In problems #2 through #6, round your answers to the nearest tenth if necessary.
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1 Math 254CM Name Essential Mathematics Date Study Guide #5 Exam #5 is closed book. You will be given the Geometry handout and the Measurements handout. You may use a calculator on this exam. You must show your work in order to receive any partial credit. Do these problems on separate paper. 1. Convert as indicated. Use only whole numbers. a) 16,250 feet = miles feet b) 3156 pounds = tons pounds In problems #2 through #6, round your answers to the nearest tenth if necessary. 2. Convert 114 inches to feet. 3. Convert.25 tons to pounds. 4. Convert 120 fluid ounces to quarts. 5. Convert 1 2 yards to inches. 6. Convert 2 quarts to cups.. a) Convert 435 centigrams to grams. b) Convert 0.68 kiloliters to milliliters. c) Convert 1. meters to centimeters. For problems #8 thru #12, perform the indicated operation. Simplify the result if possible ft 2 in 9 ft 8 in 9. 2 lb 5 oz kg 2410 g
2 ml L tons 81 lbs + 1 ton 26 lbs 13. To feed its pandas a zoo grows a small patch of bamboo. Two weeks ago the bamboo was 5ft 8in. Since then it has grown 2ft 5in. How tall is the bamboo now? Write your answer in simplest form using the given units. 14. A can of soda weighs 336 grams. Find the weight, in kilograms, of 24 cans. 15. According to the Guinness Book of Records, the heaviest baby born in good health weighed 22 pounds 8 ounces. How much heavier is this than a pound 10 ounce baby? Write your answer in simplest form using the given units. 16. A large bottle of juice contains 1.42 L. A smaller bottle contains 946 ml. How much more juice is in the larger bottle? (Answer can be written using either L or ml.) 1. a) Vitamin C tablets come in 500 milligram caplets. Convert this to ounces. b) How many caplets would you need to have a pound of Vitamin C? 18. a) Convert 102 F to degrees Celsius. If necessary, round to the nearest tenth of a degree. b) Convert 48º C to degrees Fahrenheit. If necessary, round to the nearest tenth of a degree. 19. a) Find the supplement of a 65º angle. b) Find the complement of a 65º angle. 20. a) Find the measure of BEA in the figure. A 50º B 38º C 35º b) Find the measure of BED in the figure. E D 21. The two horizontal lines are parallel. Find the measures of angles w, x, y and z in the figure. 115º x z y w
3 22. Are the following statements true or false? A rhombus is also a square. An obtuse angle measures between 0º and 90º. A parallelogram is always a rectangle. 23. Use the triangle given to find the measure of x. 25º 95º x 24. Find the perimeter of the figure below. 8 feet 20 feet 13 feet 14 feet 6 feet 25. Find the area of the following figure feet 14 feet 8 feet 26. a) Find the exact circumference of the circle shown. 9 (b) Then use 3.14 to find the approximate circumference of this circle. Round to the nearest hundredth.
4 2. (a) Find the exact area of the circle shown (b) Then use to find the approximate area of this circle. Give your answer as a mixed number with the fraction part in lowest terms. 28. Find the perimeter of the triangle. in 4 in 6 in 29. Find the area of the triangle. Write your answer as a whole number or a mixed number with the fraction part in lowest terms. yd yd 30. a) Find the perimeter of the trapezoid. 11 feet b) Find the area of the trapezoid feet 10 feet 20 feet
5 31. a) How much fencing is needed to enclose a rectangular garden that measures 105 feet by 60 feet? b) If the fencing material cost $3.50 per foot, what is the total cost of the fencing material? 32. A rectangular picture frame measures feet by 4 feet. Find how many square feet of glass the frame requires. Write the answer as a whole number or a mixed number with the fraction part in lowest terms. 33. A swimming pool company advertises that solar covers are on sale for $1. per square foot. How much would a cover cost for a 36-foot by 18-foot rectangular pool? 34. Find the volume of a right circular cylinder that has a height of 14 yards and a diameter of 8 yards. Use 22 for. Write the answer as a whole number or a mixed number with the fraction part in lowest terms. 35. Find the volume of the sphere, in cubic feet. Use 22 number with the fraction part in lowest terms. for. Write the answer as a whole number or a mixed r 9 ft. r 36. An ice cream cone with a 6 centimeter diameter and a height of 5 centimeters is filled exactly level with the top of the cone. Approximate how much ice cream is in the cone. Use 22 for. Write the answer as a whole number or a mixed number with the fraction part in lowest terms. 3. a) Find square root of 121. b) Find the square root of c) Circle the correct answer: 40 is between (i) 4 and 5 (ii) 5 and 6 (iii) 6 and
6 38. The two triangles below are similar. Find the ratio of the corresponding sides. Write your answer in simplest form Given that the pair of triangles is similar, find the length of the side labeled x. Write a proportion to receive full credit. x Given that the pair of triangles is similar, find the length of the side labeled x. Write a proportion to receive full credit x 6. 8
7 41. If a 30-foot tree casts an 18-foot shadow on the ground, find the length of the shadow cast by a 24-foot tree. Write a proportion to receive full credit. 42. At a certain time of day, a 24-foot telephone pole casts a 6-foot shadow on the ground. If another telephone pole casts a shadow that is 5 feet long, how tall is the second telephone pole? Write a proportion to receive full credit. 43. On a certain map, 1 inch = 30 miles. If on this map two cities are 2.5 inches apart, how many miles apart are the actual cities?
Be prepared to find the volume, area, and volume of any of the shapes covered in lecture and/or homework. A rhombus is also a square.
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