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Questions tagged [word-problem]

A word problem is an exercise with its main challenge being in translation from words to mathematical concepts and language including symbols and formulas. This tag is not about the unrelated topic in group theory.

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Relative density word problem

So I am having a issue with this problem and cant see a way of solving it. The world discus champion is temporarily living on a planet which has half the radius of the Earth. He discovers that he ...
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2answers
31 views

How to find any day using given date and year?

I am posting after a long time here. I am having trouble finding solution to this types of problem. Please help me out on this case: If the 1st December, 1994, was Thursday, then what was the day ...
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1answer
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How many way can you encode a five letter word

I have a solution for this problem, but the way iv carried it out seem a bit long and am wondering if and only if my ans is correct if there is a shorter method or maybe and alternate way of looking ...
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1answer
43 views

10th Grade Algebraic Rate of Bacteria Growth Problem

"A certain type of bacteria doubles every 6.5 hours. If there were 60 bacteria to start with, what is the hourly growth rate of the bacteria? How many bacteria will there be after a day and a half? ...
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System of algebraic equations concerning rates

I'm not even sure where to start on the problem. Is this possible to solve without logarithms? "A certain type of bacteria doubles every 6.5 hours. If there were 60 bacteria to start with, what is ...
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1answer
28 views

At least probability of two students

I have been trying to view this problem for a while and I have come unstuck, because of the at least at least part. Calculate the probability that at least one of two students A and B, who ...
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34 views

Probability distribution of a moving particle

I am having a issue with the wording of this question. Find the probability of the following. The velocity $v$ of a randomly selected particle, whose distribution obeys the probability density ...
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combinations word problems math

There are two different problems I am stuck on. In how many ways can we divide ten candies of the same kind among four children? I haven't found a way to solve this one 2.In how many ways can we ...
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In how many ways can we select $5$ children from this group so that Mary and Jane are always in the selection?

In a group of $10$ children no two kids have the same name. We know that Mary and Jane are among these children. In how many ways can we select $5$ children from this group so that Mary and Jane are ...
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1answer
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How can I derived the equation?

The present age of a woman is 30 years older than her daughter. 15 years ago she was twice as old as her daughter. How old is her daughter at present. How old would the woman be 12 years from now. ...
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Is this dual linear program correct? If so, how would I interpret its variables/contstraints/optimum?

I'm confronted with the following situation: A company has $5$ employees (conveniently numbered from $1$ to $5$). Each employee is paid at a fixed rate per task completed. The company also has an ...
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Two packs of cards each containing cards numbered 1 to n are shuffled and placed on the table

Let $ n ∈ N $. Two packs of cards each containing cards numbered 1 to $ n $ are shuffled and placed on the table. One by one, two cards are simultaneously turned over from the top of the packs. What ...
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1answer
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Three bags each contain balls numbered from 1 to 10

Three bags marked A, B and C each contain a set of balls numbered from 1 to 10. We pull a ball from each bag. Describe the appropriate sample space.Assuming all outcomes are equally likely calculate ...
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1answer
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Modelling Sales in a software company: Poisson or simple linear algebra?

Let's assume I have 1 year of weekly sale data for software A and 1 year of weekly sale data for software B. Software B is related to software A, because it's a maintenance/security upgrade, so the ...
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2answers
38 views

Shortest Distance Between Pair of Beetles on a Cube

This is a problem from the AMT (an Australian paper) from 2011: The first thing I thought was when the first beetle was directly over the line FH or the second beetle directly over AC, the distance ...
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1answer
46 views

System of Equations Algebraic Equations Word Problem

The problem is "In a math class that contains both 7th and 8th graders, each student must do a class presentation on a famous mathematician. Each student may do the presentation alone or with a class ...
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In solving Real World Quadratic Equations, why does 𝑐 change value, and when do i have to change value? [closed]

When solving for the equation I entered 32, not -32. When I watched the video paired with this course it did not explain in what cases to do this. All help is appreciated :D
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High School Math Help Word Problem Precalculus

The frequency of a sound wave is called its pitch. The pitch p of a musical tone and its wavelength w are related by the equation p=v/w, where v is the velocity of sound through air. Suppose a sound ...
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1answer
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Different Differences between an Arrangement of Numbers

This was an optional problem given to me which I just don't know how to approach. The full question states: "An arrangement of numbers has 'different differences' when the differences between all the ...
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1answer
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Write a function for a river word problem

My problem: The river flows at 1.5 meters per second. Write a rational function rule for the total time required to travel a distance $d$ downstream and back in a river flowing at a rate $v_r$....
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Is reversing a string an example of a one to one function?

The word "apple" reversed yields "elppa". No other input can produce the same output. And in such a scenario can palindromes also be included in the list of permissible strings. Was wondering about ...
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1answer
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Ambigious Word Questions Involving Ratios (Or Do I Not Know The Conventions?)

I am just curious if I was at fault here for the way I answered these questions, or if the book was at fault for not being clear enough. Perhaps I'm missing something regarding the conventions of ...
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1answer
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Interpretation of Notation $[k,k)$

I'm trying to understand a prove and struggling with the following introduction of a Notation: "Furthermore, let us introduce the notation $[k,l) = \{k,k+1,\dots,l-1\}$", with the numbers taken ...
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1answer
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SAT Math practice problem about seating arrangements that seems impossible! Can anybody offer any insight?

A teacher is figuring out seating charts. If she assigns 2 people/table, she needs 4 extra tables. If she assigns 4 people/table, she has 4 empty tables. how many students are there in the class? ...
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2answers
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How to convert a rate involving radians to something that can be applied to a straight direction in a related rates problem.

I can do related rates problems a little bit, but I've been given one that requires me to use a rate of $\frac{-\pi}{6}$ radians per second to figure out how fast a plane is going. Since I assume that ...
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1answer
51 views

Probability of there being a bullet in the chamber

Suppose we have three $6$-chambered guns: The first has no bullets. The second has one bullet. The third has two bullets in consecutive chambers. The cylinder advances automatically as the trigger ...
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2answers
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A bus carries $67$ travelers of three types

A bus carries $67$ travelers of three types: travelers who pay the entire ticket, which costs $\$3200$. students who have a $43$% discount. local retirees who only pay $23$% of the ticket ...
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1answer
51 views

What numbers should I not pick?

I have a problem on my hands and I am a little confused on how to solve it. Say you have $50$ people and each chooses a number from $0$ to $100$. Now you take the average of all the numbers and ...
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Piecing Together Parts Needed for Multivariable Chain Rule

The Question You want to estimate the rate at which the temperature (degrees F) in a concert hall changes per hour, dT/dt, based upon how many people are in the room, p, and the total heat output of ...
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2answers
79 views

Related rates problem: what is $\frac{dh}{dt}$ when the height is 35 in?

The following is the problem at hand: The volume of oil in a cylindrical container is increasing at a rate of 150 cubic inches per second. The height of the cylinder is approximately ten times the ...
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1answer
24 views

Find posterior distribution given beta prior

The output of a certain integrated-circuit production line is checked daily by inspecting a sample of $100$ units. Over a long period of time, the process has maintained a yield of $80$ percent, that ...
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1answer
44 views

Question from the 2011 IMC (international mathematics competition) key stage III paper, about a logical sequence

There are two kinds of students in a cerain class, those who always lie and those who never lie. Each student know what kinde each of the other students is. In a meeting today, each student tells what ...
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Weird Answer involving Minimum

Given the isosceles triangle $ABC$, in which $AB$ is 12 inches and the altitude $CD$ is 3 inches, find the point $P$ on CD such that the sum of the distances of P from the vertices is a minimum. ...
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1answer
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How do I measure distance in this problem?

I am posting here again after a long time. I have this distance measuring problem that I have been trying to solve. Please help me out here. TIA. ***A bullet covers distance of 1540 feet per second. ...
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2answers
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How to compute the different number and ways to read a given phrase forming a pile or a stack?

I'm totally lost in this riddle, does it exist a way to calculate the different ways to read a word using a systematically approach?. In my initial attempt what I tried to do is drawing a circle over ...
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Did I formulate this problem in the correct way?

A company makes two products, product 1 (X1) and product 2 (X2). Profits per unit are $\$30.00$ for $X_1$ and $\$15.00$ for $X_2$. Hours per unit for each of the three departments are: Dept. A (hrs....
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conversion question with liters

A tank has a square base of 3 m by 3 m. Water is poured into the tank at a constant rate. The mass of water in the tank is observed to increase at a rate of dm/dt = 500 kg/s. You may assume ...
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3answers
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Is it possible to know the result of a match between three teams with only knowing their goals for and goals against?

I've found this problem in my book and left clueless on how to make the right interpretation to come up with a solution. The situation involves a hockey match. Typically when you have a goals for and ...
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1answer
28 views

How to do the computation to find the number of coins in a chest if there are different denominations?

This problem has left me going in circles, since I don't know how to relate the number of coins and denominations to obtain a maximum quantity. Does this problem requires the use of derivatives?. If ...
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1answer
38 views

How can I determine the maximum profit in a problem involving inequations in both sides?

Needless to say that what I've already tried it didn't work hence I'm requesting assistance on this. Overall I want to know if there is some graphical approach on this problem. Can this be expressed ...
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1answer
53 views

Precalculus Composition of Functions Question

The prompt: Amparo bought a jacket with a \$50 gift certificate she received as a birthday present. The jacket was marked 33% off, and the sales tax in her area is 5.5%. If she paid $45.95 for the ...
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1answer
20 views

Does a problem involving finding the least amount of trials in weighing to reach a certain quantity can be solved without derivatives?

I've been going in circles with this kind of problem, hence need some help into trying to find if this kind of situation can be solved without the use of derivatives. The problem is as follows: In ...
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1answer
40 views

Fibonacci's sequence to calculate growth of a family

I'm trying to solve the following mathematical dilemma: On the 1st of July 2000 a Lizard bears 4 babies. On the 1st July 2001 each of those Lizard bears in turn 4 babies. And so on. Assumed that ...
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1answer
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How to find the least number of containers required to fill up a certain quantity?

I'm still stuck on this problem involving finding the least number of bottles. I am not sure whether if this problem belongs to combinatorics or maybe does it has to do with greatest common divisor or ...
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0answers
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How to find the number of machines given a set of rental prices?

I'm stuck in a situation involving rental. Typically I would assign a set of constants based on their price but I'm confused on how to use it or if it applies here. The problem is as follows: A tv ...
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2answers
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Particle on a line question with integrals calc2

I have a question for calculus two regarding a particle on a line. Question: A particle moves along a line with acceleration $a(t)=−1(t+3)~2\text{ft}/\text{sec}^2$. Find the distance traveled by ...
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Does there exist a way to simplify or build a table to find the truth in a set of given statements involving 5 individuals?

This problem has got me going in circles for several hours and I'm not sure what to do, the problem is as follows: At a semiconductor laboratory in Hsinchu a security guard caught five ...
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1answer
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Word problem regarding finding torque of a shoulder

Question: What is the torque about the shoulder if the arm is held in an abducted position at 60 degrees from the body in the frontal plane while holding a 10 kg dumbbell? Assume that the mass of the ...
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1answer
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Need help with a survey word problem…

I am unable to solve this problem in attached screen shot and need help
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Forming a constrained optimization from a given problem?

A workshop produces a product out of three infinitely divisible ingredients X, Y , and Z. The ingredients cost p, q, and r pounds per kg, respectively, with p, q, r > 0 all different, and the factory ...