text:
Rate (mathematics)
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For other uses, see Rate.
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In mathematics, a rate is the ratio between two related quantities.[1] If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable.
The most common type of rate is "per unit of time", such as speed, heart rate and flux. Ratios that have a non-timedenominator include exchange rates, literacy rates and electric field (in volts/meter).
In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.
Often rate is a synonym of rhythm or frequency, a count per second (i.e., Hertz); e.g., radio frequencies or heart rate or sample rate.
Contents
[hide]
1 Introduction
2 Rate of change
3 Temporal rates
3.1 Counts-per-time rates
4 Economics/finance rates/ratios
5 Other rates
6 See also
7 References
Introduction[edit]
Rates and ratios often vary with time, location, particular element (or subset) of a set of objects, etc. Thus they are often mathematical functions. For example, velocity v (distance traveled per unit time) of a transportation vehicle on a certain trip may be represented as a function of x (the distance traveled from the start of the trip) as v(x). Alternatively, one could express velocity as a function of time t from the start of the trip as v(t). Another representation of velocity on a trip is to partition the trip route into N segments and let vi be the constant velocity on segment i (v is a function of index i). Here each segment i, of the trip is a subset of the trip route.
A rate (or ratio) may often be thought of as an output-input ratio, benefit-cost ratio, all considered in the broad sense. For example, miles per hour in transportation is the output (or benefit) in terms of miles of travel, which one gets from spending an hour (a cost in time) of traveling (at this velocity).
A set of sequential indices i may be used to enumerate elements (or subsets) of a set of ratios under study. For example, in finance, one could define i by assigning consecutive integers to companies, to political subdivisions (such as states), to different investments, etc. The reason for using indices i, is so a set of ratios (i=0,N) can be used in an equation so as to calculate a function of the rates such as an average of a set of ratios. For example, the average velocity found from the set of vi's mentioned above. Finding averages may involve using weighted averages and possibly using the Harmonic mean.
A ratio r=a/b has both a numerator a and a denominator b. a and/orb may be a real number or integer. The inverse of a ratio r is 1/r = b/a.
Rate of change[edit]
Consider the case where the numerator f {\displaystyle f} of a rate is a function f ( a ) {\displaystyle f(a)} where a {\displaystyle a} happens to be the denominator of the rate δ f / δ a {\displaystyle \delta f/\delta a} . A rate of change of f {\displaystyle f} with respect to a {\displaystyle a} (where a {\displaystyle a} is incremented by h {\displaystyle h} ) can be formally defined in two ways:[2]
Average rate of change = f ( a + h ) − f ( a ) h Instantaneous rate of change = lim h → 0 f ( a + h ) − f ( a ) h {\displaystyle {\begin{aligned}{\mbox{Average rate of change}}&={\frac {f(a+h)-f(a)}{h}}\\{\mbox{Instantaneous rate of change}}&=\lim _{h\to 0}{\frac {f(a+h)-f(a)}{h}}\end{aligned}}}
where f(x) is the function with respect to x over the interval from a to a+h. An instantaneous rate of change is equivalent to a derivative.
An example to contrast the differences between the unit rates are average and instantaneous definitions: the speed of a car can be calculated:
An average rate can be calculated using the total distance travelled between a and b, divided by the travel time
An instantaneous rate can be determined by viewing a speedometer.
However these two formulas do not directly apply where either the range or the domain of f ( ) {\displaystyle f()} is a set of integers or where there is no given formula (function) for finding the numerator of the ratio from its denominator.
Temporal rates[edit]
Main category: Temporal rates
See also: Time derivative
In chemistry and physics:
Speed, being the distance covered per unit of time; e.g., miles per hour and meters per second
Acceleration, the rate of change in speed, or the change in speed per unit of time
Reaction rate, the speed at which chemical reactions occur
Volumetric flow rate, the volume of fluid which passes through a given surface per unit of time; e.g., cubic meters per second
Counts-per-time rates[edit]
Main article: Frequency
Radioactive decay, the amount of radioactive material in which one nucleus decays per second, measured in Becquerels
In computing:
Bit rate, the number of bits that are conveyed or processed by a computer per unit of time
Symbol rate, the number of symbol changes (signalling events) made to the transmission medium per second
Sampling rate, the number of samples (signal measurements) per second
Miscellaneous definitions:
Rate of reinforcement, number of reinforcements per unit of time, usually per minute
Heart rate, usually measured in beats per minute
Economics/finance rates/ratios[edit]
Exchange rate, how much one currency is worth in terms of the other
Inflation rate, ratio of the change in the general price level during a year to the starting price level
Interest rate, the price a borrower pays for the use of money they do not own (ratio of payment to amount borrowed)
Price–earnings ratio, market price per share of stock divided by annual earnings per share
Rate of return, the ratio of money gained or lost on an investment relative to the amount of money invested
Tax rate, the tax amount divided by the taxable income
Unemployment rate, the ratio of the number of people who are unemployed to the number in the labor force
Wage Rate, the amount paid for working a given amount of time (or doing a standard amount of accomplished work) (ratio of payment to time)
Other rates[edit]
Birth rate, and mortality rate, the number of births or deaths scaled to the size of that population, per unit of time
Literacy rate, the proportion of the population over age fifteen that can read and write
Sex ratio or Gender ratio, the ratio of males to females in a population
See also[edit]
Derivative
Gradient
Harmonic mean
Hertz
Slope
References[edit]
Jump up ^ See Webster's new international dictionary of the English language, second edition, unabridged. Merriam Webster Co. 2016. p.2065 definition 3. while this definition doesn't say "related" and while the ratio of two non-related quantities is technically a ratio, such a ratio has little (if any meaning). For example, what would be the utility of finding the ratio of such unrelated numbers as ratio of the weight of ones residence to an integer selected at random between -10−9 and +109?
Jump up ^ Adams, Robert A. (1995). Calculus: A Complete Course (3rd ed.). Addison-Wesley Publishers Ltd. p. 129. ISBN 0-201-82823-5.
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Hawthorne, Florida
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Hawthorne, Florida
City
City Hall and water tower
Location in Alachua County and the state of Florida
Coordinates: 29°35′17″N 82°5′2″W / 29.58806°N 82.08389°W / 29.58806; -82.08389Coordinates: 29°35′17″N 82°5′2″W / 29.58806°N 82.08389°W / 29.58806; -82.08389
Country
United States
State
Florida
County
Alachua
Incorporated (city)
1881
Government
• City manager
Ellen Vause
• Mayor
Matthew Surrency
• Vice Mayor
Tommie Howard
Area[1]
• Total
7.03 sq mi (18.20 km2)
• Land
6.77 sq mi (17.53 km2)
• Water
0.26 sq mi (0.67 km2)
Elevation
148 ft (45 m)
Population (2010)
• Total
1,417
• Estimate (2016)[2]
1,525
• Density
225.26/sq mi (86.97/km2)
Time zone
Eastern (EST) (UTC-5)
• Summer (DST)
EDT (UTC-4)
ZIP code
32640
Area code(s)
352
FIPS code
12-29275[3]
GNIS feature ID
0283829[4]
Website
www.cityofhawthorne.net
Hawthorne is a city in Alachua County, Florida, United States. The population was 1,417 at the 2010 census.[5]
Contents
[hide]
1 History
2 Geography
3 Demographics
4 Education
5 Notable people
6 References
7 External links
History[edit]
Hawthorne was laid out in 1881 on land owned by James H. Hawthorne.[6] A post office was established as Hawthorn in 1880, and the spelling was changed to Hawthorne in 1950.[7]
Geography[edit]
South Bull Pond at Sunset in Hawthorne, FL
Hawthorne is located at 29°35′17″N 82°5′2″W / 29.58806°N 82.08389°W / 29.58806; -82.08389 (29.587943, -82.083859).[8]
According to the United States Census Bureau, the city has a total area of 5.0 square miles (13.0 km2), of which 4.8 square miles (12.4 km2) is land and 0.23 square miles (0.6 km2) (4.33%) is water.[5]
Demographics[edit]
Historical population
Census
Pop.
%±
1900 296 —
1910 324 9.5%
1920 543 67.6%
1930 600 10.5%
1940 741 23.5%
1950 1,058 42.8%
1960 1,167 10.3%
1970 1,126 −3.5%
1980 1,303 15.7%
1990 1,305 0.2%
2000 1,415 8.4%
2010 1,417 0.1%
Est. 2016 1,525 [2] 7.6%
U.S. Decennial Census[9]
As of the census[10] of 2010, there were 1,417 people, 561 households, and 357 families residing in the city. The population density was 295.2 inhabitants per square mile (114.2/km²). There were 681 housing units at an average density of 141.9 per square mile (54.9/km²). The racial makeup of the city was 52.4% European American, 45.3% African American, 0.1% Native American, 0.3% Asian, 0.5% from other races, and 1.5% from two or more races. Hispanic or Latino of any race were 2.0% of the population.
There were 561 households out of which 31.6% had children under the age of 18 living with them, 38.3% were married couples living together, 21.0% had a female householder with no husband present, and 36.4% were non-families. 31.4% of all households were made up of individuals and 12.0% had someone living alone who was 65 years of age or older. The average household size was 2.534 and the average family size was 3.15.
In the city, the population was spread out with 23.2% under the age of 18, 2.4% from 18 to 21, 52.9% from 21 to 62, and 20.1% who were 62 years of age or older. The median age was 41.5 years. For every 100 females there were 86.2 males. For every 100 females age 18 and over, there were 86.6 males.
According to the 2005-2009 American Community Survey,[11] the median income for a household in the city was $36,818, and the median income for a family was $44,1672. The per capita income for the city was $15,331. About 11.9% of families and 18.9% of the population were below the poverty line, including 23.1% of those under age 18 and 30.4% of those age 65 or over.
Education[edit]
The City of Hawthorne is served by the School Board of Alachua County, which operates Shell Elementary School and Hawthorne Middle/High School in the city.[12] The Alachua County Library District operates a branch library in the city.[13]
Notable people[edit]
Bo Diddley, rock & roll legend
James B. Edwards, Governor of South Carolina
Cornelius Ingram, National Football League player
D. R. "Billy" Matthews, congressman from North Florida 1953-1965
Marjorie Kinnan Rawlings, author
References[edit]
Jump up ^ "2016 U.S. Gazetteer Files". United States Census Bureau. Retrieved Jul 7, 2017.
^ Jump up to: a b "Population and Housing Unit Estimates". Retrieved June 9, 2017.
Jump up ^ "American FactFinder". United States Census Bureau. Retrieved 2008-01-31.
Jump up ^ "US Board on Geographic Names". United States Geological Survey. 2007-10-25. Retrieved 2008-01-31.
^ Jump up to: a b "Geographic Identifiers: 2010 Demographic Profile Data (G001): Hawthorne city, Florida". U.S. Census Bureau, American Factfinder. Retrieved May 6, 2013.
Jump up ^ "Florida town has two spellings". The Miami News. Jul 16, 1946. pp. 9A. Retrieved 7 June 2015. [dead link]
Jump up ^ "Alachua County". Jim Forte Postal History. Retrieved 7 June 2015.
Jump up ^ "US Gazetteer files: 2010, 2000, and 1990". United States Census Bureau. 2011-02-12. Retrieved 2011-04-23.
Jump up ^ "Census of Population and Housing". Census.gov. Retrieved June 4, 2015.
Jump up ^ "American Factfinder". United States Census Bureau. Retrieved 17 October 2011.
Jump up ^ "American Community Survey". United States Census Bureau. Retrieved 17 October 2011.
Jump up ^ Alachua County Public Schools: Schools and Centers Archived 2011-12-17 at the Wayback Machine.
Jump up ^ Alachua County Library District: Hawthorne
External links[edit]
City of Hawthorne official website
HawthorneFlorida.org
Hawthorne Branch Library
Former official website
Student project from 1997
[hide]
v
t
e
Municipalities and communities of Alachua County, Florida, United States
County seat: Gainesville
Cities
Alachua
Archer
Gainesville
Hawthorne
High Springs
Newberry
Waldo
Towns
LaCrosse
Micanopy
Unincorporated
communities
Bland
Cross Creek
Earleton
Evinston
Hague
Haile
Haile Plantation
Hasan
Island Grove
Jonesville
Lochloosa
Melrose
Rochelle
Tioga
Windsor
Footnotes
‡This populated place also has portions in an adjacent county or counties
Retrieved from "https://en.wikipedia.org/w/index.php?title=Hawthorne,_Florida&oldid=813957416"
Categories:
Cities in Alachua County, Florida
Gainesville, Florida metropolitan area
Populated places established in 1881
Cities in Florida
1881 establishments in Florida
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This page was last edited on 6 December 2017, at 03:44.
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Hansen (surname)
From Wikipedia, the free encyclopedia
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Hansen or Hanssen (Danish pronunciation: [ˈhænsn̩]) is a Scandinavian patronymic surname, meaning son of Hans. As of 2008, it is the third most common surname in Denmark, shared by 4.3% of the population.[1] As of 2000, Hansen is the single most common surname in Norway, not counting spelling variations such as Hanssen, which are also quite common.[2] In the Faroe Islands Hansen is the second most common surname, while in the North German federal states of Schleswig-Holstein and Hamburg Hansen is the third and fifth most common surname, respectively.[3] In Sweden the parallel form is Hansson. The frequent occurrences of Hansen as a surname outside Denmark,[4] Norway and Schleswig-Holstein is due to immigration, though Nordic immigrants to English-speaking countries often anglicised their names to Hanson in order to accommodate English orthographic rules.
Contents
[hide]
1 Notable people
1.1 Arts and entertainment
1.2 Politics
1.3 Science
1.4 Sport
1.5 Other
2 References
3 See also
Notable people[edit]
Notable people with the surname include:
Arts and entertainment[edit]
Aime Hansen (born 1962), Estonian poet, writer, and artist
Al Hansen (1927–1995), American artist
Andrew Hansen (1974–), Australian comedian
Anna Hansen, Canadian chef
Asta Hansen (1914–1962), Danish stage and film actress
Beck Hansen, also known as Beck (1970–), American musician, songwriter
Betsy Hansen (dates unknown), woman who charged actor Errol Flynn with statutory rape in 1942
B. Andreas Bull-Hansen (1972–), Norwegian fantasy writer and former championship weightlifter
Carl G. O. Hansen (1871–1960), Norwegian-American journalist, musician and author
Carl William Hansen (1872–1936), Danish author
Chris Hansen, American journalist
Christian Frederik Hansen (1756–1845), Danish architect
Constantin Hansen (1804–1880), Danish artist
Courtney Hansen (contemporary), American model and television personality
C. & V. Hansen (1906–2001 & 1900–1992), Danish comics authors
Dinah-Jane Hansen (born 1996), Singer of Female American group Fifth Harmony
David Hansen (actor) (contemporary), actor, director, and playwright
Derek Hansen (contemporary), Australian writer
Erhardine Adolphine Hansen (1815–1893), Danish actress
Erik Hansen (1927–2016), Danish architect
Erik Fosnes Hansen (1965–), Norwegian author
Gunnar Hansen (1947–2015), Icelandic-American actor
Ib Hansen, pseudonym of Austrian poet H. C. Artmann (1921–2000)
Henriette Hansen, Norwegian ballerina, singer and actor
Joachim Hansen (actor) (1930–), German actor
Johannes Hansen (sculptor) (1903–1995), Danish sculptor
Joseph Hansen (writer) (1923–2004), author
Joseph Hansen (dancer) (1842–1907), Belgian dancer
Kai Hansen (1963–), German power metal musician
Liane Hansen (contemporary), American radio journalist and radio show host
Lisa M. Hansen an American producer, actress, assistant director, and writer
Mary Hansen (1966–2002), Australian guitarist and singer
Max Hansen (tenor) (1897–1961), Danish singer
Peter Hansen (actor) (1921–2017), American actor
Ron Hansen (novelist) (1947–), American novelist, essayist, and professor
Politics[edit]
Ann Hansen (contemporary), Canadian anarchist and bomber
Bernie Hansen (contemporary), American politician in Chicago politics
Clifford Hansen (1912–2009), American politician from Wyoming
Colin Hansen (contemporary), Canadian politician from British Columbia
Connor Hansen, American jurist from Wisconsin
Dave Hansen (1947–), American politician from Wisconsin
Eva Kjer Hansen (1964–), Danish politician
Flemming Hansen (politician) (1939–), Danish politician
George V. Hansen (1930–), American politician from Idaho
Glenna Hansen (1956–), Canadian Inuvialuit politician
H. C. Hansen (1906–1960), Danish Prime Minister (1955–1960)
James V. Hansen (1932–), American politician from Utah
Joseph Hansen (socialist) (1910–1979), American Trotskyist and leader of the American Socialist Workers Party
Merle Hansen (1919–), American farmer, Founder of the North American Farm Alliance
Peter Hansen (UN) (1941–), Danish UN official
Robert W. Hansen, American jurist from Wisconsin
Ron Hansen (politician) (1943–), Canadian politician from Ontario
Stephanie Hansen (1961–), American politician from Delaware
Urban Hansen (1908–1986), Danish politician
Science[edit]
Alvin Harvey Hansen (1887–1975) American economist
Emil Christian Hansen (1842–1910), Danish fermentation physiologist
Gerhard Armauer Hansen (1841–1912), Norwegian physician, discover of the cause of leprosy
Hans Jacob Hansen (1855–1936), Danish zoologist
James E. Hansen (1941–), American climatologist
Julie Vinter Hansen (1890–1960), Danish astronomer
Per Brinch Hansen (1938–2007), Danish computer scientist
Peter Andreas Hansen (1795–1874), Danish astronomer
Thomas Blom Hansen (born 22 January 1958), Danish anthropologist
W.W. Hansen (1909–1949), American physicist
Sport[edit]
Abraham Løkin Hansen (1959–), Faroese footballer (né Hansen)
Adam Hansen (1981–), Australian road cyclist
Adrian Hansen (born 1971), South African squash player
Alan Hansen (1955–), Scottish footballer
Ashia Hansen (1971–), British athlete, Olympic contestant
Bob Hansen (1961–), American basketballer
Brendan Hansen (1981–), American swimmer
Craig Hansen (1983–), American professional baseball player
Curt Hansen (chess player) (1964–), Danish chess grand master
Dale Hansen (1948–), American sportscaster
Dave Hansen (baseball player), American baseball player
Einar Hansen, Faroese soccer player
Eric Hansen, Canadian chess player
Erika Hansen (1970–), American swimmer
Fred Hansen (1940–), 1964 Olympic Gold medalist and world record pole vaulter
Jan Knobelauch Hansen (1971–), Danish athlete, Olympic contestant
Jannik Hansen (born 1986), Danish Ice Hockey Player
Joachim Hansen (MMA) (1979–), Norwegian Mixed martial artist
Joan Hansen (1958–), American long-distance runner
John Hansen (footballer born 1924), Danish footballer
John Hansen (footballer born 1950), Scottish footballer
Johnny Hansen (footballer born 1943), Danish footballer
Kevin Hansen (volleyball) (1982–), American indoor volleyball player
Martin Lundgaard Hansen (1972–), Danish badminton player, Olympic contestant
Niels Jørgen Hansen, Danish darts player
Nikolaj Hansen (1987–), Danish footballer
Paul Snow-Hansen, New Zealand sailor
Per Joar Hansen (1965–), Norwegian football coach
Phil Hansen (American football) (born 1968), American former football player
Rasmus Grønborg Hansen, Danish football (soccer) player
Rick Hansen (1957–), Canadian paraplegic athlete and humanitarian
Ron Hansen (baseball) (1938–), American professional baseball player
Søren Hansen (1974–), Danish professional golfer
Stan Hansen (1949–), American professional wrestler
Sune Berg Hansen, Danish chess player
Travis Hansen, American Basketball Player
Trine Hansen (1973–), Danish rower
Other[edit]
Annika Hansen a fictional character from Star Trek: Voyager better known as Seven of Nine
Elaine Tuttle Hansen (contemporary), president of Bates College
Georg Emil Hansen (1833–1891), Danish photographer
Georg Hansen (1904–1944), German army officer
Gesa Hansen (born 1981), German-Danish designer
Gus Hansen (1974–), Danish professional poker player
Helmer Hanssen (1870–1956), Norwegian polar explorer
John Hansen (judge) (1945–), retired New Zealand judge
Lars Peter Hansen (1952–), American economist and econometrician
Matthew Hansen, Canadian screenwriter, author and editor
Max Hansen (SS officer) (1908–1990)
Monica Hansen, Norwegian model
Percy Howard Hansen (1890–1951), Danish recipient of the Victoria Cross
Robert Hanssen (1944–), American FBI agent convicted of spying for Russia
Sig Hansen (1966–), American Captain of the Seattle-based crab fishing boat Northwestern, featured in the documentary Deadliest Catch
Theodore Marcus Hansen (1886–1973), Danish-American pastor, theologian, and churchman
Theophil Freiherr von Hansen (1813–1891), Danish-Austrian architect
References[edit]
Jump up ^ "Navne - Danmarks Statistik". dst.dk. Retrieved 2018-03-17.
Jump up ^ "Navn". SSB. Retrieved 2018-03-17.
Jump up ^ "Verteilung des Namens "Hansen" in Deutschland". verwandt.de. Retrieved 2018-03-17.
Jump up ^ "Danskernes Navne – University of Copenhagen - Name Research Section". danskernesnavne.navneforskning.ku.dk. Retrieved 2018-03-17.
See also[edit]
Hansen (disambiguation)
Hanson (surname)
Henson
Surname list
This page lists people with the surname Hansen. If an internal link intending to refer to a specific person led you to this page, you may wish to change that link by adding the person's given name(s) to the link.
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