RI REVIEW MSTC

A measure of the difficulty in excavating and loading of soil

Loadability

Crystal Lake Village is building a sewage treatment facility that has a 35-year design life.This facility includes a pump that costs $13,000 and that will last 7 years. The pump has no salvage value,and its energy costs are included with other energy costs.If i=8%,find the EAC for the series of five pumps.

$2497

A construction equipment is badly needed for a certain project so as to shorten the time of completion of the project. The equipment cost P1.2 M and has a life of 5 years with a salvage value of P200,000 at the end of its life. This machine can be bought with money borrowed at the rate of 20% per annum. Annual operating cost is P10,000. Determine the capitalized cost of using this equipment.

1,291,899

What is the exponential form of the complex number 5 +12i?

13 e^1.176i

HeavyMetal Recovery specializes in removing transuranic elements fromhazardous waste streams. It is considering a large expansion of an existing facility in eastern Washington. The expansion requires $3M in working capital. If HeavyMetal's interest rate is 12%,find the EAC for its required working capital.

360k

A ramp meter operates during the morning peak period. Ramp meter cycles vary with time as shown in the table below. The metering scheme allows one vehicle per cycle to pass the signal. The table below gives the number of vehicles demanding service on the ramp during particular time intervals, the cumulative demand for the ramp for the morning peak, and the ramp meter cycle for each interval. What are the service rates for meter cycle 12, 10, and 6?

75, 90, 150 veh

A loan of $8000 is borrowed to be repaid with uniform periodic payments at a nominal rate of 12% over 5 years.What is the payment if made annually? What is the payment if made monthly? Why isn't the annual payment 12 times the monthly payment?

Annual = $2219 Monthly =$177.6 Twelve times the monthly payment is $2131, which is $88 less than the annual payment.

The primary consideration in the design of geometric cross sections for highways, runways and taxiways is.

Carriageway

The red, yellow, or green light that is displayed to drivers in a given movement is called

Indication

The design element which is the most affected by the volume of traffic.

Number of Traffic Lanes

This drawing has elevation as its vertical axis, and horizontal distance, as measured along the centerline of the facility, as its horizontal axis.

Profile

In the measures of congestion of highway capacity, what will happen as the density continues to increase?

The point is reached at which speed declines noticeably

The traffic characteristics which has the greatest effect on highway design.

Volume of Traffic

Moretech Drilling company may buy a patent with 14 years of life left. If MoreTech spend $1.5M implement the technology, it expects net revenues of $650,000 per year for the patent's life. If MoreTech's discount rate for money's time value is 10%, what is the maximum price that MoreTech can pay for the patent?

$3.3M

A spherical balloon is inflated with gas at the rate of 20 cu cm per min. How fast is the radius of the balloon changing at the instant if the radius is 2 cm?

0.199 cm/min

The 8-kg block is moving with an initial speed of 5 m/s. If the coefficient of kinetic friction between the block and plane is μk=0.25, determine the compression in the spring when the block momentarily stops. T=1150(9.9-0.664)

0.6875m

The Department of Highways will be widening a two-lane road into a four-lane freeway this summer. The project requires the purchase of $22M worth of land for the additional two lanes. If the department uses an interest rate of 6%, what is the EAC of the right-of-way?

1.23M

If $10,000 is borrowed and payments of S2000 are made cach year for 9 years,what is the inter-cst rate?

13.704%

Find the EAC for a 5-year life of a S680 overhaul at the end of year 3

135.2

The National Monuments Commission is considering the imposition of viewing fees for several monuments. At one monument, these fees would bring in $800K for the first year, and this should ncrease by $50K per year as the number of tourists increases. If the government uses an interest rate of 10% and perpetual life is assumed, what is the EAW for the income stream?

13M

A boy is 25 years younger than his father. In 10 years, his father will be twice his age. Find the age of the boy.

15

If the stationing of PT is at 15+480.14, what is the stationing of PCC? D1=4°, D2=5°,I1=30°,I2=36°

15+624.14

Indirect Mail Inc. had been mailing out coupons for a clearance sale at a constant rate for 4 days, when they counted the coupons, they still had mail out and discovered they had 120,000 left. After 7 total days of work they had 75,000 left. At what rate are they mailing coupons out?

15,000 per day.

The Asian Transmission Co. makes and sells certain automotive parts. sales volume is 500,000 units a year at a selling price of P0.50 per unit. Fixed expenses total P80,000 per year. Determine the present total profit for a year.

170,000

A conical pendulum has a length of 50 cm. Its bob of mass 100 g performs a uniform circular motion in a horizontal plane in a circle of radius 30 cm. Determine the period of the pendulum in seconds.

2.961

An investor pays P1,100,000 for a mine, which will yield a net income of x pesos at the end of each year for 10 years and this will become valueless He accumulates a replacement fund to recover his capital by annual investments at 4.5%. Find x if he desires 11.5% return on his investment.

217,016

A strip of uniform width is shaded along both sides and both ends of a rectangular poster with dimensions 12 inches by 16 inches. How wide is the strip if one-half of the area of the poster is shaded?

3 inches

In a certain barangay,80% of the population have cellphone. Two people from the barangay were selected at random. Find the probability that one has cellphone and the other has none.

32%.

A grain silo has the shape of a right circular cylinder with a hemisphere attached to the top. If the total height of the structure is 30 feet, find the radius of the cylinder that results in a total volume of 1008π ft3.

4 ft

A 20-kg block resting on a horizontal surface is pushed down by a 50-N force with angle of 30° with the horizontal. If the coefficient of kinetic friction is 0.12, find the velocity after it moves 10 m from rest.

4.09 m/s

is the bucket volume contained within the bucket when following the outline of the bucket sides.

Heaped volume

Ship Atlantis started sailing N 40°32' E at a rate of 3 mph. After 2 hours, ship Potomac started from the same point going S 45° 18' E at a rate of 4 mph. What would be the direction of Potomac from Atlantis 3 hours after Potomac start from the same port?

S 4°11' W

During a test, a rocket travels upward at 75 m/s, and when it is 40 m from the ground its engine fails.Determine the maximum height reached by the rocket if while in motion, the rocket is subjected to a constant downward acceleration of 9.81 m/s2 due to gravity. Neglect the effect of air resistance.

S =327 m ; v = 80.06 m/s

Elevator and counterweight (Atwood's machine). A system of two objects suspended over a pulley by a flexible cable,as shown in Fig. 23a,is sometimes referred to as an Atwood's machine.Consider the real-life application of an elevator (mE) and its counterweight (mc). To minimize the work done by the motor to raise and lower the elevator safely, mg and mc are made similar in mass. We leave the motor out of the system for this calculation, and assume that the cable's mass is negligible and that the mass of the pulley, as well as any friction,is small and ignorable. These assumptions ensure that the tension Frin the cable has the same magnitude on both sides of the pulley. Let the mass of the counterweight be mc=1000kg. Assume the mass of the empty elevator is 850 kg, and its mass when carrying four passengers is mE = 1150kg.For the latter case(mE=1150kg), calculate (a) the acceleration of the elevator and (b) the tension in the cable.

T= 10.5 kN ; a= 0.684 m/s^2

Ability of a soil to support the weight of vehicles under repeated traffic.

Trafficability

Consider a family with four children. A survey indicates that it is reasonable to believe that the probabilities of having 0,1,2,3, or 4 sons in such a family are respectively, 0.1, 0.3, 0.35, 0.2, and 0.05. Find the probability that in the family with four children there will be: a) at least two sons b) at most two sons

a) at least two sons = 0.6 b) at most two sons = 0.75 a) at least two sons = p(two sons) + p(three sons) + p(four sons) p(0.35) + p(0.2) + p(0.05) b) at most two sons = p(zero sons) + p(one sons) + p(two sons) p(0.1) + p(0.3) + p(0.35)

Charley is selecting materials for a state-subsidized housing development

high quality shingles: $1 per square meter ; nearly $2 over the minimum quality shingles

If interest is compounded monthly,what nominal interest rate will result in an effective interest rate of 9.3%?

r = 12(1+9.3%)^1/12 r = 8.926%

The 100-kg crate shown is originally at rest on the smooth horizontal surface. If a towing force of 200 N,acting at an angle of 45°,is applied for 10 s, determine the final velocity and the normal force which the surface exerts on the crate during this time interval.

v = 14.142 m/s

On a flight from Orlando to Washington D.C., the airline sold 52 economy seats, 25 business-class seats, 12 first-class seats, and there were 20 empty seats. The airline has determined that it makes a profit of $550 per first-class seats and $100 profit per business-class seat. However, the airline incurs a loss of $20 per economy seat and a loss of $75 per empty seat. Determine the profit (or loss) for the flight. C. $3280 loss

$6560 profit

The 1.8-kg block A sliding toward the right with the velocity vA1 = 1.2 m/s when it hits block B, which is moving to the left with vB1 = 2.0 m/s. The impact causes block A to stop. The coefficient of restitution for the impact is 0.5. Calculate the mass of block B.

0.9 kg

Assume a population of fish grows exponentially. A pond is stocked initially with 500 fish. After 6 months, there are 1000 fish in the pond. The owner will allow his friends and neighbors to fish on his pond after the fish population reaches 10,000. When will the owner's friends be allowed to fish?

17 months

The radius of the moon is 1080 miles. The gravitational acceleration at the moon's surface is 0.165 times the gravitational acceleration at the earth's surface.What is the velocity of escape from the moon in miles/second?

2.38

24.1 km of gravel road require reshaping and leveling. You estimate that six passes of a motor grader will be required. Based on operator skill, machine characteristics, and job conditions, you estimate two passes at 6.4 km/h, two passes at 8.0 km/h, and two passes at 9.7 km/h. If job efficiency is 0.80,how many grader hours will be required for this job?

21.3

An engineer selects a sample of 5 iPods from a shipment of 100 that contains 5 defectives. Find the probability that the sample contains at least one defective.

22.55%. or 23%

The distance traveled by a train is given by the equation x = 3t2 +2t +4 where x is the distance in kilometers and t is the time in hours. Determine the velocity of the train after travelling 10 kilometers.

23.5 kph

A job can be done in 14 days by a crew of 10 men working 10 hours a day. How long will it take a crew of 7 men working 8 hours a day to complete the job?

25 days

Northern Construction and Engineering plans on opening an office in Duluth.Over the next 25 years,the office is expected to have a positive cash flow of $250,000 per year.At an interest rate of 12%, what is the equivalent present worth (PW)?

250K x 7.843 = $1961K

Geologist took measurements at two points B and C, 928 m apart. The angle of elevation from B to the top of the mountain A is 47°10'. The angle of elevation from C to B is 8°40' and the angle of elevation from C to A is 32°30'. It is known that the elevation at C is 1537 m. What is the elevation at A?

2592.87 m

Alice is a recent chemical engineering graduate. One of her first jobs is to calculate a large pump's cost using the following data. The first cost will be $54,000, the annual operating costs for energy and maintenance will be $18,000, the expected life is 10 years,the expected salvage value is 0, and the firm's interest rate is 9%. What is the EAC?

26.41k

A power-shift crawler tractor has a rated blade capacity of 7.65 LCM. The dozer is excavating loose common earth and pushing it a distance of 61 m. Maximum reverse speed in third range is 8 km/h. Estimate the production of the dozer if job efficiency is 50 min/h. Hint: Volume per cycle x cycles per hour ; Fixed Time= 0.05 min ; Dozing speed =4 km/h

271

North Central power and light has just purchased a generating unit that comes with a 2-year warranty

2805

A passenger ferry makes trips from a town to an island community that is 7 miles downshore from the town and 3 miles off a straight shoreline. The ferry travels along the shoreline to some point and then proceeds directly to the island. If the ferry travels 12 mi/hr along the shoreline and 10 mi/hr as it moves out to sea, determine the route that the ferry may travel along the shoreline having a total travel time of 45 minutes to the island.

3 miles

Find the 10th term of a geometric progression in which the first term is 12 and the common ratio is 1/2.

3/128

When the angle of elevation of the sun is 64°, a telephone pole that is tilted at an angle of 9° directly away from the sun casts a shadow 21 feet long on level ground. Approximate the length of the pole.

32.91 m

A spring of stiffness k = 500 N/m is mounted against the 10-kg block. If the block is subjected to the force of F = 500 N,determine its velocity at s = 0.5 m. When s =0, the block is at rest and the spring is uncompressed.The contact surface is smooth.

5.24 m/s

A spring is used to stop 60 kg package which is sliding on a horizontal surface. The spring has a constant k = 20 kN/m and is held by cables so that it is initially compressed 120 mm. The package has a velocity of 2.5 m/s in the position shown and the maximum deflection of the spring is 40 mm. Determine the final displacement of the package measured from the position shown when it finally stops moving.

519 mm

The number of accidents for 6 yrs. recorded in a certain section of a highway is 5432. If the average daily traffic is 476, what is the accident rate per million entering vehicles?

5211

The half life of radium is 1690 years. If 10 percent of an original quantity of radium remains, how long ago was the radium created?

5416 years ago

The scores in an examination are normally distributed with a mean of 48 and a standard deviation of 8. Approximately what percent of the scores fall between 40 and 56?

68%

An appellate court has 9 justices. The justices voted 6 to 3 in favor of the defendant on a certain case. In how many ways could this have happened?

84

Given the following cross-section notes for a road grading work:The roadbed is 9m wide and the sideslope for cut is 1:1 and for fill is 1.5:1. Determine the area of cut of the section.

9.404㎡

Find the area bounded by the two curves y= 2x2 - 2 and y y=2x2-2 and y=x2+x.

9/2

If one third of the air in the tank is removed by each stroke of an air pump, what part of the total air will be removed in 6 strokes?

91.22%

From the top of a building that overlooks an ocean, an observer watches a boat sailing directly toward the building. If the observer is 100 ft above sea level and if the angle of depression of the boat changes from 25° to 40 during the period of observation, approximate the distance that the boat travels.

98 ft

is the process of proportioning cement, water, aggregates, and additives prior to mixing concrete.

Batching

means a method of protecting workers from cave-ins by excavating the sides of an excavation to form one or a series of horizontal levels or steps, usually with vertical or near-vertical surfaces between

Benching

It may be defined as the difference between the actual travel time on a given segment of a transportation system and some ideal travel time for that segment.

Delay

A soil weighs 1483 kg/m loose, 1839 kg/m3 in its natural state, and 2106 kg/m compacted. Find the soil's load factor and shrinkage factor.

LF=0.87,SF=0.70

Blocks A and B shown have a mass of 3 kg and 5 kg, respectively. If the system is released from rest, determine the velocity of block B in 6 s.Neglect the mass of the pulleys and cord.

V_b = 35.83 m/s

An earth-filled dam of the U.S. Department of Reclamation cost $850,000 to build in 1957. Today, in 2002, it is in mint condition and worth about $5 million. At what annual interest rate has the value of the dam increased?

i= 4.02%

A special task force of a military unit requires that the recruits not to be too tall or too short.

rejected heights are 71.11 inches and 63.80 inches