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All Textbook Solutions for Elementary Technical Mathematics

Add: 435+2600+18+5184+6Subtract: 60,0004,803Multiply: 706013004R5R6R7R8R9R10R11RGiven the formula P=Fst,F=600,s=50,andt=10,findP.13R14R15R16R17R18R19R20R21R22RPerform the indicated operations and simplify: 14+512+5624R25R26R27R28R29R30R31R32R33R34R35RFill in each blank: 168ft=in.37R38R39R40R41R42RPerform the indicated operations: 8.6+140+0.048+19.6344R45R46R47R48R49R50R51R52R53R54R55R56R57R58R59R60R61RCharlotte wants to paint a room that measures 16 ft wide, 20 ft long, and 9 ft high. One gallon of the paint she selects covers 400ft2 and costs $16.99. The sales tax is 7.75%. She plans to paint the ceiling and the four walls with the same paint. How many gallons of paint should she buy? How much will it cost? She ignores the area of the two windows and the door into the room when she estimates the amount of paint she needs.A 78 -in. -thick board is being used as a base. If holes are drilled 916 in. to insert posts, what is the thickness of the board left below each hole as shown is Illustration 4? ILLUSTRATION 464R65R66R67RMaria purchased a new car for a price of $26,500. She received a rebate of $2500 and paid a sales tax of 7.25% after the rebate. She paid a down payment of 20% and obtained a loan for the balance at 6.5% APR over a 5-year period. How much is her monthly payment?1T2T3T4T5T6TFind the area of the figure in Illustration 1. ILLUSTRATION 1Find the volume of the figure in Illustration 2. ILLUSTRATION 2Ohms law states that current (in A) equals voltage (in V) divided by resistance (in ). Find the current in the circuit in Illustration 3. ILLUSTRATION 3If P=2l+2w,l=20,andw=15,findP.11T12T13T14T15T16T17T18T19T20T21T22T23T24T25T26T27T28T29T30T31T32T33T34T35T36T37T38T59.45 is 41% of what number?40TRachel receives a 6.7% increase in salary. If her salary was $612 per week, what is her new weekly salary?42T43T44TAdd: 832+9+56+2358Add: 324+973+66+9430Add: 384291147632_Add: 78107452179123_Add: 197+1072+10,877+15,532+768,098Add: 160,000+19,000+4,160,000+506,000Subtract and check: 75612397_Subtract and check: 4000702_Subtract and check: 98,40572,397Subtract and check: 417,286287,156Subtract and check: 40001180_Subtract and check: 60,0009,876_Find the total resistance in each series circuit:Find the total resistance in each series circuit:Approximately how many studs are needed for the exterior walls the building shown in Illustration 1? (See Example 4.) ILLUSTRATION 1A pipe 24 ft long is cut into four pieces: first 4 ft long, the second 5 ft long, and the third 7 ft long. What is the length of the remaining piece? (Assume no waste from cutting.)17EA welder ordered a 125-ft3 cylinder of argon gas, a semi-inert shielding gas for TIG welding. After a few days, only 78 ft3 remained. How much argon was used?Find the total input and output (I-O) in cubic centimeters (cm3)* for a patient. By how much does the input of fluids exceed the output? Input: 300 cm3, 550 cm3, 150 cm3,75 cm3, 150 cm3, 450 cm3, 250 cm3 Output: 325 cm3, 150 cm3, 525 cm3, 250 cm3, 175 cm3A student pilot must complete 40 h of total flight time as required for her private pilot certificate. She had already entered 31 h of flight time in her log- book. Monday she logged another 2 h, then Wednesday she logged another 3 h, and Friday she logged yet another 2 h. If she can fly 3 h more on Saturday, will she have enough total time as required for the certificate?Multiply: 56748_Multiply: 8374203_23EMultiply: 152032025EMultiply: 30,0104080Divide (use the remainder form with r): 4723628EDivide (use the remainder form with r): 466812Divide (use the remainder form with r): 15,64836Divide (use the remainder form with r): 67,56980Divide (use the remainder form with r): 188,000120An automobile uses gasoline at the rate of 31 miles per gallon (mi/gal or mpg) and has a 16-gallon tank. How far can it travel on one tank of gas?An automobile uses gasoline at a rate of 12 kilometers per liter (km/L) and has a 65-litre tank. How far can it travel on one tank of gas?A four-cylinder engine has a total displacement of 1300 cm3. Find the displacement of each piston.An automobile travels 1274 mi and uses 49 gal of gasoline. Find its mileage in miles per gallon.An automobile travels 2340 km and uses 180 L of gasoline. Find its fuel consumption in kilometers per liter.To replace some damaged ductwork, 20 linear feet of 8-in. 16-in. duct is needed. The cost is $13 per 4 linear feet. What is the cost of replacement?The bill for a new transmission was received. The total cost for labor was $516. If the car was serviced for 6 h, find the cost of labor per hour.The cost for a set of four tires is $596. What is the cost of each tire?A small Cessna aircraft has enough fuel to fly for 4 h. If the aircraft cruises at a ground speed of 125 miles per hour (mi/h or mph), how many miles can the aircraft fly in the 4 h?A small plane takes off and climbs at a rate of 500 ft/min. If the plane levels off after 15 min, how high is the plane?Inventory shows the following lengths of 3-inch steel pipe: 5 pieces 18 ft long 42 pieces 15 ft long 158 pieces 12 ft long 105 pieces 10 ft long 79 pieces 8 ft long 87 pieces 6 ft long What is the total linear foot of pipe in inventory?An order of lumber contains 36 boards 12 ft long, 28 boards 10 ft long, 36 boards 8 ft long, and 12 boards 16 ft long. How many boards are contained in the order? How many linear feet of lumber are contained in the order?Two draftspersons, operating the same computer plotter, each work 8 hours per day. One produces 80 drawings per hour; the other produces 120 drawings per hour. What is the difference in their outputs after 30 work days?A shipment contains a total of 5232 linear feet of steel pipe. Each piece of pipe is 12 ft long. How many pieces should be expected?The wall is 10 ft high and the vertical length of the window is 54 in. The center of the window needs to be at a distance of 5/8 of the height of the wall above the floor (to meet the special Fibonacci ratio criteria). How should a window 75 in. wide be horizon- tally placed so that it is centered on a wall 17 ft 5 in. wide? How high is the bottom of the window above the floor?A farmer expects a yield of 165 bushels per acre (bu/acre) from 260 acres of corn. If the corn is stored, how many bushels of storage are needed?A farmer harvests 6864 bushels (bu) of soybeans from 156 acres. What is his yield per acre?A railroad freight car can hold 2035 bu of corn. How many freight cars are needed to haul the expected 12,000,000 bu from a local grain elevator?On a given day, eight steers weighed 856 lb, 754 lb, 1044 lb, 928 lb, 888 lb, 734 lb, 953 lb, and 891 lb. a. What is the average weight? b. In 36 days, 4320 lb of feed is consumed. What is the average feed consumption per day per steer?What is the weight (in tons) of a stack of hay bales 6 bales wide, 110 bales long, and 15 bales high? The average weight of each bale is 80 lb (1 ton = 2000 lb.)From a 34-acre field, 92,480 lb of oats are harvested. Find the yield in bushels per acre. (1 bu of oats weighs 32 lb.)A standard bale of cotton weighs approximately 500 lb. How many bales are contained in 15 tons of cotton?A tractor costs $175,000. It has a 10-year life and a salvage value of $3000. What is the annual depreciation? (Use the straight-line depreciation method. See Example 10.)How much pesticide powder would you put in a 400-gal spray tank if 10 gal of spray, containing 2 lb of pesticide, are applied per acre?Daylilies are to be planted along one side of a 30-ft walk in front of a house. The daylilies are planted 5 in. from each end and 10 in. apart along the walk. How many daylilies are needed?A potato patch has 7 rows with 75 hills of potatoes per row. If each potato hill yields 3 lb of marketable potatoes, how many pounds of marketable potatoes were produced?Using Ohms law, find the current I in amps (A) in each electric circuit (see Example 9):Using Ohms law, find the current I in amps (A) in each electric circuit (see Example 9):Ohms law, in another form, states that in a simple circuit the voltage E (measured in volts, V) equals the current I (measured in amps, A) times the resistance R (measured in ohms, ). Find the voltage E measured in volts (V) in each electric circuit:Ohms law, in another form, states that in a simple circuit the voltage E (measured in volts, V) equals the current I (measured in amps, A) times the resistance R (measured in ohms,). Find the voltage E measured in volts (V) in each electric circuit:A hospital dietitian determines that each patient needs 4 ounces (oz) of orange juice. How many ounces of orange juice must be prepared for 220 patients?During 24 hours, a patient is to receive three 60-mg doses of phenobarbital. Each tablet contains 30 mg of phenobarbital. How many milligrams of phenobarbital does the patient receive altogether in 24 hours? How many pills does the patient take in 24 hours?To give 800 mg of quinine sulfate from 200-mg tablets, how many tablets would you use?A nurse used two 5-g tablets of potassium permanganate in the preparation of a medication. How much potassium permanganate was used?A sun room addition to a home has a wall 14 ft 6 in. long measured from inside wall to inside wall. Four windows are to be equally spaced from each other in this wall. The windows are 2 ft 6 in. wide including the inside window molding. What is the space between the wall and windows shown in Illustration 2? ILLUSTRATION 2A solid concrete block wall is being built around a rectangular storage building with outside dimensions 12 ft 8 in. by 17 ft 4 in. using 16-in.-long by 8-in.-high by 4-in.-thick concrete block. How many blocks will be needed to build the 8-ft-high wall around the building as shown in Illustration 3? (Ignore the mortar joints and a door.) Suggestion: First, change dimensions to inches.A sheet of plywood 8 ft long is painted with three equally spaced stripes to mark off a hazardous area as shown in Illustration 4. If each stripe is 10 in. wide, what is the space between the end of the plywood and the first stripe? ILLUSTRATION 3In a small machine shop, eight 5-gallon drums of oil are on hand. If 2 gallons are used each day and the owner wants a 30-day supply on hand, how many drums should be ordered?Using a process called cruising timber, foresters can estimate the amount of lumber in board feet in trees before they are cut down. In a stand of 1000 trees, a forester selects a representative sample of 100 trees and estimates that the sample contains 8540 board feet of lumber. If the entire stand containing 2500 trees is harvested, how many board feet would the landowner expect to harvest?In tilapia aquaculture production, a feed conversion ratio of 2 lb of high-protein pelleted feed per pound of weight gain, after death losses, is not unusual. At that rate of feed conversion, if fish food costs $520 per ton (2000 lb), what would be the feed cost per pound of live fish produced?A banquet facility has section areas separated with folding walls. Section A has a total of 50 seats, Section B has a total of 125 seats, Section C has a total of 110 seats, and Section D has a total of 35 seats. What is the maximum number of guests who could be seated using all sections?Each beef export loin will yield 11 prime rib servings. a. How many beef export loins are needed to serve prime rib to 125 guests? b. How many total end cut servings are possible for these guests?A delivery to the kitchen includes the following: 2 boxes of bakers (potatoes, 90 per box), 3 boxes of beef roast 109s (prime ribs, 4 per box), and 2 boxes of pork loins (pork, 4 per box). How many total individual items are in all the boxes?The Sun Rise Restaurant has 10 tables that seat 6 people each plus 12 tables that seat 4 people each. Each server is assigned at most 6 tables. What is the least number of servers needed when the restaurant is full of customers?The wait staff decides to pool (combine and divide evenly) their tips for the evening shift. The three servers have rounded tips of: $131, $152, and $128. a. What is the total amount to be divided? b. How much does each server receive?Evaluate each expression: 83(42)2E3E4E5E6E7EEvaluate each expression: 1233(8+9)+179E10E11E12E13E14E15E16E17EEvaluate each expression: 2284(7+6)8(62)19E20E21E22E23E24E25E26EEvaluate each expression: 3+17(22)6728E29E30E31E32EEvaluate each expression: 3159+(135)/24234E35E36E37E38E39E40E41E42E43E44EHow many square yards (yd2) are contained in a rectangle 12 yd long and 8 yd wide?How many square metres (m2) are contained in a rectangle 12 m long and 8 m wide?At a small airport, Runway 11-29 is 4100 ft long and 75 ft wide. What is the area of the runway?A small rectangular military operating zone has dimensions 12 mi by 22 mi. What is its area?An automobile measures 191 in. by 73 in. Find the area it occupies.Five pieces of sheet metal have been cut to form a container. The five pieces are of sizes 27 by 15, 15 by 18, 27 by 18, 27 by 18, and 15 by 18 (all in inches). What is the total area of all five pieces?In exercises assume that corners are square and that like measurements are not repeated because the figures have consistent lengths. Note: All three of the following mean that the length of a side is 3 cm: Find the area of each figure:In exercises assume that corners are square and that like measurements are not repeated because the figures have consistent lengths. Note: All three of the following mean that the length of a side is 3 cm: Find the area of each figure:In exercises assume that corners are square and that like measurements are not repeated because the figures have consistent lengths. Note: All three of the following mean that the length of a side is 3 cm: Find the area of each figure:In exercises assume that corners are square and that like measurements are not repeated because the figures have consistent lengths. Note: All three of the following mean that the length of a side is 3 cm: Find the area of each figure:In exercises assume that corners are square and that like measurements are not repeated because the figures have consistent lengths. Note: All three of the following mean that the length of a side is 3 cm: Find the area of each figure:In exercises assume that corners are square and that like measurements are not repeated because the figures have consistent lengths. Note: All three of the following mean that the length of a side is 3 cm: Find the area of each figure:How many tiles 4 in. on a side should be used to cover a portion of a wall 48 in. long by 36 in. high? (See Illustration 1.) ILLUSTRATION 1How many ceiling tiles 2 ft by 4 ft are needed to tile a ceiling that is 24 ft by 26 ft? (Be careful how you arrange the tiles.)How many gallons of paint should be purchased to paint 20 motel rooms as shown in Illustration 2? (Do not paint the floor.) One gallon is needed to paint 400 square feet (ft2). ILLUSTRATION 2How many pieces of 4-ft by 8-ft drywall are needed for the 20 motel rooms in Exercise 15? All four walls and the ceiling in each room are to be dry walled. Assume that the drywall cut out for windows and doors cannot be salvaged and used again.The replacement cost for construction of houses is $110/ft2. Determine how much house insurance should be carried on each of the one-story houses in Illustration 3. ILLUSTRATION 3The replacement cost for construction of the building in Illustration 4 is $90/ft2. Determine how much insurance should be carried for full replacement. ILLUSTRATION 4Find the volume of each rectangular solid:Find the volume of each rectangular solid:Find the volume of each rectangular solid:Find the volume of each rectangular solid:Find the volume of each rectangular solid:Find the volume of each rectangular solid:Find the volume of a rectangular box 10 cm by 12 cm by 5 cm.A mountain cabin has a single room 20 ft by 10 ft by 8 ft high. What is the total volume of air in the room that will be circulated through the central ventilating fan?Common house duct is 8-in. by 20-in. rectangular metal duct. If the length of a piece of duct is 72 in., what is its volume?A furnace filter measures 16 in. by 20 in. by 1 in. What is its volume?A large rectangular tank is to be made of sheet metal as follows: 3 ft by 5 ft for the top and the base, two sides consisting of 2 ft by 3 ft, and two sides consisting of 2 ft by 5 ft. Find the volume of this container.Suppose an oil pan has the rectangular dimensions 14 in. by 16 in. by 4 in. Find its volume.Find the weight of a cement floor that is 15 ft by 12 ft by 2 ft if 1 ft3 of cement weighs 193 lb.A trailer 5 ft by 6 ft by 5 ft is filled with coal. Given that 1 ft3 of coal weighs 40 lb and 1 ton 5 2000 lb, how many tons of coal are in the trailer?A rectangular tank is 8 ft long by 5 ft wide by 6 ft high. Water weighs approximately 62lb/ft3. Find the weight of water if the tank is full.A rectangular tank is 9 ft by 6 ft by 4 ft. Gasoline weighs approximately 42lb/ft3. Find the weight of gasoline if the tank is full.A building is 100 ft long, 50 ft wide, and 10 ft high. Estimate the cost of heating it at the rate of $55 per 1000ft3.A single-story shopping center is being designed to be 483 ft long by 90 ft deep. Two stores have been preleased. One occupies 160 linear feet and the other will occupy 210 linear feet. The owner is trying to decide how to divide the remaining space, knowing that the smallest possible space should be 4000 ft2. How many stores can occupy the remaining area as shown in Illustration 5? ILLUSTRATION 5A trophy company needs a shipping box for a trophy 15 in. high with an 8-in.-square base. The box company is drawing the die to cut the cardboard for this box. a. What are the dimensions of the smallest rectangular sheet of cardboard needed to make one box that allows 1 in. for packing and 1 in. for a glue edge as shown in Illustration 6? b. What is the area of the rectangular cardboard to be mass produced? c. What is the total area of the cardboard to be removed? ILLUSTRATION 638E39EA municipal wastewater treatment plant has a settling tank that is 125 ft long and 24 ft wide with an effective depth of 12 ft. What is the surface area of the liquid in the tank and what is the volume of sewerage that the settling tank will hold?Three inches of mulch need to be applied to a rectangular flower bed 8 ft by 24 ft between a house and a walk. How many cubic feet of mulch are needed?How many 44 inch plant containers can be placed in a greenhouse on a table 4 ft wide and 8 ft long?Use the formula W=fd, where f represents a force and d represents the distance that the force is applied. Find the work done, W: f=30,d=20Use the formula W=fd, where f represents a force and d represents the distance that the force is applied. Find the work done, W: f=17,d=9Use the formula W=fd, where f represents a force and d represents the distance that the force is applied. Find the work done, W: f=1125,d=10Use the formula W=fd, where f represents a force and d represents the distance that the force is applied. Find the work done, W: f=203,d=27Use the formula W=fd, where f represents a force and d represents the distance that the force is applied. Find the work done, W: f=176,d=236Use the formula W=fd, where f represents a force and d represents the distance that the force is applied. Find the work done, W: f=2400,d=120From formulas a. to f. on page 19, choose one that contains all the given letters. Then use the formula to find the unknown letter: Ifm=1600anda=24,findf.From formulas a. to f. on page 19, choose one that contains all the given letters. Then use the formula to find the unknown letter: IfV=120andR=24,findP.From formulas a. to f. on page 19, choose one that contains all the given letters. Then use the formula to find the unknown letter: IfE=120andR=15,findI.From formulas a. to f. on page 19, choose one that contains all the given letters. Then use the formula to find the unknown letter: Ifv=372andt=18,findd.From formulas a. to f. on page 19, choose one that contains all the given letters. Then use the formula to find the unknown letter: IfI=29andE=173,findP.From formulas a. to f. on page 19, choose one that contains all the given letters. Then use the formula to find the unknown letter: IfI=11,E=95,andt=46,findW.Find the area of each triangle: b=10in.,h=8in.Find the area of each triangle: b=36cm,h=20cmFind the area of each triangle: b=54ft,h=20ftFind the area of each triangle: b=188m,h=220mFind the area of each rectangle: b=8m,h=7mFind the area of each rectangle: b=24in.,h=15in.Find the area of each rectangle: b=36ft,h=18ft20EFind the area of each trapezoid: a=7ft,b=9ft,h=4ftFind the area of each trapezoid: a=30in.,b=50in.,h=34in.23EFind the area of each trapezoid: a=450m,b=750m,h=250mThe volume of a rectangular solid is given by V=lwh, where l is the length, w is the width, and h is the height of the solid. Find V if l=25 cm, w=15 cm, and h=12 cm.