







Retiring athletes numbers 
20171218 

From Robin: I am wondering if you can explain in layman terms how to figure out how many different ways the numbers 0099 can be arranged? The discussion that sparked this question revolved around the practice of retiring athletes numbers and how many actual number combinations there are. So if I were to use 00, 01, 02 03, 04, 05, 06, 07, 08, 09, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ....99. I say there are only 109 different numbers. I'm being told I'm wrong that there are way more than that. Please help. Thank you, Robin Answered by Penny Nom. 





Doubling the area of a pamphlet 
20151031 

From Mariam: A pamphlet has the following dimensions: 4 cm by 6 cm
If the area of the pamphlet is doubled, what will be the length of each side if sides can be integer values only? Answered by Penny Nom. 





The center and radius of a circle 
20150206 

From ariana: I need to find the center and the radius of this circle. I don't know how to put 9/2
than square it into a fraction.
x^2 + 2x + y^2 +9y=5 Answered by Penny Nom. 





Arrangements of ten letters 
20110415 

From Mustafa: In how many ways can the ten letters of the word GELATINOUS be arranged
in a line so that the vowels are in alphabetical order (not necessarily together)
when read from left to right? Answered by Penny Nom. 





Sixletter words 
20091124 

From christine: How many sixletter words (not necessarily an English words) are there in which exactly three of the letters are z's? Answered by Claude Tardif. 





A sequence of letters and numbers 
20091110 

From Maria: What is the last ten letters and numbers in the following series and how do I work it out so I can explain it to an eleven year old.
J1F8M1A0M1J0J1 Answered by Robert Dawson, Claude Tardif and Harley Weston. 





Completing the square 
20091002 

From christopher: how do i find the factors of x^2+3x+2 by completing the square ? Answered by Robert Dawson. 





The inverse of F(x)=x^26x+13, for x>3 
20090726 

From Juan: The function F is given by F(x)=x^26x+13, for x>3.
A. Write F(x) in the form (xa)^2+b
B.Find the inverse function F^1
C.State the domain of F^1 Answered by Penny Nom. 





Completing the square 
20090616 

From rebecca: Find the roots of the equation by Completing the square. Express your answer in exact form and in decimal form to 2 decimal places.
a) x(squared)+10x+23
b)3y(squared)+12y+3 Answered by Stephen La Rocque. 





Completing the square 
20090427 

From Daniel: I tried following an example of yours but I still couldn't figure it out.
Here is my question,
2x^2  6x + 1 = 0.
Any help would be greatly appreciated. Answered by Stephen La Rocque. 





Some 9 letter permutations 
20090224 

From Cecilia: If the letters G, H, S are used exactly 3 times how many 9 letter combinations can be generated? Answered by Penny Nom. 





A wine decanter 
20081210 

From Suzanne: I am trying to buy a wine decanter for my dad for Christmas. One big
problem I am having shopping online is finding the right size. Wine is sold
by metric ml, with a standard bottle holding 750ml of wine. Decanters are
measured by oz, and the sizes are all over the place, with one site alone
having sizes 25oz, 26 1/2oz, 50oz, 59 1/8oz, and 68oz.
Can you help me with metric conversions so I can figure out how much wine
these decanters hold? Like everybody else, I need this as soon as possible
so I can get it shipped in time for Christmas. (I'm disabled & don't drive, so
online shopping is my only way to get gifts.)
Thanks for your help!
Suzanne Answered by Chris Fisher and Robert Dawson. 





Factor 9x^2 + 6x + 4 
20081121 

From Jonah: how can i solve this by factoring: 9x^2 + 6x + 4 Answered by Harley Weston. 





Three letter combinations 
20080815 

From Shelbie: How many 3 letter combinations are possible, if you can repeat each letter?
I learned an easy way to do this in school, but fail to remeber what that was... Answered by Penny Nom. 





A rectangle word problem 
20080410 

From Nick: A rectangle is twice as long as it is wide. If the length and width are both increased by 5cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original. Answered by Penny Nom. 





A chain letter 
20080410 

From Lesley: In the mail you receive a chain letter with a list of ten names on it. The instructions tell you to send $2 to the person named on the top of the list, cross his name out, and place your name on the bottom. YOu then have to send ten copies of this letter to friends with the same instructions. If no one breaks the chain how much money should you receive? Answered by Stephen La Rocque and Harley Weston. 





Complete the square 
20080409 

From jessica: can you check my answer please thanks
f(x)=2x^24x+5
I got 2(x+2)^23 for when it asked to simplfy it to standard form of a quadratic
equation Answered by Stephen La Rocque. 





Complete the square 
20080409 

From jessica: Use the technique of completing the square to put f(x)= 2x^24x+5
in the form f F(x)= a(xh)^2+k were h,k=vertex of the parabola.
identify the coordinate (h,k)of the maximum or minimum point
of the associated parabola Answered by Penny Nom. 





Completing the square 
20080311 

From Ryan: solve for x by completing the squares,
x^2+4x8=0 Answered by Stephen La Rocque. 





Permuting the letters in ELEVEN 
20080123 

From Beth: (i) Find the number of distinct permutations that can be formed from all
of the letters of the word ELEVEN.
(ii) How many of them begin and end
with E?
(iii) How many of them have the 3 E's together?
(iv) How many
begin with E and end with N? Answered by Stephen La Rocque. 





Find the lengths, and explain in a 'let statement' 
20071220 

From Cordilla: the length of the sides of a triangle are 3 consecutive whole numbers. The perimeter of the triangle is 102 meters. Find the lengths, and explain in a' let statement'. Answered by Stephen La Rocque and Harley Weston. 





More on completing the square 
20071129 

From June: x^2  6x = 16 I found you already had this question but the answer you gave did not help me to explain how to answer the problem for my daughter. I do not understand how to complete the square for this paticular question and the example you showed did not help. I would appreciate any further help you could give me. Answered by Penny Nom. 





Completing the square 
20071126 

From Julie: x^2  6x = 16 Please, Help I am stuck on this math problem. I need to solve by completing the square. I need the steps of solving the problem and the answer, Please. Answered by Penny Nom. 





Completing the square 
20071101 

From Mark: An architect is designing a museum entranceway in the shape of a parabolic arch represented by the equation y = x2 + 20x, where 0 x 20 and all dimensions are expressed in feet. Determine the maximum height, in feet, of the arch. Answered by Stephen La Rocque. 





What fraction of the letters of the alphabet is each word? 
20070802 

From Clayton: How do I figure this out, the math question has the answers but I have no idea how to get it.
my Mom can't figure it out either.
What fraction of the letters of the alphabet are each word
Man = 3/26
Glasses = 7/26
Integrity = 1/4
computer = 2/9 Answered by Paul Betts and Harley Weston. 





An athletic track 
20070730 

From tammy: The inner boundary ABCDEF of an athletic track cinsists of two straight parts each 90m long and two semi circular ends as shown in the diagram.If the perimeter of the inner boundary is 400m, calculate the diameter AE of the inner semi circle.
Part 2. If the track is 3.5m wide an athlete starts the 400m run at X and remains in the outer lane . He finishes at Y(1) Calculate the outer diameter YZ
(2)The distance XY (take pie as 22/7) Answered by Penny Nom. 





Using Heron's Formula to help maximize the area of a triangle 
20070627 

From Claire: Given one side of a triangle is 4 cm and the ratio 1:3 for the other 2 sides. What is the largest area of the triangle? Answered by Stephen La Rocque and Harley Weston. 





Finding the center of an ellipse 
20070620 

From Sima: find the center of the ellipse with the equation 3x^2 +4y^2+18x32y5=0 Answered by Penny Nom. 





Factor Completely 
20070529 

From Ema: Question 1:
Factor completely.
3x(x – 4) + 5(x – 4)
Question 2:
Factor completely.
x^2 + 2x + 3 Answered by Penny Nom. 





mls and grams 
20070119 

From JJ: If I have a 2000litre pool and need to put 2mg of chlorine per litre, how many mls do I need to add? Answered by Penny Nom. 





I have to design a lettering on corrugated plate 
20061129 

From Tim: For a client of mine I have to design a lettering on corrugated plate. The lettering has to appear "normal" when viewed from the front (100%) I am so far now to consider the shape of the plate to be two halves of an oval/ellipse. What I would like to know is a way to calculate the percentage in which I have to "stretch" my design in order to let it appear "normal". Answered by Stephen La Rocque and Penny Nom. 





Sally plays roulette 
20061121 

From Sherry: Sally plans to bet 100 bets of $1.00 each on red roulette. the probability of the ball landing on red is 18/38 what is the probability that Sally will win at least half the time Answered by Penny Nom. 





How much did I have in my wallet when I lost it? 
20060615 

From Marangeo: I recently lost my wallet and when it came to completing the police report I couldn't remember how much money I had in there. I do remember thinking that the first time I bought something that it cost me 10 per cent of what I had. Then I noticed that the second purchase had also cost me exactly 10 per cents of what I had left. My receipts totalled $19. How much did I have in my wallet when I lost it? Answered by Stephen La Rocque. 





How many arrangements are there? 
20060416 

From Jim: Can you tell me how many different combinations there are using 3 letters and 4 numbers. Letters first then numbers, example aaa0001, aaa0002, aaa0003,baa0001, baa0002, zzz9999. Answered by Stephen La Rocque. 





Seven consecutive reds in roulette 
20050904 

From Joe: I know that the odds are a little less than 50% for either black or red comming up on a spin of the roullette wheel. My question is what are the odds of red or black comming up 7 times in a row? Answered by Penny Nom. 





Aunt Lucy's letter 
20040627 

From Olivia: "Dear bob,
now that i am getting on (70 today). i want to give you some of my money, i shall give you a sum each year, starting now. you can choose which of the following schemes you would like me to use.
a) £100 now, £90 next year,£80 the yaer after and so on.
b) £10 now, £20 next year, £ 30 the next year and so on.
c) £10 now, 1.5 times as much next year, 1.5 times as much the year after that and so on.
d)£1 now, £2 next year, £ 4 the year after, £8 the year after and so on.
of course these schemes will only operate while i am alive. i look forward to hearing which scheme you choose and why!
Best wishes,
Aunt Lucy." Answered by Penny Nom and Claude Tardif. 





The quadratic formula 
20030831 

From Alex: I am using Houghton Mifflin's Precalculus with Limits book, 2nd edition. However, the first chapter encompasses Algebra review, and I am stuck on a problem. All that's required is to solve the following and verify using a calculator: 3y2+6y+2=0 I have solved the problem using the quadratic formula, but from what I remember, the quadratic formula is used in the case of equations following the AX2+BX+C=0 pattern. As the problem I am attempting uses a yvariable, can I still use the quadratic formula? Since I am not sure what route to take in solving this problem, I am hoping you can assist me. Answered by Harley Weston. 





Percentage change in completion rate 
20030221 

From Remo: In the year 2000 300 out of a possible 600 completed a phone survey for a total of 50% completion rate. In the year 2001 20 out of 100 possible people completed the survey when it was redone. This is a completion rate of 20% To figure out the percentage change between the years can just use the difference between the percentage figures I already have? Or can I calculate it the same as you would for nonpercentage numbers. For example you gave an example here of a salary increase from $20 to $95 being an increase of 375%. Would I solve my problem the same way expect substituting my percentages (.5 and .2) in place of $20 and $95? Answered by Penny Nom. 





Jack and Jill wrote letters 
20020619 

From Angel: jack and jill each bought a stationary # of sheets of paper in each box were the same # of envelopes were the same jill wrote letters consisting of 3 pages jack wrote letters consisting of 1 page
when they wrote all letters jill had 50 envelopes left and jack had 50 sheets of paper left how many pieces of paper and how many envelopes? Answered by Leeanne Boehm. 





Factor 12x^2  20x  8 
20020430 

From Crystal: Factor Completely: 12x^{2}  20x  8 Answered by Penny Nom. 





Solving x^23x+5=0 
20011130 

From Katy: How do you find the solution to x^{2}3x+5=0? Answered by Penny Nom. 





Four sequences 
20010924 

From Nicole: I have a few questions I couldn't figure it out. So any help will be great to find the next three numbers or letters. Here's the patters...  DEGHNORY, EHILMU, HIILMTU, BEILLMRUY,...
 50, 33, 25, 20, 16, 14, 12,...
 1777, 1795, 1818, 1819, 1820, 1822, 1836, 1837..
 A,H,I,M,O,T,...
Answered by Chris Fisher and Penny Nom. 





Fourier transform 
20010807 

From Adbul:
 Sir, we have the Dirichlet's condition for the Fourier transform : " The function should be integral over the real line " But why we are we neglecting this for example when we take the Fourier transform of an impulse train?
 Suppose we want to travel from one corner of a square of side 'a' to the diagonally opposite corner. We can travel along the sides which gives a pah length of '2a'. We can also do it in steps as shown below:
_  _PATH  _ _____
Suppose The step size =DELTA x Then the path length will be again '2a'. Now in the limit DELTA x >0 again we get '2a' But when we take the limit we get the straight line diagonal whose length is 'SQRT(2)X a' Where did I go wrong? Answered by Chris Fisher. 





Election in Angletown 
20010607 

From Zoe: At the last school election in Angletown 4620 votes were cast. Candidate Acute received 236 more votes than Candidate Obtuse. Candidate Right received 698 votes more than Candidate Acute. Candidate Straight received 256 votes less than Candidate Right. How many votes did each receive? Answered by Penny Nom. 





Spins of a roulette wheel 
20010302 

From Bob: Here's a problem I'm working on myself.....If you look at six consecutive spins of a roulette wheel, how many combinations of red and black are possible? I.E. BRRBRB, BBBBBR, BBRRRB......ETC..... Answered by Claude Tardif. 





Completing the square 
20010112 

From Jacky Lam: A friend told me that completing square not only can find the vertex but also the roots of a quadratic equation. Is it possible? How? Can you show me how to find the roots of the following equation using completing the square? 8x^{2} + 8x + 4 Answered by Penny Nom. 





Completing a square 
20000710 

From Lexa Michaels: How do you complete a square? the textbook question is: x^{ 4} + 64 Answered by Penny Nom. 





Six letter words 
20000515 

From Karl Freitag: An anthroplogist discovers an isolated tribe whose written alphabet contains only six letters (call the letters A,B,C,D,E, and F). The tribe has a taboo against using the same letter twice in the same word. It is never done. If each different sequence of letters constitutes a different word in the language, what is the maximum number of sixletter words that the language can employ? Answered by Penny Nom. 





Completing the square 
20000311 

From Sandra: How do i complete the square and leave in simple radical form? x squared + 18x  17=0 Answered by Penny Nom. 





The Quadratic Formula 
19990122 

From Eric Morgan: Hi my name is Eric Morgan and I m in 8th Grade honors math (middle) and I'd like to know how to prove the quadratic formula b±sqrt of b(a)(c)over 2(a) Answered by Penny Nom. 





A Puzzle 
19981027 

From Bruce Bragnu: We are trying to solve what SHOULD BE a simple 7th grade problem and have run into a wall. It is: ABCD ABCD ABCD ABCD  EBEA It is an addition problem. Each particular letter represents the same digit. We are looking for what number "B" represents. We have tried a multitude of solutions and have come up empty. Answered by Penny Nom. 





Marie achète un croissant et une tartelette 
20040201 

From M. et Mme Simoneton: Marie achète un croissant et une tartelette. Elle paie 1,64 €
Isabelle achète un croissant et un pain au chocolat. Elle paie 1,51 €
Marc achète un poain au chocolat et une tartelette. Elle paie 1,77 €
Trouver le prix d'un croissant, d'une tartelette et d'un pain au chocolat.
Answered by Claude Tardif. 





Minesweeper 
20011024 

From Un eleve: J'espere que vous pourrez m'aider. Est ce que vous connaissez un algorithme ou une strategie de resoulutiom pour le jeu du demineur (8x8 avec 10 mines)(Minesweeper). Answered by Claude Tardif. 





Sens d'un mot 
20000601 

From Edward Brisse: Seraitil possible de connaître le sens précis du mot "PORISME". Exemple : "le porisme de Poncelet". Answered by Claude Tradif. 

