Practical Questions - Math Part 1-10

Deterministic queuing models

So far, the queuing models presented have assumed that arrival (and possibly service) functions vary over time in some known fashion. Such queuing models are known as:

Benching

2. A method of protecting employees 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 levels is known as:

Landing

A platform at the end of a flight of stairs is known as:

Under capacity with a volume to capacity ratio of 0.70.

Volumes for each approach of the intersection shown below are given in the table. All left turns have protected phasing and all right turning share lanes with through movements. Assume that PHF = 0.90 and that the intersection is not in a central business district. Cycle lengths may vary from 60 to 120 sec. Determine whether the intersection is under capacity, near capacity, at capacity, or over capacity.

Mobile Scaffold

A powered or unpowered, portable, caster or wheel mounted supported scaffold is known as:

two including the host

A Solid State Physicist gives a small stag party. He invites his father's brother-in-law, his brother's father-in-law, his father-in-law's brother, and his brother-in-laws father. Find the number of guests.

3, 3, 2

A bricklayer has 8 bricks. Seven of the bricks weigh the same amount and 1 is a little heavier than the others. If the man has a balance scale how can he find the heaviest brick in only 2 weighings?

President - white Professor - brown Instructor - black Janitor - green

A college president, a professor, an instructor, and a janitor are named Mr. Brown, Mr. Green, Mr. White, and Mr. Black, but not respectively. Four students with the same names will be designated here as Brown, Green, White and Black. The student with the same name as the professor belongs to Black's fraternity. Mr. Green's daughter-in-law lives in Philadelphia. The father of one of the students always confuses White and Green in class, but not absentminded. The janitor's wife has never seen Mr. Black. Mr. White is the instructor's father-in-law and has no grandchildren. The president's oldest son is seven. What are the names of the president, professor, instructor, and janitor?

4

A drawer contains red socks and black socks. When two socks are drawn at random, the probability that both are red is 1⁄2. a) How small can the number of socks in the drawer be?

21

A drawer contains red socks and black socks. When two socks are drawn at random, the probability that both are red is 1⁄2. b) How small if the number of black socks is even?

Ramp2=500, Ramp3=500, Ramp4=685

A freeway has the ramp configuration shown below. The origin-destination pattern (given as the fraction of each input bound for each output), demand input flows, and minimum metering rates are as follows: (see table) Determine the optimal metering rates for each onramp.

He lost

A gambler devised a game to be played with a friend. He bet 1⁄2 the money in his pocket on the toss of a coin; heads he won, tails he lost. The coin was tossed and the money handed over. The offer was repeated and the game continued. Each time the bet was for 1⁄2 the money then in his possession. Eventually the number of times he lost was equal to the number of times he won. Quickly now! Did he gain, lose, or break even?

99

A jig-saw puzzle contains 100 pieces. A "move" consists of nonnecting two clusters (including "clusters" of just one piece.) What is the minimum number of moves required to complete the puzzle?

Excavation

A man made cut, cavity, trench, or depression in earth surfaces, form by earth removal is known as:

Hoist

A manual or power-operated mechanical device to raise or lower a suspended scaffold is known as:

Benching

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 levels is known as:

15

A neat computer programmer wears a clean shirt every day. If he drops off his laundry and piucks up the previous week's load every Monday night, how many shirts must he own to keep him going?

Between 10 and 3

A novice librarian shelved a twelve volume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will the annual supplement, Volume 13, go?

Stilts

A pair of poles or similar supports with raised foot rests, used to permit walking above the ground or working surface is known as:

$11,920,257

A proposed new bus route is expected to require 8 new buses and to operate a total of 560,000 vehicle- kilometers (veh-km) per year and 29,000 vehicle-hours (veh-h) per year. Buses cost $200,000 each, have a 10-year life, and a salvage value after 10 years of $25,000 each. Operating costs include labor costs (wages, benefits, etc.) at $45.00 per veh-h, maintenance costs at $0.16 per veh-km, and cost of fuel, oil, tires, etc. at $0.38 per veh-km. Calculate the life-cycle cost (present value) of adding this route and operating it for 10 years, assuming an annual interest rate of 7.5 percent.

2nd wife

A rich farmer had 15 children by first wife 15 by his second. The second wife wished to insure the heritage to one of her own children and persuaded him to seat all 30 in a circle and count off every tength child until 1 remained. The first 14 thus eliminated were all his first wife's children. From this point on he insisted that they count backward from his first wife's lone remaining child. In what order were his first wife's children? Who became heir?

a) Level service C with a volume to capacity ratio of 0.722 b) 3 lanes

A rural freeway has two 12-ft lanes in each direction, with obstructions within 4 ft. on the median side but no obstructions on the right side of the one-way roadway. Traffic consists of 13 percent trucks and buses and 8 percent recreational vehicles. The design speed is 70 mph, and the adjustment for driver population factor is estimated to be 0.8. If the maximum 15-min flow rate is 1,760 vehicles per hour, a) What is the level of service on a 1-mile-long 3 percent upgrade? b) If the freeway is rolling, how many lanes are required to provide level of service B?

10

A sample of 8 travel time runs is conducted over a 2-km section of roadway. The mean travel time is 1.48 min. with a standard deviation of 0.20 min. If it is desired to determine the mean travel time to within 0.15 min, with a confidence level of 95 percent, what sample size is required? Assume that the estimate of standard deviation does not change with the sample size.

System scaffold

A scaffold consisting of posts with fixed connection points that accept runners, bearers, and diagonals that can be interconnected at predetermined levels is known as:

travel time

A second major issue in the analysis of traffic systems is the analysis of travel times and delays. The time required to covered a fixed distance and will of course be the reciprocal of the average piece at which that distance is covered is known as:

network

A set of nodes connected by links in the traffic analysis techniques is called:

Outrigger

A structural member of a supported scaffold used to increase the base width of a scaffold in order to provide support for and increased stability of the scaffold is known as:

Double pole (independent pole)

A supported scaffold consisting of a platform resting on cross beams supported by ledgers and a double row of uprights independent of support from any structure is known as:

Form scaffold

A supported scaffold consisting of a platform supported by brackets attached to formwork is known as:

Shore Scaffold

A supported scaffold which is placed against a building or structure and held in place with props is known as:

Float (Ship) scaffold

A suspension scaffold consisting of a braced platform resting on two parallel bearers and hung from overhead supports by ropes of fixed length is known as:

Interior hang scaffold

A suspension scaffold consisting of a platform suspended from the ceiling or roof structure by fixed length support is known as:

Personal Fall Arrest System

A system used to arrest an employee's fall. It consists of an anchorage, connectors, a body belt or body harness and may include a lanyard, deceleration device, life line or combination of these is known as:

4/7

A tennis tournament has 8 players. The number a player draws from a hat decides his first-round rung in the tournament ladder. Suppose that the best player always defeats the next best and that the latter always defeats all the rest. The loser of the finals gets the runner-up cup. What is the chance that the second-best player wins the runner-up cup?

Both three-man jury and one-man

A three-man jury has two members each of whom independently has probability p of making the correct decision and a third member who flips a coin for each decision (majority rules). A one- man jury has probability p of making the correct decision. Which jury has the better probability of making the correct decision?

Level of service is C with actual flow rate of 353 vehicles per hour.

A two-lane rural highway has a design speed of 60 mph. Lane widths are 11 ft. and should widths are 4 ft. The roadway is located in rolling terrain with about 60 percent no-passing zones. The two-way traffic volume is 300 vehicles per hour, with a peak hour factor of 0.85. The directional split is 70/30. Traffic includes 5 percent trucks, 12 percent recreational vehicles, and 1 percent buses. Determine the level of service.

Guardrail system

A vertical barrier consisting of, but not limited to, top rails, mid rails, and ports, erected prevent employees from falling off a scaffold platform or walkway to lower levels is known as:

Hazardous atmosphere

An atmosphere which by reason of being explosive, flammable, poisonous, corrosive, oxidizing, irritating, oxygen deficit, toxic or otherwise harmful, may cause death, illness or injury is called:

Pay at least as much to play the second game as the first.

An urn contains 10 black balls and 10 white balls, identical except for color. You choose "black" or "white". One ball is drawn at random, and if its color matches your choice, you get $10, otherwise nothing. Write down the maximum amount you are willing to pay to play the game. The game will be played just once.

Scaffold

Any temporary elevated platform (supported or suspended) and is supporting structure (including points of anchorage) used for supporting employees or materials or both is known as:

Lower Levels

Areas below the level where the employee is located and to which an employee can fall is known as:

25 miles

Between Kroflite and Beeline are five other towns. The seven towns are an integral number of miles from each other along a straight road. The towns are so spaced that if one knows the number of miles a person has traveled between any two towns he can determine the particular towns uniquely. What is the minimum distance between Kroflite and Beeline to make this possible?

18 dBA

Calculate the barrier attenuation for a noise barrier located 12 m from the source and 20 m from the receptor. The source is exhaust stack noise from a heavy truck, and is assume to 2.4 m above the pavement. The receptor is a window located 2 m above the pavement. The barrier is 6 m high.

Benefit-cost ratio = 1.6

Capital cost of a rural highway project is $10,000,000. This project will shorten the road by 2 km and reduce journey times by an average of 5 min. each. The project is also expected to reduce traffic accidents by an average of 5 per year and to reduce annual maintenance costs by $5,000. Average daily traffic on this road is currently 7,000, with a load factor of 1.5 persons per vehicle. Traffic is expected to increase linearly by 10 percent over the 20-year life of the project. If vehicle operating costs are $0.10/km, travelers value their time at $3.00/h, and the average cost of a traffic accident is $20,000, what is the benefit-cost ratio? Assume an interest rate of 8 percent.

0.079 say 8%

Chuck-a-Luck is a gambling game often played at carnivals and gambling houses. A player may bet on any one of the numbers 1, 2, 3, 4, 5, 6. Three dice are rolled. If the player's number appears on one, two or three of the dice, he receives respectively one, two, or three times his original stake plus his own money back; otherwise he loses his stake. What is the player's expected loss per unit stake? (Actually the player may distribute stakes on several numbers, but each such stake can be regarded as a separate bet.)

track resurfacing

Common maintenance tasks include restoration of horizontal and vertical alignment, replacement of worn or defective ties or rails, and cleaning or restoration of ballast. When possible, these are combined into a single operation, often referred to as:

14 minutes layover at A 13 minutes layover at B Total layover both terminals = 14 + 13 = 27 minutes

Construct a bus route schedule based on the running times given below. Headways are 30 min. and minimum layovers are 7 min. at each end or 10 percent of running time (total both layovers), whichever is greater. The first bus from A to D should leave at 8:00 a.m. The schedule should cover the time block from 8:00 a.m. to 12:00 noon. Segment travel time:

11.42

Coupons in cereal boxes are numbered 1 to 5, and a set of one of each is required for a prize. With one coupon per box, how many boxes on the average are required to make a complete set?

A

Five suspects were rounded up in connection with the famous"Cock Robin Murder." Their statements were as follows: A: "C and D are lying." B: "A and E are lying." C: "B and D are lying." D: "C and E are lying." E: "A and B are lying." Who is lying?

10 cent/number

Dr. Fubisher LaRouche, the noted mathematician, was shoping at a hardware store and asked the price of certain articles. The salesman replied. "One would cost 10 cents, eight would ost 10 cents, seventeen would cost 20 cents, one hundred and four would cost 30 cents, seven hundred and fifty six would aslo cost 30 cents, and one thousand and seventy two would cost 40 cents." What was Dr. LaRouche buying?

1/6

Duels in the town of Discretion are rarely fatal. There, each contestant comes at a random moment between 5 a.m. and 6 a.m. on the appointed day and leaves exactly 5 minutes later, honor served, unless his opponent arrives within the time interval and then they fight. What fraction of duels lead to violence?

4

Four players played a hand of hearts at $1 a point (pairwise payoffs). Dave lost $10 to Arch, $12 to Bob, and $20 to Chuck. How many hearts did poor Dave take in?

15 cm

Each end of a platform of a scaffold, unless cleated or otherwise restrained by hooks or equivalent means shall extend over the centerline of each support at least _____ .

a) average queue length b) average waiting time c) average total delay time spent in the system (queue, waiting time plus service time)

Features of interest for stochastic queuing system includes the following:

Horizontal tangents, circular curves, and possibly transition curves

Horizontal alignment for linear transportation facilities such as highways and railways consists of:

25 pitches

In a fast Major League baseball game, pitcher Hi N. Outside managed to get by with the minimum number of pitches possible. He played the entire game, which was not called prior to completion. How many pitches did he make?

saturated

In a stochastic queuing system, if the traffic intensity is greater than one is called:

undersaturated

In a stochastic queuing system, if the traffic intensity is less than one is called:

P= 2b/a+b when a = b P = 1.0

In an election, two candidates, Albert and Benjamin, have in a ballot box a and b votes respectively, a > b, for example, 3 and 2. If ballots are randomly drawn and tallied, what is the chance that at least once after the first tally the candidates have the same number of tallies?

a) travel time under free flow condition b) travel time at capacity

In practice, the ideal travel time chosen will depend on the situation, in general, however, there are two particular travel times that seem best suited as benchmarks for comparison with the actual performance of the system.

center-bound track

In railroad practice, there is danger that repeated loads will further compact the ballast under the end of the ties, leaving them supported only at their centers, a condition known as:

9

In the game "subtract-a-square," a positive integer is written down and two players alternately subtract squares from it with the restriction that the remainder must never be less than zero. The player who leaves zero wins. What square should the first player subtract if the original number is 29?

Sloping

It involves cutting back the trench wall at an angle inclined away from the excavation is known as:

Shielding

It protects workers by using trench boxes or other types of supports to prevent soil cave-ins is known as:

wetlands

It refers to a wide variety of plant and animal communities is called:

Shoring

It requires installing aluminum hydraulic or other types of supports to prevent soil cave-ins is known as:

9 pm or 3 am

Maynard's Grandfather Clock is driven by two weights, one for the striking mechanism which strikes the hours only, the other for the time mechanism. When he hears the clock strike his bedtime, he immediately winds the clock and retires. After winding, the weighs are exactly opposite each other. The weighs are again opposite every six hours thereafter. What is Maynard's bedtime?

queuing delay

Most recent research has found that for highway systems, there is comparatively little difference between these two speeds. That being the case, the analysis of delay normally focuses on delay which results when demand for a facility exceeds its capacity, such delay is known as:

Kind Friend will be cured first.

Mr. Brown always bets a dollar on the number 13 at roulette against the advice of Kind Friend. To help cure Mr. Brown of playing roulette, Kind Friend always bets Brown $20 at even money that Brown will be behind at the end of 36 plays. How is the cure working? (Most American roulette wheels have 38 equally likely numbers. If the player's number comes up, he is paid 35 times his stake and gets his original stake back; otherwise he loses his stake.)

30 cm

On scaffold where platforms are overlapped to create a long platform, the overlap shall occur only over supports and shall not be less than _____ . ANS:

6

On the average, how many times must a die be thrown until one gets a 6?

Competent Person

One who is capable of identifying existing and predictable hazards in the surroundings or working conditions which are unsanitary, hazardous, or dangerous to employees and who has authorization to take prompt corrective measures to eliminate the hazards is called:

a) server b) stream of customers who demand service c) queue, or line of customers waiting to be served

Queuing theory involves the analysis of what is known as queuing system, which is composed of the following:

Maximum intended load

The total load of all persons, equipment, tools, materials, transmitted loads and other loads reasonably anticipated to be applied to a scaffold or scaffold component at any one time is known as:

Excavation

The vertical or inclined earth surfaces as a result of excavation work is known as:

1.0

Two strangers are separately asked to choose one of the positive whole numbers and advised that if they both choose the same number, they both get a prize. If you were one of these people, what number would you choose?

Empire State Building

Two strangers who have a private recognition signal agree to meet on a certain Thursday at 12 noon in New York City, a town familiar to neither, to discus an important business deal, but later they discover that they have not chosen a meeting place, and neither can reach the other because both have embarked on trips.

10

Six boys on a hockey team pick a captain by forming a circle and counting out until only one remains. Joe is given the option of deciding what number to count by. If he is second in the original counting order what number should he choose?

3.7 dollars

Six grocers in a town each sell a different brand of tea in four ounce packets at 25 cents per packet. One of the grocers gives short weight, each packet of his brand weighing only 3 3⁄4 ounces. If I can use a balance for only one weighing, what is the minimum amount I must spend to be sure of finding the grocer who gives short weight?

0, 3, 6, 8

State University won their first football game of the season 17 to 0. Though they scored no safeties, they managed to score more points each quarter than they had scored in the previous quarter. What were State's quarter scores?

1/4

Suppose King Arthur holds a jousting tournament where the jousts are in pairs as in a tennis tournament. The 8 knights in the tournament are evenly matched, and they include the twin knights Balin and Balan. What is the chance that the wins meet in a match during the tournament?

analysis of traffic flow

The basis for design of transportation system operating strategies, traffic control systems, and certain physical features of transportation system is known as:

Failure

The breakage, displacement, or permanent deformation of a structural member or connection so as to reduce its structural integrity and its supportive capabilities is known as:

36 cm

The front edge of all platforms of a scaffold shall not be more than _____ from the face of the work unless guardrail systems are erected along the front edge and or personal fall system are used to protect employees from falling.

0.4923

The game of craps, played with two dice, is one of America's fastest and most popular gambling games. Calculating the odds associated with it is an instructive exercise. The rules are these. Only totals for the two dice count. The player throws the dice and wins at once if the total for the first throw is 7 or 11, loses at once if it is 2, 3, or 12. Any other throw is called his "point". If the first throw is a point, the player throws the dice repeatedly until he either wins by throwing his point again or loses by throwing 7. What is the player's chance to win?

Cross braces

The horizontal members of a shoring system installed perpendicular to the sides of the excavation, the ends of which bear against either uprights or wales is known as:

0.366

The king's minter boxes his coins 100 to a box. In each box he puts 1 false coin. The king suspects the minter and from each of 100 boxes draws a random coin and has it tested. What is the chance the minter's peculations go undetected?

Runner (ledger or ribbon)

The lengthwise horizontal spacing or bracing member which may support the bearers is known as:

8 cm

The maximum distance from the face for outrigger scaffolds shall be _____ cm.

15 and 16 in the 3rd group, 17 in the 2nd group

The numbers are divided into three groups as follows; 0, 3, 6, 8, 9,.... in the first group, 1, 4, 7, 11, 14,.... in the third. In which groups would 15, 16 and 17 be placed?

rate of trave

The reciprocal of speed which is represent by the slope in a space time diagram of a traffic analysis technique is known as:

Cave-ins

The separation of a mass of soil or rock material from the side of an excavation, or the loss of soil under a trench shield or support system, and its sudden movement into the excavation, either by balling or sliding, in sufficiently quantity so that it could entrap, bury or otherwise injure and immobilize a person is called:

speed of the vehicle

The slope of trajectory on a space time diagram for a traffic analysis technique is called:

3 times its rated load

The stall load of any scaffold hoist shall not exceed ______ .

198 days

Very few people are aware of the growth pattern of Jack's beanstalk. On the first day it increased its height by 1⁄2, on the second day by 1/3, on the third day by 1⁄4, and so on. How long did it take to achieve its maximum height (100 times its original height)?

52 x 12!

We often read of someone who has been dealt 13 spades at bridge. With a well-shuffled pack of cards, what is the chance that you are dealt a perfect hand (13 of one suit)? (Bridge is played with an ordinary pack of 52 cards, 13 in each of 4 suits, and each of 4 players is dealt 13.)

23

What is the least number of persons required if the probability exceeds 21 that two or more of them have the same birthday? (Year of birth need not match.)

0.08

When 100 coins are tossed, what is the probability that exactly 50 are heads?

253

You want to find someone whose birthday matches yours. What is the least number of strangers whose birthdays you need to ask about to have a 50-50 chance?