Review#2 graphs&change
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The document reviews different types of graphs and maps that are important for understanding Earth science concepts and that may appear on the Earth science Regents exam, including: direct/inverse/no relationship graphs; cyclical graphs; isolines/contour maps that connect points of equal elevation/temperature/air pressure; how to read information from graphs like seasonal temperature and daylight changes. It emphasizes being able to draw graphs and maps, identify relationships, read contour intervals, and calculate slope from provided topographic maps.
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COMENIUS - Webquest eratosthene
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The Mesopotamian culture is often called Babylonian, after the large metropolis of that name. We could “babble on”1 and on about their many fine achievements in architecture, irrigation, and commerce, but it is their mathematics that is truly remarkable, dwarfing that of other contemporary civilizations. One might not be impressed by their use of a vertical mark for “one” and a horizontal mark for “ten” – ten being a common unit in the mathematics of many societies, including Egypt, China, Rome, and our own society today. On the other hand, they were the first to employ a “positional” system which, except for minor changes, survives to this day!
1The authors would like to apologize for the easy pun, but we couldn’t resist.
Let’s remind ourselves how our current number system works. It does not suffice to say that it is based on grouping by tens. The Egyptians did this – yet we have left them in the dust by taking a giant step forward to the “position system.” We require only ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Nevertheless, we can handle numbers of any size without the need to define a new symbol. This is because the value of a number is determined not just by the symbol. We must note the positionof the symbol as well. The two 3’s in the number 373 represent different quantities. You would rather have three hundred dollars than three dollars, right? To summarize, our number system employs a mere ten symbols, whose values depend on their position in the number. Moving one digit to the left multiplies its place value by ten, while moving to the right (not surprisingly) divides its place value by ten.
Observe, by the way, that this is true on both sides of the decimal point! In the number 3.1416, the 1 near the 6 is worth only one hundredth of the 1 near the 3. There is no number in the entire universe that is too large or too small for our clever (ten-digit!) number system (of Hindu-Arabic origin, by the way). We call our system the decimal system, because ten is the base.
The Babylonians used instead the sexagesimal system because they chose 60 as their base. While we are not sure why, we are fairly certain they did not have 60 fingers. One theory (which is very popular) is that 60 has a multitude of factors, that is, many numbers go into 60. Put another way, $60 can be divided without coin among 2, 3, 4, 5, 6, 10, 12, 15, 20, or 30 people. We shall follow the common practice of using commas to separate groups. Thus (3, 50)60 shall mean 3 sixties and 50 ones for a total of 230. What does (2, 3, 50)60 mean? Well in our position system, 357 means 3 hundreds, 5 tens, and 7 ones, right? Each column is ten times more valuable than its neighbor. In the same way, each column to the left in the Babylonian system is sixty times bigger! In the number (2, 3, 50)60, the 2 represents 2 3600’s – because 60 × 60 = 3600. The next column to the left would represent 60 × 3600 or 216000.
The Babylonians only used two symbols: a vertical mark for 1 and ...
Term Paper Coordinate Geometry
The document provides a summary of coordinate geometry. It begins with definitions of key terms like the coordinate plane, axes, quadrants, and coordinates. It then discusses finding the midpoint, distance, and section formula between two points. Methods for finding the coordinates of the centroid and area of a triangle are presented. The document outlines different forms of equations for straight lines, including their slopes and the general equation of a line. It concludes with some uses of coordinate geometry, such as determining if lines are parallel/perpendicular.
1. A small accounting firm pays each of its five clerks $35,000, t.docx
1. A small accounting firm pays each of its five clerks $35,000, two junior accountants $80,000 each, and the firm's owner $350,000. What is the mean salary paid at this firm? (Round your answer to the nearest whole number.)
$
How many of the employees earn less than the mean?
employees
What is the median salary?
$
2. A small accounting firm pays each of its five clerks $35000, two junior accountants $90000 each, and the firm's owner $256000.
What is the mean salary paid at this firm?
How many of the employees earn less than the mean?
What is the median salary?
If this firm gives no raises to the clerks and junior accountants, but the owner now has a salary of $435000.
How does this change affect the mean?
The mean increases by $ .
How does it affect the median?
The median increases by $ .
3. A study of diet and weight gain deliberately overfed 16 volunteers for eight weeks. The mean increase in fat was x = 2.63 kilograms and the standard deviation was s = 1.21 kilograms. What are x and s in pounds? (A kilogram is 2.2 pounds.)
x
=
s
=
4.Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Suppose these are the last few national mean scores, on a scale of 0 to 500.
Year
1990
1992
1996
2000
2003
2005
2008
Score
265
266
270
271
278
279
281
(a) Make a time plot of the mean scores, by hand. This is just a scatterplot of score against year. There is a slow linear increasing trend. (Do this on your own.)
(b) Find the regression line of mean score on time step-by-step. First calculate the mean and standard deviation of each variable and their correlation (use a calculator with these functions). Then find the equation of the least-squares line from these. (Round your answers to two decimal places.)
= + x
Draw the line on your scatterplot. What percent of the year-to-year variation in scores is explained by the linear trend? (Round your answer to one decimal place.)
%
(c) Now use software or the regression function on your calculator to verify your regression line. (Do this on your own.
5. A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. The data (heights in inches) are listed below.
Women (x)
65
63
63
64
69
64
Men (y)
72
67
69
69
69
68
(a) Make a scatterplot of these data. (Do this on paper. Your instructor may ask you to turn this in.) Based on the scatterplot, do you expect the correlation to be positive or negative? Near ± 1 or not?
The correlation should be positive. It should be near 1.The correlation should be negative. It should be near -1. The correlation should be positive. It should not be near 1.The correlation should be negative. It should not be near -1.
(b) Find the correlation r between the heigh ...
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- 2. “A PICTURE IS WORTH A THOUSAND WORDS”
- 3. SCIENTISTS USE “PICTURES” IN THE FORM OF GRAPHS AND TABLES TO ORGANIZE OBSERVATIONS.
- 4. GRAPHS AND TABLES MAKE IT EASIER TO UNDERSTAND THE “STORY” THAT THE DATA IS “TELLING” US!
- 5. THE EARTH SCIENCE REGENTS HAS MANY, MANY, MANY TABLES!
- 6. A DIRECT RELATIONSHIP GRAPH: AS THE X-AXIS INCREASES, THE Y-AXIS ALSO INCREASES.
- 7. A INVERSE RELATIONSHIP GRAPH: AS THE X-AXIS INCREASES, THE Y-AXIS DECREASES.
- 8. A NO RELATIONSHIP GRAPH: AS THE X- AXIS INCREASES, THE Y-AXIS DOES NOT INCREASE OR DECREASE.
- 9. A CYCLICAL RELATIONSHIP GRAPH: AS THE X-AXIS INCREASES, THE Y-AXIS INCREASES AND DECREASES OVER AND OVER AGAIN
- 10. MOST NATURAL PROCESS ARE CYCLICAL (EX. TIDES, THE SEASONS, CELESTIAL MOTION OF PLANETS ARE CYCLICAL)
- 11. I MUST BE ABLE TO READ THE GRAPHS ON THE EARTH SCIENCE REGENTS.
- 12. Base your answer on The GRAPH below indicates the average number of daylight hours and the average surface air temperature over a 12-month period at a specific location on the Earth. Based on the graph, the highest average surface air temperature occurs • a. on June 21 • b. between June 21 and September 23 • c. on December 21 • d. between December 21 and March 21
- 13. Which statement is best supported by the graph? • a. The infrared radiation given off by the Sun occurs at a wavelength of 2,000 angstroms. • b. The maximum intensity of radiation given off by the Sun occurs in the visible region. • c. The infrared radiation given off by the Sun has a shorter wavelength than ultraviolet radiation. • d. The electromagnetic energy given off by the Sun consists of a single wavelength.
- 14. I WILL HAVE TO DRAW AT LEAST ONE GRAPH ON THE EARTH SCIENCE REGENTS!
- 15. ISOLINES (TOPOGRAPHIC MAPS), CONTOUR LINES, ISOTHERMS, ISOBARS ARE GRAPHS THAT CONNECT POINTS WITH EQUAL MEASUREMENTS.
- 16. I MUST REMEMBER TO “CONNECT THE DOTS”. TO CONNECT THE SAME MEASURES TO EACH OTHER.
- 17. Does the map below show isolines, isotherms or isobars? How do you know?
- 18. Draw the 1024- and 1028-millibar isobars on the weather map provided below.
- 19. Remember: isobars are always circular
- 20. are these HIGH pressure or LOW pressure system? How do you know/
- 21. Is this an isoline, isobar or isotherm? How do you know?
- 22. On the field map provided, draw only the 15°C and the 20°C isotherms. Isotherms must be extended to the edge of the map.
- 23. Remember: I must draw isotherms from the edge of the field map to another edge.
- 26. Contour maps (topographic maps): connect points of equal elevation (height above sea level)
- 27. Contour maps (topographic maps): connect points of equal elevation (height above sea level)
- 28. CONTOUR INTERVAL shows the distance in elevation between two contour lines
- 29. I must be able to find the contour interval, if it isn’t given.
- 30. What is the contour interval of this map? • a. 10 m • b. 50 m • c. 100 m • d. 150 m
- 31. On contour maps, v-shaped lines represent a stream (river)
- 32. The point of the v-shaped lines show where a stream (river) comes from.
- 33. This stream comes from the north west and flows towards south east.
- 34. On a contour map, the steepest slope is where the contour lines are close together.
- 35. On a contour map, the gentle slope is where the contour lines are far apart.
- 36. A hole (a depression) is represented by hachure lines
- 37. A contour profile is “side view” of a contour map. I will have to draw one on the regents.
- 40. I will also have to calculate the gradient (the slope) of a contour map. Turn to page 29 of the green workbook.