







Three digit codes 
20190714 

From Jessica: I need to find the total number of 3 digit codes using the digits 1 through 9. How many of these codes would be odd numbers, and how many even? Answered by Penny Nom. 





A three digit code 
20190714 

From Hannah: I have a briefcase with a threedigit code. I can set the code myself using digits 1 through 9, assuming that each digit can only be used once. How many possible codes are there? Answered by Penny Nom. 





4 digit codes 
20190227 

From Sophia: How many 4 digit codes can you get out of a numbered key pad ? Answered by Penny Nom. 





A four digit pass code 
20180226 

From Jessica: I was trying to fond out how many combinations could there be for a four digit pass code to a phone when no numbers are repeated? Answered by Penny Nom. 





The code on a new phone 
20180202 

From Maria: Hi 
My husband gave me a new Samsung Galaxy mobile for out anniversaire gift. He set me a challenge which I have to solve before I can use the Phone. He has set the pin code with numbers 4, 7 and 0 and created a four digit code with the said numbers. Is there a way I can somehow list all possible combinations and try them all? Thanks! Answered by Penny Nom. 





4 digit codes with repeating digits 
20170601 

From Morgan: what are all possible 4 digit code repeating numbers? cuz i know that you have one website on it but, it doesn't repeat 2 numbers in a code. Answered by Harley. 





A lost iPhone pass code 
20170417 

From Sam: I have a locked iPhone and it has all my of my holiday photos on it. I changed the password and then I think I did a incorrect number pattern but anyway I know it ends with 99 and the first 4 digits are 235 and 6 could you please send all of the combinations for this password (without the 99) Thx and plz get back ASAP I need it for school Answered by Penny Nom. 





A six digit code 
20160506 

From Ralph: How many combinations are possible if a "safe" has four buttons and you can use a six digit code? (these are just single press buttons..)For example, this could be one possible combination: Button 4 Button 1 Button 1 Button 3 Button 2 Button 4. Thanks! Answered by Penny Nom. 





A fivedigit pass code 
20150425 

From Mary:
Question from Mary:
More on your published question:
I have the same type of lock, but set up a 5digit pass code. Is that more or fewer possibilities than a 4digit code. How many digits would make the lock most secure? I don't believe Werner specified this, but each number can only be used once. Thanks, Mary Answered by Penny Nom. 





A model of the sun and the Earth 
20140614 

From Lynn: There is a model of the sun that is 2 1/2 inches in diameter. This is the only clue we have! How far away is the earth from this model? Answered by Penny Nom. 





A 4 digit code 
20130326 

From chris: I saw a previous question about a 4 digit code type thing and I was wondering if you could email me that same type of thing.
I changed the pin number on my phone's lock screen and I tried hard to remember it, then I had to go help my mom with something and I automatically forgot it and there is no way for me to get back on my phone.
I need all of the possible 4 digit number combinations without the numbers 0, 1, or 2. It cannot be repeating, ascending, or descending.
I know you may not want to do all of them, but I really need it. Answered by Robert Dawson. 





A valid UPC number 
20121222 

From Jacob: A valid UPC number , ABABABABAB C must end in a 2 after using the rule: 3A +B+3A+B+3A+B+3A+B+3A+B+C=##2. What would term C need to be in order to make the following UPC valid? 2741825293C Answered by Harley Weston. 





A security code 
20120901 

From Breanna: The code is made up of five two digit numbers from 01 to 20 entered in a certain order. How many different security codes are possible with this system Answered by Penny Nom. 





The spread of a rumor 
20120409 

From Roohi: The function f(t) = a/(1+3e^(bt)) has also been used to model the spread of a rumor. Suppose that a= 70 and b=3 0.2. Compute f(2), the percentage of the population that has heard the rumor after 2 hours. Compute f'(2) and describe what it represents. Compute lim t approaches infinity and describe what it represents. Answered by Penny Nom. 





Sales as a function of advertising 
20101208 

From Adori: The sales S(in thousands if units) of a product after x hundred dollars is spent on advertising is given by S=10(1e^kx). Find S as a function of x if 2500 units are sold when $500 is spent on advertising. Answered by Penny Nom. 





A punchcode lock box 
20101129 

From Doug: I am a real estate agent that uses punchcode lock boxes on houses to store the keys. I need to crack the code on one of our boxes, so I need a list of the possible combinations.
Rules:
4 digit code
Numbers 09
Each number can only be used once
Order of the numbers does not matter.
With advice from this site, I have calculated that there should be 210 possibilities.
10x9x8x7 (5040) gives me the total number possibilities and 4x3x2x1 (24) gives me the total number of ways to arrange those numbers.
So if I divide the possibilities by the arrangement, I get 210. (5040 / 24 = 210) GREAT!!!
Now, how do I develop a list of those 210 combinations?
Thanks for your help. Answered by Robert Dawson. 





A linear relationship 
20100622 

From Laura: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $300 to drive 480 miles and in June it cost her $460 to drive 800 miles.
Question: Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. Answered by Robert Dawson. 





My phone is "sim locked" 
20100610 

From Daniel: Question from daniel:
got a phone that says sim locked, it requires 09 digit code to get in, how many combinations could there be if you could please list the possibilities, the number can be repeated. Answered by Penny Nom. 





A scale model of a city 
20100518 

From Briana: Well I have to create a three dimensional city for a geometry project and it requires us to use precise scal factor and well we want to build a medium sized city but our teacher said that If we make or buildings to high our houses would look like super small compared to the tall building were trying to figure out if we were to build a medium sized city what scale factor should we use to make the houses big enough to see and design? Answered by Walter Whiteley and Tyler Wood. 





Modelling an underpass 
20100511 

From Sue: An engineer at the Ministry of Transport is creating the plans for a new road. This road
will cross the path of a busy railway track so it will be necessary to built an underpass for this road.
This underpass will be in the shape of a parabolic arch.
The specifications include:
the road must be at least 10 m wide and it must have shoulders at least 2 m wide on either
side of the road.
there must be a clearance of 3 m over all areas of the road.
What quadratic equation could you use to model this bridge. Answered by Penny Nom. 





A three digit entry code 
20100414 

From Bryon: The entry code for the executive bathroom is a threedigit odd number
with no repeated digits. If you want to try to break in, what is the
maximum number of numbers you'll have to try?
(Remember that the threedigit numbers cannot start with zero.) Answered by Stephen La Rocque and Penny Nom. 





A model for the population of a Canadian city 
20100407 

From jess: Let t^2 represent tsquared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000? Answered by Penny Nom. 





A linear relationship 
20100224 

From Mel: This table shows the linear relationship between an aeroplane's height (above sea level) and the outside air temperature.
h (cm) 
120 
340 
480 
600 
1040 
T (degrees C) 
14.28 
12.96 
12.12 
11.4 
8.76 
Find the gradient and vertical intercept of the function. Write the formula for T. Answered by Penny Nom. 





A code on my pedometer 
20100219 

From Jacqui: Hi I need to break a code on my pedometer. I have only 3 digits 1 2 and 3 but need to fill a 5 digit code. I have tried to find answers but they seem to relate to if the digits are only used once. I can use them in any order and repeated as many times. How many possibilities are there and is there an easy way to run through them. Many thanks Answered by Tyler Wood. 





Can a line segment curve over two planes? 
20100214 

From Graham: I am working on a math fair project.
Can a line segment curve over two planes?
Such as, if I had a three dimensional L bracket and I drew a line segment
on it with a marker starting on the bottom of the L and had it curve
around the corner and up the top, would it still be considered one line
segment? Or is that two line segments?
Is there a rule that a line segment can only occupy one plane?
Thank you.
Graham Answered by Chris Fisher. 





A 3D cardboard cupcake 
20100130 

From Margaret: Hi,
I'm an art student and I'm attempting to build a 3D cupcake out of cardboard.
I want it to have a circular base of 8.5 inches and sides that are 7'' tall and slope outward so the top of the base is 29'.
The top with the frosting would be a detachable lid made from a cone with a base circumfrance of 29".
My problem is how to cut the side so they will slope out, I'm pretty sure there needs to be a curve, however I don't how to calculate the degree of it.
Ideally I want the sides to be a single piece of cardboard.
I also don't know how to calculate the arc needed to make a cone who's circular base's circumfrence is 29''.
Thanks,
Margaret Answered by Stephen La Rocque. 





A 4digit phone code 
20100121 

From pat: my daughter can`t remember her 4digit code to unlock her phone. she is pretty sure it starts with a 4. can you help us? my brain is locked up Answered by Robert Dawson. 





Constructing a scale model 
20090927 

From Colleen: What is the formula i need to use to find out how to state a reasonable scale in the question below;
Suppose you were constructing a model that must sit on a piece of cardboard that is 22cm by 28cm. STATE THE REASONABLE SCALE that you can use to build a model to represent the following items. Determine the dimensions of the model.
a) a rectangular prism with a length of 5m and a width of 2m? Answered by Penny Nom. 





Fitting the curve y=a*exp(b*x)+c 
20090812 

From aika: Could one show me the complete algorithm and formula for finding the coefficients (a,b, and c) in exponential regression model
y=a*exp(b*x)+c Answered by Robert Dawson. 





Math in everyday life 
20090803 

From Naveen: Dear sir,
We are advised to do a project on "Mathematical modeling to solve various problems
of our everyday life/environmental related problems...... Can u plz help us by mailng some
ideas, suggestion,reference to make my project successful.... Thanking you......
Waiting for your favourable reply...... Answered by Penny Nom. 





A simple digraph 
20090323 

From Shabkhal: Show that the sum of in degrees of all the nodes of a simple digraph is equal to the sum of out degrees of all its nodes and this sum is equal to the number of edges of the graph. Answered by Victoria West. 





The scale for a model train 
20090313 

From Shelly: Lindy is planning to build a model of a train using a scale where 2 inches represents 25ft. If the train is 60 feet long, what is the length in inches that Lindy should build the model of the train? Answered by Stephen La Rocque and Penny Nom. 





A four digit passcode 
20090112 

From john: i have a machine at home that has a four digit passcode and the numbers range from 1 to 4 how can i get all the ways those numbers can be used Answered by Harley Weston. 





A wooden deck around a pool 
20090109 

From lupio: a 20' pool is surrounded by a 3' wood deck, find the amount of material needed for the project Answered by Robert Dawson and Penny Nom. 





Zip codes, postal codes and 5 digit codes 
20080708 

From Mike: Sorry if you have answered this before but I don't understand the explanations I have seen.
How many possible combinations are in a 5 digit code (like a Zip Code). Is there an equation that can be used for this type of question? Answered by Penny Nom. 





The mean, the median and the mode 
20080623 

From Crystal: Hi my name is Crystal,
My question is
under what circumstances will the mean, the median, and the mode all have the same value? Answered by Stephen La Rocque and Harley Weston. 





A linear model 
20080509 

From Shelby: How would you write a linear model to represent the population of a city that has a population of 547,725 and a growth rate of 25,195 per year with t represents the number of years since 1994? Answered by Penny Nom. 





Break this code 
20080416 

From Kim: The most common letter used in the English Language is E. The next is T. Vowels O,A and I are the next most common;then comes the letter N.
Use this information to break this code.
DMRA EXCEFX GC RCQ JRCL QBMQ QBX NQOGA CS DMQBXDMQTUN UMR BXFE QBXD WXMG CW LWTQX M UCGX Answered by Claude Tardif. 





A three dimensional object 
20080304 

From Briana: what is the 3d term for pentagon? like a circle is a shhere? Answered by Penny Nom. 





A 4 digit passcode 
20080216 

From Rob: If there is a 4 digit passcode with only 6 punch in symbols, how many possibilities are there and what are they?
symbols are: Y, X, RB, RT, LB, LT. Please get back to me, thanks for your time and help. Answered by Stephen La Rocque. 





Zip codes 
20071203 

From Natalie: How many 5 digits zip codes are possible if digits can be repeated? Answered by Penny Nom. 





How many three button codes are possible? 
20070823 

From kim: A home security device has ten buttons and is disarmed by pushing three buttons in sequence. How many three button codes are possible if each button can be pushed more than once in the code? Answered by Stephen la Rocque. 





I need all the possible 4 digit combinations... 
20070718 

From Jo: I have lost the code for my car stereo. I need all the possible 4 digit combinations using the numerals 1 2 3 4 5 and 6. Thank you Answered by Penny Nom. 





A model for a building 
20070717 

From Carl: A model for a building is 50 centimeters long, 38 centimeters wide, and 225 centimeters tall
on model 1 centimeter represents 2.5 meters.
I need to find the volume of the actual building in cubic meters,and the surface area of the building including
ceilings and floors. round to the nearest tenth of a square meter. Answered by Harley Weston. 





Five button push lock 
20070706 

From Jeffrey: We have a 5 button push lock and we were wondering how many different codes were possible in this situation. In this lock each button can only be pressed once (ie it's not a numbered key pad) and order matters. How would we find out the # of possible codes? Answered by Stephen La Rocque. 





The "mode" of a set of numbers 
20070606 

From Anthony's mom: we have a graph: Kindergarten has 1, 1st has 5, 2nd has 4, 3rd has 3
is the mode "1st grade" because there are more children in that grade? Answered by Stephen La Rocque. 





Using a stem and leaf plot 
20070522 

From Maegan: The students in Mr.Smiths PE class collected data on the number of sit ups the students were able to do in three minutes. Use the data to create a stem and leaf plot. What is the median for the class data? range? mode? Answered by Penny Nom. 





Can you have median < mode < mean? 
20070411 

From Kaliela: Can the Median > mode > mean?
Can the Mean > Mode > Median?
I don't think either of these can occur but I'm unsure why? Answered by Penny Nom. 





A missing observation 
20070402 

From destinee: please help me my problem is 5,11,19,3,15,17,5,n find n given the following info.range:16 mode:5 median:8 mean:10 what the heck is the answer Answered by Penny Nom. 





A scale model 
20061130 

From Adrianna: 1) A model of a storage compartment is to a scale of 1:40. If the surface area of the model is 25 square centimeters, what is the surface area of the actual storage compartment?
a) The storage compartment in the last question has an actual volume of 8 cubic metres. What is the volume of the model? Answered by Penny Nom. 





The perimeter of a regular octagon 
20060420 

From Martin: I would like to make an octagon out of 2x4 lumber. I know that the lumber needs to be cut at 67.5 degree angles, but how do I determine the length of each piece if I want to make, say, a 2.5 ft diameter octagon? Answered by Stephen La Rocque. 





A scale factor 
20060325 

From Jackie: I need a formula or step by step help to show my child how to find missing dimensions for example: The scale factor for a model is 10 inches = ________ feet
Model 39.7 in
Actual 11.9 ft Answered by Penny. 





A train model is created using a scale of 1:60 
20060101 

From Jennifer: An "n gauge " train model is created using a scale of 1:60. If an actual train engine, the "K4" an early twentiethcentury engine,is 45 feet long, what is the length of an "N gauge" model of the engine in inches? Answered by Penny Nom. 





A 4digit access code 
20050102 

From Missi: I need to find the 4 digit number to access my voice mail. These numbers will be 09 & numbers can be repeated. Could you provide me with a list of possibly combinations? If not, do you know anywhere that I could get a list of combinations so I don't have to write it all down? Answered by Harley Weston. 





Modelling monthly temperature with a cosine 
20041225 

From Regis: The average monthly temperature for a location in Ontario as a function of month number can be modelled using the equation y = a cos[k(t + b)] + d. Answered by Harley Weston. 





An ODE 
20041110 

From David: I have a question that i really cant do, it is as follows:
The ODE dy/dx + 0.5y = 0.5e^(1.5x) ; y(5) = 2
Solve the ODE subject to the given condition using exact methods and evaluate the solution y for x = 5 x=5.2 x=5.4 x=5.6 x=5.8 x=6 Answered by Harley Weston. 





Diagonals in a regular dodecahedron 
20040515 

From Joshua: A dodecahedron has twelve faces, all of which are regular pentagons. Three edges meet at each vertex of the dodecahedron. An interior diagonal is a segment connecting two vertices such that the segment is not an edge or along a face of the dodecagedron. How many interior diagonals does a regular dodecahedron have? Answered by Penny Nom. 





Two modes 
20021212 

From ali: I have a math assignment to pick the mode in a set of data. 12 and 21 both appear twice in the data set. What is the mode? Answered by Penny Nom. 





Mean, median and mode 
20020908 

From Ramona:
 How do you calculate the mean, median, and mode?
 what are each of their definitions?
Answered by Leeanne Boehm. 





Sanding a wooden block 
20020907 

From Wanda: If a wooden block, 2in height, 3in width, and 6in length is sanded and 1/8 of an inch is removed from the top and from the bottom, how much is the volume of the block decreased? Answered by Penny Nom. 





The Dugout, Don's Basement, Cd Corner,... 
20020430 

From A student: The Dugout, Don's Basement, Cd Corner, Harry's Deli, Bill's Software, Anne's Footwear, and Joanne's House cleaning. The gift certificates are each in multiples of $5. There is a $100 range in the value of the gift certificates, which start at $25. The mean value of all seven gift certificates is $80, and the median and mode are both $70. The certificate from The Dugout is worth the most and the one from Joanne House cleaning is worth the least. The total value of the gift certificates from CD Corner, Harry's Deli, and Anne's Footwear is $270, but Anne's Footwear certificate is worth $50 more than the one from Harry's Deli. The Cd Corner gift certificate is equivalent to the mean for this group of three. What is the value of the gift certificates from each store? Answered by Penny Nom. 





The best linear model 
20010729 

From Rebeca: I am a student (senior) summer hire working for Dept of the Army Resource Management. I've been assisting the Analyst in developing a model to predict training costs. The technique we used was simple linear regression. Now I've been asked for my opinion in choosing the best model I feel is better. I've chosen #1. Garrison Training but I want a second opinion before I give my choice. I've taken basic statistics last year in high school and will probably be taking more this year. Could you look over the information and give me a reason my choice would not be best? The dep variabley, is Training costs in dolars per day. Model  Ind Variable X  a  b  r  sy.x  1.  Garrison Training  126.31  0.982  0.9055  117.2  2.  Local Training  212.16  1.37  0.7937  142.7  3.  Man Rig Area  116.38  2.47  0.6481  175.6  4.  Major Training  346.12  4.67  0.7280  167.2  Answered by Andrei Volodin. 





Conservation, consumption and population growth 
20010604 

From Steve: I'm trying to quantify the relation between conservation/consumption and population growth. For instance let's consider California: The 2000 census states that California's population grew from 29,760* in 41990 to 33,871 in 42000. I want to find r or rate of growth per year. Based on the exponential growth formula for population growth: . . . Answered by Penny Nom. 





Toy bricks 
20010513 

From Sarah: A regularsized brick weighs 4 kilograms. How much will a similar toy brick, made of the same material, but all of the same dimensions of which are four times smaller, weigh? The 300metre tall Eiffel tower is made of steel and weighs 8 000 000 kg. An exact replica, made of the same material, weighs 1 kg. How high is the replica Answered by Penny Nom. 





What is the difference between Mean and Average? 
20001213 

From Julie: What is the difference between Mean and Average? My thinking is the average, is the equal to the sum of all numbers divided by the number of numbers added together. But the mean, I think should be calculated by adding the largest and smallest numbers in the set and them dividing by 2. (which is the point where 1/2 the numbers are higher and 1/2 the numbers are lower) Answered by Patrick Maidorn and Penny Nom. 





A zip code problem 
20001026 

From Rob Mathis: Find the zip code of a place in a county so that the product of it and the zip code of another place in another county of the same name, but in a different state, is an exact multiple of the number 123456789 Answered by Claude Tardif. 





Mode 
20000922 

From James Barton: I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others. Answered by Claue Tardif and Harley Weston. 





A model area 
19991215 

From John Ost: Hello, I am a college student taking an elementary math course I need if possible assistance to developing an area model 36 x 25 that shows each of the four separate partial products. I must know how to do the computation 36x25 showing each of the four partial products separately, and indicate how each corresponds to the drawing that is required of the area model. Answered by Penny Nom. 





Mean, median and mode 
19991207 

From J William Morning: Using the data values 2,2,10,6,5, determine the median, mode and mean. Answered by Penny Nom. 





Linear models 
19991109 

From Helen Moreno: What is a linear model? Answered by Harley Weston. 





Mean, median and mode 
19991106 

From Rick: I have five number places and the mean and median are both "0". The mode is greater than the mean. The sum of the absolute values of all of the numbers is 20. The smallest number is 4 less than the next smallest number. What are the five numbers. (negative integers can be used) All of the numbers are integers. Answered by Penny Nom. 





Platonic Solids Surface Area 
19981202 

From Rachel Bidwell: How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch Answered by Harley Weston. 

