Mathematics

Question 1

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.

Answer 1

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 × 10 9

Question 2

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

Answer 2

A— Byte.

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

Question 3

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

Answer 3

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.

Question 4

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

Answer 4

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.

Question 5

8381. (Refer to Figure 52.) Solve the equation.
      A — 115
      B— 4.472
      C— 5

Answer 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.

Question 6

8382. Find the square root of 3722.1835.
      A— 61.00971
      B — 61.00
      C— 61.0097

Answer 6

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.

Question 7

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

Answer 7

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:

Question 8

8383-1.
(Refer to Figure 69.) Solve the equation.
A— 12
B— 60
C— 76

Answer 8

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

Question 9

8384. 64 cubed equals
      A— 4
      B— 192
      C— 262,144

Answer 9

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

Question 10

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

Answer 10

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).

Question 11

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

Answer 11

A— 32

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

Question 12

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

Answer 12

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

Question 13

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

Answer 13

A— 1.63 × 10 to the fourth power.

1.63 × 10 4 = 16,300
1.63 × 10-3 = 0.00163
163 × 10-2 = 1.63

Question 14

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

Answer 14

C— 1,118 × 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

Question 15

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

Answer 15

C— 256

The square root of 16 is 4.
4 raised to the fourth power is 256.

Question 16

8391. (Refer to Figure 53.) Solve the equation.
      A— .0297
      B— .1680
      C — .0419

Answer 16

C — .0419

Question 17

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

Answer 17

A— 349.24

7 raised to the third power is 343.
The square root of 39 is 6.245.
The sum of these two numbers is 349.245.

Question 18

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

Answer 18

C— .42708 × 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

Question 19

8393-1.
(Refer to Figure 65.) Which of the figures is using scientific notation?
A— 1.
B— 2.
C— both 1 and 2.

Answer 19

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 tenth power does not qualify as scientific notation.

Question 20

8393-2.
(Refer to Figure 70.) Which alternative answer is equal to 5.59?
A— 1.
B— 2.
C— 3.

Answer 20

A— 1.

Question 21

8393-3.
(Refer to Figure 67). Solve the equation.
A— 5.58.
B— 12.16.
C— 0.042.

Answer 21

C— 0.042.

Question 22

8393-4.
(Refer to Figure 68.) Which results in the largest number?
A— 1.
B— 2.
C— 3.

Answer 22

B— 2.

1. 4.631 5 = 2129.97205201
2. 4.631 × 10 5 = 4.631 × 1000 = 463,100
3. 4.631 × 10-5 = 4.631 × 0.00001 = .00004631

Question 23

8394. The total piston displacement in a reciprocating engine is
      A— the volume displaced by only one piston during one-half revolution of the crankshaft.
      B— the volume displaced by all the pistons during one revolution of the crankshaft.
      C— the volume displaced by all the pistons during two revolutions of the crankshaft.

Answer 23

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.

Question 24

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

Answer 24

B— 315.375 square inches

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 × 6 = 315.375 square inches.

Question 25

8395. (Refer to Figure 54.) Compute the area of the trapezoid. A— 52.5 square feet. B— 60 square feet. C— 76.5 square feet.

Answer 25

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.

Question 26

8395-1. (Refer to Figure 71.) 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.

Answer 26

C— 381.7 cubic inches.

Question 27

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

Answer 27

C— 20 inches × 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.

Question 28

8397. (Refer to Figure 55.) Find the area of the triangle shown. A— 12 square inches. B— 6 square inches. C— 15 square inches.

Answer 28

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.

Question 29

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.

Answer 29

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.

Question 30

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

Answer 30

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.

Question 31

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.

Answer 31

B— 8.0 cubic feet.

Question 32

8401. (Refer to Figure 56.) Compute the area of the trapezoid. A— 24 square feet. B— 48 square feet. C— 10 square feet.

Answer 32

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.

Question 33

8402. (Refer to Figure 57.) Determine the area of the triangle formed by points A, B, and C. A to B = 7.5 inches A to D = 16.8 inches A— 42 square inches. B— 63 square inches. C— 126 square inches.

Answer 33

B— 63 square inches.

Question 34

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.

Answer 34

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 to be 7.0686 cubic inches.

Question 35

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

Answer 35

B— 75

Question 36

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. 3 6 6 B— 8.83 C — 170.156

Answer 36

B— 8.83

Question 37

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.

Answer 37

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. Stroke = 8.5 – 4 = 4.5 inches PD = Area × Stroke × Number of cylinders = 11.22 × 4.5 × 4 = 201.96 cubic inches

Question 38

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

Answer 38

C— 4,331.25

Question 39

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.

Answer 39

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 (3.5 inches in this problem) and multiplying this by the constant 0.7854 (one fourth of π). When the area of 9.621 square inches is multiplied by the stroke of 4.5 inches, we find that the displacement of one cylinder is 43.295 cubic inches. This is a six-cylinder engine, so the total displacement is six times that of a single cylinder. The total displacement is 259.77 cubic inches.

Question 40

8409. Select the fraction which is equal to 0.0250. A— 1/4 B— 1/40 C— 1/400 1/40 is equal to 0.025. 1/4 is equal to 0.25. 1/400 is equal to 0.0025.

Answer 40

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

Question 41

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

Answer 41

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.

Question 42

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

Answer 42

C— 6:1

Question 43

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

Answer 43

C— 87.5 percent.

Question 44

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.

Answer 44

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.

Question 45

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

Answer 45

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.

Question 46

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.

Answer 46

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.

Question 47

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

Answer 47

A— 1/16

Question 48

8416-1. Examples of units used in the conventional (U.S. or English) measurement include A— inch, meter, and gram. B— inch, kilo, and liter. C— inch, ounce, and pound.

Answer 48

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

Question 49

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

Answer 49

C— 62.5 percent.

Question 49

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

Answer 49

C— 62.5 percent.

Question 50

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

Answer 50

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

Question 51

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

Answer 51

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.

Question 52

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

Answer 52

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.

Question 53

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.

Answer 53

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.

Question 54

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

Answer 54

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 1.12. $145.60 ÷ 1.12 = $130.00

Question 55

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

Answer 55

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

Question 56

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

Answer 56

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

Question 57

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

Answer 57

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.

Question 58

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

Answer 58

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

Question 59

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

Answer 59

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.

Question 60

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

Answer 60

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.

Question 61

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.

Answer 61

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

Question 62

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

Answer 62

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

Question 63

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.

Answer 63

A— 14.6 amperes.

Question 64

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

Answer 64

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

Question 65

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

Answer 65

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

Question 66

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

Answer 66

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

Question 67

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

Answer 67

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.

Question 68

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

Answer 68

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

Question 69

8437. (Refer to Figure 58.) Solve the equation. A — 174.85 B— 68.037 C — 14.002

Answer 69

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

Question 70

8438. (Refer to Figure 59.) Solve the equation. A— +31.25 B— -5.20 C— -31.25

Answer 70

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

Question 71

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

Answer 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

Question 72

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

Answer 72

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

Question 73

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

Answer 73

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

Question 74

8442. (Refer to Figure 60.) Solve the equation. A — 11. 9 B — 11.7 C — 11.09

Answer 74

A — 11. 9

Question 75

8442-1. (Refer to the Figure 66.) Solve the equation. A— 35,998 B— 36,002 C— 62,208

Answer 75

B— 36,002 -4 + 6 + 10 3 ( √ 1 296 ) simplifies to: 2 + 1,000(36), which equals 36,002.

Question 76

8595. (Refer to Figure 71.) Solve the equation. A— 47.71 cubic inches B— 381.7 square inches C— 381.7 cubic inches

Answer 76

C— 381.7 cubic inches The radius, 4.5 inches, is half of the diameter so the diameter is 9 inches. Answer A is incorrect and would result from using the 4.5 in. radius instead of the 9 in. diameter. Answer B is incorrect because the volume of any 3-dimensional shape such as a sphere is measured in cubic inches, not square inches.

Question 77

8593. Which of the following is equal to the square root of 3844? A— 31(2) + 7 + (-3.5 × 2) = B— 480(4) + (-4) – (-3 × 2) = C— 960 × 4 – (-2) + 2 =

Answer 77

A— 31(2) + 7 + (-3.5 × 2) = Use your calculator to find that the square root of 3844 is 62. The following is also equal to 62. 31(2) + 7 + (-3.5 × 2) = 62 + 7 – 7 = 62 Answer B is incorrect because 480(4) + (-4) – (-3 × 2) = 1920 – 4 + 6 = 1922 Answer C is incorrect because 960 × 4 – (-2) + 2 = 3840 + 2 + 2 = 3844

Question 78

10004. Round 57.2338 to the nearest hundredth. A— 57.23 B— 57.2 C— 57.24

Answer 78

A— 57.23 57.2338 rounded to the nearest hundredth is 57.23. When the digit immediately to the right of the last retained digit is 5 or greater, round up by 1. When the digit immediately to the right of the last retained digit is less than 5, leave the last retained digit unchanged. Answer B is incorrect because 57.2 is rounded to the nearest tenth not the nearest hundredth. Answer C is incorrect because the 3” in the thousandths place of 57.2338 is less than 5, but the answer choice rounded up instead of leaving the last remaining digit unchanged.