Operating Expenses. Fuel, Maintenance Items, or Repairs. Cost per Unit. Number. = Subtotal Time = Hour. 1 Oil Filter $22.50 = $22.

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1 4 Operating Expenses Operating equipment costs money. To know just how much money it costs requires keeping careful record of all the expenses such as fuel, maintenance, and repairs. Operating costs are calculated by finding the cost per mile or per hour of running time. Example : Find the total operating costs per hour for changing oil in the skidder every 200 hours. Fuel, Maintenance Items, or Repairs nit = Subtotal Time = Hour Oil Filter $22.50 = $ Gallons of oil $5.60 = $28.00 Total Operating Cost Per Hour $ hours = $0.25 The cost of an oil change for the skidder is $0.25 per hour. Example 2: Find the total operating cost per hour for running the skidder. Fuel, Maintenance Items, or Repairs nit = Subtotal Time = Hour 4.5 Gallons of Fuel $2.65 = $.93 hour = $.93 Engine Overhaul $5,250 = $5,250 0,000 hours = $ Tires $2,350 = $9,400 6,000 hours = $.57 8 Gallons of Coolant $4.75 = $ ,500 hours = $0.0 2 Oil Filters $22.50 = $ hours = $0.09 Total Operating Cost Per Hour $4.3 The cost of running the skidder is about $4.3 per hour. 7

2 Lesson 4 Find the cost per mile for operating a pickup truck with these expenses. Round all answers to the nearest cent. Fuel, Maintenance Items, or Repairs nit = Subtotal Miles = Mile. a. b. d. Gallons of fuel $3.9 = 2.5 miles = 4 Tires $25.00 = 40,000 miles = Repairs $ = 5,000 miles = Total Operating Expense Per Mile Find the operating costs per hour for running a lawnmower with these expenses. Round all answers to the nearest cent. Fuel, Maintenance Items, or Repairs nit = Subtotal Time = Hour 2. a. b. d. 2 Gallons of Gasoline $3.5 = hour = Mower Repairs $ = 240 hours = 5 Quarts of Oil $.95 = 240 hours = Total Operating Expense Per Hour We R e m e m b e r Solve. se the distance formula. 3. A horse trotted at an average speed of 8 mph. How far did it travel in H hour? List the prime factors using exponents. Then list each factor with the largest exponent. Multiply to find the LCM. 4. a. 0 = b. 5 = d. e. LCM = 8 40 =

3 Lesson x S k i l l B u i l d e r s a b Find the final cost after discount. 6. The cost was $22.99 before an 8% discount. The final cost is. Look at the graph on page 70. Write the ordered pair for each point. 7. a. J b. M N d. R e. V From the graph on page 70, write the letter of the point for each ordered pair. 8. a. (3, 3) b. ( 4, 0) ( 5, 6) d. (2, 5) Find the prime factors and the GCF. 9. a. Factors of 96 = b. Factors of 08 = GCF = Find the mean, median, mode, and range. Round to the nearest whole. 0. 4, 9, 20, 4, 0, 6, 9, 6, a. mean b. median mode d. range se a compass and a straightedge to construct a perpendicular from point L to the line. L. 9

4 Lesson 4 M a s t e r y D r i l l 2. Opposite angles always have measures. 3. The formula for finding the volume of a triangular prism is. 4. The difference between the least and greatest number in a list is the. 5. The correct order of operations is ; ; and ; and. 6. a. The parallel symbol is. b. kilogram pounds 7. a. The intersection symbol is. b. The union symbol is. 8. a. The a member of symbol is. b. The subset symbol is. 9. a. The not a member of symbol is. b. The perpendicular symbol is. 20. a. 2 6 = b. 2 3 = 3 3 = d. = % a. = % b. = % = % d. 69 = Simplify the expressions. 22. a. x x 3 x b. x x x + 3x + x d. 8n + n Convert to decimals. Write the repeating decimals with a bar = = Convert. Round to the nearest whole yd m m yd Solve. 27. $,500 loaned out at 5% interest for 0 months. a. Amount of interest owed: b. Total amount to repay: Maple sap harvested straight from the tree contains to 3% solids. Sap needs to be boiled down to concentrate the solids to no less than 65% to be considered maple syrup. 20

5 Lesson 4 Finish the Venn diagram to illustrate the sets. Complete the sentences. 28. Set = all the trees in New York Set A = hard maples in New York Set B = hardwood trees in New York 29. Set of Set B. 30. Set A B = all the in New York. Find the total income. 3. A salesman receives a salary of $,875 per month plus 2% commission on sales of $4,575. Find the area of the irregular shape Find the cost per copy for operating a photocopier with these yearly expenses. Round to the nearest cent. Fuel, Maintenance, or Repairs nit = Subtotal of Copies = Copy 33. a. b. d. e. 2 Toner Cartridges $78.00 = Developer $45.00 = Drum $25.00 = Maintenance Technician $50.00 = Total Operating Expense Per Copy 50,000 copies = 2

6 5 Quiz Tell your teacher when you are ready to take Quiz. Fa s c i n a t i n g D i s c o v e r i e s A Problem With Length 2 feet = 24 inches and foot = 6 inches Since 2 =, then multiplying the inch equivalents should also equal foot. 2 feet foot = 24 inches 6 inches foot = 44 inches Wait a minute! Doesn t foot = 2 inches? What did we do wrong? The problem lies in the fact that when we multiplied the numbers, we neglected to also multiply the units. A correct solution looks like this: 2 ft ft = 24 in 6 in ft 2 = 44 in 2 REMEMBER: Multiply units as well as numbers. 22

7 6 Venn Diagrams for Intersection of Sets When members belong to two different sets at the same time, we show it on the Venn diagram with overlapping circles. The overlap, or intersection, of the two circles represents the members which belong to both sets. = People who like outdoor sports A = People who like fishing A B B = People who like hunting A B = People who like both hunting and fishing The intersection of two sets of factors is the common factors. = All s C 3, 6, D Set C = Factors of 2 {, 2, 3, 4, 6, 2 } Set D = Factors of 8 {, 2, 4, 8 } C D = Common factors of 8 and 2 {, 2, 4 } When two sets are multiples, the intersection is the common multiples. E F = All s Set E = Multiples of 2 { 2, 24, 36, 48, 60 } Set F = Multiples of 6 { 6, 2, 8, 24, 30 } E F = Common multiples of 2 and 6 { 2, 24 } 23

8 Lesson 6 Disjoint Sets Sometimes two different sets have nothing in common. We call these sets disjoint sets. Sets A and B below are disjoint sets. A B = All students in the school A = Girls in seventh grade B = Boys in seventh grade The Empty Set When a particular problem has no answers, or a set has no members, the answer is the empty set ( ). For the Venn diagram above, we could say that A B =. In other words, there is no intersection. Draw a Venn diagram to illustrate the intersection of sets. Answer the questions.. Set = All students Set A = Students who like to play chess Set B = Students who like to play Monopoly (Some students like to play both games.) Complete the sentence. 2. A B represents students who like to play both and. Write the letter of each set shown on the Venn diagram. 3. a. cats b. all pets 4. a. poodles b. dogs C D E Write T for true or F for false. 5. a. Sets C and D are disjoint sets. b. C D is the empty set. 6. a. D E =. b. E C E D 24

9 Lesson 6 We R e m e m b e r Find the cost per mile for an oil change for Clark s pickup. Round to the nearest cent. Fuel, Maintenance Items, or Repairs nit = Subtotal Distance = Mile 7. a. b. Oil Filter $5.50 = 6 Quarts of Oil $.45 = Total Operating Expense Per Mile 2,000 miles = 8. Bingham Lumber uses one chain saw with a 36-inch bar. This saw uses chain with a pitch of inches. All the other saws the men use regularly have 20-inch bars and use chain with a pitch of I inch. How much longer is the pitch of the larger saw chain than the pitch of the smaller saw chains? The pitch of a saw chain is the distance between any first and third rivet. Convert. Round to the nearest whole L gal in cm. 39 kg lb Read Kings 8:32. Complete the sentences. se seah 6.5 quarts. 2. The trench Elijah made around the altar was big enough to hold seahs (measures) of seed. 3. The trench held about quarts. Solve. se the distance formula. Change the time to a fraction of an hour. 4. The flight was 450 miles long and took 45 minutes. What was the average speed of the airplane? 25

10 Lesson x S k i l l B u i l d e r s 7 lb 9 oz x 5. a. 6 lb 2 oz b. 30 = hr 36 min + 7 hr 33 min 6. A late-season snowfall of 4 inches was equivalent to inches of rain. At this density, how many inches of snow were equivalent to inch of rain? se a proportion. Round to the nearest whole inch. Simplify the expressions. 7. a b d Solve. Graph the solution. 8. a. x 8 5 b Round to the nearest,000 to estimate. Then copy and solve. 9. 7, ,26 + 0, ,367 = = 26

11 Lesson 6 M a s t e r y D r i l l 20. A reflex angle measures between and. 2. The number that occurs most often in a list is the. 22. Any number with an exponent of equals the number itself. 23. The sum of the measures of complementary angles equals. 24. In the formula V = Bh, the capital B stands for the of the. 25. a. meter yards b. foot 2 = inches a. The union symbol is. b. mile kilometers 27. a. Distance = time b. The a member of symbol is. 28. a. 2 5 = b. 5 3 = = % d. = % Draw two Venn diagrams to illustrate the two groups of sets. Then Complete the sentences. 29. Set = All numbers Set A = Positive numbers Set B = Negative numbers 30. Set = All numbers Set C = Factors of 2 {, 2, 3, 4, 6, 2} Set D = Factors of 20 {, 2, 4, 5, 0, 20} 3. Sets and are disjoint sets. 32. Sets and overlap. Their intersection represents the common factors of and. 33. a. C D = b. A B = Complete the sentences. 34. The symbol for the empty set is. 35. Sets that have nothing in common are called sets. 27