Questions on Word Problems: Miscellaneous Word Problems answered by real tutors!

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Question 1185698: being the first grandson, your grandparents decided to give you a rectangular field for your coming wedding. If you are given 200m wires of fencing, what dimensions would you choose to get the maximum area?
a. List all the possible dimensions of the rectangular field.
b. Make a table of values for the possible dimensions.
c. Compute the area for each possible dimension.
d. What is the maximum area you obtained?
e. What are the dimensions of the maximum area you obtained?
Click here to see answer by CPhill(1959)

Question 1184943: a vector of 13.2 units acts upward, and a vector of 45 units acts east. what is their resultant? indicate the direction with respect to east.
Click here to see answer by ikleyn(52747)

Question 1185083: Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.
Probability
0.2
0.5
0.3
Design A
180
230
350
Design B
520
310
270
What is the variance of your profit when Design A is chosen?
What is the standard deviation of your profit when Design B is chosen?
What is the covariance of the profits from the two different designs?
What is the expected profit, the total variance, and the total standard deviation if you increase the shift of your production lines and choose to produce both designs?

Click here to see answer by CPhill(1959)

Question 1183001: The average lifespan of a Ghanaian is 57years. The average lifespan of males in Ghana is known to be 55 years while the average lifespan of females in Ghana is known to be 60 years. The average lifespan of people from the Northern region of Ghana is known to be 58 years while the average lifespan of people in the East region of Ghana is known to be 54 years.
Use the above information to answer the following questions:
(i).With your reasons, discuss all possible population parameters from the above information.
(ii).With your reasons, discuss all possible sample statistics from the above information.
(iii) Compare and contrast the average lifespan of males and females. Which group average is more likely to represent the corresponding population parameter? Give reasons for your answer.
Click here to see answer by CPhill(1959)

Question 1209708: Hi
The average usage of water is 4000 litres per month. During the months of May June and July the usage is 4500 litres per month. What should the average usage of water be for the rest of the months so that the total consumption for the year is the same.

Click here to see answer by CPhill(1959)

Question 1209718: Hi
A container is filled with 300 litres of water and 100 litres of chemical. 80 litres of the mixture is removed and another 80 litres of chemical is added to obtain the original volume. What is the percentage of the chemical in the final mixture.

Click here to see answer by timofer(104)

Question 1181818: A rectangular brass bar of mass M has dimensions a, b, c as shown in the
figure below. The moment of inertia I about the axis at the centre of the ab
face and perpendicular to it, is given by:
I=(M/12)(a^2 + b^2)
The following measurements are made:
𝑀=135.0±0.1𝑔
𝑎 =80±1 𝑚𝑚
𝑏 =10±1 𝑚𝑚
𝑐 =20.00±0.01 𝑚𝑚
Calculate the standard error in:
a) the density ρ of the material
b) the moment of inertia I
Click here to see answer by CPhill(1959)

Question 1181444: An epidemic is spreading through a large western state. Health officials estimate that the number of persons who will be afflicted by the disease is a function of time since the disease was first detected.
Specifically, the function is 𝑛 = 𝑓(𝑡) = 350𝑡 3 − 22𝑡 2 Approximate the instantaneous rate of change at which the disease is expected to be spreading at t=20 days, using,
i. Three Point Central Difference Formula
ii. Three Point Forward Difference Formula
iii. Five Point Central Difference Formula
Also calculate the respective Absolute Relative Error. Let spacing between points equivalent to 0.01
Click here to see answer by CPhill(1959)

Question 1209737: The dots on the opposite faces of a die have a sum of 7. How many different sum of dots on three adjacent faces are there on a die?
Click here to see answer by CPhill(1959)

Question 1179182: A drug is administered to a patient every 4 hours. The patient's metabolism cause the concentration of the drug in the patient's blood to decrease by 75% between doses. The dose causes an instantaneous rise in blood concentration of 0.2 units. Then what will be the concentration of drug in patient's blood immediately after the nth dose

Click here to see answer by CPhill(1959)

Question 1179016: Find the daily interest rate for each quarter. Round to the nearest millionths' place.
April, May, June at 3 1/2% interest
Click here to see answer by CPhill(1959)

Question 1178345: The rate of change of atmospheric pressure P with respect to altitude h is proportional to P, provided that the temperature is constant. At a specific temperature, the pressure is 103.5 kPa at sea level and 89 kPa at h = 1,000 m. (Round your answers to one decimal place.)
(a) What is the pressure at an altitude of 3500 m?
kPa
(b) What is the pressure at the top of a mountain that is 6251 m high?
Click here to see answer by CPhill(1959)

Question 1178007: Suppose that you are attempting to buy a house, and you are bargaining with the current owner over the sale price. The house is of value $200,000 to you and $150,000 to the current owner; so, if the price is between $150,000 and $200,000, then you would both be better off with the sale. Assume that bargaining takes place with alternating offers and that each stage of bargaining (an offer and a response) takes a full day to complete. If an agreement is not reached after seven days of bargaining, then the opportunity for the sale disappears (you will have no house and the current owner has to keep the house forever). Suppose that you discount the future according to the discount factor 0.4 per day and the current owner discounts the future at a discount factor of 0.8 per day. The real estate agent has allowed you to decide whether you will make the first offer. Should you make the first offer or let the current owner make the first offer? Why? Suppose that you have to make the first offer, what will be your offer that is going to be acceptable to the current owner?
Click here to see answer by CPhill(1959)

Question 1177643: 9. At the Fitness place, there are 12 weight machines that Amy liked to use: 6 upper body machines and 6 lower body machines. All machines were in one row, with 8 feet between each upper body machine and 8 feet between each lower body machine. The upper body machines were separated from the lower body machines by 16 feet. The lower body machines were numbered 1 through 6, and the upper body machines were number 7 through 12. Amy started at machine 6 (lower body) and then walked to machine 7 (upper body), then to machine 5 (lower body), then to machine 8 (upper body), and so on, alternating between lower body and upper body. After each 3 lower body machines, she would walk to the mat that was 20 feet past machine 1 and do some stretches. After each 3 upper body machines, she would walk to the wall that was 30 feet past machine 12 and do some stretching. When she finally finished lifting and stretching (the last thing she did was upper body stretching on the wall) how many feet had she walked in all?
Click here to see answer by CPhill(1959)

Question 1177642: Linda, Rumi, Liz, Amy, Adam, and Sam ran an 800-meter race. Adam BEAT Liz by 7 meters. Sam beat Linda by 12 meters. Adam finished 5 meters AHEAD of Amy but 3 meters BEHIND Sam. Rumi finished HALFWAY between the first and last woman. In what order did the women finish? What were the distances between them?
Click here to see answer by CPhill(1959)

Question 1176288: A 6-string guitar is being strummed by a guitarist once. When he strummed the strings, he hit the 6th string
(topmost string) first and released it before hitting the 5th string consequently. The 6th string went back to its initial
position after 50 milliseconds from its initial position. When the 6th string reaches its maximum point, the 5th string
went back to its normal position for the first time. Assume an equal tension applied to both strings.
A. Find the equation of the 6th string and graph.
B. Find the equation of the 5th string and graph.
1. Assume that the 5th string is released when the 6th string went back to its initial position for the first time.
2. Assume that the oscillation of the 5th string started when the 6th string reached its maximum point.
Click here to see answer by CPhill(1959)

Question 1176040: A car dealership sells 0, 1 or 2 luxury vehicles each day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car.
Let X denote the number of luxury cars sold in a given day. Let Y denote the number of extended warranties sold.
X Y Probability
0 0 0.07
1 0 0.13
1 1 0.1
2 0 0.15
2 1 0.11
2 2 0.44
Use the table to find the variance of X.
Click here to see answer by CPhill(1959)

Question 1175988: A 6-string guitar is being strummed by a guitarist once. When he strummed the strings, he hit the 6th string (topmost string) first and released it before hitting the 5th string consequently. The 6th string went back to its initial position after 50 milliseconds from its initial position. When the 6th string reaches its maximum point, the 5th string went back to its initial position for the first time. Assume an equal tension applied to both strings.
A. Find the equation of the 6th string and graph.
B. Find the equation of the 5th string and graph.
1. Assume that the 5th string is released when the 6th string went back to its initial position for the first time.
2. Assume that the oscillation of the 5th string started when the 6th string reached its maximum point.

Click here to see answer by CPhill(1959)

Question 1175966: Are all cycles planer? If they are, can you explain why? If they are not, you should be able to find a nonplanar tree.

Click here to see answer by CPhill(1959)

Question 1175631: A consultant has issued an environmental report on the cost of cleaning up a property that was previously the site of a chemical factory. Costs can increase dramatically depending on the percent of pollutants that needs to be removed. Her report gives the cost, C, in dollars, of removing p% of the pollutants from the site as C(p)=50000/100-p
a) Determine the average rate of change in the cost of cleaning up between 15% and 20% of the pollutants on the property.
b)Estimate the rate of change in the cost of cleaning up 95% of the pollutants on the property.
Click here to see answer by CPhill(1959)

Question 1209840: I came across the following question today:
A rectangular parcel of length x metres, width k metres and height k metres is to be sent through the post. The total length and girth of the parcel is to be exactly 2 metres. Show that the volume of the parcel is
V = x/16(2-x)^2
What I do not understand is, is the x in the volume equation the length of the parcel (ie 2m) or a different variable?
Also, does (2-x)^2 mean
(2-x)(2-x) ie 4-4x+x^2?
Click here to see answer by ikleyn(52747)

Question 1172981: The Truth in Lending Law requires all lending institutions to fully disclose interest rates on all loans.
$5000 is loaned for 36 months with monthly payments of $162.50. Determine annual interest rate.
Not sure how to continue.
Click here to see answer by CPhill(1959)

Question 1170693: Using 1 lb. of lead, and allowing 5% for waste, determine amount of shot 1/16 in. in diameter that can be produced.
Lead weighs .410 lbs. per cu. in.
Lead shot are spheres.
Sphere volume = 4/3 * pi * r^3
1.333 * 3.1416 * .03125 * .03125 * .03125 = .0001278 cu. in.
5% waste = .95 lb. remaining.
Not sure how to proceed.

Click here to see answer by CPhill(1959)

Question 1209951: Hi
When tara was 3 years old Joe was 1/3 of Tara's current age. When Joe was 13 years old Tara was 1/3 of his current age. How old are each of them now.
Click here to see answer by Edwin McCravy(20054)

Question 1167558: A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 25% real fruit juice and Drink B contains 20% real fruit juice. Company made 280 liters of fruity drinks with 61 liters of real fruit juice. Write a system of equations that could be used to determine the number of liters of Drink A made and the number of liters of Drink B made. Define the variables that you use to write the system.
Click here to see answer by ikleyn(52747)

Question 1210149: Hi
The ratio of adults to boys is 9 to 1. The ratio of adults to girls is 3 to 2. When half of the adults and 2/3 of the girls leave, what was the ratio adults to boys to girls at the end.
Click here to see answer by Edwin McCravy(20054)

Question 1165790: You plan to go ice skating often this winter. The skating rink charges $2 for admission. You can either rent ice skates at the skating rink for $5 per day or buy your own pair for $40. How many times do you have to use the ice skates in order for the cost of buying them to be less than the total cost of renting them?
Click here to see answer by ikleyn(52747)

Question 1168521: A retail outlet for calculators sells 700 calculators per year. It costs $2 to store one calculator for a year. To reorder, there is a fixed cost of $5, plus $2.35 for each calculator. How many times per year should the store order calculators, and in what lot size, in order to minimize inventory costs? The store should order ___ calculators ___ times per year to minimize inventory costs.

Click here to see answer by CPhill(1959)

Question 1168364: This question is related to electricity and magnetism in physics, more specifically transformers.
A coil of 600 turns, wound using 90.0 m of copper wire, is connected to a 6.0-V battery and is just able to support the weight of
a toy truck. If 200 turns are removed from the coil but the wire is
uncoiled and left in the circuit, what battery voltage would be
needed in order to support the truck?
The supposedly correct answer was 18 volts however I don't know how they got there
Click here to see answer by CPhill(1959)

Question 1210215: Hi
Tim and Michelle drove from A to B which was 285km away. Tim set off for B at an average speed of 75km per hour. 48min later Michelle set off for B at a speed of 95km per hour.
How long would Michelle take to catch up with Tim .
How far away was Tim from B when Michelle completed her journey

Click here to see answer by CPhill(1959)

Question 1168213: To help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 9% of the students in the district, based on the scores on a reading achievement exam. If the average score for the students in the district is 115.8, find the cutoff score that will make a student eligible for the program. The standard deviation is 23. Assume the variable is normally distributed. Round z-value calculations to 2 decimal places and the final answer to the nearest whole number.
Cutoff score
Click here to see answer by CPhill(1959)

Question 1168212: If the average price of a new one-family home is $246,300 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 88% of the market. Assume that the variable is normally distributed. Round z-value calculations to 2 decimal places and final answers to the nearest dollar.
Minimum Price
Maximum Price
Click here to see answer by CPhill(1959)

Question 1210256: The volume of water increases by 8 1/2% when freezing. Determine amount of space water will occupy when frozen the volume is 1085 cu. ft.
Unsure how to solve.
Click here to see answer by greenestamps(13195)

Question 1210257: Ran across this:
"The weight of a fraction of a square foot of any material can be quickly computed by the breakdown method;
The weight of 1 sq. ft. of steel, 0.22 in. thick, is 8.976 lbs., how much will 81 sq. in. of this thickness weigh ?
72 sq. in. (1/2 of 8.976 lbs.) = 4.488 lbs.
9 sq. in. (1/8 of 4.888 lbs.) = .561 lbs.
------------------------------------------
81 sq. in. = 5.049 lbs. "

My question:

Why was 1/2 and 1/8 used ?

Click here to see answer by greenestamps(13195)

Question 1210266: A sq. ft. of wrought iron weighs 40 lbs. Determine weight of a portion 11 in. by 9 in.
11 ( ? of 40 lbs.) = ? lbs.
9 ( ? of ? ) = ? lbs.
----------------------
99 sq. in. = ? lbs.
How do I determine the first two ?'s ?

Click here to see answer by josgarithmetic(39613)

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20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690