properties of divisibility : Part 2
Session # 5 Euclid's Division Lemma : Part 1
Session # 6 Euclid's Division Lemma : Part 2
Session # 7 Euclid's Division Lemma : Part 3
Session # 8 Proof of the Euclid's Division Lemma
Session # 9 Euclid's Division Lemma - Applications
## Problems
Problem Solving Session # 1 Show that n^2-1 is divisible by 8 if n is an odd positive integer.
Problem Solving Session # 2 Show that the square of any positive integer is of the form of 3m or 3m+1 for some integer m.
Problem Solving Session # 3 Prove that one of every three consecutive positive integers is divisible by 3
## Concept Lectures
Session # 10 Euclid's Division Algorithm
Session # 11 Euclid's Division Algorithm: What is GCD?
## Problems
Problem Solving Session # 4 Find the GCD/HCF of 237 and 81 and express it as a linear combination of 237 and 81
Problem Solving Session # 5 Find the GCD/HCF of 72 and 56 and express it as a linear combination of 72 and 56. Also show that the linear combination is not unique.
Problems Solving Session # 6 Word Problem
Problems Solving Session # 7 Word Problem
## Concept Lectures
Session # 16 Fundamental Theorem of Arithmetic
## Problems
Problems Solving Session # 8 Express 168 and 234 as a product of prime factors
Problems Solving Session # 9 Prove that there is no natural number n for which 4^n ends with digit zero
Problem Solving Session # 10 Prove that there are infinitely many prime numbers
Problem Solving Session # 11Prove that a positive integer n is a prime number, if no prime less than or equal to square root of n, divides n | 480 | 1,864 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2021-49 | latest | en | 0.787967 |
https://es.mathworks.com/matlabcentral/answers/1815800-how-to-quickly-identify-a-list-of-nearby-stations | 1,670,164,413,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710974.36/warc/CC-MAIN-20221204140455-20221204170455-00174.warc.gz | 274,415,125 | 38,868 | # How to quickly identify a list of nearby stations?
3 views (last 30 days)
Leon on 2 Oct 2022
Answered: Walter Roberson on 2 Oct 2022
I have a total of 1 million stations numbered from 1 to 1 million. For each of them, how do I quickly identify the rest of the stations (Station numbers) that are within 2 km of distance? I wrote the below program, but it was extremely slow. Any recommendations would be greatly appreciated. Many thanks!
%% calculate the distance between the stations:
m2 = numel(Sta); % The list of profile numbers
B0 = zeros(m2*m2, 6);
n0 = 0;
for i=1:m2
for j=1:m2
if Sta{i}.lon <= 180
Lon1 = Sta{i}.lon;
else
Lon1 = Sta{i}.lon-360;
end
if Sta{j}.lon <= 180
Lon2 = Sta{j}.lon;
else
Lon2 = Sta{j}.lon-360;
end
n0 = n0+1;
B0(n0,:) = [i, j, Sta{i}.lat, Lon1, Sta{j}.lat, Lon2];
end
end
Dis = distance(B0(:,3), B0(:,4), B0(:,5), B0(:,6), 6371); % The radius of the earth is 6371km.
%units: km.
D = []; % cell array storing the list of stations that are close to this profile:
for i=1:m2
Ind1 = B0(:,1)==i; % Index of the distance values for Station i.
B = [B0(Ind1,2), Dis(Ind1)]; % Two columns: List of profiles, Distance.
Ind = B(:,2) <= 2; % distance is less than 2km.
if sum(Ind) >= 2 % at least two profiles identified, one of them is itself.
C0 = setdiff( B(Ind,1), i ); % list of profiles that are close to this station (excluding itself)
D{i} = C0;
else
D{i} = [];
end
end
Torsten on 2 Oct 2022
Edited: Torsten on 2 Oct 2022
And for your double loop, you should replace
for i=1:m2
for j=1:m2
by
for i=1:m2
for j=i+1:m2
to save computation time.
Image Analyst on 2 Oct 2022
You accepted this answer but we don't know how you solved the problem of needing 8000 GB of memory to hold your B0 array for your trillion distances. How did you do it?
Image Analyst on 2 Oct 2022
Well let's see why it's slow. You have a million elements and you create an array that is a million by a million by 8 bytes. So that is 8000 gigabytes! Now maybe you have an 8 terabyte drive in your computer for swap space, but it will still be slow. I don't even know if MATLAB can handle an array that big even if you had infinite memory.
The second reason it is slow is the use of cell arrays. Cell arrays are very slow and memory inefficient. Put all your locations into standard double arrays, not cell arrays.
Now I don't know what this distance function you're using is (there are several) but it might be slow because it is general purpose with lots of overhead or maybe it takes the square root or even some more complicated formula. That could be avoided by using the simple Euclidean distance formula but not taking the square root. If you want the distance to be less than 2 km, that is the same as wanting the squared distance to be less than 4. Hence just square the distances and compare to 4 but don't take the square root. That is just an extra, unnecessary operation that will slow it down.
So why do I think the square distance will probably be better? Well if you're trying to find stations that are within 2 km of each other you're probably not considering stations placed all over the globe. You're probably not worried about whether a station in Beijing is within 2 km of one in Miami. You wouldn't need that kind of precision. You're probably considering a much smaller area, like just stations in Belgium or some country or state. Though why you'd have a million stations in a small area, I don't know. What is a station anyway? A radio station? A train station? An antenna location? So if you're using a small area of the globe you can convert the lats and lons to linear (x,y) locations. But you'll say "oh but it won't be accurate" and I'll say "who cares?" Certainly not us/you. It will be accurate enough to find stations within 2 km since there is no earth curvature effect over such a small distance, and if it's inaccurate for stations separated by 500 km, who cares? You don't want to identify a pair of stations like that (very distant) anyway so who cares if it says the distance is 480 km instead of 500 km? It doesn't matter. In the end all you care about are stations where the squared distance is less than 4, not the absolutely precise distance down to the nearest millimeter.
So just have a 2-D array where you compute the squared distance of every station to every other station using the Pythagorean theorem and your (x,y) coordinates (not cell arrays). Try meshgrid. But you still have the problem of having a trillion distances to compute. You're just going to somehow reduce that down to something more manageable - a trillion distances is not realistic. So now once you have the square distances in your array, finding the ones closer than 4 is trivial
mask = (squaredDistances > 0) & (squaredDistances <= 4);
% Find station indexes
##### 2 CommentsShowHide 1 older comment
Leon on 2 Oct 2022
Wow, thank you so much for the very insightful comments! I find it very helpful.
Walter Roberson on 2 Oct 2022
First, divide the stations into subsets:
• stations close enough to the North Pole that the smaller distance between degrees of longitude could start substantially affecting the calculation of which stations are close to each other. For the moment, call this NorthStations
• A subset of NorthStations that is potentially within 2 km of the sourthern boundary of the NorthStations. Call this NorthBorderStations for the moment
• Likewise, create SouthStations and SouthBorderStations
• Take the remaining stations that are not in NorthStations or in SouthStations, and add copies of NorthBorderStations and SouthBorderStations to that. Call this OtherStations at the moment
• Take a subset of OtherStations that are potentially within 2km of -180 degrees (remember that OtherStations is clipped at 2km North/South of the boundary you decided earlier so the curve at the North/South boundary will be limited.) Add 360 to those longitudes and add that subset back into OtherStations
Now NorthStations and SouthStations are substantially reduced subsets of the original data. You can use the Haversine distance formula within each subset, perhaps using pdist(). This will compare every point in each of the subsets to every other point within the subsets, but the subsets should only be including the locations where the curve introduces notable risk of unexpected connections. The distances calculated within each of the subsets will be exact on the first pass for each of the two subsets.
Now take OtherStations and use knnsearch and Euclidean distance, with the radius set to the largest euclidean distance that maps to 2km right at the border you used for dividing into the North / South subsets. For example if you choose to put the boundary at acosd(1/3) (70.5 degrees) then use a radius corresponding to 1/(1/3)*2 = 6 km. knnsearch with these settings with create a quadtree and search it for nearby points. This will, if I recall, take roughly N * log(N) time where N is the number of points in the subset.
The list of neighbours you get will be an overestimate -- but now you can take the points and their neighbours and do pairwise havershine formulas to get exact distances.
The higher/lower you put the latitude boundaries the more you reduce the size of the NorthStations and SouthStations subsets that have to be compared pairwise, but the more you overpopulate the search in OtherStations (because the more extreme the boundary, the larger you need to make the euclidean search radius so as to be able to find the matches right at the boundary.
I guess perhaps this search strategy could end up with some duplicates, if you happen to have pairs that lie exactly within the NorthBorderStations or SouthBorderStations, or entirely within the band that is duplicated at -180, so be sure to do a final filtering pass.
Walter Roberson on 2 Oct 2022
If you have the Mapping Toolbox then use distance
Leon on 2 Oct 2022
Edited: Leon on 2 Oct 2022
The stations can be anywhere in the global ocean. Some of them will be close to the poles.
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Translated by | 2,023 | 8,230 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2022-49 | latest | en | 0.887496 |
https://www.ques10.com/p/13168/an-lti-system-is-characterized-by-the-system-fun-1/? | 1,632,815,340,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780060538.11/warc/CC-MAIN-20210928062408-20210928092408-00243.warc.gz | 954,870,229 | 7,049 | 0
1.8kviews
An LTI system is characterized by the system function:$H(z) = \dfrac {z}{(z-\frac 14)(z+\frac14)(z-\frac12)}$
write down possible ROCs for different possible ROCs. Determine causality and stability and impulse response of the system.
Mumbai University > EXTC > Sem 4 > Signals and Systems
Marks : 10
Year : DEC 2014
0
9views
$$H(z) = \dfrac z {(z-\frac14)(z+\frac14)(z-\frac12)}$$
Poles at: $z=1/4, -1/4, ½$
Pole zero plot:
Since exterior part of circle (r=1/2) lies within the unit circle. Hence the given system is causal. Also all the pole of the system lies inside the unit circle, thus having bounded output for every bounded input. Hence is a stable system
Impulse response:
$H(z) = \dfrac z {(z-\frac14)(z+\frac14)(z-\frac12)} \\ \dfrac {H(z)}z = \dfrac 1 {(z-\frac14)(z+\frac14)(z-\frac12)}$
By using partial fraction,
$\dfrac {H(z)}z = \dfrac A{(z-\frac 14)}+ \dfrac B{(z+\frac14)}+ \dfrac C{(z-\frac12)}$
Put $z=1/4$ we get, $A=-8$
Put $z=-1/4$ we get, $B=2/3$
And Put $z=1/2$ we get, $C=4/3$
$\dfrac {H(z)}z=\dfrac {-8}{(z-\frac14)} + \dfrac {2/3}{(z+\frac14)} + \dfrac {4/3}{(z-\frac12)} \\ H (z) = \dfrac {-8z}{(z-\frac14)} + \dfrac {2z/3}{(z+\frac14 )} + \dfrac {4z/3}{(z-\frac12)}$
By Inverse z-transform,
$h [n] = -8(\dfrac14)^n u(n)+\dfrac23 (\dfrac {-1}{4})^n u(n)+\dfrac43 (\dfrac12)^n u(n)$ | 524 | 1,341 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2021-39 | latest | en | 0.604219 |
https://calculator.academy/full-load-current-calculator/ | 1,652,864,449,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662521883.7/warc/CC-MAIN-20220518083841-20220518113841-00785.warc.gz | 212,822,782 | 62,036 | Enter the full load power (watts) and the full load voltage (volts) into the calculator to determine the Full Load Current.
## Full Load Current Formula
The following formula is used to calculate the Full Load Current.
If = Pf/(1.732*Vf)
• Where If is the Full Load Current (amps)
• Pf is the full load power (watts)
• Vf is the full load voltage (volts)
## How to Calculate Full Load Current?
The following two example problems outline how to calculate the Full Load Current.
Example Problem #1:
1. First, determine the full load power (watts). In this example, the full load power (watts) is measured to be 67.
2. Next, determine the full load voltage (volts). For this problem, the full load voltage (volts) is calculated to be 8.
3. Finally, calculate the Full Load Current using the formula above:
If = Pf/(1.732*Vf)
Inserting the values from above and solving the equation with the imputed values gives:
If = 67/(1.732*8) = 4.83 (amps)
Example Problem #2:
Using the same process as example problem 1, we first define the variables outlined by the formula. In this case, the values are:
full load power (watts) = 90
full load voltage (volts) = 4
Entering these values into the formula above gives :
If = 90/(1.732*4) = 12.99 (amps) | 327 | 1,253 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2022-21 | longest | en | 0.787966 |
https://drugtruthaustralia.org/and-pdf/1801-scatter-plots-and-lines-of-best-fit-worksheet-pdf-166-204.php | 1,653,195,510,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662543797.61/warc/CC-MAIN-20220522032543-20220522062543-00015.warc.gz | 259,839,185 | 8,917 | Wednesday, May 26, 2021 7:23:55 PM
# Scatter Plots And Lines Of Best Fit Worksheet Pdf
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Scatter plot line of best fit worksheet.
## Sample Worksheets
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Line Of Best Fit - Displaying top 8 worksheets found for this concept.. There are 9 questions asking for the Slope-Intercept Form Equation of the trend line line of best fit given the scatter plot and 12 questions asking students to make a 9. Big Idea The emphasis in this lesson is to take students a little beyond the basics of Scatter Plots to explain the correlation coefficient r and the coefficient of determination r squared. Answer the questions: 80 72 56 48 40 32 16 Earnings at Work Hours Worked 1. Line of best fit: smoking in
When we have two separate data sets we can see if they have a relationship by plotting their points on in this manner. When we plot these points on an XY graph, we can see if a pattern forms. If a pattern forms, a relationship exists. We can examine this relationship using a Line of Best Fit Trend line. To create a Line of Best Fit we draw a line so that we are as close as possible to all the points.
## Print Scatter Plots and Line of Best Fit Worksheets
By: Published on: Dec 15, Categories: Uncategorized 0 comments. Approximately half of the data points should be below the line and half of the points above the line. Do not use the day on the scatter plot identify the data sets as having a positive a negative or no correlation. The teacher records the number of hours each student studied and the marks scored by the respective student on the test. The scatter plots and lines of best fit worksheet can be used to help those who have questions about scatter plots and lines of best fit.
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## 31 Scatter Plot And Lines Of Best Fit Worksheet
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A Scatter XY Plot has points that show the relationship between two sets of data. The data is plotted on the graph as " Cartesian x,y Coordinates ". The local ice cream shop keeps track of how much ice cream they sell versus the noon temperature on that day.
Draw a scatter plot and determine what relationship if any exists in the data.
Или мы придем к соглашению. - Какому соглашению? - Немец слышал рассказы о коррупции в испанской полиции. - У вас есть кое-что, что мне очень нужно, - сказал Беккер.
Он не мог поверить в свою необыкновенную удачу. Он снова говорил с этим американцем, и если все прошло, как было задумано, то Танкадо сейчас уже нет в живых, а ключ, который он носил с собой, изъят. В том, что он, Нуматака, в конце концов решил приобрести ключ Энсея Танкадо, крылась определенная ирония.
Пора отсюда сматываться. - Куда ты девал мои бутылки? - угрожающе зарычал парень. В его ноздрях торчала английская булавка. Беккер показал на бутылки, которые смахнул на пол. - Они же пустые.
Стратмор знает, что я это видел! - Хейл сплюнул. - Он и меня убьет. Если бы Сьюзан не была парализована страхом, она бы расхохоталась ему в лицо.
Он решил было обратиться в полицию - может быть, у них есть данные о рыжеволосых проститутках, - но Стратмор на этот счет выразился недвусмысленно: Вы должны оставаться невидимым. Никто не должен знать о существовании кольца. Может быть, стоит побродить по Триане, кварталу развлечений, и поискать там эту рыжую девицу. Или же обойти все рестораны - вдруг этот тучный немец окажется .
Фонтейн вздохнул и обхватил голову руками. Взгляд его черных глаз стал тяжелым и неподвижным. Возвращение домой оказалось долгим и слишком утомительным. Последний месяц был для Лиланда Фонтейна временем больших ожиданий: в агентстве происходило нечто такое, что могло изменить ход истории, и, как это ни странно директор Фонтейн узнал об этом лишь случайно.
Ошеломленный потерей жены и появлением на свет неполноценного, по словам медсестер, ребенка, которому скорее всего не удастся пережить ночь, он исчез из больницы и больше не вернулся. Энсея Танкадо отдали в приемную семью. Каждую ночь юный Танкадо смотрел на свои скрюченные пальцы, вцепившиеся в куклу Дарума note 1и клялся, что отомстит - отомстит стране, которая лишила его матери, а отца заставила бросить его на произвол судьбы. Не знал он только одного - что в его планы вмешается судьба.
Так долго. Сьюзан нахмурилась, почувствовав себя слегка оскорбленной. Ее основная работа в последние три года заключалась в тонкой настройке самого секретного компьютера в мире: большая часть программ, обеспечивавших феноменальное быстродействие ТРАНСТЕКСТА, была ее творением. Шифр в миллион бит едва ли можно было назвать реалистичным сценарием.
Сьюзан отвернулась. - Не имеет значения. Кровь не .
Она была абсолютно уверена, что не вводила такой команды - во всяком случае, намеренно. Подумала, что, может быть, спутала последовательность нажатия клавиш. Немыслимо, - подумала. Согласно информации, появившейся в окне, команда была подана менее двадцати минут .
- Я ничего не знаю. Беккер зашагал по комнате. - На руке умершего было золотое кольцо.
И мы, те, кто близко к сердцу принимает интересы страны, оказались вынужденными бороться за наше право служить своей стране. Мы больше не миротворцы. Мы слухачи, стукачи, нарушители прав человека. - Стратмор шумно вздохнул. - Увы, в мире полно наивных людей, которые не могут представить себе ужасы, которые нас ждут, если мы будем сидеть сложа руки.
Кольцо? - Он вдруг забеспокоился. Вгляделся в полоску на пальце и пристыжено покраснел. - О Боже, - хмыкнул он, - значит, эта история подтверждается. Беккеру даже сделалось дурно. - Прошу прощения.
Похоже, он снискал благословение - шичигосан. Скоро Нуматек станет единственным обладателем единственного экземпляра Цифровой крепости. Другого нет и не. Двадцать миллионов долларов - это очень большие деньги, но если принять во внимание, за что они будут заплачены, то это сущие гроши. ГЛАВА 19 - А вдруг кто-то еще хочет заполучить это кольцо? - спросила Сьюзан, внезапно заволновавшись.
Все вокруг светилось ярко-красными огнями. | 2,029 | 7,376 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2022-21 | latest | en | 0.901886 |
http://www.mathcaptain.com/geometry/parabola-equation.html | 1,540,263,739,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583516003.73/warc/CC-MAIN-20181023023542-20181023045042-00055.warc.gz | 495,396,764 | 10,672 | A quadratic equation always represents a parabola.Every quadratic form of equation when graphically represented, forms a parabola. When a ball is thrown or kicked, It follows a parabola.
The equation of parabola is can be written as
Where,
a, b and c are constants.
(x, y) is an arbitrary point lying on the parabola.
a $\neq$ 0. If a equals zero, then equation will be no more a quadratic equation. Hence it will not represent a parabola.
## Standard Form of a Parabola
The equation of parabola is defined above, but more generally and specifically, the standard and general form of a parabola is given below.
Where,
A, B, C, D, E and F are constants.
x and y are coordinates of an arbitrary point (x, y) lying on the parabola.
## Vertex Form of a Parabola
Sometimes, the equation of parabola is given in vertex form. The general and standard form of parabola is deducible to the vertex form of parabola. The equations of parabola in vertex form are:
Where,
(h, k) is vertex of parabola.
(x, y) is any arbitrary point on parabola.
If vertex of parabola is origin (0, 0), then h = 0 and k = 0. So, following are the parabolic equations in this case are
## Equation of Parabola
Equation of parabola can be in any of the given forms:
• Standard Form
• Vertex Form
Standard form is referred as quadratic form. It can be in below two formats:
• y = ax2 + bx + c
• Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Vertex form can be as follows:
Vertex at origin:
• y2 = 4ax
• y2 = -4ax
• x2 = 4ay
• x2 = -4ay
Vertex at (h, k):
• (y - k)2 = 4a (x - h)
• (y - k)2 = - 4a (x - h)
• (x - h)2 = 4a (y - k)
• (x - h)2 = - 4a (y - k)
## Solving Parabola Equations
Here, let us see how to solve parabolic equations.
While solving parabola equation, following points should be kept in mind:
• Deduce given equation in standard parabolic form.
• Determine "a" by comparing it with standard form.
• Now, determine the coordinates of focus, vertex, directrix etc. according to given format.
Let us consider few examples:
### Solved Example
Question: Consider a parabola: y2 - 12x = 0. Determine its vertex and focus.
Solution:
y2 = 12x
Comparing it with standard parabola equation, y2 = 4ax:
Vertex = (0, 0)
4a = 12
a = 3
Focus = (a, 0) = (3, 0)
Example 2: Deduce the quadratic equation y2 - 4x - 3 = 0 in vertex form of parabola and find its vertex, focus and equation of directrix.
Solution: y2 - 4x - 3 = 0
y2 = 4x + 3
y2 = 4(x + $\frac{3}{4}$)
Comparing it with standard parabola equation, (y - k)2 = 4a(x - h):
Vertex = (-$\frac{3}{4}$, 0)
4a = 4
a = 1
Focus = (h + a, 0)
= (-$\frac{3}{4}$ + 1, 0)
= ($\frac{1}{4}$, 0)
Directrix:
x = -$\frac{3}{4}$ - 1
x = -$\frac{7}{4}$
## Graphing a Parabola Equation
Following steps should be followed while graphing a parabolic equation:
If equation is in quadratic form:
1. Find a, b and c by comparing it with standard quadratic form y = ax2 + bx + c.
2. Calculate x coordinate of vertex with the help of formula $x = -$$\frac{b}{2a}$. Plugging x in given equation, find y coordinate of vertex.
3. Find x intercept by putting y = 0 in the equation.
4. Find y intercept by substituting x = 0 in the equation.
5. Now plot the graph of parabola with the help of information so obtained.
If equation is in vertex form:
1. Compare it with vertex parabolic form and determine the vertex (h, k).
2. Find coordinates of focus.
3. Determine the equation of directrix.
4. Now plot vertex, focus, directrix, and other required points and graph the parabola.
Let us consider an example:
### Solved Example
Question: Graph the quadratic equation y2 - 2x - 4 = 0
Solution:
Deduce the given equation in vertex form:
y2 = 2(x + 2)
Comparing it with standard form (y - k)2 = 4a (x - h)
h = -2 and k = 0
So, vertex = (-2, 0)
4a = 2
a = $\frac{1}{2}$
Focus = (h + a, 0) = (-$\frac{3}{2}$, 0)
Equation of Directrix:
x = h - a
x = -$\frac{5}{2}$ = -2.5
Finding the value of Y intercept by substituting x = 0
y2 = 4
y = $\pm$ 2
By using above information, we get the following graph of a parabola: | 1,277 | 4,014 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2018-43 | latest | en | 0.860212 |
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