Math - Others Questions

In old gangster movies on TV you often hear of number runners or the numbers racket This numbers game which is still played today involves betting 1 on the last three digits of the number of stocks sold on a particular day in the future as reported in The Wall Street Journal If the payoff is 800 what is the expectation for this numbers game X

a b 36 hands Four of a kind 624 hands Full house 3 744 hands Flush 5 108 hands Straight 10 200 hands Three of a kind 54 912 hands Two pair 123 552 hands One pair 1 098 240 hands Other hands 1 302 540 hands P three of a kind x P two pair x probabilities are mutually exclusive That is the 36 straight flushes do not include the 4 royal flushes and the 5 108 flush hands do not include the better

Perform the experiment tally your results and calculate the probability Toss a coin 100 times Make sure that each time the coin is flipped it rotates several times in the air and lands on a table or on the floor Keep a record of the results of this experiment Suppose the results of this experiment were as follows Let H tossing a head and T tossing a tail HHTHTTHTTTHHHHHTTTTH HHTTHTHTHTH HTTHTHTTH TTHHHTHTTHTHTHTTH HHT HTTHTH HTTTHHHTTHTHTH HT TTHHHHTH HH TT HTTTH T Based on the given results what is P heads Enter the probability as a fraction

In dice a pair of ones is called snake eyes What is the probability of losing a dice game by rolling snake eyes Enter the probability as a fraction

A game involves tossing two coins and receiving 78 if they are both heads What is a fair price to pay for the privilege of playing this game twice

Assume that a dart is randomly thrown at the dartboard shown here and strikes the board every time The payoffs are listed on the board How much should you be willing to pay for the opportunit play this game Round your answer to the nearest cent 8 16 2 MY NOTES 5 ASK YOUR TEACHE

hat is the expectation for the 1 bets on a U S roulette wheel See the figure Round your answer to the nearest cent Six number bet

A box contains one each of 1 5 10 20 and 100 bills It costs 12 to reach in and withdraw one bill What is the expected value

A company held a bingo contest for which the following chances of winning were given PLAY ONE CARD AND WIN YOUR CHANCES OF WINNING ARE AT LEAST 1 TIME 7 TIMES 25 prize 3 prize 1 prize Any prize 1 in 21 252 1 in 2 125 1 in 886 1 in 609 1 in 3 036 1 in 304 1 in 127 1 in 87 13 TIMES 1 in 1 630 1 in 163 1 in 68 1 in 47 What is the expectation to the hearest cent from playing one card 13 times hearest

A punch out card contains 100 spaces One space pays 300 five spaces pay 15 and the others pay nothing How much should you pay to punch out one space Assume that you wish to pay the fair price

The game of Dungeons and Dragons uses nonstandard dice Consider a die with eight sides marked one two three four five six seven and eight Write a sample space for rolling a pa dice Die One Die One 1 2 3 4 5 6 7 8 1 2 3 4 5 6 1 1 1 0 0 2 2 3 1 3 2 0 0 0 0 4 3 5 1 0 0 5 3 0 0 7 2 8 Die Two 3 4 0 0 1 4 2 3 0 0 0 0 0 0 0 6 2 0 0 6 4 7 1 0 0 0 0 7 4 0 0 8 2 8 3 0 Die Two 5 6 7 1 5 0 0 0 8 1 8 0 0 2 6 2 7 0 0 3 5 0 0 3 7 0 0 0 0 4 6 0 0 4 8 5 5 5 6 0 0 0 0 6 8 0 0 0 0 6 7 0 0 7 6 0 0 7 8 0 0 8 7 0 0

An oll drilling company knows that it costs 25 000 to sink a test well If oil is hit the income for the drilling company will be 415 000 If only natural gas is hit the income will be 145 000 nothing is hit there will be no income If the probability of hitting oil is 1 40 and if the probability of hitting gas is 1 20 what is the expectation for the drilling company x Should the company sink the test well Yes No

A magazine subscription service is having a contest in which the prize is 40 000 If the company receives 2 million entries what is the expectation of the contest

Consider a bowl containing 120 marbles 25 green 17 blue 25 gray 6 orange 4 yellow 21 cat eyes and 22 multicolored Suppose each marble has an equal chance of being picked from the bowl Find the following probabilities Round your answers to three decimal places a P orange b P cat eye c P yellow

Suppose you toss a coin and will win 1 if it comes up heads If it comes up tails you toss again This time you will receive 2 if it comes up heads If it comes up tails toss again This time you wil receive 4 if it is heads Continue in this fashion for a total of 1 000 flips of the coin after which you receive nothing if it comes up tails What is the mathematical expectation for this game X

Courtesy of Reader s Digest Inc for the Reader s Digest sweepstakes described Assume there are 186 000 000 entr 10 500 000 00 SWEEPSTAKES ENTRY DOCUMENT Official Disclosure of Dates To be eligible to win the FIVE MILLION DOLLAR Grand Prize you must return the attached Sweepstakes Entry Document by August 19 1991 Failure to respond by that date will result in the forfeiture of Grand Prize eligibility To be eligible to win any of 58 567 other prizes but not the Grand Prize return your Sweepstakes Entry Document by March 2 1992 Grand Prize Distribution Information If you are chosen Grand Prize winner you will receive FIVE MILLION DOLLARS in your choice of payment options Either 30 equal yearly payments of 167 000 00 each OR 360 equal monthly payments of 14 000 00 each You must specify your choice of payment option now by detaching the appropriate seal at left and affixing it onto the box provided on your Sweepstakes Entry Document OFFICIAL PRIZE LIST 100 000 00 50 000 00 20 000 00 5 000 00 1 First Prize 2 Second Prizes 3 Third Prizes 4 Fourth Prizes 10 Fifth Prizes 400 Sixth Prizes 58 147 Seventh Prizes Winner s choice of a Special Edition Men s or Women s Wristwatch an 89 00 approximate retail value 500 00 100 00 J P Burn SWEEPSTAKES DIRECTOR Sponsor

19 Determine the area in square units of the shaded regions 1 unit A B D E

sume that a dart is randomly thrown at the dartboard shown here and strikes the board every time The payoffs are listed on the board How much should you be willing to pay for the opportunity to y this game 3 X 1 00 6 00 8 00 4 00 10 00

An oil drilling company knows that it costs 25 000 to sink a test well If oil is hit the income for the drilling company will be 415 000 If only natural gas is hit the income will be 145 000 If nothing is hit there will be no income If the probability of hitting oil is 1 40 and if the probability of hitting gas is 1 20 what is the expectation for the drilling company X Should the company sink the test well Yes O No

Suppose that you have 5 quarters 5 dimes 5 nickels and 15 pennies in your pocket You reach in and choose a coin at random so that you can give it to your child What is the expectation Round your answer to two decimal places What is the most likely gift O a quarter O a dime O a nickel O a penny

Suppose you toss a coin and will win 3 if it comes up heads If it comes up tails you toss again This time you will receive 6 if it comes up heads If it comes up tails toss again This time you will receive 12 if it is heads and nothing if it comes up tails What is the mathematical expectation for this game

company held a contest and the following information was included in the fine print PRIZE A B C D TOTAL WIN WIN NUMBER OF PRIZES 13 52 520 28 900 29 485 PROBABILITY OF WINNING INDICATED PRIZE 0 000005 0 00002 0 0002 0 010886 0 011111 Read this information carefully and calculate the expectation to the nearest cent for this contest Assume that Prize A is 90 000 Prize B is 1 000 Prize C is 200 and Prize D

gangster movies on TV you often hear of number runners or the numbers racket This numbers game which is still played today involves betting 1 on the last three digits of the number of sold on a particular day in the future as reported in The Wall Street Journal If the payoff is 800 what is the expectation for this numbers game

Krinkles potato chips is having a Lucky Seven Sweepstakes The one grand prize is 50 000 7 second prizes each pay 5 000 77 third prizes each pay 500 and 777 fourth prizes each pay 50 What is the expectation of this contest if there are 9 million entries Round your answer to the nearest cent

Heights in inches obtained by a group of people in a random survey are reported in the following tab Height Probability 0 005 55 60 65 70 75 80 85 90 What is the expected height in inches in 0 025 0 133 0 337 0 337 0 133 0 025 0 005

A box contains one each of 1 5 10 20 and 100 bills You reach in and withdraw one bill What is the expected value

ch the tax form with the description 5p 1 W 9 Forms Requests for Taxpayer Identification 2 Form W 2 Summary of your previous year s earnings tax withholdings and other withholdings 3 Form 1040 US individual Income Tax Return a Used for long term jobs This determines how much of b This form comes from your employer and you use it as reference to complete your tax return c One of the official documents used to file your annual income tax return d Used for contract or sometimes seasonal work it is used for very short term work

Use INDEX and MATCH functions to fill in a table that extracts the amounts shipped between each pair of cities in the accompanying data which shows the solution to an optimization model that finds the minimum cost and amounts shipped from two plants to four distribution centers Your table should be set up as follows and the formulas for the Amount Shipped column should reference the names in the From and To columns Click the icon to view the data and model 8 Minneapolis Chicago 9 Minneapolis Phoenix Marietta Marietta Marietta To Cleveland Baltimore Chicago Phoenix Minneapolis Cleveland Minneapolis Baltimore Minneapolis Chicago Minneapolis Phoenix Replace the functions with the amounts shipped between each pair of cities From Marietta Amount Shipped 0 IZB 0 From 0 Marietta Marietta Marietta Marietta To Cleveland Baltimore Chicago Phoenix Minneapolis Cleveland Minneapolis Baltimore Minneapolis Minneapolis FINDEX Model MATCH H8 Plant U MAI CH 18 Center U INDEX Model MATCH H9 Plant 0 MATCH 19 Center 0 Chicago Phoenix Amount Shipped 2 3 Plant 4 Marietta 5 Minneapolis 6 Demand 7 8 Model 9 10 Plant 11 Marietta 12 Minneapolis 13 Demand 14 15 16 Total 17 18 19 20 21 22 23 24 25 26 27 28 29 Distribution Center Cleveland 13 24 9 71 200 Distribution Center Cleveland Cost 27 509 0 200 200 Baltimore Chicago 11 63 14 66 8 08 16 38 250 500 250 0 250 Phoenix 17 84 17 95 0 500 500 1000 Phoenix Baltimore Chicago Capacity 800 200 1000 1050 900 Total Shipped 1050 900

Suppose you and an opponent each pick one of the spinners shown here A win means spinning a higher number Construct a sample space to answer the question and tell which of the two spinners given you would choose in each case F plays C A D O spinner F O spinner C O either spinner Need Help 5 Read It Additional Materials acce B E 6 2 6

Suppose that you toss a coin and roll a die The sample space is shown in the figure below FOT a What is the probability of obtaining heads and a five Enter the probability as a fraction 1 12

a What is the probability of obtaining heads and a five Enter the probability as a fraction b What is the probability of obtaining heads or a five Enter the probability as a fraction Need Help Read It

a One airline has six across seating in coach three seats on either side of the aisle If seats are assigned randomly what is the probability that a person will be stuck in a middle seat Enter the probability as a fraction b Another airline has five across seating There are three seats on one side of the aisle and two seats on the other side of the aisle If seats are assigned randomly what is the probability that a person will have a window or an aisle seat Enter the probability as a fraction 24

A mad scientist has captured you and is showing you around his foul smelling laboratory He motions to an opaque formalin filled jar This jar contains one organ either a kidney or a brain he cheerily informs you His voice seems an octave too high as he gives you a twisted leer You watch as the madman grabs a brain lying on his worktable and drops it into the jar as well He then shakes the jar and quickly withdraws a single organ It proves to be a brain He turns to you and says What is now the chance of removing another brain Fearing that the scientist might remove your brain in his next ghoulish experiment you want to give him the right answer What is your response t Enter the probability as a fraction Need Help Read It

er is a common game in which players are dealt five cards from a deck of cards It can be shown that there are 2 598 960 different possible poker hands The winning hands from highest to est are shown in the table below Find the requested probability Use a calculator Show your answer to nine decimal places P royal flush Poker Hands Royal flush 4 hands Other straight flush 36 hands Four of a kind 624 hands Full house 3 744 hands Flush 5 108 hands Straight 10 200 hands Three of a kind 54 912 hands Two pair 123 552 hands Que noir 44 vv for Fore 44 4

Give the probability in decimal form correct to two decimal places A calculator may be helpful One year in Ferndale California it rained on 144 days If one day of that year is randomly selected what is the probability of rain on that day Assume that this was not a leap year Need Help Read It

Use the sample space shown in the figure to find the probability for the experiment of rolling a pair of dice Enter the probability as a fracti P eight THE 36 WAYS DICE CAN ROLL

Q4 Define isomorphism of a graph Show that the following three graphs are isomorphic X 2

8 A recovery oriented person centered approach emphasizes which of the following That recovery is the expected outcome OO OO That recovery is not the norm but it is possible That recovery from substance misuse should be the first priority That recovery is possible if individuals comply with treatment recommendations 9 Which strategy is the BEST way to include persons with severe difficulties in person centered planning Create a treatment plan focused on the provider s recommendations Allow a loved one to make planning decisions for the person Be sensitive to and aware of the numerous ways that individuals may communicate their preferences Use association guidelines to determine what is typical for persons with severe difficulties

A function and the graph of a feasible region are given f 7x 8y x 2y 19 3x 2y 29 Find both the maximum and minimum values of the function if they exist and the point at which each occurs If an answer does not exist e The maximum value of the objective function is X which occurs at x y The minimum value of the objective function is 91 which occurs at x y 5 7 X

Estimate 752 x 352 by first rounding each number so tha it has only 1 nonzero digit

Form the dual maximization problem Use X X and x3 as the variables and f as the function and use the simplex method to solve the minimization problem Assume that all variables are nonnegative Minimize g 16y 15y2 subject to the following Y Y 2 100 2y1 y 140 5y 580 6y1 Maximize f subject to X Your answer cannot be understood or graded More Information 16 The minimum value of the objective function is 15 X1 X2 X3 2 0 which occurs at y MY NOTES ASK YOUR TEACH

Example 2 9 John Dilcher is paid an hourly rate of 18 50 per hour and he worked 49 hours this week His gross pay is 40 hours x 18 50 740 00 regular earnings 249 75 overtime earnings 989 75 9 hours x 27 75 18 50 x 1 5 Total gross pay John Porter is an hourly employee of Motter Company located in New York City This week Porter had to travel to the company s regional office in Albany He left Sunday at noon and arrived in Albany at 3 00 P M During the week he worked his normal 40 hours in the Albany office Monday through Friday 9 A M to 5 P M In addition he attended the company s mandatory 4 hour work training session on Wednesday evening Porter s hourly rate of pay is 12 10 per hour Round the overtime rate to two decimal places and use the rounded amount in subsequent computations Round the final answers to the nearest cent a Porter s overtime earnings for the week are b Porter s total earnings for the week are

This problem involves mixed constraints Solve it with the simplex method Assume that all variables are nonnegative Maximize f 5x 7y subject to the following 2x 5y 37 5x y 34 x 2y 4 The maximum value of the objective function is which occurs at x y

Form the dual maximization problem Use X X2 and x3 as the variables and f as the function and use the simplex method to solve the minimization problem Assume that all variables are nonnegative Minimize g 16y 15y2 subject to the following Y1 y 100 2y1 y 2 140 6y 5y 2 580 Maximize f 16 S 15 subject to X1 X2 X3 0 The minimum value of the objective function is which occurs at y

Maximize f Form the dual maximization problem Use x and x as the variables and f as the function and use the simplex method to solve the minimization problem Assume that all variables are nonnegative Minimize g 4y 3y2 subject to the following 5y1 2y 2 16 3y1 71 2 27 S4 3 subject to X1 X 0 The minimum value of the objective function is MY NOTES which occurs at y y ASK YOUR TEACHE

Solve this linear programming problem using graphical methods Restrict x 0 and y 0 Maximize f 6x 3y subject to the following f 7x 3y 105 2x 5y 59 x 7y 70 X

Problem 1 40 Points Given A ball is thrown vertically upward from the top of a building with an initial velocity of V4 The initial height of the ball is yA The values of VA and yA are found on YOUR KEY Set the origin of the coordinate axis on the ground and assume that the ball s motion is of the rectilinear type Use the values on your KEY to Find of the the ball fo tion 09 C

tnEN Discuss the convergence or or divergence of the improper integrals fofi 160 e 15 ma

1 0 0 Step 2 Corner 0 3 0 0 1 Step 1 We want to find the maximum and minimum values of the objective function C 6x 8y given the feasible region determined by the constraint inequalities We know that the optimal values of the objective function will occur at a corner a corner of the feasible region Thus we need to test the coordinates of the corner points in our objective function 7 0 42 6 2 52 C 6x 8y 0 52 4 4 56 4 4 56 3 5 7 0 42 52 6 2 56 7 0 0 3 24 24 The maximum value of the objective function is which occurs at x y

Which two of the expressions below are equivalem x 2 4 32 A