Block 1 Math

8385. Find the value of 10 raised to the negative sixth power. A—0.000001. B—0.000010. C—0.0001.

"A—0.000001" Ten raised to the negative sixth power (10-6) is equal to 0.000 001. This negative number is the reciprocal of the positive sixth power of ten. It is found by dividing the number 1 by the sixth power of 10 (1,000,000).

8431. How much current does a 30-volt, 1/2 horsepower motor that is 85 percent efficient draw from the bus? (Note: 1 horsepower = 746 watts) A—14.6 amperes. B—12.4 amperes. C—14.3 amperes

"A—14.6 amperes. " There are 746 watts in one horsepower. The motor produces one-half horsepower (373 watts) at 100 percent efficiency, but it is only 85 percent efficient. 373 ÷ 0.85 = 438.8 watts of power used by the motor. Current drawn by the motor is found by dividing the power by the voltage: I = P ÷ E I = 438.8 ÷ 30 I = 14.62 amps

8386. What is the square root of 4 raised to the fifth power? A—32. B—64. C—20.

"A—32." The square root of four is two. Two raised to the fifth power is 32.

8427. Sixty-five engines are what percent of 80 engines? A—81 percent. B—65 percent. C—52 percent.

"A—81 percent." To find the percentage of engines represented by 65 out of 80, we find the ratio of 65 to 80 by dividing 65 by 80. 65 ÷ 80 = 0.8125 Then we change this decimal fraction into a percentage by multiplying it by 100. Sixty-five engines is 81.25 percent of 80 engines.

8439. Solve the equation. 4 - 3[-6(2 + 3) + 4] = A—82. B—-25. C—-71.

"A—82." 1. Begin this problem by working the inside parentheses, and then work outward. (2 + 3) = 5 (-6 × 5) = -30 (-30 + 4) = -26 2. Next, the multiplication is done. 3 × -26 = -78 3.Now, perform the subtraction. 4 - (-78) = 82

8397. Find the area of the triangle shown A—12 square inches. B—6 square inches. C—15 square inches. Hight= 3' base= 4' hypotenuse= 7.5'

"B—6 square inches." The area of a triangle is one half of the product of its base times its altitude. The base of this triangle is 4 inches and the altitude is 3 inches. The area is (4 × 3) ÷ 2 = 6 square inches.

8402. Determine the area of the triangle formed by points A, B, and C. A—42 square inches. B—63 square inches. C—126 square inches. A to B = 7.5 inches A to D = 16.8 inches

"B—63 square inches." The area of a triangle is equal to one-half the product of its base and its altitude. In this problem, the base is the distance A to D, which is 16.8 inches (this is the same as the distance B to C). The altitude is the distance A to B, which is 7.5 inches. Area = 16.8 × 7.5 divided by 2 = 126 divided by 2 = 63 square inches

8403. What is the piston displacement of a master cylinder with a 1.5-inch diameter bore and a piston stroke of 4 inches? A—9.4247 cubic inches. B—7.0686 cubic inches. C—6.1541 cubic inches.

"B—7.0686 cubic inches." The piston displacement of a master cylinder is found by multiplying the area of the piston head by its stroke. The area of the piston is found by squaring its diameter (1.5 inch in this problem) and multiplying this by the constant 0.7854 (one-fourth of π). When the area of 1.767 square inches is multiplied by the stroke of 4.0 inches, we find that the displacement of the master cylinder is 7.0686 cubic inches. PD = 0.7854 × B2 × S = 0.7854 × 1.52 × 4 = 7.0686 cubic inches

8393-3. Solve the equation. A—5.58. B—12.16. C—0.042. square root 31 + square root 43 over (17)^2

"C—0.042." Follow the order of operations rule:

8384. Find the cube of 64. A—4. B—192. C—262,144.

"C—262,144" The cube of a number is found by multiplying the number by itself three times. 64^3 = 64 × 64 × 64 = 262,144

8433. Solve the equation. (64 x 3/8) ÷ 3/4 = A—18. B—24. C—32.

"C—32." First work the part of the problem inside the parenthesis, and then do the division. 64 × 3/8 = 24 24 ÷ 3/4 = 32

8395-1. What is the volume of a sphere with a radius of 4.5 inches? A—47.71 cubic inches B—381.7 square inches C—381.7 cubic inches Volume= 1/6*πD^3

"C—381.7 cubic inches" V = (1/6) × πD^3 V = (1/6) × π x 93 V = (1/6) × π x 729 V = 381.7

8417. Express 5/8 as a percent. A—.625 percent. B—6.25 percent. C—62.5 percent.

"C—62.5 percent." A percentage is a decimal fraction with 100 as its denominator To convert 5/8 into a percentage, divide five by eight and multiply this by 100. 5 ÷ 8 = 0.625 0.625 × 100 = 62.5 percent

8415. A certain aircraft bolt has an overall length of 1-1/2 inches, with a shank length of 1-3/16 inches, and a threaded portion length of 5/8 inch. What is the grip length? A—.5625 inch. B—.8750 inch. C—.3125 inch.

"A—.5625 inch." The grip length of a bolt is the length of the unthreaded portion of the shank. If the shank is 1-3/16 (1.1875) inches long, and the threaded portion is 5/8 (0.625) inch, the grip length is 1.1875 - 0.625 = 0.5625 inch.

8379-3. Convert 7 to binary form. A—0111. B—0011. C—1110.

"A—0111." The binary number system has only two digits: 0 and 1. To convert a decimal number to a binary number, the place values in the binary system are used to create a sum of numbers that equal the value of the decimal number being converted. Start with the largest binary place value and subtract from the decimal number. Continue this process until all of the binary digits are determined. 7 = 0111 in binary.

8398. What force is exerted on the piston in a hydraulic cylinder if the area of the piston is 1.2 square inches and the fluid pressure is 850 PSI? A—1,020 pounds. B—960 pounds. C—850 pounds

"A—1,020 pounds." The force exerted on a piston by hydraulic fluid is found by multiplying the area of the piston by the amount of pressure acting on each square inch of the piston. In this problem the area is 1.2 square inches and a pressure of 850 pounds acts on each square inch. The force is 1,020 pounds.

8393-1. Which of the figures is using scientific notation? A—1. B—2. C—both 1 and 2. 1) 3.47*10^4=34,700 2) 2(4^10)=2,097,152.

"A—1." Equation 1 uses scientific notation, equation 2 does not. Scientific notation requires 10 to be raised to a power. Four raised to the 10th power does not qualify as scientific notation.

8393-2. Which alternative answer is equal to 5.59? A—1. B—2. C—3. 1) (square root 31) + (square root 43) divided by 17^2 2) (square root 31+ square root 43) divided by 17^2 3) (square root 31) + (square root 43) - 17^2

"A—1." You must follow the order of operations rule:

8388. Which alternative answer is equal to 16,300? A—1.63 x 10 to the fourth power. B—1.63 x 10 to the negative third power. C—163 x 10 to the negative second power.

"A—1.63 x 10 to the fourth power." 1.63 × 10^4 = 16,300 1.63 × 10^-3 = 0.00163 163 × 10^-2 = 1.63

8416. Select the fractional equivalent for a 0.0625 inch thick sheet of aluminum. A—1/16. B—3/64. C—1/32.

"A—1/16." In order to change this decimal fraction into a common fraction, divide the number by the decimal equivalent of 1/64 (0.015625). 0.0625 ÷ 0.015625 = 4/64 This is the same as 1/16 inch.

8436. Solve the equation. 1/2 (-30 + 34) 5 = A—10. B—95. C—160.

"A—10." First, solve the part of the problem inside the parenthesis, then multiply by 1/2 (divide by 2) and finally multiply by five. (-30 + 34) = 4 4 ÷ 2 = 2 2 × 5 = 10

8442. Solve the equation. A—11.9. B—11.7. C—11.09. (-5+23) (-2)+(3^-3)(square root 64) over -27 divide by 9

"A—11.9. " 1. Begin this problem by clearing the parentheses. 2. Perform the multiplication in the numerator. 18 × -2 = -36 0.037 × 8 = 0.296 3. Perform the addition in the numerator. -36 + 0.296 = -35.704 4. Perform the division in the denominator. -27 ÷ 9 = -3 5. Divide the numerator by the denominator. -35.704 ÷ -3 = 11.90

8425. A blueprint shows a hole of 0.17187 to be drilled. Which fraction size drill bit is most nearly equal? A—11/64. B—9/32. C—11/32.

"A—11/64." The hole specified on the blueprint has a diameter of 0.17187 inch. It could be drilled with a 11/64 drill. 11/64 is equal to 0.171875. 9/32 is equal to 0.28125. 11/32 is equal to 0.34375.

8383-1. Solve the equation ( square root 100+ square root 36 - square root 16) A—12. B—60. C—76.

"A—12." The square root of 100 is 10. The square root of 36 is 6. The square root of 16 is 4. 10 + 6 - 4 = 12

8399. A rectangular-shaped fuel tank measures 60 inches in length, 30 inches in width, and 12 inches in depth. How many cubic feet are within the tank? A—12.5. B—15.0. C—21.0.

"A—12.5." The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together. The volume is 12.5 cubic feet.

8406. A four-cylinder aircraft engine has a cylinder bore of 3.78 inches and is 8.5 inches deep. With the piston on bottom center, the top of the piston measures 4.0 inches from the bottom of the cylinder. What is the approximate piston displacement of this engine? A—200 cubic inches. B—360 cubic inches. C—235 cubic inches.

"A—200 cubic inches." The piston displacement of one cylinder of a reciprocating engine is found by multiplying the area of the piston head by the length of the stroke. The area of the piston is found by squaring the bore (3.78 inches in this problem) and multiplying this by the constant 0.7854 (one-fourth of π). When the area of 11.22 square inches is multiplied by the stroke of 4.5 inches (the depth of the cylinder minus the distance from the top of the piston at BDC to the bottom of the cylinder), we find that the displacement of one cylinder is 50.49 cubic inches. This is a four-cylinder engine, so the total displacement is four times that of a single cylinder. The total displacement is 201.96 cubic inches.

8392. The result of 7 raised to the third power plus the square root of 39 is equal to A—349.24. B—.34924. C—343.24

"A—349.24" 7 raised to the 3rd power is 343. The square root of 39 is 6.245. The sum of these two numbers is 349.245.

8380. Find the square root of 1,746 A—41.7852. B—41.7752. C—40.7742.

"A—41.7852." The square root of a number is the number that, when multiplied by itself, gives the number. By using an electronic calculator, we find that the square root of 1,746 is 41.785165.

8430. What is the ratio of 10 feet to 30 inches? A—4:1. B—1:3. C—3:1.

"A—4:1." Ten feet is equal to 120 inches. The ratio of 120 ÷ 30 is 4:1.

8395. Compute the area of the trapezoid. A—52.5 square feet. B—60 square feet. C—76.5 square feet. Hight= 5' base 1= 12' base 2= 9'

"A—52.5 square feet." The area of a trapezoid is found by multiplying its altitude (5 feet in this problem) by the average length of the two bases (the average of 9 feet and 12 feet is 10.5 feet). The area of this trapezoid is 5 × 10.5 = 52.5 square feet.

8435. What is the ratio of a gasoline fuel load of 200 gallons to one of 1,680 pounds? A—5:7. B—2:3. C—5:42.

"A—5:7." Gasoline has a nominal weight of 6 pounds per gallon. So, 200 gallons of gasoline will weigh 1,200 pounds. The ratio of a load of 1,200-pound load to one of 1,680 pounds is the ratio of: 1,200 ÷ 1,680 = 0.7142. The ratio 5:7 is 0.7142. The ratio of 2:3 is 0.6667. The ratio of 5:42 is 0.1190.

8429. Maximum life for a certain part is 1100 hours. Recently, 15 of these parts were removed from different aircraft with an average life of 835.3 hours. What percent of the maximum part life has been achieved? A—75.9 percent. B—76.9 percent. C—75.0 percent.

"A—75.9 percent." In this problem, 1100 hours represents 100 percent of the life of the part. The percentage represented by 835.3 hours can be found by dividing 835.3 by 1100, and multiplying this answer by 100. 835.3 ÷ 1100 = 0.759 0.759 × 100 = 75.9 percent

8414. An engine develops 108 horsepower at 87 percent power. What horsepower would be developed at 65 percent power? A—81. B—70. C—61.

"A—81." If an engine develops 108 horsepower at 87 percent power, its 100 percent power is 108 ÷ 0.87 = 124.13 horsepower. Its horsepower at 65 percent power is found by multiplying 124.13 by 0.65, or 80.68 horsepower.

8379-1. What is defined as a group of bits representing a complete piece of information? A—Byte. B—Bit. C—Word.

"A—Byte." A byte is composed of a group of 8 bits and represents a complete piece of information in a binary system.

8432. Solve the equation. [(4 x -3)+(-9 x 2)] ÷ 2 = A—-30. B—-15. C—-5.

"B—-15." In a problem of this type, work from the inside outward: 1. First solve the parts of the problem inside the parentheses. 4 × -3 = -12 -9 × 2 = -18 2. Now combine the two values just found. -12 + -18 = -30 3. Divide this answer by 2. -30 ÷ 2 = -15

8438. Solve the equation. A—+31.25. B—-5.20. C—-31.25. 125/-4 over -36/-6

"B—-5.20." This problem can be rewritten as 125 ÷ -4, divided by -36 ÷ -6. 125 ÷ -4 = -31.25 -36 ÷ -6 = 6 -31.25 ÷ 6 = -5.208

8428. The radius of a piece of round stock is 7/32. Select the decimal which is most nearly equal to the diameter. A—0.2187. B—0.4375. C—0.3531.

"B—0.4375." The diameter of the stock is two times the radius. We need to find the decimal equivalent of 2 × 7/32 or 7/16 inch. By dividing the numerator by the denominator, we find that we will need a piece of round stock with a diameter of 0.4375 inch.

8426. Which decimal is most nearly equal to a bend radius of 31/64? A—0.2065. B—0.4844. C—0.3164.

"B—0.4844." To convert the common fraction 31/64 into a decimal fraction, divide the numerator, 31, by the denominator, 64. 31 ÷ 64 = 0.484375

Select the fraction which is equal to 0.0250. A—1/4. B—1/40. C—1/400.

"B—1/40." 1/4 is equal to 0.25. 1/40 is equal to 0.025. 1/400 is equal to 0.0025.

8379-2. Convert the binary number 00001111 to a whole number. A—31. B—15. C—8.

"B—15." The binary number 00001111 is converted bit by bit into whole number: 1000 = 8; 0100 = 4; 0010 = 2; and 0001 = 1; thus the entire binary number equals 8 + 4 + 2 + 1 = 15 as a whole number

8393-4. Which results in the largest number? A—1. B—2. C—3. 1) (4.631)^5 2) 4631*10^5 3) 4.631*10^-5

"B—2." 1. 4.6315 = 2129.97205201 2. 4.631 × 105 = 4.631 × 1000 = 463,100 3. 4.631 × 10-5 = 4.631 × 0.00001 = .00004631

8441. Solve the equation. (-3 + 2)(-12 - 4) + (-4 + 6) x 3 A—20. B—22. C—28.

"B—22." 1. Begin this problem by clearing the parentheses. (-3 + 2) = -1 (-12 - 4) = -16 (-4 + 6) = 2 2. Then perform the multiplication. -1 × -16 = 16 2 × 3 = 6 3. And finally the addition. 16 + 6 = 22

8408. A six-cylinder engine with a bore of 3.5 inches, a cylinder height of 7 inches and a stroke of 4.5 inches will have a total piston displacement of A—256.88 cubic inches. B—259.77 cubic inches. C—43.3 cubic inches.

"B—259.77 cubic inches." Piston displacement formula pi*(bore divided by 2)^2 * stroke* (# cylinders) pi=3.1415

8423. If an engine is turning 1,965 rpm at 65 percent power, what is its maximum rpm? A—2,653. B—3,023. C—3,242.

"B—3,023." 1,965 rpm is 65% of 3,023 rpm. 1,965 ÷ 0.65 = 3,023

8394-1. What is the surface area of a cube where a side (edge) measures 7.25 inches? A—381.078 cu. in. B—315.375 sq. in. C—52.5625 sq. in.

"B—315.375 sq. in. " Each surface of the cube is 7.252 = 52.5625 square inches. A cube has six surfaces so the total surface area is: 52.5625 x 6 = 315.375 square inches

8442-1. Solve the equation. A—35,998. B—36,002. C—62,208. -4+6+10^3(square root 1296)=

"B—36,002." The problem in the figure is: -4 + 6 + 103 (√1296), which simplifies to: 2 + 1,000(36), which equals 36,002.

8421. A pinion gear with 14 teeth is driving a spur gear with 42 teeth at 140 RPM. Determine the speed of the pinion gear A—588 RPM. B—420 RPM. C—126 RPM.

"B—420 RPM. " The speed ratio is the reciprocal of the gear ratio. The spur gear with 42 teeth is driven by a pinion gear of 14 teeth. This is a gear ratio of 3:1. The spur gear will turn at 1/3 the speed of the pinion gear. If the spur gear turns at a speed of 140 RPM, the pinion gear will have to turn at a speed of 420 RPM.

8404. How many gallons of fuel will be contained in a rectangular-shaped tank which measures 2 feet in width, 3 feet in length, and 1 foot 8 inches in depth? (7.5 gal = 1 cu ft) A—66.6. B—75. C—45.

"B—75." The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together. V = L × W × D = 3 × 2 × 20/12 = 10 cubic feet

8400. Select the container size that will be equal in volume to 60 gallons of fuel. (7.5 gal = 1 cu ft) A—7.5 cubic feet. B—8.0 cubic feet. C—8.5 cubic feet.

"B—8.0 cubic feet." Since a one-cubic-foot container will hold 7.5 gallons, an 8-cubic-foot container will hold 60 gallons. 60/7.5=8 cubic feet

8405. A rectangular shaped fuel tank measures 27-1/2 inches in length, 3/4 foot in width, and 8-1/4 inches in depth. How many gallons will the tank contain? (231 cu in = 1 gal) A—7.366. B—8.83. C—170.156.

"B—8.83." The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together. All dimensions must be in the same units. 3/4 foot = 9 inches V = L × W × D = 27.5 × 9 × 8.25 = 2,041.875 cubic inches Since there are 231 cubic inches in each gallon, we must divide the total volume of 2,041.875 by 231 to find the capacity of the tank in gallons. Capacity = 2041.875/231 = 8.83 gallons This tank will hold 8.83 gallons of fuel.

8394. The total piston displacement of a specific engine is A—dependent on the compression ratio. B—the volume displaced by all the pistons during one revolution of the crankshaft. C—the total volume of all the cylinders

"B—the volume displaced by all the pistons during one revolution of the crankshaft" The piston displacement of an engine is the total volume swept by the pistons in one revolution of the crankshaft. The piston displacement is found by multiplying the area of the piston head by the length of the stroke (this gives the displacement of one cylinder). Multiply the displacement of one cylinder by the number of cylinders in the engine

8422. The parts department's profit is 12 percent on a new part. How much does the part cost if the selling price is $145.60? A—$128.13. B—$125.60. C—$130.00.

"C—$130.00." In this problem, the cost of the magneto is equal to 100 percent. Since a 12 percent profit is specified, the selling price must be 112 percent. If the selling price (112%) is equal to $145.60, the cost (100%) can be found by dividing the selling price by 112% (by 1.12). $145.60 ÷ 1.12 = $130.00

8440. Solve the equation. -6[-9(-8 + 4) - 2(7 + 3)] = A—-332. B—216. C—-96.

"C—-96." 1. Begin the problem by working the inside parentheses in the first term. (-8 + 4) = -4 2. Combine the factors in the first term. -9 × -4 = 36 3. Clear the parenthesis in the second term. (7 + 3) = 10 4. Multiply this value by 2. 10 × 2 = 20 5. Combine the two terms in the brackets. 36 - 20 = 16 6. Multiply this by -6. -6 × 16 = -96

8387. The number 3.47 x 10 to the negative fourth power is equal to A—.00347 B—34,700 C—.000347

"C—.000347" The value of 3.47 × 10-4 is found by multiplying 3.47 by 1 divided by 10,000 (1 × 10 4 ). 3.47 × 10^-4 = 0.000347

8391. Solve the equation. A—.0297. B—.1680. C—.0419. square root 31 + square root 43 over (17)^2

"C—.0419." The square root of 31 is 5.5677. The square root of 43 is 6.5574. The square of 17 is 289. 5.5677 + 6.5574 over 289 = 0.0419

8393. Find the square root of 1,824 A—42.708 x 10 to the negative second power. B—.42708. C—.42708 x 10 to the second power

"C—.42708 x 10 to the second power." The square root of 1,824 is 42.708. 42.708 × 10^-2 = 0.42708 .42708 × 10^2 = 42.708

8389. Find the square root of 124.9924. A—111.8 x 10 to the third power. B—.1118 x 10 to the negative second power. C—1,118 x 10 to the negative second power.

"C—1,118 x 10 to the negative second power." The square root of 124.9924 is 11.18. 111.8 × 10^3 = 111,800 .1118 × 10^-2 = 0.001118 1,118 × 10^-2 = 11.18

8418. Select the decimal which is most nearly equal to 77/64. A—0.08311. B—0.8311. C—1.2031.

"C—1.2031." To convert a common fraction into a decimal fraction, divide the numerator by the denominator 77 ÷ 64 = 1.203125

8401. Compute the area of the trapezoid. A—24 square feet. B—48 square feet. C—10 square feet. base 1= 6 base 2=4 height =2

"C—10 square feet." The area of a trapezoid is found by multiplying its altitude (2 feet in this problem) by the average length of the two bases (the average of 4 feet and 6 feet is 5 feet). The area of this trapezoid is 10 square feet.

8379. What power of 10 is equal to 1,000,000,000? A—10 to the sixth power. B—10 to the tenth power. C—10 to the ninth power.

"C—10 to the ninth power." An easy way to tell the power of 10 to which a number has been raised is to count the number of places the decimal would have to be moved to leave a number between 1 and 10. In this problem, the decimal would have to be moved nine places to the left. 1,000,000,000 is 1 × 109

8437. Solve the equation. A—174.85. B—68.037. C—14.002. (-35+25)(-7)+(pi)(16^-2) over square root 25

"C—14.002." 1. First, solve the parts of the problem inside parentheses: (-35 + 25) = (-10) 2. Combine the factors (the parts) of the first term (the part of the problem to the left of the plus sign). (-10) × (-7) = 70 3. Clear the parenthesis on the right of the plus sign by raising 16 to its -2 power. 16 -2 = 1/16 2 = 1/256 = 0.003906 4. Multiply the two factors of the second term. (3.1416) × (0.003906) = 0.01227 5. Add the two terms above the line. 70 + 0.0122 = 70.0122 6. Divide this by the square root of 25, which is 5. 70.0122 ÷ 5 = 14.002

8413. What is the speed of a spur gear with 42 teeth driven by a pinion gear with 14 teeth turning 420 RPM? A—588 RPM. B—160 RPM. C—140 RPM.

"C—140 RPM." The speed ratio is the reciprocal of gear ratio. The spur gear with 42 teeth is driven by a pinion gear with 14 teeth. This is a gear ratio of 3:1. The spur gear will turn at 1/3 the speed of the pinion gear. If the pinion gear turns at a speed of 420 RPM, the spur gear will turn at a speed of 420 ÷ 3 = 140 RPM

8383. Which of the following is equal to the square root of (-1776) ÷ (-2) - 632? A—128. B—256. C—16.

"C—16." Solve this problem in three steps: 1. Divide -1776 by -2: -1776 ÷ -2 = 888 2. Subtract 632 from 888: 888 - 632 = 256 3. Find the square root of 256:

8420. What is the speed ratio of an input gear with 36 teeth meshed to a gear with 20 teeth? A—9:5. B—1:0.56. C—1:1.8.

"C—1:1.8." The speed ratio is the reciprocal of the gear ratio. The large gear has 36 teeth and the small gear has 20 teeth. This is a gear ratio of 1.8:1, or a speed ratio of 1:1.8.

8396. What size sheet of metal is required to fabricate a cylinder 20 inches long and 8 inches in diameter? (Note: C = π x D) A—20 inches x 25-5/32 inches. B—20 inches x 24-9/64 inches. C—20 inches x 25-9/64 inches

"C—20 inches x 25-9/64 inches." The sheet metal needed to fabricate a cylinder 20 inches long and 8 inches in diameter is 20 inches long and 25-9/64 inches wide. 8 × π (3.1416) = 25.1328 25.1328 is slightly less than 9/64.

8419. An airplane flying a distance of 750 miles used 60 gallons of gasoline. How many gallons will it need to travel 2,500 miles? A—31,250. B—9,375. C—200.

"C—200" If the airplane uses 60 gallons of gasoline while flying 750 miles, it is getting 750 ÷ 60 or 12.5 miles per gallon of fuel burned. At this rate of fuel consumption, it will require 2,500 ÷ 12.5 = 200 gallons of fuel to fly 2,500 miles.

8390. What is the square root of 16 raised to the fourth power? A—1,024. B—4,096. C—256.

"C—256." The square root of 16 is 4. 4 raised to the 4th power is 256.

8410. 1.21875 is equal to A—83/64. B—19/16. C—39/32.

"C—39/32." Divide the decimal fractional part of this mixed number by the decimal equivalent of 1/64. .21875 ÷ 0.015625 = 14 The common fraction equivalent to 1.21875 is 1-14/64. This is the same as 78/64 or 39/32.

8407. A rectangular-shaped fuel tank measures 37-1/2 inches in length, 14 inches in width, and 8-1/4 inches in depth. How many cubic inches are within the tank? A—59.75. B—433.125. C—4,331.25.

"C—4,331.25." The volume of a rectangular solid figure (such as this fuel tank) is found by multiplying its length, width, and depth together. V = L × W × D = 37.5 × 14 × 8.25 = 4,331.25 cubic inches

square root (-4)^0 +6+( 4throot 1296)(square root 3)^2 A—115. B—4.472. C—5.

"C—5." To solve this equation, follow these steps: clear all of the parentheses, perform the multiplication, then the addition. Finally, take the square root of the number you have just obtained. Any number raised to the zero power is 1. (-4)^0 = 1 The fourth root of 1,296 is the same as 1,296 raised to the 1/4 power. 1,296^0.25 = 6 The square of the square root of 3 = 3

8382. Find the square root of 3,722.1835. A—61.00971. B—61.00. C—61.0097.

"C—61.0097." The square root of a number is the number that, when multiplied by itself, gives the number. By using an electronic calculator, we find that the square root of 3,722.1835 is 61.00970005.

8411. If the volume of a cylinder with the piston at bottom center is 84 cubic inches and the piston displacement is 70 cubic inches, then the compression ratio is A—7:1 B—1.2:1 C—6:1

"C—6:1" The volume of a cylinder with the piston at the top of its stroke is found by subtracting the piston displacement of the cylinder from the volume of the cylinder with the piston at the bottom of its stroke. Volume at top = Volume at bottom - displacement = 84 - 70 = 14 cubic inches The compression ratio of the cylinder is the ratio of the volume of the cylinder with the piston at the bottom of its stroke to the volume of the cylinder with the piston at the top of its stroke. C.R. = Volume at bottom ÷ volume at top = 84 ÷ 14 = 6

8434. Solve the equation. (32 x 3/8) ÷ 1/6 = A—12. B—2. C—72.

"C—72." 1. First, work the part of the problem inside the parenthesis: (32 × 3/8) = 12 2. Now divide 12 by 1/6. To divide by a fraction, invert the divisor (1/6) and multiply. 12 ÷ 1/6 = 12 × 6 = 72

8424. An engine of 98 horsepower maximum is running at 75 percent power. What is the horsepower being developed? A—87.00. B—33.30. C—73.50.

"C—73.50." Seventy-five percent of 98 horsepower is equal to 98 × 0.75 = 73.50 horsepower.

8412. Express 7/8 as a percent. A—8.75 percent. B—.875 percent. C—87.5 percent.

"C—87.5 percent." A percentage is a decimal fraction with 100 as its denominator. To convert 7/8 into a percentage, divide seven by eight and multiply this by 100. 7 ÷ 8 = 0.875 0.875 × 100 = 87.5 percent

8416-1. Examples of units used in the conventional (U.S. or English) measurement include A—inch, meter, and rod. B—inch, kilometer, and fraction. C—inch, feet, and yard.

"C—inch, feet, and yard." Some of the conventional U.S. or English units of measure are: inches, feet, yards, miles, ounces, pints, gallons, and pounds.