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RELATIVE WHITE AND COLORED POPULATION IN TEN OF THE SOUTHERN
STATES. – First line: South Carolina, Mississippi, Georgia, Alabama, Louisiana. Second line: Virginia, North Carolina, Arkansas, Tennessee, Texas
Exercise From data probably obtainable from the local Chamber of Commerce, prepare graphical diagrams setting forth concerning the city in which you live, information along the following lines :
1. Variation in temperature during twenty-four hours. 2. Monthly rainfall for a period of years. 3. The hourly electric output at some near-by power house. 4. Daily consumption of gas. 5. Daily consumption of meat, milk, eggs, or bread.
Exercise Prepare graphical charts, obtaining the data where you can, setting forth the following:
1. The number of passengers who travel on the street cars at various hours during the day, in your city.
2. Bank clearings in your city by years, months, or days for the past ten years.
3. Post-office business in the largest three cities in your state.
4. Values of various agricultural productions of your county. 5. Values of various mineral productions of your state.
Abundance of material suitable for graphic representation can be found in such publications as the Statistician's Year Book, World Almanac, Tribune Almanac, Scientific American Reference Book, and any geographical statistical atlas. Much material of this kind can usually be obtained from the local Chamber of Commerce, Bureau of Mines, Development Board, the newspaper offices, and the banks. The student will find numerous other types of graphical representation in various magazines, especially those devoted to engineering and construction work. Indeed, scarcely a book or technical article is written these days wherein the author does not have recourse to pictorial charts or diagrams.
RATIO AND PROPORTION
Ratio. - In the accompanying figure it is apparent that A is one half as large as B, and one third as large as C.
It is customary to say, then, that the ratio of A to B is one half, and
that the ratio of A
A to C is one
third. Similarly it is evident that B is two thirds as large as C. That is, the ratio of B to C is two thirds.
Ratio therefore has to do with the relative size of things and is the numerical relation between two quantities of the same kind.
Thus, since 6 is half as great as 12, the ratio of 6 to 12 is one half. The ratio of 2 pounds to 3 pounds is two thirds; the ratio of one foot to one yard is one third.
A ratio can be expressed in a variety of ways. Thus, if one number is half as great as another, their ratio can be expressed graphically thus
; or if a certain quantity is one fourth as great as another, their ratio can be expressed as in the accompanying figures.
Ratio can be expressed numerically in any one of several ways. For example, the ratio of 2 to 3 can be expressed as , 2/3, 2 + 3, or 2:3. Such an expression as 2:3 is read “ the ratio of 2 to 3,” or “ 2 is to 3.”
Definitions. In the ratio 2:3, 2 and 3 are called the terms of the ratio. Expressed in fractional form the
. same ratio reads for 2/3. The numerator or first term of the ratio is called the antecedent. The denominator or second term of the ratio is called the consequent. Thus, in the ratio 4:5, 4 is the antecedent and 5 is the consequent..
In each of the following examples determine the ratio of the first-named quantity to the second : 1. 3 ft. to 7 ft.
12. $ 3.50 to $ 14.00 2. 4 yd. to 9 yd.
13. 141 lb. to 29 lb. 3. 2 lb. to 14 lb.
14. 29 lb. to 141 lb. 4. 2 ft. to 5 yd.
15. 1 oz. to 1 lb. (Avoir.) 5. 5 ft. to 1 yd.
16. 1 oz. to 1 lb. (Troy) 6. 10 lb. to 6 lb.
ft. to 1 sq. yd. 7. 1 mi. to 2 mi.
18. 1 sq. yd. to 1
ft. 8. 14 in. to 3 yd.
19. 4} tons to 75 lb. 9. 10 yd. to 3 in.
20. 1 kilometer to 1 mi. 10. $ 7.50 to $ 3.75
21. 1 decimeter to 1 in. 11. $ 14.00 to $ .50
22. 1 millimeter to 1 in.
23. The area of a square 1 ft. on a side to the area of a square 2 ft. on a side.
24. The area of a square 2 ft. on a side to the area of a square 1 ft. on a side.
25. The volume of a 1-ft. cube to the volume of a 2-ft. cube.
26. The volume of a 12-in. cube to the volume of a 4-in. cube.
27. The perimeter of a square to one side.
36. The area of a circle to the area of a square whose side is the same as the diameter of the circle.
Rates. In a ratio the things compared are of the same kind. It frequently happens, however, that things of different kinds must be compared, and this comparison gives rise to the idea of a rate. Such expressions as so many threads to the inch, so many revolutions per minute, ,
, etc., are of common occurrence and are called rates.
Exercise 1. If a wheel makes 2000 revolutions per minute, how many does it make in 10 seconds ?
2. If a vehicle travels 55 miles an hour, what is the distance traveled in 15 minutes ? in 15 seconds ?
3. If there are 8 threads to the inch in a nut, how far will it advance in making 20 turns ?
4. If telephone poles are placed 100 feet apart, how many poles are there to the mile ?
5. If the price of gas is $.65 per M, what is the charge for 2260 cubic feet of gas ?