4. A employs a capital of $2,500 in business, and at the end. of 3 years takes into partnership B, who furnishes $4,000. Four years later they are joined by C, with a capital of $5,000. At the end of 12 years from the commencement of the business, the profits, amounting to $15,000, are divided. What amount should each receive? A's money is in the business how many years? B's, how many years? C's, how many? 5. Four butchers rent a field, and pay for 6 months' rent $152.50. The first puts in 20 oxen for 10 weeks and 50 sheep for 8 weeks; the second, 25 oxen for 8 weeks and 30 sheep for 7 weeks; the third, 18 oxen for 10 weeks and 10 sheep for 12 weeks; the fourth, 30 oxen for 12 weeks. What share will each have to pay, counting 3 sheep equal to 1 ox? 6. A wall 700 yards long was to be built in 29 days. At the end of 11 days, 18 men had built 220 yards of it. How many extra men had then to be put to work, so that the wall might be completed in the given time? 7. If 5 needlewomen can do a piece of work in 11 days of 9 hours each, how long will it take 3 needlewomen to do two such pieces, supposing them to work 10 hours each day? 8. If 14 men can mow 168 acres in 12 days of 8 hours 15 minutes each, how many acres can 20 men mow in 11 days of 7 hours 48 minutes each? 9. If 12 men can do a piece of work in 20 days, what number of men will be required to do four times as much work in a fifth part of the time? 10. A ship sailed with a crew of 60 men, and provisions for 34 days, and 10 days afterwards, 12 persons were received on board from a sinking vessel. How long would the provisions last the 72 persons then on board? How long would the provisions last the 60 persons at the time the sinking vessel was met? 11. If 76 boards, each 14 feet long and 10 inches wide, are worth $19.76, how much would 50 such boards be worth? 12. If 7 men receive $126 for 5 weeks' work, how much should they receive for 9 weeks' work? 13. If for 7s. 6d. I can buy 9 lb. of raisins, how many pounds can I buy for £56 16s.? 14. A field of grain was to be cut down by 40 men in 10 days. Eight of the men, however, failed to come. How long did it take the others to do the work? 1889 428,483,681 1,344,023 1,997,414 9,298,236 2,009,518 8,709,541 2,159,879 Av. of 10 yr. Find for each year the total tax levy, and the tax rate in dollars, cents, and mills per $1,000 of assessed value. Find the average assessment per year; the average tax levy for state, county, and city purposes; and the average tax rate. SURFACES OF PRISMS AND CYLINDERS. 1141. Slate Exercises. NOTE. The pupils should be encouraged to make cardboard models of the forms studied. 1. Find the convex surface of a square prism, one side of its base being 4 inches and its height 6 inches. Draw the development. NOTE. The convex surface is the surface exclusive of the bases. 2. Find the convex surface of a triangular prism, each side of whose base measures 4 inches and whose altitude is 6 inches. Draw the development. 3. Find the convex surface of an hexagonal prism, each side of its base being 4 inches and its altitude 6 inches. Draw the development. 4. Can you show that the convex surface of a prism is found by multiplying the perimeter of the base by its altitude (height)? 5. Find the convex surface of a cylinder, the diameter of its base being 4 inches and its height 6 inches. 6. How do you find the entire surface of a prism or cylinder? 7. What is the entire surface of a cube whose side is 7 inches? Of a cube whose side is x inches? 8. The entire surface of a cube is 216 sq. in. What is the length of one side? 9. The convex surface of a cube is 144 sq. in. Find the entire surface. 10. Find the entire surface of a square prism, one side of whose base measures 4 inches, and whose altitude is 6 inches. 11. The convex surface of a square prism is 600 sq. ft., the altitude is 15 ft. What is the length of one side of the base? 12. The entire surface of a square prism is 1,650 sq. in. One side of the base measures 15 inches. What is its convex surface? What is its altitude? 13. Find the entire surface of a square prism whose convex surface is 540 sq. in., and whose altitude is 15 inches. 14. What is the entire surface of a cylinder whose base has a diameter of 1 foot, and whose altitude is 1 foot? SURFACES OF PYRAMIDS AND CONES. 15. The convex surface of a square pyramid consists of how many equal triangles? Find the convex surface when one side of its base measures 4 inches and its slant height (AX) 6 inches. Draw the development. A B X C 16. The convex surface of a pyramid is equal to the perimeter of the base multiplied by what? 17. Find the entire surface of the above pyramid. 18. Calculate the entire surface of a square pyramid whose slant height is 18 inches, the area of its base being 144 sq. in. 19. Find the entire surface of a triangular pyramid whose three convex faces and the base are equilateral triangles, each side measuring 2 inches. 20. Draw the developed convex surface of a cone, the diameter of whose base is 4 inches, and whose slant height is 6 inches. Calculate the convex surface. 21. How many square inches of paper would 6 in. 4 in. be required to cover the side and the base of a cone 6 inches in diameter at the base, and having a slant height of 10 inches? 22. Calculate the slant height of a cone whose altitude is 12 inches, the diameter of its base being 10 inches. What is its convex surface? the 23. What is the entire surface of a cone, diameter of whose base is 6 inches, and its slant height 10 inches? Draw the development. 6 in. A B 24. A semi-circular piece 4 of paper 6 inches in diam eter is folded into a hollow cone (without overlapping). C AB of the mouth of the cone (the base)? What will be the slant height BC? 1142. Cambridge, Mass., Public Schools. Examination Questions. 1. Last year 22 per cent of the whole number of pupils in the primary schools lost on an average 138 sessions each. How many sessions were lost by these pupils, the whole number of pupils being 4,300? 2. There are 40 weeks in a school year. There are usually 10 sessions in each week. There are 36 lines in the "Psalm of Life." If pupils commit to memory one line each session, how many poems containing as many lines as the "Psalm of Life" will they learn at school during the year, the school being closed 1 per cent of the 40 weeks? 3. If to-day (June 21, 1890) Mr. Chas. P. Emerson, of Cambridge, is to give you his note for $240, without interest, on three months' time, how should the note be written? What would be the avails (proceeds) of the note at a bank July 21, 1890? 4. A man invested some money in bonds, at par, bearing 6 per cent interest, and received $300 semi-annually. What was the sum invested? |