







A system of inequalities 
20200201 

From Isaac: Austin has x nickels and y dimes, having a maximum of 15 coins worth a minimum of $1 combined. No more than 4 of the coins are nickels and no less than 11 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution. Answered by Penny Nom. 





Roll two dice and record the difference 
20191209 

From Barbara: Suppose you roll two dice 100 times. Each time you record their difference
(always subtracting the smaller one from the bigger one to get a positive
difference). The possible values you get are 0,1,2,3,4 and 5. You record
the frequency of each value in the following table:
Difference of two dice 0 1 2 3 4 5
Observed frequency 12 31 26 13 10 8
Let your null hypothesis be that the dice are fair, and the alternative
hypothesis be that they are not fair. Using a confidence level of α = 0.10,
test the null hypothesis by a goodnessoffit test.
Hint: begin by
completing table:
x 0 1 2 3 4 5
f(x) Answered by Penny Nom. 





The area of a patio 
20190623 

From Miguel: Stephanie has 60 feet of metal fencing material to only fence 3
sides of a rectangular patio. A tall metal wall serves as the fourth side
of the rectangle. write a function for the area the garden (A) in terms
of width in feet (x) What measures of the width would give an area of
at least 150 feet? Answered by Penny Nom. 





A dice game 
20190317 

From Remo: So, little game my kid came up with.
Dice are standard d6.
I roll a die, he rolls a die. If he gets the same number as me OR a bigger number he wins.
So far so good. Used the opportunity to get him to calculate the probabilities of him winning, see if I could get him interested into looking at this game from a more academic perspective. He did fine.
Then we upped the ante.
He rolls one die, I roll two dice. I his die has a number that is equal or greater than both of mine, he wins.
We had a bit of trouble solving that one, and had to resort to a table with all the results ( 6x36) to figure out where we stood.
Then again we upped.
He rolls two dice, I roll two dice.
If any one of his dice has a number equal to or greater than both of mine he wins. I only win if one of my dice is greater than both of his.
And we got stuck. Figured I would need to find a formula to resolve this one, as our earlier solution ( table everything ) suddenly is 36x36, giving well over a thousand possible results. And if we ever go bigger than that then we *really* are going to need another way to calculate it. Answered by Harley Weston. 





A parallelogram, a rhombus and a rectangle 
20180207 

From Sambo: what do parallelogram, rhombus and rectangle have in common? Answered by Penny Nom. 





A pair of linear inequalities 
20170808 

From Hempstone: Solve the inequalities 3x5<2x+5>4x+9 Answered by Penny Nom. 





A 13 game bet 
20160228 

From farah: I'm trying to calculate the odds of a 13 game bet. Each game has 2 teams with 3 possible outcomes (win,draw,lose).
What are the odds. Answered by Penny Nom. 





Seven switches with 3 stages each 
20150915 

From jeff: We are trying to solve a combination problem. If I have 7 things that can be in 3 states (say on/partially on/off), and all 7 have to a state. How many different combinations can there be? It doesn't seem like we should treat it as 21 independent things, but not sure how to break the problem apart. Answered by Penny Nom. 





An inequality 
20150419 

From mr.: Simplify the inequality √x>x and represent on a number line Answered by Penny Nom. 





A region described by inequalities in cylindrical coordinates 
20150221 

From Rahul: I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system)
0=
I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length.
It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!
Regards,
Rahul Answered by Penny Nom. 





1 + cot x divided by sin x + cos x 
20150115 

From Torrie: I need to solve this problem in terms of Sin, but I'm having trouble.
1 + cot x divided by sin x + cos x Answered by Robert Dawson and Penny Nom. 





An inequality 
20140327 

From James: a step on a stairway is at least 8 inches high. write and solve an inequality to represent the maximum number of steps between floors that are 10 feet apart Answered by Penny Nom. 





An inequality 
20140117 

From Rosie: 4x/x2<3
four x divided by x2 is less than or equal to 3 Answered by Penny Nom. 





When would one flip the inequality sign? 
20140109 

From Natasha: Would one flip the inequality symbol in this equation: (explain why)
(9a)/(9) > 81
And please explain in what circumstances one would flip the inequality sign
THANKS! Answered by Penny Nom. 





Why can't we add or subtract speed? 
20131121 

From kashish: why we cannot add or subtract "speed" / directly in any given distance , speed , time questions? Answered by Chris Fisher. 





Solve 2x^4+x^337x>26x^2+12 using a graphical approach. 
20121229 

From Tehmas: Solve 2x^4+x^337x>26x^2+12 using a graphical approach.
I don't know how to find the xintercepts or yintercepts in this form. Answered by Penny Nom. 





The last 4 digits of a cell phone number 
20121222 

From Jacob: If the last 4 digits of a cell phone number, XXXXXXABCD, are restricted where: A cannot be 0 or 1 and B cannot be 0 / how many possible 4 digit combinations are left? Answered by Penny Nom. 





5<2x+1<1 
20121111 

From Rahul: How does 5<2x+1<1 changes to 1<2x+1<5. What is the rule?
Can we apply absolute value function throughout the first inequality i.e. can we say 5<2x+1<1. But then it becomes 5<2x+1<1 which is impossible because 5 is not less than 1. Answered by Penny Nom. 





A proof by contraposition 
20121019 

From Rahul: I am not able to understand the following,
To prove that if for all e>0, x0, then x>=e. I understand the approach very well but I do not understand why if x=e then x>=e. If it is so then why not x=
Thanks in advance!'
Rahul. Answered by Penny Nom. 





Changing the sign of an inequality 
20120919 

From Bryauna: Why do you change the signs in inequalities?! Answered by Penny Nom. 





Properties of real numbers applied to subsets 
20120201 

From Mark: Hello 
The questions that I have for you is do the properties of real numbers (such as the associative, commutative, identity, inverse, and distributive law) apply to ALL the subsets of real numbers? In other words, do all those properties work for the Natural Numbers? The Whole Numbers? And so on and so forth. I understand that they are all real numbers, but for instance: the identity is whenever you add zero to a number, you get that number back. But does that work with, say, with only the odd numbers? Zero isn't odd so can that property actually apply to JUST the odd numbers? Any consideration would be greatly appreciated! Answered by Robert Dawson. 





A trig identity 
20120108 

From Joe: Prove this Trig. Identity :
((cos2θ + sinθ1) / tanθ ) + sin2θ = cosθ Answered by Penny Nom. 





Linear inequalities 
20110325 

From Alice: OK. I'm in algebra 1 and the linear inequality is
y<2x1
y>2
I don't completely know how to graph y>2 and I'm getting really frustrated
Please help me in any way possible!
Thank You! Answered by Penny Nom. 





An inequality 
20101213 

From jimmy: 1.7b1.1 <2.3 Answered by Stephen La Rocque. 





Linear inequalities with absolute values 
20101201 

From ryan: Good day!
We we're given this assignment in algebra concerning linear inequalities with absolute value.
In this number I'm confused how to isolate the absolute value, considering there is a variable in the absolute value and there is a variable in the outside.
2+5 43t+t ≤ 34t Answered by Penny Nom. 





Bbippities, bops, and boos 
20101105 

From Stacey: six bippities equal three bops,and six bops equal two boos. How many
boos are there in one bippity,one bop, and one boo?? Answered by Stephen La Rocque. 





4 > 3m7 >= 2 
20100605 

From pamela: The question is
4>3m7>=2 Answered by Penny Nom. 





6 items are taken 3 at a time 
20100412 

From Kristen: Explain the three different scenarios that could occur and would result in the following number of outcomes when 6 items are taken 3 at a time. Give reallife examples.
a. 63 = 6 x 6 x 6 = 216 possibilities
b. 6! / (6  3)! = 6 x 5 x 4 = 120 possibilities
c. 6! / (6  3)! 3! = 20 possibilities Answered by Tyler Wood. 





Frank makes picture frames 
20100220 

From Carol: Frank makes picture frames his revenue from sales is R=$13.60x for frames sold. The cost making frames is C=$5.80x+$120 for frames made. What is the minum number of frames Frank must make and sell in order for his revenue to be greater than his costs. Answered by Penny Nom and Melanie Tyrer. 





1/a + 1/b + 1/c < 1 
20100201 

From Mrityun: suppose a,b and c are natural numbers such that 1/a + 1/b + 1/c < 1. Prove that
1/a + 1/b + 1/c < = 41/42. Answered by Penny Nom and Claude Tardif. 





Growth rates 
20100126 

From Bhavya: Dear Sir/Ma'am,
I read in the text book that the growth rates of these 3 functions are as below
n^{2/3} < n/lg n < n^{0.99}
I tried the substitution method to check the correctness of this. But it gets really tough as n increase.
Is there any simpler way to understand the correctness of these growth rates?
Thanks and Regards,
Bhavya Answered by Robert Dawson. 





A trig identity 
20100124 

From Natalie: hi, i need help proving the following trig identity. i cant seem to figure out how to do it.
thanks so much.
(1+sin2x)/cos2x = cos2x/(1sin2x) 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. 





A trig identity 
20100105 

From Christine: I need help with this whole paper here is one problem
csc^2xcot^2x/1sin^2x=sec^2x
by the ^2 i mean squared pleease Answered by Penny Nom. 





sin x / 1+ cos x = csc x  cot x 
20091118 

From Mansi: i need a hint on how i could prove the following identity:
sin x / 1+ cos x = csc x  cot x Answered by Harley Weston. 





Probability 
20090927 

From Ed: My mother died 3 years to the day after her daughter died. what are the odds of that happening by chance? thanks Answered by Chris Fisher. 





2(x4)>4+2x 
20090827 

From jorna: 2(x4)>4+2x Answered by Penny Nom. 





Inequalities 
20090722 

From Sindhu: prove that
4^79 < ( (2^100) + (3^100) )< 4^80 ? Answered by Robert Dawson. 





Solve 1<52x<10 for x 
20090512 

From Helen: solve the following inequality for x
1<52x<10 Te less then sign by the one, should be less then or equal to. Answered by Stephen La Rocque and Penny Nom. 





An inequality with logs 
20090306 

From Indrajit: (x/10)^(logx  2)<100..........how to solve this one?? Answered by Stephen La Rocque. 





An annuity 
20090227 

From Jules: R 20 000 is deposited in the bank,at the end of each year R 5 000
is withdrawn from it, the interest is 13 percent compounded monthly.
Calculate how many years that person will be able to use his/her money ? Answered by Stephen La Rocque. 





How can other infinites can be larger than each other? 
20090217 

From Justin: Hello again, I was just wondering even in the context of set theory, how can other infinites can be larger than each other, I thought infinity itself is the largest possible quantity?
Justin Answered by Victoria West and Robert Dawson. 





Solving an equality 
20090210 

From Deborah: 2(v+10)<18 Answered by Penny Nom. 





Saving for his daughter's education 
20090115 

From George: To save for his daughter’s university education at the end of each month Mr McLean sets aside £50 in a savings scheme paying 10% p.a. compounded monthly. He begins saving when his daughter is 3 years old. How much will he have saved by the time his daughter is 18? Answered by Harley Weston. 





Trig identities 
20090105 

From Michael: 1) Determine if the following is an identity. If it is, prove it, If it isn't state it.
tan x + cot x = sec x * csc x
and
1  (cos^2) x = 1+ (cot^2) x Answered by Robert Dawson and Harley Weston. 





Solving an inequality 
20090102 

From jarred: 3x+8>2 Answered by Penny Nom. 





Student who is inverting digits 
20081209 

From Tammie: Do you have any strategies for addressing inversion of digits in two digit numbers. For example  The student the teacher is working with will write "14" and the number is 41. She has tried highlighting, practice writing numbers, and hundreds charts and finding patterns. Help! Thank you! Answered by Robert Dawson and Victoria West. 





Two inequalities 
20081008 

From s: 3y > 4x
2x3y>6 Answered by Stephen La Rocque. 





Three addends that sum to ten 
20080913 

From Alfred: How many probabilities are there to have 3 addends to get a sum of 10? What is the formula? Answered by Harley Weston. 





How do you solve for x when (x^4)x is greater than or equal to 0? 
20080814 

From Katie: How do you solve for x when (x^4)x is greater than or equal to 0? Answered by Penny Nom. 





5x < 25+10 
20080425 

From Courtney: What is the answer to 5x<25+10 Answered by Stephen La Rocque. 





How is the square root of 3/4 is greater than 3/4? 
20080422 

From Serena: How is the square root of 3/4 is greater than 3/4? Answered by Penny Nom. 





Two consecutive odd numbers 
20080401 

From prinsilla: of all pairs of consecutive odd integers whose sum is greater than 75. find the pair whose sum is least? Answered by Stephen La Rocque. 





2 tan theta /(1 + tan^2 theta) = sin 2theta 
20080325 

From Charmaine: I'm having trouble on where to begin proving identities. I must prove that
(2 tan theta / 1 + tan^2 theta) = sin 2theta Answered by Penny Nom. 





Drawing blocks from a box 
20080211 

From Inez: A box contains 3 red blocks and 1 green block. A block is chosen without looking and not put back. Then another block is chosen. What are the possible outcomes? Answered by Penny Nom. 





Small group activities 
20080211 

From Rain: I need to have a meet and greet with 40 people and need to do small group activities so that each person meets every other person but only once.
I'm not into math, need someone to tell me how many groups I would need to have? Answered by Victoria West. 





Blood type probabilities 
20071201 

From Noelle: Question from Noelle, a student:
Blood Type % Population
O+ 37.4%
O 6.6%
A+ 35.8%
A 6.3%
B+ 8.5%
B 1.5%
AB+ 3.4%
AB .6%
I need to make another table showing the probablility of meeting someone in each of the eight blood groups. I'm not sure how to find the probability with percentages. Thanks for your help. Answered by Penny Nom. 





Multiplying an inequality by a negative number 
20071127 

From Lisa: Why is it that you have to switch the sign of the inequality when you divide or multiply by an negative number to solve for a variable? Answered by Penny Nom and Walter Whiteley. 





A normal distribution problem 
20070927 

From m.j.: Car Loan Rates The national average for a new car loan was 8.28%. If the rate is normally distributed with a standard deviation of 3.5%, find these probabilities.
a. One can receive a rate less than 9%.
b. One can receive a rate less than 8%. Answered by Harley Weston. 





Variable expressions  part 2 
20070904 

From lisa: how do I write a variable expression for word phrase example x less than =
2 or 2 less than p
4 fewer than job please help Answered by Penny Nom. 





Combining probabilities 
20070820 

From Arul: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/2 , and 5/8 , respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem ? Answered by Stephen La Rocque. 





Trig identities 
20070730 

From Suzanne: I'm a UR University Graduate (with High honours!) but not in math: I'm taking GeoTrig, Sk Learning version, and the text is poorly written. But I was flying through the material until I hit the Trig Identities. I just don't get WHY we have them, why we should know them? What good is this "theory". All that "simplying" rarely yeilds a simpleer version! Also, give me advice for how to study them.
Thanks
Suzanne Answered by Harley Weston. 





Trig identities 
20070705 

From Alex: Use the identities tan_=sin_/cos_ and/or sin*_+cos*_=1 to simplify 1cos*_ Answered by Stephen La Rocque. 





Simultaneous inequalities 
20070618 

From Freddy: Watson Electric has production facilities in Valley Mills, Marlin,and Hillsboro.
Each one produces radios,stereos,and TV sets.
There production capacities are
Valley Mills: 10 radios, 12 stereos, and 6 TV sets per hour
Marlin: 7 radios, 10 stereos, and 8 TV sets per hour
Hillsboro: 5 Radios, 4 Stereos, amid 13 TV sets per hour
QUESTION
How many hours should each plant be scheduled to fill an order of 1095 radios, 1230 stereos,
and 1490 TV sets? Answered by Stephen La Rocque. 





An inequality 
20070616 

From jerry: Two real numbers a and b satisfy the equation ab=1.
i) Prove that a^6 + 4b^6 >4
ii) Find out whether the inequality a^6 + 4b^6 >4 holds for all a and b such that ab = 1 Answered by Stephen La Rocque. 





A linear system 
20070323 

From Adam: Solve the system by graphing: 4y>6x
3x+2y<6 Answered by Stephen La Rocque and Penny Nom. 





3x > 12 
20070111 

From Jen: In the following inequality, would one flip the inequality symbol?
3x > 12 Answered by Stephen La Rocque. 





x + 2y < 6 
20070106 

From Mike: I understand solving by graphing, but i am having trouble with the graphing of in equalities. i solved : x + 2y<6 Answered by Penny Nom. 





The proof of inequality by mathematical induction 
20061207 

From Carol: S(n) = 2^n > 10n+7 and n>=10 Answered by Stephen La Rocque. 





Linear inequalities 
20061201 

From Susan: how would I graph a linear inequality of y>3. Answered by Stephen La Rocque. 





2x > 6 and x  4 < 3 
20061127 

From Alyssa: 2x > 6 and x  4 < 3 , i need to know how to solve it and how to graph it. Answered by Stephen La Rocque. 





Inequalities 
20061003 

From Maleeha: a)Use algebra to find the set of values of 'x' for which x(x5)>36.
b)Using your answer to part a, find the set of values 'y' for which y^{2}(y^{2}5)>36 Answered by Penny Nom. 





Two trig questions 
20060404 

From mandy: I have a few questions that I need help with for my precal class in college. The following have to prove the trigonometric identities:
cos^{4}x + 2cos^{2}x sin^{2}x + sin^{4}x = 1
sin^{4}x  cos^{4}x = 1  2cos^{2}x
thanks you, Answered by Stephen La Rocque. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) Answered by Penny Nom. 





A pair of trig equations 
20051205 

From Kevin:
I am trying to solve for A and B but haven't been able to find a trig identity that will help me.
1.414 = .5cosA + cosB
.5 = .5sinA  sinB
how do I solve this?
Answered by Penny Nom. 





The distributive property 
20051112 

From Jennifer: I am trying to help my daughter . How do you name the property for 6(4w  3z)=(6 x 4w)(6 x 3z) Answered by Penny Nom. 





Open dots and closed dots 
20050929 

From Cynthia: When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot? Answered by Penny. 





Graphing a linear inequality 
20050826 

From Gina: When graphing a linear inequality, how do you know if the inequality represents the area above the line? Answered by Penny Nom. 





50^99 and 99! 
20050523 

From Romel: Which number is greater, 50^{99} or 99! Answered by Claude Tardif. 





Graphing an inequality 
20050502 

From Janice: I need to know how to graph inequalities. I need to know just abot everything. From graphing an equation to shading. Answered by Leeanne Boehm. 





An inequality 
20050331 

From Ambross: demostrate the following inequality:
2.Sqrt(K+1)2.Sqrt(k)<1/Sqrst(K)<2.Sqrt(K)2.Sqrt(k1)
Answered by Penny Nom. 





Graphing inequalities 
20050215 

From Melanie: Solve and Graph the following variable inequalities:
y<2x+4
y>2x+6
3x+4y<24
4x6y>24 Answered by Penny. 





0.999..., asymptotes and infinity 
20041217 

From Mike: My Name is Mike and I teach high school. I had a student ask me to explain why .9 repeating is equal to 1. Then he asked me about an asymptote, or why a parabola or any other curve for that matter can continually approach a value (like 1) and yet never attain a value of 1. He is thinking that these two should represent the same concept and yet they contradict each other. Do you have a solid explanation for him? Of by the way he is a 7th grader. Great little thinker!!!!! Answered by Claude Tardif and Harley Weston. 





Probabilities in poker 
20041104 

From Ben: Please can someone tell me the odds of getting a royal flush while playing texas hold em.
Please can you also let us know the odds of a royal flush while playing texas hold em if you must be dealt two of the needed cards. Answered by Chris Fisher. 





Square roots and inequalities 
20041025 

From Waheed: Q1. What is the simplest way of finding a square root of any number using just a pen and paper? (I am asking this question because I browsed a few sites a didn't find any method that is simpler than the one I use. so I am just curious.)
Q2. Is it possible that you take an equation and turn it into an inequality by performing same mathematical operations on both sides? Answered by Claude Tardif and Penny Nom. 





An ineqlality with absolute values 
20040705 

From Uneeza: abs(x^{2}  4x) > 3 Answered by Claude Tardif. 





Undercapatalized small businesses 
20040626 

From Greg: Suppose that 30% of all small businesses are undercapitalized. 40% of all
undercapitalized small businesses fail and 20% of all small businesses that
are not undercapitalized fail. A small business is chosen at random. The
probability that the small business succeeds if it is undercapitalized is? Greg
Answered by Penny Nom. 





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. 





Some trig expressions 
20040523 

From A student: Prove:
sin A + sin B = 2sin(A+B/2)cos(AB/2)
cos A  cos B = 2sin(A+B/2)sin(AB/2)
cos A + cos B = 2cos(A+B/2)cos(AB/2)
sin A  sin B = 2cos(A+B/2)sin(A+B/2) Answered by Penny Nom. 





Solving inequalities 
20040503 

From Joe: Let x be a real number find and graph the solution to the following sentances:
2x10+9
4X+2<15
5X+3>(x1) Answered by Peny Nom. 





Probabilities and olivies 
20040214 

From Annetta: A bowl contains five green olives and eight black ones. Wilma sticks a fork into a bowl and brings out two olives. What is the probability that she gets one green and one black olive? Answered by Harley Weston. 





Inequalities 
20040108 

From Michael: How do you use inequalities in your job and in your everyday life? Answered by Penny Nom. 





An inequality whose solution is all points 
20031125 

From Katie:
Hi my name is Katie and I am in the 9th grade and I would like help on this question. Is it possible to have a system of inequalities whose solution is all points?
1.I need to know why (explanation)
2.how to do it(example)
Answered by Penny Nom. 





Cathy's Clothing 
20030715 

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. 





A binomial probability 
20030430 

From Erica: In a biathlon, athletes shot at 20 targets. A particular athlete had a probability of 0.18 of missing a target. Assuming a binomial distribution, what is the probability, to the nearest thousandth, that the athlete hit exactly 16 targets? Answered by Andrei Volodin. 





A fractional inequality 
20030408 

From Jessica: Solve for x. Write in interval notation.
[(x^{2})9]/[x5] >= 0 Answered by Penny Nom. 





y < 2x + 1 
20030301 

From Erika: how can I solve and graph y<2x+1 and which side in the graph should i shade after i finish solving my inequality? Answered by Penny Nom. 





The horse race 
20021119 

From Pat: The Horse Race Three horses run a race. In how many different ways can the three horses finish the race if ties are allowed? Answered by Penny Nom. 





An identity in trigonometry 
20021017 

From Alex: I really need help with proving this identity. (1+cosx+sinx)/(1+cosxsinx) = secx + tanx Answered by Penny Nom. 





Three algebra problems 
20021013 

From Veronica: Solve the following inequality: 5(xsqured4)/(xto the 5th(2x5)to the 3rd) < or equal 0 Solve the following equations for all roots square root of x+2=1+square root of 2x+3 what's ZERO FACTOR PROPERTY??? The hypotenuse of an isosceles right triangle is 7cm. long. Determine the lenghts of the other sides. Answered by Leeanne Boehm. 





When does an inequality represent the area above the line? 
20020825 

From Tamara: How do you determine that an inequality represents the area above the line and when do you include the line in the solution? Answered by Penny Nom. 





Some inequalities 
20020725 

From A student:
1)5 <= 3X+1 < 1 2)4X2 < 6 OR X+2 > 9 Answered by Penny Nom. 





The median with ties 
20020227 

From Marcel: What, exactly, is the proper way to determine the median of a set of numbers when doubles or triples of a number are part of that set? Do the doubles count as two and the triples three, or does each count only as one toward determining the median. Answered by Harley Wston. 





Inequalities 
20011113 

From Pat: When writing the solution to an inequality, why is the solution written in set notation? {x/ } Answered by Penny Nom. 





Theme day 
20011014 

From A teacher: I woulld like a math theme for a theme day in a high school, grades 912. Our last theme was fractal fest. Answered by Penny Nom and Claude Tardif. 





Binomial probabilities 
20011008 

From Amna: I had a few binomial probability questions which I can not use from the tables as instructed:  If 60 % of television viewers are watching a certain program, what is the probability tha tmore than half of those selected in a random sample of five will be watching the specified program?
 If it is known according to Mendel's Law, that we can expect in teh long run to have 3 white, 1 brown rabbits in every 4 rabbits of a certain type, what is the probability that 2 in a litter of 3 will be white?
 On the average, 2% of the items sold in a department store are returned for refunds. what is the probability that of its next five items sold, at most two will be returned for refunds?
Answered by Leeanne Boehm. 





A linear inequality 
20010917 

From Eric: How can I solve x + y + x  y< =6? Answered by Penny Nom. 





Don't worry too much about your difficulties in math... 
20010907 

From Matt: Do you know who said,"Don't worry too much about your difficulties in math, I assure you that mine are still greater"? Thanks for your help. this for extra credit and I can't find it ANYWHERE! Answered by Penny Nom. 





Probabilities and dice. 
20010504 

From Carmen: Hi! My name is Carmen! I am a member of a grade 5 class in Edmonton, AB. We were talking about probability in math, and I was wanted to know what the probability (odds) of rolling two sixes would be rolling two dice? If it is not to diffucult could you tell me what the probability (odds) of rolling any number with two dice were? Answered by Andrei Volodin and Penny Nom. 





Winning percentages 
20010221 

From Mike: TEAM A WINS 55% OF GAMES PLAYED TEAM B WINS 40% OF GAMES PLAYED AGAINST THE SAME OPPONENTS WHAT WINNING PERCENTAGE SHOULD BE EXPECTED WHEN TEAM A PLAYS TEAM B (NEUTRAL SITE)? Answered by Harley Weston. 





Two inequalities 
20010212 

From A student: If 3 Answered by Leeanne Boehm. 





Which fraction is greater? 
20010201 

From Carol: Hello My name is Carol I am a student teacher! I am asked to aproach these students on their problems. I am unsure of how to explain to them that these are wrong. Can you help? Thanks. Iris claims that if we have two positive rational numbers, the one with the greatest numerator is the greatest. Shirly claim that if we have two positive rational numbers, the one with the greatest denominator is the least. Thanks! Answered by Claude Tardif. 





A problem with distance 
20010116 

From A student: For what values of a is the distance between P(a, 3) and Q(5, 2a) greater than the square root of 26. Answered by Penny Nom. 





< and > Which one is which? 
20001206 

From Alice: This grandmother forgot and wants to know the correct for greater and the one for lesser..... the two are < and > Which one is which? Answered by Penny Nom. 





False Positives 
20001029 

From James: A rare disease infected 1 in 1000 people in the population. A test for the disease is accurate 99% of the time when given to an infected person and also when given to a heathy person.  Fill out a twotier tree diagram and find the probability of the false positive(i.e the conditional probabily of being healty even when tested postive by the test) Comment on the result?
 ...
Answered by Penny Nom. 





Larger and smaller 
20001010 

From Nicole: which one of these arrows < , > points to the greater number? which arrows points to the smaller number. Answered by Penny Nom. 





Inequalities 
20000902 

From Jennifer: I would like some help with equations and inequalities. My first inequality is 3p6>21 and 3q+11+8q>99. Answered by Paul Betts. 





Graphing an inequality 
20000802 

From Lori: How do I find x and y and graph this problem 3x + y < 5 Answered by Penny Nom. 





Phone Number Possibilities 
20000109 

From Hamilton Weston: How do phone companies arrive at the possible number of phone numbers that can be generated for customers? Answered by Harley Weston. 





Proving a trigonometric identitiy 
19991217 

From Ryan: I need to figure out how to prove that sec^{2}x + csc^{2}x = sec^{2}x csc^{2}x. I am not sure where to start out with it and whether I should use reciprocal, quotient, or pythagorean. Answered by Penny Nom. 





Inequalities and absolute values 
19991207 

From Austin Cline: Solve for x: The absolute value of x1 is less than or equal to the absolute value of x2 Answered by Harley Weston. 





62x<4 
19991020 

From Tchilco: Solve 62x<4 Answered by Harley Weston. 





A trig problem 
19990603 

From Stu Barnes: cos(theta) / 1+ sin(theta)=sec(theta)tan(theta) I've being having trouble with this one on my correspondance course. Answered by Harley Weston. 





Work jobs 
19990419 

From Cindy Miller: Hi. I'm a college student, majoring in Elementary Education. This semester I am taking a math class for elementary school teachers. I'm not sure if you can help out, but here is what I need. For the class, I am supposed to make 10 work jobs for students. Simple things that teach math that students can work on individually, for example after finishing a test. If you have any suggestions, I would really appreciate it. Answered by Penny Nom. 





Reversing the direction of an inequality. 
19990306 

From Mallory White: If the Problem was 4a plus 5 is less than or equal to 14, why would you change the sign to greater than or equal to? Answered by Jack LeSage and Harley Weston. 





Rowing on the Charles River. 
19970917 

From Fawwaz Muraisi: On the Charles River in Boston, the Harvard bridge and the Longfellow bridge are 1 mile apart. The MIT crew starts rowing upstream at the Longfellow bridge. As the crew passes under the Harvard bridge, the coxswain's hat falls into the river. Ten minutes later, the coxswain notices and turns the boat around instantaneously. He has t he crew row back to get it, rowing at the same constant rate. By the time the team reaches the hat, they are back at the Longfellow bridge.How fast is the river flowing? Answered by Harley Weston. 





Graphing Inequalities of Conic Sections 
19970324 

From James Sheldon: I'm trying to graph Systems of Conic Sections with inequalities, but I'm running into problems on which area to shade: x^2+y^2 is greater than or equal to 16 xy > 4 So I graph these two equations, and then my teacher said to substitute a point into it but I'm still not sure how to do it... Answered by Penny Nom. 





How do you graph these inequalities? 
19960517 

From Robert: How do you graph the inequalities 5+gg, and g+h>6 on one coordinate plane? Answered by Harley Weston and Maxine Stinka. 





A trig identity 
19960311 

From Azmat Hussain: Is there an easier/another way to prove the trig identity cos(a+b) = cos(a)cos(b)sin(a)sin(b)? Answered by Penny Nom. 





Trig identities 
19951130 

From Azmat: Why do we work on the two sides of a trig identity separately? Answered by Harley Weston. 





Ses points de discontinuités est les irrationnelles 
20020108 

From Un eleve: Je voudrait montrer qu'il n'existe pas de fonction de R>R tels que ses points de discontinuités est les irrationnelles, en utilisant la methode de "baire". Answered by Claude Tardif. 

