Every year a company pays a bonus of 30,000 to his most industrious assistant, and 75,000 each to the rest of his staff. After how many years...

A father and his son can dig a hole if the father works 6 hours and his son works 12 hours, or they can do if the father works 12 hours and the son works 8 hours. how will it take for the father to dig the hole alone?

A trainee in a computer company takes 0.8 times as long as to assemble each computer as he took to assemble the preceding computer. if it took him 30 mns to to assemble the first computer, find how long it takes him to assemble the five computer units?

If a radioactive element has a half-life of 3 hours, then x grams of the element dwindles to x/2 grams after 3 hours. if a nuclear reactor has 600 grams of that radioactive element, find the amount of radioactive material after 12 hours.

A ball dropped from a height of 12 feet. It rebiynds one-half the distance on each bounce. what is the total distance it travels?

A bolt making machine has a 0.05 chance of producing a defective product each time it produces a bolt. if three bolts are selected randomly, what is the probability of finding no defective profuct in the three samples?

In 1990, a subtle flaw of Pentium chip would affect 1 in 9 billion division problems. Suppose a computer performs 20 million divisions in the cpurse of a particular program. What is the probability of no error and of at least one error.

In a common carnival game, a player tosses a penny from a distance of about 5 feet onto surface of a table ruled by 1-inch squares. if the penny (3/4 inch in diameter) fall entirely inside a square, the player receives 5 centavos but does not get the penny back; otherwise he losses his oenny. if the penny hands on the table, what is the chance to win if the lines are 1/16 in thick?

Find two angles such that the angles are supplementary and the larger is twice the smaller

Given the point P on side BC of triangle ABC. Given that AB=AC=BP and AP=CP, what is the value of angle ABC?

Four towns are located at the corner of a square highway network... At the end of one hour the first and third cars are 204 km, and the second and fourth 212 (beeline) km apart. what is the rate of the first car?

In a certain network, there are 4 nodes and 4 regions. How many arcs are there in the network?

Determine the time of oscillation (in minutes) of a pendulum having a length of 15 m

A 100-kg block initially at rest is acted upon by a constant force of 80 N for 5 seconds after which an opposite force of 52 KN is applied. In what additional time will the block come to rest?

A centrifuge rotor is accelerated from rest to 23,000 rpm in 5 min. what is the average angular acceleration?

Between two towns the road is level for half the distance, the rest being part uphill and part downhill. A bicyclist takes 1 hr 28 min one way and 1 hr 22 min to return. He travels 10, 15, and 20 km per hr, uphill, on level road, and downhill respectively. Determine the length of the level portion of the road.

Determine the length of the chord common to the circles: x2 + y2 = 64 and x2 + y2 - 16x = 0

A small circle is inscribed in a circular sector of radius 12cm and a central angle of 60°. Compute the area of the small circle if it is tangent internally to the radius and the arc of the sector.

PA and PB are tangents at A and B of a circle having a diameter of AC. If AC and PB is prolonged, it will intersect outside the circle at Q. If the value of the angle PQA is 20°, find the value of angle BAQ.

A closed triangular traverse has the ff. data: An area of 320,000 m? is cut off starting from corner A to point F on line BC. What is the length of line AF?

The ground makes a uniform slope of +5.2% from A (Sta.8+890) to B. At point A, the center height of the roadway is 4.13m fill. At the other point, the center height is 7.57m cut. If the finish road has a uniform grade of -2.6%, what is the stationing of B?

The areas of two similar polygons are 80 and 5. If the side of the smaller polygon has a length 2, find the length of the corresponding side a larger polygon.

In a city, streets run north and south, and avenues run east and west. Streets and Avenues are 850 feet apart. The city plans to construct a straight freeway from the intersection of 25th Street and 8th Avenue to the intersection of 115th Street and 64th Avenue. How long will the freeway be?

The measure of the largest angle of triangle is 800 more than the measure of the smallest angle and the measure of the remaining angle is 100 more than the measure of the smallest angle. Find the measure of each angle.

A topographic surveying map using a scale 1 cm = 40 m and with a contour interval of 1 m. The distance scaled on the map between two adjacent contours is 15 mm. Determine the slope of the ground in percent.

The maximum allowable rate of crashes at intersections is 9 per million entering vehicles. At an intersection of 2 roadways, average daily traffic (ADT) values are 10,000 and 8,265. Determine the maximum number of crashes per year before corrective action is needed.

signs that instruct road users to meet certain traffic rule requirements on road condition

Signs which warn road users of condition on or adjacent to the road maybe unexpected or hazardous

Signs which warns or advise temporary hazardous conditions that could endanger road users or the men and equipment on roadworks

Signs which provide means of displaying essential traffic information on wide multi-lane roads, where some degree of lane use control is required or where side of road clearance is insufficient to accomodate a road side sign.

Signs which inform and advise road users of directions, distances, routes and the location of services for road users and point of interest

From point O on the ground of a square courtyard of area 160,000 ft?, the angles of elevation of three flagstaffs of equal heights at three consecutive corners of the yard at A, B and Care 450, 60° and 60° respectively. Find the height of each flagstaff in meters.

A highway fill at stations 5+040 has a uniform ground slope. It has a sideslope of 2:1 and width of roadway is 12 m. Find the area of Sta. 5+040.

The famous pyramid of Egypt has an altitude of 15 m and weight of 4000 kg. It has a square base. At what distance from its base must it be cut by a plane parallel to its base so that the two solids of equal weight will be formed?

A sphere of radius 5cm and a right circular cone of base radius 5cm and altitude of 10cm stand on the same horizontal plane. How far from this plane is the plane, parallel to the former; which will cut the two solids into two equal circular sections?

A car travels from point A northward for 30 minutes, then eastward for one hour, then shifted N 30° E. If the constant speed is 60 kph, how far directly from A will it be after 2 hours?

A trapezoidal lot ABCD (BC parallel to AD is to be divided into two equal areas by a line parallel to BC and AD. If the angle BAD = 70°, angle CDA = 58°, AD = 300m and BC = 200m, how far is the end of the dividing line from vertex A?

Two tangents were drawn from T to a circle and has its point of tangency on the circle at A and B. The angle between the tangents is 54°. Point C is along the periphery of the circle and is nearer to T than A and B. If the lines AC and BC are constructed, determine the angle between the lines AC and BC at point C.

Points A, B, and C are on a circular track with AB as a diameter of the track. The angle of elevation of the top of a vertical pole standing at A as observed from B is 25°. If the horizontal angle subtended by BC at A is 30°, what is the angle of elevation of the top of the pole as observed from C?

Compute the deflection angle at the end point of the spiral if the length of spiral is 80 m and the degree of curve of the central curve is 6.5°.

11. The grading works of a proposed National Road shows the following data: FHD = 50 m LEH = 450 m Cost of Haul = P0.25 per meter station Compute the cost of borrow.

Conjugate hyperbolas are such that the transverse and conjugate axes of one are respectively the conjugate and transverse axes of the other. If the eccentricity of one is 1.25, what is the eccentricity of the other?

The slope of the curve b2x2 - a2y2 = a2b2 at the upper end of its latus rectum to the right of the origin is 4/3. What is the eccentricity of the curve?

Two circles whose radii are 12cm and 16cm respectively, intersect at two points. The angle between the lines tangent to the circles at their point of intersection is 29.5°. Find the distance between their centers.

A triangle inscribed in a circle of radius 8cm have two of its sides equal to 8cm and 14cm respectively. Compute the altitude upon the third side of the triangle.

rectangular barge is 20 m long, 12 m wide and 8 m deep. It enters the harbor of Cebu City having a low tide (DLT) equal to -0.30 m. The harbor facility is protected by riprap to prevent scouring. The weight of the barge when empty is equal to 1000 tons. Assuming sp. gr. of seawater to be 1.03 and that max. depth of water in the harbor is 6.4 m deep, determine the maximum weight of tons that the barge can carry safely based on the specification of the (PPA) Phil. Ports Authority regarding standard water depth.

A horizontal curve has a radius of 270m and a central angle of 55°. Compute the area of the fillet of the curve in square meter:

A 50 m tape weighing 1.075 kg has a standard pull of 8 kg. The tape's cross-sectional area and modulus of elasticity are 0.05 cm? and 200 GPa respectively. What pull is required in order that the effect of sag will be eliminated when the tape is supported at the end points only?

A scalene triangle ABC is a triangle having three unequal sides. The distance from the centroid of a triangle to the circumcenter is 6 units. How far is the centroid of the triangle from the orthocenter?

A plane travels in a direction of N 30° W at an air speed of 600kph. If the wind has a speed of 80kph on a direction of N 40° E, what is the speed of the plane relative to the ground?

Side AB and AD of a corner lot ABCD are on two streets intersecting at an angle of 75°. AB = 12m while AD = 16m. Side BC is perpendicular to AB and CD is perpendicular to AD. Find the area of the lot.

Highway appurtenances designed to prevent vehicular penetration from the travel way to areas behind the barrier such as to minimize damage to impacting vehicles and their occupants, and to reduce the risk of injuries to pedestrians and workers.

Warning devices used to supplement other controls and devices necessary to alert motorists of construction and maintenance activities or obstructions in the roadway.

Light retro-reflecting devices mounted at the side of the roadway, in series, to indicate the roadway alignment.

Devices which may be conical in shape or tubular shaped capable of performing channelization of traffic which may be set on the surface of the roadway or rigidly attached for continued use.

Roadwork devices consisting of precast concrete sections, sandbag and others which may be used to guide traffic at the construction site.

Device used in place of rigid cones with a minimum of 450 mm by 50 mm wide with alternate bands of contrasting color as seen by approaching traffic for delineation of traffic.

Means any traffic control device marked on the surface of the carriageway used to regulate traffic or to warn or guide road users.

Looking at the possibility of injury or harm occurring to a person if exposed to a hazard.

Recognizing of things which may cause injury or harm to a person.

Introduction of measures which will eliminate or reduce the risk of a person being exposed to a hazard.

Rule____ is the guidelines regarding PPE

It is an impervious membrane applied to concrete pavement before its initial setting that prevents rapid evaporation of water from the mix.

This should be done during the first seven days in order that the expected development of strength will be obtained and the occurrence of plastic cracks will be prevented or minimized.

A mixture of cementitious materials and water, with or without aggregate, proportioned to produce a creamy consistency.

The interior of a satellite TV antenna is a dish having the shape of a (finite) paraboloid that has diameter 12 ft and is 2 ft deep. Find the distance from the center of the dish to the focus.

A concrete pavement 8 m wide and 150 mm thick is to be provided with a center longitudinal joint using 12 mm bars The unit weight of concrete is 2400 kg/m°. Coefficient of friction of the slab on the subgrade is 2.0. Assuming an allowable stress in tension for steel at 138 MPa, determine the spacing of bars in mm.

During Typhoon Ondoy, due to strong winds, it causes a wave length of a shallow water wave of 80 m long. If the wave period (the time for two consecutive crests to pass a given point) is 72 sec, determine the depth of water at that point assuming it to be uniform.

A tsunami also called seismic sea wave of tidal wave is a catastrophic ocean wave, usually caused by a submarine earthquake occurring less than 50 km beneath the sea floor, with a magnitude greater than 6.5 on the Richter Scale. Under water or coastal landslides or volcanic eruptions also may cause a tsunami. The term tidal wave is more frequently used for such a wave, but it is a misnomer, for the wave has no connection with the tides. If the depth of water at a certain point in the ocean is 1200 m, determine the velocity of the wave propagation in kph.

Tropical typhoon "Yolanda" hits the country with an estimated wind speed of 140 kph. This causes a storm surge in Tacloban City with a period of 7.47 sec. in a point having a depth of 9 m. Compute the height of the wave if it has a steepness of 0.14. Hint: L = 1.5672

An earthquake is usually measured by the magnitude M on the Richter Scale. The intensity I of an earthquake and the magnitude M are related by the formula M= log (1/1.) where I, is the intensity of an arbitrary chosen earthquake. The earthquake that hit Kobe, Japan, measured 5.7 on the Richter Scale. The earthquake that hit Baguio, Philippines measured 7.8. How many times stronger is the earthquake that hit Baguio?

Three spheres made of steel having a radius of r, 2r, and 4r respectively are melted to form a new sphere of radius R. The ratio of the volume to the surface area of the new sphere is equal to 4.18. Compute the radius r.

One side of an equilateral triangle lies on the line 3x + 4y - 12 = 0 while the opposite vertex is on the line 3x + 4y + 20 = 0. What is the area of this triangle?

In many parts of the world, the high waters reach their greatest height and the low waters at the least height. soon after the time of full moon and new moon. These tides are called

When the lines connecting the earth with the sun and the moon form a right angle, that is the moon is in its quarters, then the actions of the moon and sun are subtractive, and the lowest tides of the month occur, this is called:

Tides which occurs only high tide a day

The avrage hieght of the sea for all stafes of the obtained from systematic observations of sea levels at equal intervals over a long period of time along a given coastline

The 1986 explosion at the Chernobyl nuclear power plant in the former Soviet Union sent about 1000 kilograms of radioactive cesium-137 into the atmosphere. The function f(x) = 1000(0.5)^ (×/30) describes the amount, f(x), in kilograms, of cesium-137 remaining in Chernobyl × years after 1986. If even 100 kilograms of cesium-137 remain in Chernobyl's atmosphere, the area is considered unsafe for human habitation. Find the remaining amount of cesium particles after 80 years.

A plane flies 465 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 20 mph, find the speed of the plane in still air.

Ifone pump can fill the tank in 16 hours, two pumps can fill the thank in 6 hours, how fast can the other pump can fill the tank?

Dr. Irving Weiman, who is always in a hurry, walks up an upgoing escalator at the rate of one step per second. Twenty steps bring him to the top. Next day he goes up at two steps per second, reaching the top in 32 steps. How many steps are there in the escalator?

A politician states, "If you elect me to office, I promise to cut your taxes for each of my first three years in office by 10% each year, for a total reduction of 30%. Evaluate the accuracy of the politician' statement.

what are the positive and negative co-terminal of 10degrees?

A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave towards the point of intersection of the two tangents. Each tangent and the arc of the circle is 1-mile long. What is the radius of the circle?

In a room, 40 feet long, 20 feet wide, and 20 feet high, a bug sits on an end wall at a point one foot from the other floor, midway between the sidewalls. He decides to go on a journey to a point on the other end wall which is one foot from the ceiling midway between the sidewalls. Having no wings, the bug must make his trip by sticking to the surfaces of the room. What is the shortest route that the bug can take?

A cross section through the center of a football is a circle × inches in circumference. The football is › - 8 inches long from tip to tip and each seam is an arc of a circle ¾ x inches in diameter. Find x.

A semi-ellipse and a parabola rests on the same base 60m wide and 20m high. Using the common base as x-axis, determine the difference of ordinates at a point 25m from the center of the base.

Two chords AB and AC are equal and OB is also equal to OC where point O is the center of the circle circumscribing triangle ABC. If the angle BOC is 228°, find the value of angle ABO.

If the length of the latus rectum of an ellipse is three-fourths of the length of the minor axis, determine its eccentricity.

The perpendicular distance between the parallel tangents of a reversed curve is 7.5 m. If the long chord is 60 m long, what is the common radius?