SET 6 (p. 90)

Question 1

1. A box open at the top is to be made from tin 48 square ft. Find the maximum volume of the box that can be made.

Answer 1

32 ft^2

Question 2

6. Which of the following is not a true statement about the normal curve?
   A. The area under a normal curve is always equal to 1, no matter the mean and standard deviation.
   B. The smaller the standard deviation of a normal curve, the higher and narrower the graph is.
   C. Normal curves with different means are centered around different numbers.
   D. The area under the standard normal curve between 0 and 2 is twice the area between 0 and 1.

Answer 2

D

Question 3

11: There are three consecutive odd integers. Three times the largest is seven times the smallest. What is the largest integer?

Answer 3

7

Question 4

12. Three numbers are in direct proportion in the following manner: A is to B as 24.5 is to 20.2 while B is to C as 36 is to 15. If C is 52.8 , what is the value of A?

Answer 4

153.7

Question 5

13. An elevated concrete tank is filled through its inlet pipe and then is emptied through the outlet pipe, in a total time of 9 hours. If the water enters through the inlet pipe and simultaneously allowed to leave through the outlet, the tank is filled in 20 hours. How long will it take to fill the tank if the outlet is closed?

Answer 5

4 hrs

Question 6

17. Determine the velocity of escape of Mars if the acceleration of gravity at the surface of Mars is 0.38 g where g = 9.18 m/sec² and the radius of Mars is 2,100 miles.

Answer 6

3.10 m/sec

Question 7

21. Find the area in sq. m. of a spherical triangle whose angles are 115°, 98°, and 82° if the radius of the sphere is 40 m.

Answer 7

2,478.9 m²

Question 8

23. An arithmetic progression has its 4th term 25 and 11th term 102.
    Find the first term.

Answer 8

-8 (p. 97)

Question 9

30: Given in the accompanying tabulation are the observed data for a closed traverse obtained from a transit-tape survey.
(p. 12)
Determine the Linear Error of Closure.

Answer 9

1.74 m

Question 10

31. Given in the accompanying tabulation are the observed data for a closed traverse obtained from a transit-tape survey.
    (p. 12)
    Determine the bearing of the side of error.

Answer 10

S 13°32’ E

Question 11

32: Given in the accompanying tabulation are the observed data for a closed traverse obtained from a transit-tape survey.
(p. 12)
Determine the precision of the measurement.

Answer 11

1/600

Question 12

33: Find the angle between the planes 3x - y + z -5 = 0 and x + 2y + 2z + 3 = 0.

Answer 12

72.45°

Question 13

34. What color is used of markings of islands in line of traffic?

Answer 13

Yellow

Question 14

35. Find the area enclosed by the curve r = 2cos3θ.

Answer 14

π/3 sq. units

Question 15

37. Find the equation of a sphere with center at ( 3, 2, -4 ) and tangent to the plane x + 2y - 3z + 9 = 0.

Answer 15

x^2 + y^2 + z^2 - 6x - 4y + 8z = 27 (p. 99)

Question 16

40: The ground makes a uniform slope of 5% from station 8 + 340 to station 8 + 420. At station 8 + 340, the center height of roadway is 1.6 m fill, and at station 8 + 420, the center height is 3.2 m cut. Find the grade of the finished road.

Answer 16

-1%

Question 17

42. The length of the common tangent of a compound curve is 226.5 m. Given that D1 = 3°, I1 = 32°, I2 = 54°, and the stationing of the P.C. is 12 + 442.68.
    Find the degree of the second curve.

Answer 17

5° (p.100)

Question 18

43. The length of the common tangent of a compound curve is 226.5 m. Given that D1 = 3°, I1 = 32°, I2 = 54°, and the stationing of the P.C. is 12 + 442.68.
    Find the stationing of the P.T.

Answer 18

12 + 872.37

Question 19

45. Find the amplitude of y = 4sin2x.

Answer 19

4

Question 20

51. A 30-m tape is supported only at its ends and under a steady pull of 10 kg. If the tape weighs 1.20 kg, determine the sag correction.

Answer 20

0.018 m

Question 21

52: Find the volume of a regular octahedron whose edge measures 8 cm each.

Answer 21

241.36 cm^3 (p. 102)

Question 22

53. Find the value of B in the given fraction and its partial fractions.
    (p. 12)

Answer 22

-1 (p. 102)

Question 23

55: An airplane has an airspeed (in still air) of 240 mph with the bearing S 30° W. If a wind is blowing due west at 40 mph, find the final bearing of the plane.

Answer 23

S 38° W

Question 24

60. A point moves so that its distance from the point (3,5) is always equal to its distance from the line y=1. Find the eccentricity of the curve.

Answer 24

1 (p. 104)

Question 25

61. What is the effective rate of interest corresponding to a nominal rate of 10% compounded continuously?

Answer 25

10.52%

Question 26

62: Find the expected number of boys on a committee of 4 selected at random from 5 boys and 3 girls.

Answer 26

2.5 (p. 104)

Question 27

63. A sample is taken from the scores of a 10-item test: 8, 9, 8, 7, 10, and 7. Find the standard deviation.

Answer 27

1.367

Question 28

64. What is the maximum area of a triangle inscribed in a semicircle with radius 12 cm if the hypotenuse of the triangle is on the diameter of the circle?

Answer 28

108.54 cm²

Question 29

65. In the year 2000, approximately 40 million tourists visited South America and the Caribbean. The number of tourists to that area had been increasing at an average rate of 0.80 million tourists per year. In the same year, 17 million tourists visited the Middle East. The number of tourists to the Middle East had been increasing at an average rate of 1.8 million tourists per year. If the trend continues, when would you expect the number of tourists of the two places be equal?

Answer 29

2023 (p. 104)

Question 30

70: A sector of a circle AOB has a radius “r” and a central angle of 45° at O, the center of the circle, with AB as the arc. A line is drawn from point A to point X, where X is the midpoint of OB. If the area of section ABX is 4.5 cm², compute the radius of the circle, “r”.

Answer 30

5 cm (p. 105)