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	The area of an odd shaped piece of property		2003-07-24
		From Barry: What is the formula for figuring the square footage of an odd shaped piece of property? Answered by Penny Nom.
	Surface area of a sphere		2003-07-23
		From Rob: I have a shere with a circumference of 12 feet. What is the total surface area of the shere in square feet and how did you find it? Answered by Penny Nom.
	nine digit numbers		2003-07-23
		From John: With a nine digit number, with each of the nine digits having a possibility of 10 different numbers then what is the total number of possible mathematical variations in the nine digit number. i.e. Social Security numbers have nine digits and if each of the nine digits have a possibility of being any one of ten numbers, i.e. 0,1,2,3,4,5,6,7,8,9. Then what is the formula to calculate the maximum possible number of variations in this nine digit number and what is the mathematical maximum possible number of variations of this nine digit number? Answered by Penny Nom.
	Natural logarithms		2003-07-22
		From Amanda: I'm going into my senior year of high school. I will be taking AP calculus, and my teacher gave us some homework over the summer. However, there are two things that I do not understand how to do. The first is, she wants us to be able to generate a unit circle by hand using 30, 60 and 90 degree triangles. I have used the unit circle in trigonometry, however I was never taught how to draw it. Secondly, I need to know how to do natural logarithms without a calculator. I was not taught how to do this, and the worksheet I was given only showed me how to complete them using a calculator. Answered by Claude Tardif.
	A pyramid with its top cut off		2003-07-21
		From David: What is the name given to a 3D shape that looks like a pyramid with its top cut off? Answered by Penny Nom.
	Slope		2003-07-20
		From Brian: You are placing a pipe 60 feet long at a slope of 1.5%. How would you figure the amount of drop from the inlet of the pipe tot he outlet of the pipe? and what is the answer . If you are trying to keep a shoulder slope of a road between 3/4'' per foot and 11/2'' per foot . If the shoulder is 10 feet wide, how would you figure how much lower should the outside of the shoulder be than the edge of pavement and what is the answer ? Answered by Penny Nom.
	|x+3| = -15x		2003-07-19
		From Nathan: Without the use of trial and error, is there a way of solving for x where |x + 3| = -15x? I know that x = -0.1875, but how do I find whether x + 3 is positive or not if I did not have this information (In other words, how would I solve whether the x-value was -3 or less, or if it was more than -3)? Answered by Claude Tardif and Penny Nom.
	"cubic feet" of a refrigerator		2003-07-16
		From Ron: Is the volume of a home appliance (e.g. fridge or freezer) calculated in a different way? I am planning to replace both my fridge and my freezer but I'm unable to determine what size replacement to get. For example, one company descibes their fridge as being 32"(L) x 30"(W) x 66" (H). I converted those measurements to feet (2.67 x 2.5 x 5.5) and I calculate the fridge to be 36.7 cubic feet. However, the company says the fridge is 18 cf. Answered by Chris Fisher.
	Cathy's Clothing		2003-07-15
		From Cathy: I am supposed to write a practical and useful word problem that would use the following algebriac inequality to solve it: 12x + 25 > 15x + 10. State the quanity that represents x and solve the inequality. Answered by Penny Nom.
	Preparing 100ml of a 30% alcohol solution		2003-07-13
		From Justin: My question is how do you prepare a 100ml of a 30% alcohol solution using 95% alcohol? Answered by Penny Nom.
	Sunshine?		2003-07-11
		From lori: It is noon, your lunch hour, but you cannot go out because there is a terrific hailstorm. Turning on your radio you hear the weathercaster predict that the hail will change to rain and that it will pour all day today. How can you determine whether the sun will be shining in 36 hours? Answered by Claude Tardif.
	A problem with lugs		2003-07-11
		From Lori: A young man's car developed a flat tire as he was driving along a deserted street. He pulled over to the curb and did all the usual things: removed the hub cap, unscrewed the lugs and rested them carefully in the hub cap, jacked up the car. As he was putting the spare tire onto the axle he accidentally kicked the hub cap. The lugs rolled out, and all five of them fell down a nearby grate. Peering through the bars of the grate the man thought that he could see the lugs about 6 feet below in a shallow water puddle. He had a problem. How do you think he solved it? Answered by Penny Nom.
	A mixture problem		2003-07-10
		From A student: Having a problem with word problems. example A chemist mixes a 10% acid solution with a 50% acid solution to form 400mL of a 40% solution. How much of each solution should be used. Answered by Penny Nom.
	A triangle in the complex plane		2003-07-10
		From Scott: The vertices O and A of an EQUILATERAL triangle OAB in the complex plane are located at the origin and 3 + 3i. Find all possible values for the complex number representing the vertex B. Give the location of B in both polar and cartesian form (to 2.d.p) Answered by Penny Nom.
	E(X + Y) and V(X + Y)		2003-07-10
		From Reuben: I'm a teacher trying to find a way to make some stats work from first principles. The topic is expectation algebra and it is for the top age level in high school. By using a set of data I can show how the mean is the same as the expected value ie 2,2,3,4,4 is 15 / 5 = 3 also, 2x0.4+3x0.2+4x0.4=3. I can also show this to work for the variance in the same style but using Sum(x-mean)2/n and the Var(X) version of squaring x then multiplying by the probability ( all this for random independant samples). Now comes the tricky bit.....when I try to show E(X+Y) = E(X) + E(Y) from setting up two data sets I get it to work only if I add each item from X to each item from Y. However, I can't get it to work for V(X+Y)=V(X) + V(Y) from two sets of data. There must be something missing in my knowledge of how the sets are required to add together or my knowledge of expectation algebra. I am familiar with proofs but still want to show my students that the basic formulae work from groups of data whether done the long way or by use of formulae. Can you help please? Answered by Penny Nom.

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