







Filling a candy box 
20181016 

From Stephanie: My child had the question: A candy box has the following measurements.
10x6x4Find the total volume. (We got that one right 240in3)
But... then it said “How many 1/2 inch cubed pieces of candy can fit in the box?
This is where we disagree. Please help. Answered by Penny Nom. 





Significant digits 
20170806 

From Pat: The directions for a problem are: "Solve the problem, expressing your answer
using the correct number of significant figures."
Problem
0.0043 divided by 2.04
Answer before using the correct number of significant figures is
0.002107843
Is the correct number of significant figures the number below?
2107843
Pat Answered by Penny Nom. 





Canada's population as a percentage 
20170511 

From bethmarie: What percentage of the world population (7.5 billion) is Canada's population (36 million).
Thank you very much! Answered by Penny Nom. 





Shooting a ball at a target 
20160216 

From Thys: Hi
I have a problem with the formula that i use .(for programming)
I have looked all over the web to find a solution but no luck.
I have a cannon that shoots a ball at a target
I use this formula to calculate what my initial velocity must be to hit the target
at a angle of 30 degrees and a distance of 15m (the cannon and target position is known)
It works perfectly if both is at same height but if one is higher or lower it miss.
In an example I am working with the range is 30m, the angle is 45 degrees and the target is 10m higher than my position.
Please help
Formula = V0 = √RG / Sin(2α) Answered by Harley Weston. 





Prove that you cannot factor x squared + 5 
20150528 

From lily: the question is: prove that you cannot factor x squared + 5 Answered by Robert Dawson. 





Percentage of water in a soil sample 
20120301 

From avi: what i need is the formula in getting the percentage from gram.
situation:
i need to know how many percent will i declare in getting the moisture of a soil sample
i weighed 2,000 grams of soil before i dried it out in the oven, after few hours the recovery
of the dried out soil is 1,700 grams. How many percent will be the water content?
kindly send me a formula in computing this.
thank u very much! Answered by Penny Nom. 





Designing a tin can 
20110331 

From Tina: A tin can is to have a given capacity. Find the ratio of the height to diameter if the amount of tin ( total surface area) is a minimum. Answered by Penny Nom. 





Multiplication and order 
20110121 

From Janet: IN A MULTIPLICATION SENTENCE BASED ON A DRAWING..IS THERE ANY ORDER FOR THE MULTIPLICAND ANG MULTIPLIER FOR THE ANSWER TO RIGHT? Answered by Robert Dawson. 





[sec^2x]*[sec^2x] 
20101216 

From Hari: [sec^2x]*[sec^2x]=...? Answered by Penny Nom. 





How many zeros? 
20100318 

From jeff: 1 light yr is 6,500 billion miles, the galaxy "Andromeda" is 2,500,000 million light yrs, how many zeros are in this equation ? Answered by Robert Dawson. 





More on millions and billions 
20100311 

From julio: shouldn't the thousands of millions, tens of thousands of millions, and hundreds of thousands of millions be called what they are? technically they are not billions because billions come after 999,999,999,999 . It would sound better to call the numbers by their real name when economists talk about the national deficit besides mathematics is a very precise science that doesn't admit mistakes. Or am I wrong? I know that in other countries is expressed different than here. I have this question to different people and nobody has a "logical" explanation to it. " that's the way is here in the US" does not explain any thing Answered by Penny Nom. 





A circle problem 
20091214 

From Fawad: AP is a tangent at P to a circle centre O, where AP=6cm. The straight line AQC is such that QC= 9cm.
Find the length, in cm of AQ. Answered by Chris Fisher. 





Divide and reduce to lowest terms. 
20090906 

From Karen: Divide and reduce to lowest terms.
Use the cancellation technique as needed
4 2/3 divided by 12
14/3 divided by 12/1 not sure wheer to go from here with the cancellation technique Answered by Penny Nom. 





Paddling downstream 
20090904 

From Nicole: You head downstream on a river in a canoe. You can paddle at 6 km/h and the river is flowing at 2.4 km/h. How far downstream will you be in 55 minutes? Answered by Penny Nom. 





Fred in his canoe 
20090221 

From Susan: Fred paddled for 4 hours with a 7 km/hr current to reach a campsite. The return trip against the same current took 9 hr. Find the speed of Fred's canoe in still water. (Remember to include correct units) Answered by Penny Nom. 





More on infinity and Set Theory 
20090217 

From Justin: I greatly appreciate your help I was just wondering from your previous answer, why doesn't Cantor's cardinal numbers in set theory apply to the limit x>0, y=infinity?
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. 





Why is the difference between british and american counting? 
20081215 

From Muhammad: Why is the difference between british and american counting?
Example 1 Billion american = 1,000,000,000 but,
1 Billion British = 1,000,000,000,000 Answered by Robert Dawson and Harley Weston. 





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. 





A canal with cross section a semicircle 
20081019 

From Connor: a canal with cross section a semicircle is 10m deep at the centre.
Find an equation for the semicircle and use it to find the depth 4m
from the edge Answered by Penny Nom. 





Distance, time and rate 
20080911 

From Pauline: During the first part of a trip, a canoeist travels 100 miles at a certain speed. The canoeist travels 25 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip? Answered by Penny Nom. 





Alpha level 
20080723 

From anonymous: What is the advantage of using an alpha level of .01 versus a level of .05, What is the disadvantage of using a smaller alpha level? Answered by Janice Cotcher. 





Cantor's diagonal argument 
20080126 

From David: Cantor's theory using a diagonal across a list of real numbers to proven uncoutability has always puzzled me.First in base ten, it feels like hocus pocus so I began thinking of the Boolean numbers as truer representations of place value (on,off). Secondly his list was always arbitrary or so I recollect. Therefore, I suggested using a seriesA=.10000....,B=.01000. C=.11000, etc.
Any diagonal is already located among the numbers listed. My only alteration is that since the final digit is always unrepresentably either one or zero, but it must be one or the other, I make an assumption that if x= .abc...1 and y= .abc...2 the only two possibilities and I choose to count F=x+y then then the numbers are countable= Z=sumFi,where I=2+2^2+2^3...
I hope this sketch is enough description, I asked Rudy Rucker more formally but got no mathematical response, someone else gave me some tale about slippery epsilon. What do tyou think of recasting his proofs in more rigorous form?
David French Answered by Claude Tardif and Walter Whiteley. 





What would be the cost of a 10 in * 15 in canvas? 
20071201 

From Jasmine: a 40in *60 in canvas is sold for $60.00 if the price is determined by the cost of the material what would be the cost of a 10 in * 15 in canvas Answered by Stephen La Rocque. 





Countable and uncountable sets 
20070724 

From Mac: Hi, i tried to read few webpages related to the countably infinite and uncountable sets.
Even i read few questions from this forum.
But i am not convinced with this explanation. If you have any good book that
explains this in layman term, please redirect me to that.
1) Can you please explain what is the difference between these too ?
2) How could you say set of Natural number and set of even numbers are countably
infinite ?
N={1,2,3,...} and Even= {2,4,6,...}
When an element in the even set is some 2n, we will map it to 'n'.So
now we have a bigger number(2n) right ?
Sorry, i didn't understand that.
...
Can you please help me out to understand that ? Answered by Harley Weston. 





A statistical difference 
20070703 

From a student: I am writing a paper for a grad class in which I am comparing achievement levels of boys and girls. I have data that shows the average marks for girls and boys in each grade 12 subject for the entire province.
My prof want me to show there is a statistical difference. What do I have to do to show this? I don't have access to the raw data, so don't know the SD. Is there anything I can do mathematically with the data that I have? (I can determine n for each set of data, it ranges between 2400 and about 13000 for each subject area.) Answered by Chris Fisher and Harley Weston. 





Surface area of a cylinder 
20070513 

From Nina: if a cylinder is 23 ft high with a 12 ft radius, how do I find the surface area? Answered by Penny Nom. 





A point inside a circle 
20070504 

From edgemitter: There is a point inside a circle (but not in its center) where two perpendicular secants intersect, dividing the circle into four regions with different area. Calculate the area of the four regions Answered by Walter Whiteley. 





What is the value of csc (2pi/3)? 
20060604 

From Kishor: What is the value of csc (2pi/3)? Answered by Stephen La Rocque. 





A tangent to a parabola 
20051102 

From A student: Find the point on the curve y=x^{2} where the tangent to the curve is parallel to the secant line connecting (1,1) and (2,4) Answered by Penny Nom. 





Cubic feet and imperial gallons 
20051027 

From Dave: What is the volume in cubic feet which is occupied by 1080 Canadian gallons of water? Answered by Harley Weston. 





Different infinities 
20040527 

From Plober: How can I explain to a friend (in a bar, using as a pen and a paper napkin) that the integer's infinity is 'smaller' than the irrationals's one? The demo I tried was that you couldn't match the integers with the real numbers between 0 and 1 (that 0.xxxxx replacing the Nth number from a different one... that demo), but she used my argument >: saying that you can add one to the integer's infinite, and the number I was creating was only one more...
I can't think of any other way, and I KNOW the real's cardinality is greater than the integer's one Answered by Claude Tardif and Penny Nom. 





Acres and square miles 
20040217 

From Richard:
How many acres are in .17 square miles? and How many acres are in .6 square miles?
The two areas I am requesting information about are Vatican City and San Marino, the two smallest countries in the world. If I can transfer the sq. miles into acres , I can relate the size of these countries to our school grounds and the students will better understand their sizes.
Answered by Penny Nom. 





Multiplier and multiplicand 
20031217 

From Karen: The K5 curriculum states that at a grade 5 level students should "understand and use the terms multiplier, multiplicand" The curriculum defines 'multiplicand' as " a number being multiplied by another number. A factor." There is no definition given for 'multiplier'
Question: Define these words are they just other words for 'factors'. If so, how important is it that students use these terms? It would seem like 'factors' would be the better choice of words to use. If multiplcand refers to eg. the first factor in the equation and the 'multiplier' the seond term, (if in fact it does) is this not confusing for students when we teach them that multiplication is commutative? Answered by Penny Nom. 





7,473,000,000 divided by 52000 
20030906 

From A student: I am having trouble with a question. 7,473,000,000 divided by 52000. Our calculater gets 147311.5385. I come up with 143711.53846, and then the number starts to repeat itself Answered by Penny Nom. 





Gallons in a tank 
20030320 

From Leslie: I am trying to figure the liquid gallons in a water tank that is 19" wide by 29.25" long and is 12.25" high. Could you tell me the formula to figure this out. Answered by Penny Nom. 





Sasha's candies 
20030218 

From Pat: Ticktactoe
Sasha and Trudy are playing ticktactoe. Sasha agrees to give trudy two pieces of candy for each game Sasha loses, and Trudy agrees to give Sasha three pieces of candy for each game that Trudy loses. After playing thirty games, Sasha has the amount of candy that he started with. If no ties occurred, how many games did Sasha win? Answered by Paul Betts. 





What is larger than infinity? 
20030112 

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





How many billions equal one trillion? 
20021207 

From Ryan and Aylah: How many billions equal one trillion? We believe that the answer is one thousand times one billion equals one trillion. Please help us with the answer to this question. Answered by Penny Nom. 





Radicals with fractional radicands 
20021111 

From A student: how do I simplify radicals with fractional radicands? ex. 7sqrt(2) + sqrt(50)  2sqrt(18) 10sqrt(3/5)  24sqrt(5/3) 3sqrt(2/9) + 1/2sqrt(32) + sqrt(9/8) Answered by Penny Nom. 





Rounding 27.27 
20021103 

From A parent: If you have a problem 27.27 and you need to round to the first 7 the answer would be 27 Would 27.0 be acceptable as well or is it completely wrong. Answered by Penny Nom. 





For 7 the multiplicand is 143 
20011212 

From Cory: For 7 the multiplicand is 143 I am asked to solve this, if you could help me it would be greatly appreciated! Answered by Penny Nom. 





Gallons 
20011119 

From Shawn: Do we use British or American gallons in Canada? Answered by Chris Fisher. 





A trig identity 
20010727 

From Jeff: prove this identity and show steps tan(x/2+pi/4)=secx+tanx Answered by Harley Weston. 





A sugar cane crop 
20010327 

From A student: a sugar cane farmer harvested only 1/4 of his crop. he sold 2/3 of his harvest to the mill. what fraction of the total crop did he sell. darens recipe for florida fudge calls for 5/8 cup of sugar. if he wants to make only 1/2 of the recipe how much sugar should he use. Answered by Penny Nom. 





The path of a cannonball 
20010115 

From A student: Artillerymen on a hillside are trying to hit a target behind a mountain on the other side of a river. Their cannon is at (x, y) = (3, 250) where x is in kilometers and y is in meters. The target is at (x, y) = (2, 50). In order to avoid hitting the mountain on the other side of the river, the projectile from the cannon must go through the point (x, y) = (1, 410). Write the equation for the problem. Answered by Penny Nom. 





Minimizing the metal in a can 
20000502 

From May Thin Zar Han: A can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. Answered by Harley Weston. 





Cross multiplication 
20000216 

From J E Swinton: Why does cross multiplication work? How come canceling work? Answered by Penny Nom. 





Two candles 
19991124 

From Skip Simpson: You have two candles the same length. They are lit at the same time. One burns down in 4 hours; the other in 5 hours. How long does it take before one candle is three times the length of the other candle? Answered by Walter Whiteley. 





Cannonballs 
19990127 

From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom. 

