







Alex rents a car for one day 
20191031 

From Arshia: Alex rents a car for one day. The charge is $25 plus $0.20 per mile. Alex wants to spend exactly $110. How many miles can he drive? Answered by Penny Nom. 





A tube through a board at 45 degrees 
20190615 

From Guy: I need to insert a tube 5/8" diameter into a board at a 45 degree angle. What size hole must I drill for the tube to fit snugly? Answered by Harley Weston. 





A car on a rough road and a concrete road 
20170827 

From Ken: A car is driven on a rough road at a speed of 25km and then on a concrete road with a speed of 70kph. The car has 5.5 hours to travel 225km. How long did the car travel on concrete road? Answered by Penny Nom. 





Baseball Cards 
20170420 

From Raquel: A minor league baseball team gave away baseball cards to each person entering the stadium. One group receives 28 baseball cards. A second group received 68 baseball card. If each person entering the stadium receive the same number of cards, what was the greatest possible number of baseball cards that each person could have received? Answered by Penny Nom. 





Renting an electric cart 
20170107 

From Desiree: Vacation Rentals rents electric carts for travel on their grounds. The economy plan rents
carts for $26 per day and the premium plan rents a carts for $12 per day plus a one time fee of $126.05
For how many whole days would it be cheaper to rent from the economy plan then from the premium plan? Answered by Penny Nom. 





A car chase 
20160925 

From Ms.: Car 1 is traveling down the road at 50 mph and passes Car 2 is
sitting on the side of the road. Car 2 needs to catch Car 1 one half mile
down the road. How fast must Car 2 drive to catch Car 1 if Car 2
waits 10 seconds before pursuing Car 1?
Yes, the assumption is that the Car 2 can accelerate from a standing position and over take Car 1 rate. What is the answer or formula for this type of question?
Respectfully
Befuddled Mom? Answered by Penny Nom. 





How fast and how far must Car 2 travel before catching Car 1? 
20160925 

From Ms.: Car 1 is traveling down the road at 50 mph and passes Car 2 is
sitting on the side of the road. Car 2 needs to catch Car 1 one half mile
down the road. How fast must Car 2 drive to catch Car 1 if Car 2
waits 10 seconds before pursuing Car 1?
Yes, the assumption is that the Car 2 can accelerate from a standing position and over take Car 1 rate. What is the answer or formula for this type of question?
Respectfully
Befuddled Mom? Answered by Penny Nom. 





Carlos, Mark, Jeremy, and Alan collect Yugioh cards 
20160808 

From justin: Carlos, Mark, Jeremy, and Alan all collect Yugioh cards. Mark has twice as many cards as Jeremy. Carlos has 3 times as many cards as Jeremy, and Alan has collected 12 less than 3 times as many cards as Jeremy. Together the four players have collected 456 cards. How many does each person have? Answered by Penny Nom. 





A cubic equation 
20160725 

From Chinmay: x³2x²7x+5 Answered by Penny Nom. 





A two car competition 
20160202 

From Christian: Question: Two cars are racing to a fixed point and back. One car travels 70 MPH both ways
While the other travels 60 MPH there and 80 MPH back, which car won the race?
It is not a tie. Answered by Penny Nom. 





Dealing cards to Melissa and Robert 
20150324 

From Karena: 92 cards in all. Melissa has 3 times as many cards as Robert. How many cards does Robert have? Answered by Penny Nom. 





4 card hands 
20141102 

From Ronaldo: How many Mus hands (combination of 4 cards allowing repetitions)
can be made from a deck containing 8 types of cards?
RRRR, RRRC, RRRS, RRR7, RRR6, RRR5, RRR4, RRRA,
RRCC, RRCS, RRC7, RRC^, RRC5, RRC4, RRCA,
RRSS, RRS7, etc.
I think 330. If so, what is the formula? Answered by Penny Nom. 





A car passing a bus 
20140824 

From Athish: the driver of the car is travelling at 36 km/hr and spots a bus 80 m ahead of him after 1 hr the bus is 120 m behind the car what is the speed of the bus Answered by Penny Nom. 





Selecting a card 
20140216 

From Akarsh: Cards numbered 1 to 1000 were put in a box.Ali selects cards at random.What is the probability that Ali selects a card containing at least one'3'? Answered by Penny Nom. 





Sharing in a car rental 
20130409 

From Marilyn: 8 persons are planning to share equally the cost of a rental car.
If 1 person withdraws from the arrangement and the others share
equally the entire cost of the car, then the share of each of the
remaining persons is increased by? Answered by Penny Nom. 





Driving a rental car 
20130313 

From teresa: Driving a rental car x miles cost y= 0.25x + 25 dollars.
(a) How much would it cost to rent the car but not drive it?
(b) How much does it cost to drive the car 1 additional mile?
(c) What is the yintercept of y= 0.25x + 25? What does it represent?
(d) What is the slope of y= 0.25x + 25? What does it represent? Answered by Penny Nom. 





Drawing cards from a standard 52card deck 
20120707 

From Fatima: My daughter has to complete the project in probability chapter.Her gave her a complete probability chapter and told her to do all the problems.Out of them some questions I am not getting
The question is like this please give me a detailed explanation.
When drawing cards without replacement from a standard 52card deck, find the maximum number of cards you could possibly draw and still get
a. fewer than three black cards
b. fewer than six spades
c. fewer than four face cards
d.fewer than two kings Answered by Penny Nom. 





Two cars in a race 
20120130 

From Christine: In a car race, the speed of one car is 120kph and the other car is 105 kph. If the faster car finished the race 20 mins before the slower one, what was the distance of the race? Thanks for the answer and the previous answer to my question. Answered by Penny Nom. 





Decartes' circle theorem 
20110907 

From Joseph: Given 3 circles of diameters 50, 55, and 60 units,
Place them externally tangent.
What is the diameter of the outer circumscribing circle,
tangent to all 3 circles? I can attach a pdf if this description is not clear.
Not urgent, this has nothing to do with current assignments,
just wondering if I have developed the best methods? Answered by Chris Fisher. 





Geometry Related Careers 
20110901 

From Richard: Good morning,
I am hoping to find a list of careers that would relate to geometric constructions and tessellations.
I have searched the internet some and some of the sites I have found are a bit questionable or dated. Are there sites that Math Central would recommend?
I could not find anything when I did a search on the site.
Thanks in advance,
RVD Answered by Walter Whiteley. 





Two piles of cards 
20110709 

From maribie: a standard deck of playing cards contains 26 black cards and 26 red cards, or 52 cards in all. a deck is randomly divided into two unequal piles, such that the probability of drawing a red card from the small pile is 1/3. at the same time, the probability of drawing a black card from the larger pile is 5/14. how many cards are in the larger pile? Answered by Penny Nom. 





What is the speed of each car? 
20101104 

From Jennifer: two cars are 420 miles apart and traveling towards each other along the same road. They meet in 3.5 hours. One car is traveling 15mph slower than the other. What is the speed of each car?
This must be solved using a system of equation, I have no idea? Answered by Stephen La Rocque. 





A train passes a car 
20101024 

From Mary: A train, whose speed is 75 mph, takes 3 minutes to pass a car that is going 60 mph in the same direction. How long is the train? Answered by Stephen La Rocque. 





The angles in an mgon and genrealizations 
20101016 

From Michael: Hello:
In answer to a student's question, someone named Penny from
your organization provided a proof that the sum of the interior
angles of a triangle in the plane is pi radians (or 180 degrees).
I am interested (and I'm sure many other people would be too) in
3 potential generalizations of this basic fact in plane geometry: Answered by Walter Whiteley. 





Electronic cars around a circular track 
20101011 

From Taylor: Cory and Melissa are racing electronic cars around a circular track. They begin at the same time going in the same direction. Cory's car completes a revolution in 35 secs, while Melissa's car completes a revolution in 30 secs. How long will it take them before both cars reach the starting point again simultaneously? Answered by Stephen La Rocque and Penny Nom. 





Two cars 
20100930 

From Amanda: Two cars, 142 miles apart, start moving towards each other at the same
time. One is moving 3 times as fast as the other. If they meet 1.7 hrs
later, find the average speed of the slower car in miles per hour? Answered by Penny Nom. 





Two cars on a circular track 
20100812 

From david: If two cars starts to drive at point 1 and go in a circle when will they meet?
(one cars speed is faster the other ) all I need is a formula Answered by Tyler Wood. 





More on carbon 14 dating 
20100526 

From Malachi: I am doing carbon 14 dating and i figured out the rule for taking the percent of the original C14 to figure out how old it is. how do I work the equation the other way around to find the percent remaining, from how long ago the objects organic mater died Answered by Harley Weston. 





When are the cars exactly 40 miles apart? 
20100501 

From Maryanne: A car traveling east at 45 mph passes a certain intersection at 3pm. Another car traveling north at 60mph passes the same intersection 25 minutes later. To the nearest minute, figure out when the cars are exactly 40 miles apart. Answered by Penny Nom. 





A 12 foot by 12 foot room 
20100420 

From Dominique: The room is 12ft by 12ft. How many yards must be purchased for the carpet? Answered by Penny Nom. 





How many 5 card hands in a deck of 52 have 2 aces and 3 other cards? 
20100323 

From Travis: How many 5 card hands in a deck of 52 have 2 aces and 3 other cards? Answered by Penny Nom. 





Probability, counting and cards 
20100115 

From Julie: Hello,
 Select a card from the deck(card deck of 52 cards). Place the card back in the deck. What is the probability that both cards will be black? Is it 25/104, 24%?
 Select a card from the deck. Do not replace the card. Select another card. What is the probability that a red and a face card are the two cards you selected? Is it 2/221, .9%?
 Remove the red cards from the deck and assume that the remaining cards have been shuffled: select a card from the remaining deck. Place the card back in the deck. Select another card. What is the probability that both cards will be black? Is it 26/26 x 26/26= 1 x 1 = 1 , 100%?
Select a card from the remaining deck. Do not replace the card. Select another card. What is the probability that a red 3 and a face card are the 2 cards you selected? Is it 0/26 x 6/26 = 0, 0%?
 Seperate 12 face cards from the rest of the deck. Assume that the face cards have been shsuffled. Select 3 cards from the pile of face cards. How many different arrangements can be made by selecting 1 of each card (jack, king, queen) from the pile? is it 1/4 x 1/4 x 1/4 x 1/4 = 1/64?
 How many different ways are there of selecting the queen of clubs, then the king of diamonds, and then the jack of hearts from the pile? Is it 1/12 x 1/12 x 1/12 = 1/1728?
Answered by Robert Dawson. 





How fast is the distance between the two cars decreasing? 
20091208 

From Jenny: Two cares are on a collision course toward point P. The paths of the two cars make a 30 degree angle with each other. The first car is 40 km from P, and traveling toward P at 16 km/hour. The second car is 50 km from P, traveling at 20 km/hour. How fast is the (straight line) distance between the two cars decreasing. (Hint: Law of Cosines) Answered by Harley Weston. 





A truncated cone 
20091111 

From Lucian: I need to calculate the bottom inside diameter of a truncated cone.
The top insdie diameter is 1450mm.
The material is 6mm thick
The cone angle is 20 degrees
The slant length is 152mm
I would like a formula so that I can build a spread sheet Answered by Penny Nom. 





The cardinality of the prime numbers 
20091107 

From Justin: Hello there, I was just wondering since the number of primes is infinite,
are they equal to infinity or Alephnull?
Justin Answered by Robert Dawson and Victoria West. 





Cardinality of infinite sets 
20090901 

From Brian: I was reading an answer to a question on your site regarding infinite sets (http://mathcentral.uregina.ca/QQ/database/QQ.09.01/carlos1.html), and I think they may have got the answer wrong.
I his example, he claims that the set of real numbers BETWEEN 0 AND 1 is larger than the set of positive integers.
Please correct me if I am wrong, but I believe those two sets are  pardon the expression  equally infinite. For any integer, there is a corresponding real number between 0 and 1, and vice versa.
For instance, using the decimal as a "mirror", you can create a mirror image of any real number between 0 and 1 as an integer (i.e. 0.1234 gets mirrored as the integer 4321  I could write it out algebraically, if you want, but you get my point)
Am I wrong?
Thanks,
Brian Answered by Victoria West. 





Two cars 
20090809 

From Jayna: If a car was traveling 20mph east and another car was traveling 30mph west,
assuming they were 300 miles apart, at what point would they collide at the center? Answered by Penny Nom. 





InfiniteDimensional Spaces 
20090626 

From Justin: Hello again, I was also just wondering (in Hilbert Space and Function Space) are there infinitedimensional spaces larger than each other in terms of cardinality? Thanks a lot for your help again!
All the Best,
Justin Answered by Victoria West. 





5 spades 
20090515 

From Dee: From a standard deck of 52 cards, how many cards would you have to draw, without looking at them , to be absolutely certain (a probability of 1) that you had 5 spades? Answered by Robert Dawson. 





A car loan 
20090506 

From Cindy: A person takes out a car loan in the amount of $11,170.00 @ 4.5% interest. The person makes 17 payments of $500.00, then for the 18th payment (this person 'finds' some $) and pays off the whole thing. How much was their last (18th) payment? How much overall did they pay in principle? and interest?
The person who made the initial loan then takes $11,156.25 and places it into a High Interest Savings Account @ 2.25% annually on Nov 18, 2003. How much is now in the High Interest Savings Account if no futher funds have been added to the account and no withdrawls have been made?
Thanks for your help with this. I have been trying on and off for 3 years to figure this out.
C Answered by Robert Dawson. 





The odds against drawing a red queen 
20090315 

From tabyia: 7. The common deck of 52 cards has 26 black cards (13 spades and 13 clubs) and 26 red cards (13 hearts and 13 diamonds). Each suit consists of ace, king, queen, jack, ten, nine, eight, seven, six, five, four, three and deuce. 13in all.
A single card is chosen at random. Find the odds against its being a red queen?
How many cards will I have to draw to be absolutely certain that I have drawn three black cards Answered by Harley Weston. 





More on cardinal numbers 
20090218 

From Justin: Hello again, I was just wondering that since the rules of Cantor's cardinal numbers in set theory do not apply to the infinity obtained by limits in calculus (ex. x>0, y=1/x=infinity), does that mean that this infinity is the largest quantity in both calculus and mathematics?
Justin Answered by Robert Dawson. 





Infinity and Set Theory 
20090217 

From Justin: I was just wondering is the limit x>0, y=1/x=infinity, the biggest uncountable infinity according to Cantor's cardinal numbers in set theory?
Justin Answered by Robert Dawson. 





Cantor's cardinality 
20090216 

From Justin: Hello, I was just wondering why the infinity from real numbers is smaller than Beth Two in the context of Cantor's cardinality set theory?
Justin Answered by Robert Dawson. 





A semi circular room 
20090211 

From Taylor: being 450pi (the area of a semi circle)
how much money would it cost to lay carpet at $2.57 per foot???
if the area of a semi circular room is 450 pi ft
then what is the volume being that the diameter is 60 feet
and the ceiling is 16 feet tall Answered by Robert Dawson and Penny Nom. 





An octagonal carpet 
20090124 

From Larry: I am cutting a piece of carpet that is 9 feet x 9 feet and need to cut it into an octagon. How far do I cut from the corner of the square. thank you for any help. Answered by Harley Weston. 





A seven card poker hand 
20090112 

From Sean: from a standard card deck, seven cards are chosen at random.
find the probability that the set chosen contains exactly three of each
of two different face values.
the second part of the problem asks the probability that the card hand contains
exactly three 2's and exactly three 5's. Answered by Robert Dawson. 





(a x b) intersect (b x a) 
20090108 

From sean: is it possible to have two sets such that
n((a X b) intersect (b X a) =3 Answered by Harley Weston. 





A five card hand of playing cards with all 4 tens 
20080625 

From shari: of the 2598960 different five card hands from a deck of 52 playing cards. how many would contain all ten's? Answered by Janice Cotcher. 





Escort cards on a rectangular table 
20080613 

From Susan: What size rectangular table will we need to put 230 2" X 3.5" escort cards on for my daughter's wedding reception with a spacing of .5 inch between them on all sides? Thanks so much for your help Answered by Penny Nom. 





Rectangular cards on a round table 
20080611 

From Susan: How many 4" X 3.5" wide escort cards will fit on a 48" diameter table. These are for my daughters wedding. I have already added the extra spacing between the cards into the size of the cards.Thanks for your help Answered by Janice Cotcher and Harley Weston. 





How many different ways can cards fall when shuffling? 
20080609 

From Twyla: How many different ways can cards fall when shuffling? In other words,
if you have 52 numbers, each one unique, how many different ways can
they be arranged, using each number only once? Answered by Penny Nom. 





x^36x^2+3x+5=0 
20080522 

From faiz: x36x2+3x+5=0 Answered by Janice Cotcher and Harley Weston. 





A car tire full of concrete 
20080327 

From robert: I want to build a volleyball net support. I am using a car tire 24"odx16"id filled with concrete. how much will this weigh? thanks Answered by Penny Nom. 





A ton of carbon dioxide 
20080311 

From claire: I want to know the size of a box if it contained a ton of Co2? Answered by Stephen La Rocque. 





A new carpet 
20080228 

From Rhiannon: The Gatlins are buying a new carpet for their house. They need about
1,175 square feet of carpet. The carpet they buy is sold by the square yard.
Estimate the number of square yards of carpet they need. Do I use the
formula to find the volume or are? Answered by Penny Nom. 





Maximum volume of a box 
20080115 

From Rajesh: A square piece of a cardboard of sides ten inches has four equal peices are removed at the corners, then the sides are turned up to form an open box. What is the maximum volume such a box can have? Answered by Stephen La Rocque. 





Protecting a carrot patch 
20080103 

From Kate: A farmer has a problem with rabbits and skunks
in his rectangular carrot patch that is 21m^2 in area. Determine the
dimensions that will require the least amount of fencing if a barn can
be used to protect one side of the garden. Answered by Stephen La Rocque. 





Two cars drive in opposite directions 
20071223 

From dale: 2 cars starting from the same point in opposite direction on a straight highway drove 6 miles then turn left and drove 8 miles. How far apart are the cars? Answered by Penny Nom. 





The largest number you can add ... 
20071026 

From Dryden: What is meant by asking what is the greatest number you can add to that number without having to regroup in any place? Answered by Penny Nom. 





How many sq yards did i use? 
20071003 

From Rose: i used 12 x 19 of carpet. how many sq yards did i use? What is the formula for this? Answered by Victoria West. 





Three circles 
20070929 

From Kevin: 3 given circles of R80, R56 & R24 are all in contact. The 2 smaller ones are inscribed in the big one.
Find by calculation or graphically (both if possible) the radiusof a 3rd circle which will be in contact with all 3 given circles. Answered by Chris Fisher. 





Who was the mathematician that united algebra and geometry? 
20070508 

From Victor: who was the mathematician that united algebra and geometry Answered by Penny Nom. 





Find the amount of carpet you need. 
20070411 

From lakisha: you want to buy carpet for a room that is 15 feet wide and 18 feet long. Find the amount of carpet you need.
What information do you need to know to solve this problem. Answered by Penny Nom. 





exponential decay of Carbon14 
20070312 

From Christine: How do I set up the exponential decay formula for Carbon 14 with an initial amount of 1500 grams. Answered by Stephen La Rocque. 





Write the digits 1 to 9 on index cards, ... 
20061019 

From Kim: Write the digits 1 to 9 on index cards, arrange the cards to form three 3digit numbers (using each card only ONCE). The third number is the sum of the first two numbers ** how many different ways can you do this?? ** Answered by Penny Nom. 





Plotting coordinates on a number plane 
20060908 

From Victor: I need to plot coordinates (0,2), (2,2), (2,0), and (0,0) on a number or coordinates plane, I am not sure how to do this, and get lost after the first point, can you please help? Answered by Penny Nom. 





Building an octagonshaped deck 
20060711 

From Maurice: I'm a landscaper and one of my customers wants me to build her an octagon shaped deck in the back yard that has a measurement of 16 by 16. I'm not sure of the way to measure for materials required. It will be built with 2 by 6 lumber with a half inch spacing between the 2 by 6. Answered by Stephen La Rocque. 





Buying some carpet 
20060605 

From Russ: My room is 24 ft. long and 17 ft. wide. I need to know how many square feet are in 1 yd.² Answered by Penny Nom. 





Probability of getting their stories straight 
20060405 

From Amy: Four students drive to school in the same car. They claim they were late because they had a flat tire. Assuming they did not have a flat tire what is the probability that they all would choose the same tire if asked which one was flat. Answered by Stephen La Rocque. 





Polar to Cartesian coordinates 
20060115 

From Linden: How do you convert six units at 30 degrees Polar Coordinate into a Cartesian Coordinate? Answered by Penny Nom. 





One car leaves a spot traveling at 100 km per hour 
20051228 

From Jason: One car leaves a spot traveling at 100 km per hour. The second car leaves the same spot 15 minutes later and traveling at 120 km per hour. How long does it take for the second car to catch up to the first car? Answered by Penny Nom. 





How many three digit numbers can I make from the four cards 
20050312 

From Sue: I have four playing cards 2,3,4,5 of hearts. How many three digit numbers can I make from the four cards. Answered by Penny Nom. 





Select a card from the deck. 
20041202 

From Heidi: Select a card from the deck. What is the probability that this card will be red? Show the number of expected outcomes versus the number of total possible outcomes. What type of event does this represent? Answered by Penny. 





Converting coordinates 
20041025 

From Allen: I am trying to help my son with his home, but I don't remember these conversions. Please help.
1. Convert the following coordinates
Cartesian x = 7, y = 24
2. Convert the following coordinates
Polar r = 4, theta = pi / 3 Answered by Penny Nom. 





A new way to measure randomness 
20031231 

From Stephanie:
Last year, I did a science project in which I asked, "Which shuffles better, an automatic card shuffler or shuffling by hand?" To measure this I decided the "best" shuffler was the one to become random first. Last year, to measure randomness, I numbered cards 152 and had the subjects shuffle them until they broke up the rising sequences or reached 10 shuffles. (Usually 10 shuffles came first...) Anyway, I did the same thing with the automatic card shuffler, and, as hypothesized, the automatic card shuffler randomized the deck first.
This year, I have decided to continue the project. The problem is, I need a new way to measure randomness without the use of fancy computers or something. I have searched the Internet, I have posted my query on websites based on math, and I have searched the local library.
I have found many useful things on the Internet, but none of them can tell me a new way to measure randomness. I cannot do a perfect shuffle, and I am not terribly gifted in the art of using computers. If you have any information (anything will help) or advice, I would be greatly obliged. Answered by Andrei Volodin. 





Math jobs 
20031212 

From Veronica: Do you know a couple of jobs I can get when I am older in Math? Answered by Harley Weston. 





Two cars 
20030709 

From Nicole: Two cars start off at the same point on a striaght highway facing opposite directions. Each car drives 6 miles, talkes a left turn, and drives for 8 miles. How far apart are the two cars. Answered by Penny Nom. 





A radio controled car 
20030608 

From Robert: I have a radio controled car (scale size 1/43). This car can travel 490 ft. per minute. I would like to know how fast that is at that scale size in miles per hour (and Kilometers per hour)? Answered by Penny Nom. 





Two piles of cards 
20030524 

From Sam: A standard deck of 52 cards (26 red, 26 black) is separated into two piles, not necessarily equal in size. The first pile contains seven times as many black cards as red cards. The second pile contains a number of red cards that is a multiple of the number of black cards in that pile. How many red cards are in the first pile? Answered by Penny Nom. 





A royal flush 
20030324 

From Vikki:
A poker hand consists of 5 cards selected randomly from an ordinary deck of cards: find the probability of a ROYAL FLUSH : the 10 , jack, queen,king and ace of the same suit. I was thinking somewhere along the lines of: *the number of ways to get the suit is 4C1 *the number of ways to get a 10 out of the 13 cards etc.... ...but Im not sure I am going about this the right way, could you help? Answered by Andrei Volodin. 





What is larger than infinity? 
20030112 

From Dana: What is larger than infinity? Answered by Claude Tardif and Harley Weston. 





Painting a car 
20020924 

From A student: Dan can paint a car in 4 hours. Luke can pain the same car in 6 hours. Working together, how long would it take them to pain the same car? Answered by Penny Nom. 





Equivalence relations on a set of cardinality n 
20020706 

From Siddhartha: what is the no. of equivalence and transitive relations on a set of cardinality n? Answered by Penny Nom. 





Drawing cards 
20020611 

From Ed: What is the probability of drawing without replacement from a standard deck of 52 cards the following 5 card hand ...... the ace of spades, 2 tens and 2 face cards Solution 1: ^{1}/_{52} x ^{4}/_{51} x ^{3}/_{50} x ^{12}/_{49} x ^{11}/_{48} Solution 2: Using Combination theory ..... (1C1 x 4C2 x 12C2) divided by (52C5) Can you help us understand which answer is correct and why the other is not? Answered by Penny Nom. 





Day care 
20020513 

From Sonam: In many familes, both parents work. as a result, there is increasing need for day care. data was collected; and in one year in Canada, approximately 32% of children aged 0 to 11 years were in day care for at least 20h per week. (a) what is the probability, in a random poll of 60 children form the age of 0 to 11, that more than 15 children are in day care at least 20 h per week? nearest tenth of one %
ANSWER: P(children are in daycare at least 20h)= 60/60C14 = to the answer (b) what is the probability, in a random pool of 60 children that fewer than 20 are in day care at least 20 h per week?
ANSWER: P= 20/60= 33.3% stay in day care for 20h per week, I dont know if these answers are right please help me out. Answered by Andrei Volodin. 





Some 5 card hands 
20020328 

From A student: From a standard deck of cards how many 5 card hands are possible consisting of a. exactly 4 hearts
b. two cards of one kind and three of another(like a full house). Answered by Penny Nom. 





Can a infinite set be smaller than another infinite set? 
20011129 

From Carlos: Can a infinite set be smaller than another infinite set? If so why? Answered by Chris Fisher and Penny Nom. 





Cardinality of sets 
20011119 

From Tania:
 Show that the cardinality of P(X) (the power set of X) is equal to the cardinality of the set of all functions from X into {0,1}.
 Show that (the cardinality of the natural numbers set) N = NxNxN.
 Show that the cardinality of the set of prime numbers is the same as the cardinality of N+
Answered by Walter Whiteley. 





Counterclockwise 
20010914 

From Rolanda: When Descartes invented the coordinate system he decided to number them counterclockwise. Why? Answered by Chris Fisher. 





72 cards 
20010903 

From A student: What would be the probability of dealing a deck of 72 cards out in the exact orderly sequence that they were in when they were packaged after they have been throughly shuffled? Answered by Andrei Volodin. 





Buying a car 
20010606 

From Steph: How do you figure a percent. Say you want to buy a car listed for 21,500. You tell the dealer you want to pay 19,600. The dealer says they'll sell it to you for 20,450. how do you figure what the percent is between 20,450 & 19,600? Answered by Penny Nom. 





Choosing a car 
20010428 

From Ashley: THE CAR DEALERSHIP IN TOWN OFFERS 32 DIFFERENT MODELS OF VIHICLES.EACH MODEL HAS A CHOICE OF EIGHT INTERIOR COLORS,EIGHT EXTERIOR COLORS,AND ALSO THE OPTION OF AUTOMATIC OR MANUAL TRANSMISSION. HOW MANY COMBINATIONS ARE POSSIBLE? Answered by Penny Nom and Andrei Volodin. 





Cash advance 
20010328 

From A student: dulani has a new credit card. it says: you can get cash advances wherever you are. whenever you want. also if you pay off your balance in full each month for a small transaction fee, the cash is interest free. (see important information on reverse side. On reverese side it says: cash advance transaction fee: $500 or less 2.5%; $500.01 to $1000.002%; $1000.01 or more 1.5%; $2.00 minumum.
Annual percentage rater for cash advances 19.8%. dulani wants to know what a cash advance will really cost. Analyze the cash advance terms given here. how much would he pay for a $20 cash advance? What about a $450 cash advance? What annual interest rate are these charges equivalent to? choose other amounts. determine cost and annual ratees for these as well. make recommendations to dulani. Answered by Penny Nom. 





The price of a carpet 
20010301 

From Amber: i have to calculate the square footage of carpet for me room and im not quite sure how to do that. the carpet is $2.08 per sq. ft. and my room is 12x11ft. Answered by Penny Nom. 





Books and cars 
20010213 

From Aquilya:
 A pile of books is 96.08cm. If each book is 0.8cm thick. How many books are in th pile?
 2. A car travels 9.84km on 0.6 litres of petrol. How far will the car travel on 3.7 litres of petrol?
Answered by Penny Nom. 





Chris' cards 
20010211 

From A student: Chris gave Jane x cards. He gave Bety one card more than he gave Jane and he gave Paul two cards fewer than he gave Betty. In terms of x, how many cards did Chris give Bety, Jane, and Paul together? Answered by Penny Nom. 





Subsets of the natural numbers 
20010130 

From Christina: How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets? Answered by Penny Nom. 





Motivators 
20010116 

From Michelle Stapley: Do you know of any (or where I can find) student motivators for math at the secondary level? Basically any way I can motivate my students to WANT to learn math. Answered by Penny Nom. 





5 spades 
20001121 

From Matt: In a standard deck of 52 card how many would you have to draw (without looking at them) to be absolutely certain that you had 5 spades? Answered by Claude Tardif. 





A cycloid in Cartesian form 
20000920 

From Billy: The parametric equation of cycloid is given: x=r(tsint) y=r(1cost) How to eliminate t? Answered by Harley Weston. 





Review problems 
20000918 

From Dee: A card is selected from an ordinary deck of cards. What is the probability of. . . selecting 2 aces in a row? If you toss two dice, what would be your probability of the following? . . . Answered by Penny Nom. 





Math in various careers 
20000418 

From Jennifer Jones: I am a Fifth grade student researching how math is used in various careers. What kind of math is used in your career? How do you use math? Answered by Harley Weston. 





Uniting algebra and geometry 
20000416 

From Beth: Who is the mathmatician that united algebra and geometry??? Answered by Claude Tardif. 





All the roots of x^6  64 
20000415 

From Dakota: Find ALL zeros of P(x) = x^{ 6}  64 Answered by Walter Whiteley. 





Infinite sets 
20000412 

From Brian Provost: Here's the deal: There are an infinite amount of integers (1,2,3...). Agreed? There are an infinite amount of even integers, too (2,4,6...). Agreed? By convention, infinity equals infinity. Yet common sense tells us there are obviously more integers than there are even integers. Prove this to be true mathematically. Answered by Harley Weston. 





Careers after a math degree 
20000331 

From Jeanne Hyer: What type of careers can a person have with a math degree, and what is the closest thing that you have to an undergraduate degree in financial mathematics? (Administration, math, actuarial science, etc.) Answered by Harley Weston. 





A valentines project 
20000221 

From Courtney Dohoney: I was assigned a valentines project. Our job is to make a valentines card that has a math theme. On my valentines card I would like to include the set of equations that when graphed look like a heart. If you can figure out a set of equations and get it back to me I would be very happy. Answered by Harley Weston. 





A 16th century mathematician 
20000204 

From Danielle Dombrowski: My name is Danielle Dombrowski, I am in the 7th grade and my teacher gave us a riddle to figure out which mathemtician we would have to do a report on. The only problem is that I don't know what the answer is. Can you help? The riddle is "This 16th century mathematician, having predicted the day of his death, took poison to make sure it came true. Who is it?" Answered by Penny Nom. 





Cutting a carpet 
19991215 

From Heather: A rectanglular piece of carpeting is 90 inches long and 90 inches wide. How can the carpet be cut into two pieces of equal sides and shape to cover an area of 100inches? There can only be one cut and no scraps. Please show me how. Answered by Penny Nom. 





A donkey and his carrots  part 2 
19991002 

From Sarah Klink and Brenda Gamble: Does anyone know the solution of the donkey who had to carry 3000 carrots to the market which was 1000 miles away? The donkey can only carry 1000 carrots at a time and he eats one carrot every mile he walks but this is only when he is carrying carrots. How many carrots can get to the market with the donkey carrying them? Answered by Claude Tardif. 





How to carpet a room 
19990531 

From Appleby: A room which is 9X12 is to be covered with carpet but the carpet has been provided in one 8X1 piece and one 10X10 piece. The larger piece is to be cut into two pieces so that the room can be covered in carpet. Answered by Stacey Wagner. 





Question about 3rd degree polynomials 
19990423 

From Patrick Bryan: What is the general solution to the equation with the form: a*x^3 + b*x^2 + c*x + d = 0 I have once seen a solution to this a few years ago, but I do not recall if it was a general solution. What I do know, is that you could simplify this equation to: a*x'^3 + p*x' + q = 0... Answered by Doug Farenick. 





A Car Wash 
19980404 

From Lisa GotimerStrolla: Al washes a car in six hours. Fred washes a car in eight hours. How long will it take them to wash a car together? Answered by Harley Weston. 





Cos(x) Cos(2x) Cos(4x)=1/8 
19970924 

From Tan Wang: How many distinct acute angles x are there for which cosx cos2x cos4x=1/8? Answered by Chris Fisher Harley Weston and Haragauri Gupta. 





A Monte Carlo Procedure 
19970423 

From Donna Hall: A irregularly shaped object of unknown area A is located in the unit square 0<=x<=1. Consider a random point uniformly distributed over the square. Let X = 1 if the point lies inside the object and X = 0 otherwise. Show that E(X) = A. How could A be estimated from a sequence of n independent points uniformly distributed over the square? How would you use the central limit theorem to gauge the probable size of the error of the estimate. Answered by Harley Weston. 





A donkey and his carrots 
19970128 

From Emily Lind: There is a donkey who carries carrots. A farmer has 3,000 carrots to carry to the market. The market is 1,000 miles away. The donkey can only carry 1,000 carrots at a time and he eats 1 carrot every mile that he walks but this is only when he is carrying carrots. How many carrots can the farmer get to market by having the donkey carrying them? Answered by Penny Nom. 





Cardano's method 
19960311 

From Mike Gorski: What is Cardano's method for finding the roots of a cubic equation? Answered by Harley Weston. 





méthode pour trouver l'air d'un carré 
20080408 

From Mélodie: je doit trouver au moins 4 manieres différentes de calculer l'air d'un carré.
j'en ai déja trouvée 2 mais il m'en faut le plus possible...
1. longueur x largeur
2. division en triangles, puis air des triangles et multipler par
l'air des triangles Answered by Thierry Moisan. 





racine carre de 9 
20080101 

From hichem: racine carre de 9 Answered by Claude Tardif. 





Deux terrains 
20070604 

From Aurelie: Deux terrains, un rectangulaire et l'autre carré, ont la même superficie.
Si tu sais que la longueur du terrain rectangulaire mesure 40m et que le carré mesure 20m de côté, détermine la largeur du terrain rectangulaire. Answered by Claude Tardiff. 





Origine du signe racine carré 
20061130 

From Kévin: Je suis simplement un élève de 3eme très curieux et j'aimerais savoir d'où vien le signe de la racine carré (l'espece de V) c'est une question toute bete mais ma prof de math ne peu me répondre le pouvez vous? Answered by Claude Tardif. 





la somme des aires des deux dommaines 
20061106 

From Nina: Une ficelle de longeur L = 1m est coupée en deux morceaux. Avec l'un des morceaux, de longeur x, on forme un carré, et avec l'autre un cercle. A quel endroit doit on couper la ficelle pour que la somme des aires des deux dommaines obtenus soit minimale? Answered by Claude Tardif. 





Un carré ABCD 
20061031 

From Barrault: Dans un carré ABCD de coté a , avec I le milieu du cote AB je cherche a exprimer CI et CA en fonction de a en demontrant que les vecteur CA+CB=2CI comment faire? Answered by Claude Tardif. 





ABCD est un carré de 4 cm de côté 
20060306 

From Elodie: ABCD est un carré de 4 cm de côté. On découpe un peit carré AEFG d côté x. Que vaut x si l'aire de AEFG est la moitié de l'aire de ABCD? Answered by Claude Tardif. 





l'aire d'un carré 
20050224 

From Un eleve: calculer l'aire d'un carré parfait sachant que les diagonales mesurent 8 mètres
Je ne sais pas comment lui expliquer. Answered by Claude Tardif. 





Un problème de math 
20040910 

From Sophie: (V est en fait le signe de la racine carrée)
(3 / V27) x ( V75 ) = ??? Answered by Claude Tardif. 





Comment fait on pour justifier que... 
20020930 

From Lucie: Comment fait on pour justifier que p au carré est égal à 2 fois q au carré? Answered by Claude Tardif. 





l'équation d'une rotation dans un graphique cartésien 
20011114 

From Ghaith: je d6sir que vous me rafraichissez un peu la mémoire s.v.p. j'aimerai savoir l'équation d'une rotation dans un graphique cartésien merci Answered by Claude Tardif. 





racine carrée 
20001124 

From G. Bigorgne: Quel est donc l'origine de l'expression "racine carrée" ? Pourquoi avoir choisi cette expression ? Answered by Claude Tardif. 

