







The domain of f(g(x)) 
20180618 

From Joshua: What are the restrictions of the domain of f(g(x))? Answered by Penny Nom. 





The inverse square law 
20180605 

From Amy:
Question about inverse square law ;
Hi, I'm trying to understand some nuances about this law and
have been reading about it a lot online and trying out some homework
for personal interest (hobby )  not school related.
I understand that the simple formula is ; 1/d^2
I was wondering about what appears to be an oddity to me, that
I came across when I was working with a test example I found at this
link ;
http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/
The problem that caught my interest was this one on that page ;
"1) If a bright flashlight has a light intensity of 15.0 candela at a distance 1.00 m from the lens, what is the intensity of the flashlight 100.0 m from the lens?"
So I have a few different questions about this, but the most important
one is, what does it mean if we replace the "1" in ; 1/d^2 with a different value such as a ratio in the form of a decimal value, so instead we have something like this ;
0.75/d^2
???
Does this ratio represent a curve then?
I am thinking that the "1" in the normal formula represents a straight line
Some of the links I was researching ;
http://wisptools.net/book.php?c=3&s=2
http://www.softschools.com/formulas/physics/inverse_square_law_formula/82/
https://www.ndeed.org/GeneralResources/Formula/RTFormula/InverseSquare/InverseSquareLaw.htm Answered by Penny Nom. 





mg to ml 
20180517 

From Carolynne: I need to convert 12 mg to ml
density is 12.5mg/5ml
I can give dose of 1mg per pound . My dropper is in ml.
How much in ml can I give Answered by Penny Nom. 





Positive and negative values of a function 
20180130 

From Grayson: f(x)=x^6x^4
Interval: ( negative infinity, negative one )
Test Value: negative two
Function Value f(x): positive forty eight
Interval: ( negative one, zero )
Test Value: negative one
Function Value f(x): zero
Interval: ( zero, positive one )
Test Value: positive one
Function Value f(x): zero
Interval: ( positive one, positive infinity )
Test Value: positive two
Function Value f(x): positive forty eight
What is the sign of f(x) for each Interval? Answered by Penny Nom. 





The mass of a length of tree trunk 
20171113 

From SM: What is the mass of a length of 1m of trunk a tree trunk of uniform cross section of area 0.5 sq.m is made of wood of relative density 0.8? Answered by Penny Nom. 





f(x)=x^26x find f(x2) 
20171027 

From Kenneth: f(x)=x^26x find f(x2) Answered by Penny Nom. 





The composition of a function with itself 
20160717 

From Mel: If f(1 + 3x) = 1 * x, solve f(f(x)) Answered by Penny Nom. 





Covering a site with 6 inches of rock 
20160426 

From Carla: if a pump house that measures 20'x16' sits in the middle of a site that is 50'x60' and you apply crushed rock to the site at depth of 6", how many yards will you need to haul? Answered by Penny Nom. 





Filling a hole with 14 tons of rock 
20160408 

From Barry: If I had 14 tons of inch and one half sized aggregate rock, how large of a square or rectangular shaped hole would I need to hold that amount? Answered by Penny Nom. 





Travelling in opposite directions 
20151206 

From Roselyn: Jenny and Mark commute to work, travelling in opposite directions. Jenny leaves the house at 8 AM, and averages 35 kph. Mark leaves at 8:15 AM, and averages 40 kph.At what time will they be 40 kilometers apart? Answered by Penny Nom. 





The weight of a steel block 
20150404 

From Mark: the weight of a steel cube 37 inches X 28 inches X 7 inches Answered by Penny Nom. 





Two consecutive positive integers 
20150301 

From meha: Find two consecutive positive integers , sum of whose squares is 365. Answered by Penny Nom. 





A stone is dropped in a lake 
20150214 

From Wendy:
Hi, I have problems solving this problem. We didn't exactly go over these kind of problems and the book doesn't have an example either. Thank you for your help!
A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 80 cm/s.
(a) Find a function g that models the radius as a function of time t.
g(t) =
(b) Find a function f that models the area of the circle as a function of the radius r.
f(r) =
(c) Find f compose g.
f compose g = Answered by Penny Nom. 





Mutually prime composite numbers 
20150109 

From nivedita: Two composite number that is mutually prime? Answered by Penny Nom. 





The density of sea sand 
20141102 

From Lenny: Hi There,
I need to find out the the density of sea sand to convert one metric ton to cubic
meter as I am submitting for a tender which is in cubic meter but the requirement
is in metric ton. I searched through the web site but no density of sea sand is given
though there is specific Gravity of dry sand is available. I was given a density of
1.6 to work with. If that is true am I right to say that 1 cubic meter of sea sand is
equivalent to 1.6 metric ton? Please help as I am getting confused with what I am
able to find out on the web.
Thanks much in advance
Rgds
Lenny Answered by Penny Nom. 





Revisiting 8 golfers in two foursomes 
20140819 

From steve:
I noticed you had an answer on how can you put 8 golfers in even foursomes over 7 games so that everyone plays with everyone equally. However the formula showed the following sequence that was used but did not go past the second day. Can you change the 0s and 1s into the numbers 1 to 8 instead. Here is what you have written:
Day 0 : (0, 0, 0, 0, 1, 1, 1, 1)
Day 1 : (0, 0, 1, 1, 0, 0, 1, 1)
Day 2 : (0, 1, 0, 1, 0, 1, 0, 1)
Day 3 : (0, 1, 1, 0, 1, 0, 0, 1)
Day 4 : (0, 0, 1, 1, 1, 1, 0, 0)
Day 5 : (0, 1, 0, 1, 1, 0, 1, 0)
Day 6 : (0, 1, 1, 0, 0, 1, 1, 0)
Thank you so much for your anticipated help.
Steve Answered by Harley Weston. 





A small solid silver pyramid 
20140613 

From Jenesis: For Awards Night at Baddeck High School, the math club is designing small solid silver pyramids.The base of the pyramids will be a 2 in by 2 in square. The pyramids should not weigh more than 2.5 pounds. One cubic foot of silver weighs 655 pounds. What is the maximum height of the pyramids? Answered by Penny Nom. 





The weight of salt in a basket 
20140517 

From Sumit: I want to determine how many kg of salt or XYZ thing can be filled in a basket
Length = 4.5"
Breadth = 5"
Height = 6"
Even its formulae
is kg quantity can be different for semi solid thing Answered by Penny Nom. 





A slab of wet clay 
20140412 

From Karen: How many square feet ( at 1/4 inch thickness) are in 100 lbs. of wet clay? Answered by Penny Nom. 





A silver figurine 
20130503 

From Renee: I have a silver figurine, the density of silver is 10.5g/cm3. if the figurine weighed 149 g. to determine the volume, he dropped it into a cylindrical glas of water. the diameter of the glass is 6 cm and the figurine was pure silver, by how much should the water level in the glass rise? Answered by Penny Nom. 





The continuity of f(x,y)=ln(x^2+y^2) 
20130217 

From anu: the question says we have to find the points in the plane where the function is continuous:
f(x,y)=ln(x^2+y^2) . here we aren't given a particular point (x,y) where we have to check a function's
continuity.
what is to be done if we have to check continuity over the whole domain of the function?
please help . Answered by Harley Weston. 





A relation on a collection of sets 
20130204 

From raji: suppose R be a non empty relation on a collection of sets defined by ARB if and only if A intersection B is nullset.then.....the correct answer is R is symmetric and not transitive...my doubt is how it is symmetric Answered by Penny Nom. 





The weight of a pipe full of water 
20130116 

From joe: how do you figure out the weight of a pipe full of water Answered by Harley Weston. 





Transposition error 
20121203 

From Carol: What is the correct term for when a child writes 61 instead of 16, or 83 for 38when they switch the place values of a number? Answered by Chris Fisher. 





A function problem 
20121118 

From nahla: f: IN > IN
n > f(n)
for every n that belongs the IN : fof(x) = 4n  3
and for every n that belongs to IN f(2^n) = 2^(n+1) 1
Calculate f(993) 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. 





Composition of functions and one to one 
20121017 

From Ariana: If f o g are one to one function,does it follow that g is one to one? Give reasons for your answers Answered by Penny Nom. 





The position of an aircraft relative to the airport 
20120608 

From Dennis: "Air traffic controllers usually describe the position of an aircraft relative to the airport by altitude, horizontal distance, and bearing. Suppose an aircraft is at altitude 500m, distance 15km, and bearing 35 degrees east of north. What are the x,y, and z components (in meters) of the position vector. The xaxis is east, the yaxis is north and the zaxis is vertical. Answered by Penny Nom. 





A uniform probability density function 
20120326 

From Noeline: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 ≤ x ≤12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





One acre of dirt 6 inches deep 
20120111 

From Cameron: Ok what im wanting to know is how many pounds of dirt are in 80
acres of land that is 6 inches deep? My friend and I are stumped on this question Answered by Penny Nom. 





Limits and composition 
20111230 

From Rahul: I want to know about limit proofs of composite functions. Like limit of log of a function equals log of limit of the function Answered by Penny Nom. 





The weight of 36 inch steel pipe 
20111222 

From Keith: What is the weight of 36 inch steel pipe 3/4 wall per foot in lbs. Answered by Penny Nom. 





The LCM of 6,15 and x is 90 
20111030 

From Richie: Hi there,
There are 2 parts to the question.
#1. Factorise 90. This is easy, 90=2x3x3x5
#2
LCM of 6,15 and x is 90. What are possible values of x if x is odd?
From #1, since 90=6x15, how can this be used to work out possible values of x?
Thanks in advance,
Richie Answered by Penny Nom. 





Composition of functions 
20110905 

From Jenna: Let f(x)=x^21 and g(x)=12x. Find the indicated values.
1. f(g(1)) and g(f(1))
Thanks,
Jenna Answered by Penny Nom. 





The mass of a metal box 
20110311 

From Pamela: A metal block has the dimensions of 3.16 inches wide, 2.15 inches
high, 4.98 inches long. What is the volume of the block in cm^3?
What is the block's mass if the metal has a density of 5.89g/cm^3. Answered by Robert Dawson. 





The weight of a tank 
20110111 

From tom: A tank, open at the top is made up of thin sheet iron 1in. thick. The internal
dimensions of the tank are 4 ft. 8in. in long ;3 ft. 6 in.in wide ;4ft 4 in. in deep
Find the weight of the tank when empty, and find the weight when full of salt
water. (Salt water weighs 64 lbs. per cu. ft., and iron is 7.2 times as heavy as
salt water) Answered by Harley Weston. 





How many gallons of water will it take to fill a classroom? 
20101201 

From deena: How many gallons of water will it take to fill a classroom that is 26 feet long by 19 feet wide and 9 feet high? How many tons of water will that be? Answered by Stephen La Rocque. 





The weight of some dirt 
20101103 

From Maggie: I am wanting to know how many tons of dirt we r going to need to fill a basement.
The measurements we r going with r 15ftx15ftx8ft. Answered by Penny Nom. 





Disposing of some concrete 
20100812 

From Kathy: We are needing to dispose of concrete that we are tearing out of our
backyard and I need to figure the dimensions and weight.
I figured we have approx. 419 sq ft of concrete at 4" thick.
Could you tell me the how much that comes to in cubic ft,
cubic yards and weight. So I can get some estimates on pricing to
haul off and dispose of. thank you Answered by Harley Weston and Tyler Wood. 





70 cubic meters of mulch 
20100730 

From zsuzsi: i have 70 cubic meters of mulch to move and an 8 tonne truck to use
how much tonnage is to 1 square meter so that i can work out how many trips i need to make Answered by Penny Nom. 





The tonnage of some gravel 
20100722 

From Gregory: i have a road that is 8 miles long 20 feet wide and 4 inches deep what is the tonnage for gravel i would need Answered by Penny Nom. 





The test for some disease is 99% accurate 
20100224 

From baaba: Assume that the test for some disease is 99% accurate. If somebody tests positive for that disease, is there a 99% chance that they have the disease? Answered by Chris Fisher. 





4digit positive numbers 
20100215 

From marjon: Find the sum of all the 4digit positive numbers with no zero digit. Answered by Penny Nom. 





The intervals where the function is positive and negative 
20100110 

From Ron: Hello
I'm trying to find out the intervals where the function is positive and negative.
It's for a polynomial function y= (x+2)^2 (x2) and y= (x+1)(x+4)(x3)
I have tried the right and left side of each xintercepts, but I still don't understand the
results
thank you for your help Answered by Penny Nom. 





Finding Density Given Volumetric Thermal Expansion Coefficient 
20091226 

From florence: Hi
Please help me to apply the formula for this problem. The coefficient of volumetric for gold is 4.20 X 10^5 C degrees. The density of gold is 19,300 kg/m^3 at 0.9 C degrees. What is the density of gold at 1050 degrees C.
Could you please explain how to get the solution of 18,500 kg/m^3
Thank you for your help
Florence Answered by Janice Cotcher. 





A number base that's not a positive integer 
20091211 

From Nick: Is it possible for a number to have a base that's not a positive integer?
Base 1 gives a result that's meaningless but possible. I have no concept of a base 0, a negative base, or a fractional base, never mind any other base. I think there isn't any base that's not a positive integer, but, knowing that math keeps jumping ahead and sometimes has inventions before anyone knows how to exploit them, I think I'd better ask.
Thank you.
Nick Answered by Robert Dawson and Claude Tardif. 





Density of dirt and gravel 
20091026 

From ken: if digging a load of dirt and gravel in mining how many yards of material to the ton thanks Answered by Penny Nom. 





Sawdust 
20090929 

From joel: What is the density of saw dust Answered by Harley Weston. 





Gravel in an aquarium 
20090809 

From Bev: Hi...I worked this part out, but want to know how many kilograms of gravel I will need...thanks
Bev
Cylinder shape.
A cylindrical shape that has a radius of 82 centimeters and a depth of 7 centimeters has a volume of:
Volume
= 0.14787 cubic meters
= 147870 cubic centimeters
= 0.1934 cubic yards
= 5.2219 cubic feet
= 9023.5 cubic inches
= 39.063 U.S. gallons
= 147.87 liters
* calculations accurate to 5 decimal places of precision Answered by Harley Weston. 





Cubic meters of gravel in a 7 ton lorry 
20090621 

From Jackie: I have to transport gravel in a 7 ton lorry and I know how many cubic meters of gravel I need, but I need to know how many cubic meters of gravel a 7 ton lorry can hold.
Thanks, Jackie Answered by Penny Nom. 





Percent increase from a negative number to a positive number 
20090421 

From Brian: I have no problem calculating year over year net profits but am having trouble when it comes to a negative.
2007 Net Profit = 110,333.00
2008 Net Profit = 66,054.00
Brian Answered by Harley Weston. 





Comparing positive and negative fractions 
20090324 

From Christyrose: Hello. I am a sixth grade math student and i need help on how to compare negative and positive fractions.
Here is is:
3/4 2/3 7/10 5/6
I'm not sure how to do the negative parts because i was absent for a couple days. Thank you!
Christyrose Answered by Penny Nom. 





The amount of material remaining on a reel 
20090304 

From James: Question from james:
I am after a standard calculation so that after each usage of the Reel I can get the Remaining Quantity in kilos left on the roll
below is an example of roll
THICKNESS: 30 MICRON
REEL WIDTH: 7.5 CM
REEL DIAMETER: 76 CM
REEL WEIGHT: 7.13 KILOS
The core centre has a 9cm diameter, the weight of the roll is excluding the core , and after each use the diameter of the role is measured.
I am a factory supervisor working on project and need this calculation info for template.. Thanks James Answered by Harley Weston. 





Pressure at Given Depth 
20090222 

From Tamara: A sea is 3km deep. The average density of sea water there is 1020 kg/m^3. What is the water pressure at the bottom? Answered by Janice Cotcher. 





The volume of a yogurt pot 
20081204 

From Robyn: Okay, I know you have some answers on converting this already, but I can not convert the yoghurt pot I need yet into ml.
Is there some way to explain this using the yoghurt as an example?
The pot's 150g of lowfat strawberry yoghurt... would the 'lowfat' have an effect on this?
I'm sorry if this is a bother for you to answer, I just don't seem to be able to get it...
Have a nice day.
 Robyn Answered by Janice Cotcher and Penny Nom. 





A product of positive and negative numbers 
20081003 

From kaylou: Suppose you were given 13 numbers and asked to find their product.
Seven of the numbers were positive, and the rest were negative.
Would your product be positive or negative? Why? Answered by Penny Nom. 





The weight of a concrete cylinder 
20080918 

From Curtis: I am trying to calculate the weight of a concrete cylinder. The diameter is 56" and the thickness or depth is 24". Can anyone help me? If possible I would like to see the formula as to how the answer was derived. Thank you Answered by Harley Weston. 





557 mL of benzaldehyde 
20080828 

From Kara: Calculate the mass of 557 mL of benzaldehyde. The density of benzaldehyde is 1.04 g/mL. Answered by Penny Nom. 





Right Sided Limit of an Exponential Function 
20080729 

From joseph: I am trying to find the limit as X approaches 0 from the positive side of x to the sin of x
which look like this lim x^sinx
x>0+ Answered by Harley Weston. 





Three consecutive positive integers 
20080720 

From AC: find three consecutive positive integers such that the product of the first and third, minus the second, is 1 more than 4 times the third Answered by Penny Nom. 





Neither prime nor composite 
20080708 

From saloni: Give the counting number which is neither prime nor composite ? Answered by Penny Nom. 





Composition of two functions 
20080704 

From Kristian: f(x)= the square of x add to 1 and g(x)=1/x
find: (f o g)x Answered by Penny Nom. 





The weight of concrete 
20080611 

From Daniel: I need to calculate the weight of Concrete in a slab that measures 2' x 4' x 4" thick.
I am pricing out a job and have two different size stones to work with, the second stone measures
2' x 2' x 4". Answered by Harley Weston. 





.5 cu ft of sand to lbs. 
20080525 

From rogersimmons: needtocovert .5 cu ft. of sand into lbs. Answered by Penny Nom. 





Volume/weight of a salt shedweight 
20080521 

From James: How do I find the volume/weight of a salt shed. I have a 3000 ton barn, I need a better way of finding how much salt to order as it gets used. I know how to calculate volume, how do i get tonnage from there?? Answered by Harley Weston. 





The weight of a concrete column 
20080511 

From russell: a cylindrical form is filled with a slow curing concrete. The base of the form
is 10 ft in radius, and height is 25 ft. while the concrete hardens, gravity
causes the density to vary from a density of 90 lbs/ft^3 at the bottom to a
density of 50 lb/ft^3 at the top. Assume that the density varies linearly
from the top to the bottom, and compute the total weight of the resulting
concrete column Answered by Harley Weston. 





Converting metric density 
20080428 

From Hilary: 10g/100ml=?g/?l
52g/100ml=?g/?l
65g/100ml=?g/?l
100g/100ml=?g/?l
137g/100ml=?g/?l
0.15g/100ml=?g/?l Answered by Penny Nom. 





A 13 cubic foot cylinder filled with sand 
20080412 

From Thomas: I have a 100 pound bag of sand. I need to know how much sand I will need to fill a 13 cubic foot cylinder Answered by Harley Weston. 





The weight of 1 litre of milk 
20080407 

From IMRAN: WHAT WEIGHT IN KILOGRAMS DOES 1 LITRE OF MILK HAVE? Answered by Penny Nom. 





Composition of functions: feet, inches and yards 
20080405 

From Coya: write a function f(x) that converts feet to inches.Now write a function g(x) that converts yards to feet. Explain what the composite function f(g(x)) means. Then evaluate f(g(x)) for x = 3,6, and 9. Answered by Stephen La Rocque. 





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. 





Composition of functions 
20080307 

From sharon: Find FoG(x)
F(x)= the square root of x9
G(x)= x^2
and also find GoF and their domains Answered by Penny Nom. 





Why is the number 1 neither prime nor composite? 
20080207 

From ronni: why is the number 1 neither prime nor composite? Answered by Harley Weston. 





Bubbles trapped in the volumetric pipet 
20080131 

From Nursing: In determining the density of a liquid, a student left air bubbles trapped in the volumetric pipet. Did this give a density less than expected or greater than expected? Why? Answered by Penny Nom. 





The volume of a tank 
20080127 

From Fred: A cubic tank holds 1,000 kilograms of water what are the dimensions of the tank in meters? Answered by Harley Weston. 





Converting mg's to cc's 
20080117 

From sandy: i need to find out how to convert mg's to cc's i need to give 10 mg of liquid and 5 mg of liquid and i only have a dropper that measures cc's please help Answered by Stephen La Rocque and Harley Weston. 





Transformations and compositions 
20071129 

From mary: Is there any possible relationship between composite functions and the concept of function transformations? Answered by Harley Weston. 





Density 
20071129 

From jessuca: what is the density for 40g / 2 mL Answered by Penny Nom. 





I know it's heavy, but how heavy, per linear foot? 
20071119 

From Gary: I am trying to find out the weight of a linear foot of a steel bar with the following measurements.
Thickness  1.125"
Length  120"
Height  18"
Density of carbon steel  .2837
I know it's heavy, but how heavy, per linear foot? Answered by Stephen La Rocque. 





A mole of hydrogen peroxide 
20071111 

From John: i need to get a mole of hydrogen peroxide, which i know is 34g, but i don't have a way to measure grams, so do you know how many mililiters i need to have 34g of hydrogen peroxide. Thanks for all the help Answered by Stephen La Rocque. 





How do i convert milliliters to grams for water and also for copper sulfate (CuSO4)? 
20071111 

From jenn: how do i convert milliliters to grams for
water and also for copper sulfate (CuSO4)? Answered by Harley Weston. 





Why is the number 1 neither prime nor composite? 
20071108 

From amarilis: why is the number 1 neither prime nor composite? Answered by Penny Nom. 





Density 
20071030 

From Ali: Would an object sink or float in pure water if it has a mass of 10g and a volume of 5 cubic centimeters?
314 Answered by Stephen La Rocque. 





How many tons of asphalt are in 12 cubic yards? 
20071015 

From Matthew: I want to know how many tons of asphalt are in 12 cubic yards? Answered by Penny Nom. 





Motion along a line 
20071002 

From Claudette: If the position function of a particle is x(t) = sin^2(2t), find the distance that the particle travels from t = 0 to t = 2 Answered by Harley Weston. 





A 3 ounce piece of gold 
20070924 

From Helen: What would the volume (in mL) of a 3 ounce piece of gold be?
16oz= 1lb
1lb= 454oz.
first i converted 3oz to lbs and then to grams to get the mass. i got 85.125 g.
now i don't know how to get the density to get to the volume. Answered by Stephen La Rocque. 





Volume, mass and density 
20070914 

From Nathan: I have a sample of material that is 10cmx10cmx5cm and has a mass of 29 grams. How many grams would a sample of the same material that was 96cmx188cmx5cm be? Answered by Penny Nom. 





How much stone will be needed to fill the trench? 
20070914 

From Debbie: A trench 100metres long 1ft wide*18inches deep with a 4inch pipe laid. How much stone will be needed to fill the trench.
How much weight in stone would I need to fill it? Answered by Penny Nom and Victoria West. 





Is it platinum or silver? 
20070914 

From Jordan: In Chemistry we are doing a lot of problems that are much more math related than anything. One of my questions reads: A certain medallion has a mass of 55.64 g. When placed in 75.2 mL of water in a graduated cylinder,
the water level rises and then reads 77.8 mL.
Is the medallion made of platinum (D=21.4 g/mL) or silver (D= 10.5 g/mL)? Answered by Penny Nom. 





Composite angles 
20070913 

From Gilbert: what is a composite angle? please help Answered by Stephen La Rocque. 





What was the water level in the cylinder? 
20070911 

From glen: After a 5.63g sample of Wood's metal has been added to the water in a 10mL graduated cylinder, the new water level is 8.7mL. What was the water level in the cylinder before the sample was added? Answered by Stephen la Rocque. 





Grams of vodka 
20070710 

From Andrew: milliliters to grams..vodka 80 proof? Answered by Stephen La Rocque. 





Derivative of a Function 
20070709 

From Bob: What is the derivative of the function a sub n = [n/(n+1)]^n ? Answered by Stephen La Rocque. 





Tons of concrete 
20070703 

From Trey: I have 300,000 square feet of concrete and want to know how to convert this to tons? Answered by Harley Weston. 





How do I convert milliliters(powder form) to grams? 
20070628 

From ed: How do I convert milliliters(powder form) to grams Answered by Harley Weston. 





How many tons of sand? 
20070619 

From Richard: I need to know how many tons of sand it would take to fill a container 20 feet
long, 20 feet wide, and 6 inches deep. I am not sure of the makeup of the sand as
far as dry, loose, wet, etc. If you could give me calculations of all the variants it
would be appreciated. Answered by Stephen La Rocque and Penny Nom. 





The composition of functions 
20070614 

From Gilligan: Question from Gilligan, a student:
Let f(x) = x^2, g(x) = 3x and h(x) = (sqrt{x}) + 1. Express each function as a composite of f, g and/or h.
(1) p(x) = 3(sqrt{x}) + 3
(2) Q(x) = (sqrt(sqrt{x}) + 1}) + 1 Answered by Penny Nom. 





Composition functions 
20070612 

From Gilligan: Find functions f and g so that f(g(x)) = H.
(1) H(x) = (1 + x^2)^(3/2)
(2) H(x) = int(x^2 + 1)
I don't know where to start. Answered by Stephen La Rocque. 





The number of grams of sulfuric acid 
20070531 

From cookie: Hi,
Can you please let me know if I've done this correctly?
Calculate the number of grams of sulfuric acid in 0.500L of battery acid if the solution has a density of 1.28 g/mL and is 38.1% sulfuric acid by mass. Answered by Stephen La Rocque. 





How many tons of dirt is this? 
20070523 

From Deb: I need to know how many tons of dirt(6 inches deep)would it take to cover 8 acres? Answered by Stephen La Rocque. 





Converting mass of sand to volume (a sand ceremony) 
20070521 

From Linda: I'm getting married. We are having a sand ceremony. The empty bottle we are using holds 800ml. I have bags of colored sand. Each bag is 30g. There is 7 people participating in this ceremony. What I need to find out is how many grams of sand i need for 7 people to participate to fill this jar. Answered by Penny Nom. 





A ton of sawdust 
20070510 

From David: I am trying to do a conversion. A tractor trailer is loaded with 165 cubic
yards of sawdust (I do not know the actual weight). I knw the wholesale
cost as $1,000 for this amount, but would like to convert this to find out
what the equivalent cost for a metric ton would be. Answered by Stephen La Rocque. 





Probability of H.I.V. tests 
20070507 

From Danielle: A medical test detects H.I.V. Among those who have H.I.V., the test will detect the disease with probability 0.95; among those who do NOT have H.I.V., the test will falsely claim that H.I.V. is present with probability 0.0125. Among those who take this test, 4% have H.I.V. The test is given to Lucille, and indicates that she has H.I.V. What is the probability that Lucille actually has H.I.V.? Answered by Stephen La Rocque. 





How many tons of sand is needed 
20070425 

From Jennifer: How many tons of sand is needed to cover 350 cubic square feet? Answered by Penny Nom. 





How can I convert milliliters to grams? 
20070418 

From April: What if I'm using cow's milk, how can I convert milliliters to grams? Answered by Stephen La Rocque. 





Yards of sand in a ton 
20070409 

From Teresa: how many yards of sand are in a ton and how many yards of limestone does it take to make a ton Answered by Penny Nom. 





What is the intensity 5m below the surface? 
20070331 

From david: I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the diffrential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface. Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help. Answered by Penny Nom. 





Factoring a trinomial 
20070327 

From Kim: Hi, could you please help me solve this.
3x(squared) +20x  7 Answered by Leeanne Boehm. 





Concrete sand 
20070308 

From david: Can you tell me how much 4 cubic yards of concrete sand ways in tons? THANK YOU. Answered by Stephen La Rocque. 





Centimeters to cubic meters and grams to kilograms 
20070214 

From Colleen: A box of balls measures 120cm by 20cm by 20cm and weighs 48 g. One thousand boxes = x cubic meters and weighs x kilograms. Also, one million boxes = x cubic metes and weighs x kilograms. One billion boxes = x cubic meters and weighs x kilograms. Solve for x. Answered by Stephen La Rocque. 





Density 
20070209 

From Judy: How do I calculate the mass in grams of 125mL of chloroform when d=1.49g/mL. Answered by Stephen La Rocque. 





The density of an irregular wooden block 
20070130 

From Carlos: I'm trying to help my son but I don't really have too much knowledge about this topic. he is been asked to convert 10 milliliter to gram, I think that since 1 g = 1ml the answer will be 10 g also there is another question of how of the density of an irregular wooden block is affected if: a) the center is hollow: b) the block is not completely submerged when determining the volume. Answered by Stephen La Rocque and Penny Nom. 





Why zero is neither prime nor composite? 
20070117 

From Brenda: Why zero is neither prime nor composite? Answered by Penny Nom. 





I want to convert milliliters into grams. 
20061214 

From Kenchotenzin : I want to convert milliliters into grams. Answered by Penny Nom. 





What is the diameter of the planet? 
20061207 

From Niall: In April 2005, scientists claimed to have captured light from an extrasolar planet orbiting a brown dwarf in the constellation Hydra some 230 lightyears from Earth. The scientists believe the planet is about five times the mass of Jupiter.
Assume the planet has the same density as Jupiter. What is the diameter of the planet? Answered by Stephen La Rocque. 





solve; 
20061128 

From Monique: solve; f(f(x)) = 2x + 4 ; if f(x) = 1 Answered by Penny Nom. 





Composition of functions 
20061119 

From RJ: Let f0(x) = 2/2x and fn+1 = f0 o fn for n greater than or equal to 0. Find a formula for fn and prove it by mathematical induction. Recall that o represents function composition. i.e., (f o g)(x) = f(g(x)). Answered by Stephen La Rocque. 





Composition of functions 
20061118 

From Oryan: Given f(x)=2x^3 and g(x)4x5, find g(f(1)) Answered by Stephen La Rocque. 





Two problems involving density 
20061006 

From Patricia:
1. Nick has to ship 650,000 g of substance A to Singapore. The density of substance A is 3.23g/cm^3. If the delivery charge is 0.25 centavo per cm^3,how much does he need to pay?
2.Ann ordered 150 balloons for a birthday. Each balloon has a radius of 20cm. If the density of helium is 0.124g/cm^3,how many grams of helium is needed to meet the order?
Answered by Stephen La Rocque. 





How much does 1300cc of liquid weigh? 
20060428 

From Debra: How much does 1300cc of liquid weigh, and how is the formula equated? Answered by Stephen La Rocque. 





How much money can I borrow if I have $5 000 for a deposit? 
20060419 

From Chris: I have a sum of cash that I want to use as a deposit ($ 5 000) and a lender will lend me 65% of the purchase price. How do I calculate the maximum value I can borrow?
Answered by Stephen La Rocque. 





A proof by contraposition 
20060316 

From Eban:
1)by mathematical induction prove that 1^{2} + 3^{2 }+ 5^{2 }+ ...... + (2k1)^{2} = (1/3)k(2k1)(2k+1) for all positive integers k.
2)show that the contrapositive of the following statement is true. if 1 + M^{7} is even, then M is odd.
Answered by Stephen La Rocque. 





An account that earns 6% annually 
20060301 

From Christine: How much do you have to deposit to an account that earns 6% annually if you want to earn $1200 on the account? Answered by Stephen La Rocque. 





Percentage increase in sound intensity 
20060129 

From David: I am doing some emotion response mapping.
Being a composer I know how to push the heart beat tempo by a % increase of BPM in my music. I want to know how to calculate an increase in intensity of sound. Now I have 60 decibels. I want an increase of intensity by a factor n% with out going over 156 decibels.
Answered by Penny Nom. 





Composite triples 
20060124 

From Laeah: question 1 Find the smallest integer n such that n+1, n+2,and n+3 are all composites.
question 2 If n = 5! +1, show that n+1, n+2, and n+3 are all composite.
question 3 Find the sequence of 1000 consecutive composite numbers. Answered by Penny Nom. 





I need to order sand for playgrounds 
20060118 

From Jody: I need to order sand for playgrounds. I have their square footage and the various depths of sand needed for each, but sand comes in tons.
What is the formula for converting square footage and depth to tons (for example: 6 inches of sand needed for a 200sq ft area = how many tons?) Answered by Penny Nom. 





fog 
20051112 

From Janice: I am having problem with the (fog) function
(fog) (x). Given f(x)= 2x^{2} ; g(x)= 34x Answered by Penny Nom. 





Whole numbers 
20051010 

From Kirk: Can the sum of two or more whole numbers be less than any of those numbers? Answered by Penny Nom. 





Adding positive and negative numbers 
20050903 

From Billy: 46 + 24 =
38 + 22 =
19  20 = Answered by Penny Nom. 





Spraying roses 
20050303 

From A student: A litre and a half of water has 0.045 grams of herbicide added for spraying roses. How many grams of herbicide per litre is this? Answered by Penny Nom. 





A seating arrangement 
20050203 

From Kay: If you have 5 married couples, how many arrangements can be made if they must sit across from each other? Answered by Penny Nom. 





Strategies for teaching operations with positive and negative decimal numbers 
20050202 

From Erin: I am wondering if you can suggest any strategies for teaching operations with positive and negative decimal numbers that do not rely on rules that must be memorized? Answered by Diane Hanson. 





An isosceles triangle 
20050103 

From Abraham: The question is,"Triangle ABC is not isosceles.Prove that if altitude BD were drawn, it would not bisect AC."My question is If an altitude is drawn wouldn\'t that mean automatically its isosceles because, In a triangle the sides opposite congruent angles(in this case the right angles)are congruent? What am I thinking wrong? Answered by Harley Weston. 





1/4 tsp salt = ??? grams 
20041116 

From Julie: if i have 1/4 teaspoon of salt how many grams does that equal Answered by Penny Nom. 





Visitor wins or home wins 
20040929 

From Paavn and Laddi: I have a math question i am stumped on for one of my classes. The question states that there are 14 baseball games with 2 possible outcomes for each game, visitor win or home win. How many different total combinations are possible from the 14 games? Answered by Penny Nom. 





Pizza for Jack? 
20040916 

From Grace: Jack is playing pool with Jim for $1 a game. He has only $2 and decides to play until he goes broke or has $5, at which point he will quit and go out for a pizza with Jim(Dutch treat). Jack knows from past experience that he beats Jim 60% of the time. What is the probability that Jack will get to eat pizza? Hints: Let A be the 6x6 matrix defined by A=[aij], where aij is the probability that Jack will have $(i1)after one game is he starts with $(j1). For example, a23  .40 since there is a 40% probability that Jack will end up with $1 after a game is he starts the game with $2 (If Jack wins 605 of the time, he must lose 40% of the time). Also, for example, a52 = 0 since there is no way jack can have $4 after one game if he had $1 at the beginning of the game. Since Jack will stop if he goes broke or accumulates $5, a11 and a66 are both 1.
Let x0 = [0 0 1 0 0 0 ] transposed, which we interpret as saying that initially Jack has $2 with a probability 1. Then Ax0 will represent the porbability of each amount of money, $0$5, after one game. What is the probability that Jack will be able to eat pizza by computing Akx0 for large k and finding a limiting value. Answered by Penny Nom. 





Limits and composite functions 
20040807 

From Sue: I have two questions, one about a limit and the other about a composite function. If you could help me, I'd really appreciate it.
1. Find the limit:
lim[x>0] (x*csc(x))
I converted csc(x) to cos(x)/sin(x), but I didn't know what to do after that.
2. f(g(x)) = ln(x^2 + 4), f(x) = ln(x^2) and g(x) > 0 for all real x, find g(x):
I'm having trouble with this one because x^2 + 4 isn't a perfect square.
Sue Answered by Penny Nom. 





The sum of some positive integers 
20040607 

From A student: Find the sum of all positive integers not greater than 10000 that are divisible by neither 3 nor 7. Answered by Penny Nom. 





A probability density function 
20040414 

From A student: The label on a bottle of liquid detergent shows contents to be 12 ounces per bottle. The production operation fills the bottle uniformly according to the following probability density function:
f(x) = 8 for 11.975 <= x <= 12.10
and
f(x) = 0 elsewhere
a. What is the probability that a bottle will be filled with 12.02 or more ounces?
b. What is the probability that a bottle will be filled between 12 and 12.05 ounces?
c. Quality control accepts production that is within .002 ounces of number of ounces shown on the container label. What is the probability that a bottle of this liquid detergent will fail to meet the quality control standard? Answered by Penny Nom. 





A snowball melts 
20031211 

From Adam: A spherical snowball has diameter 10cm and density 0.75g/cm3. It is placed in a cylindrical can with diameer 12cm. After the snow melts it turns to water with density 1.0g/cm3. What will be the depth of the water in the can (to 1 decimal place)? Answered by Penny Nom. 





A fish tank 
20031126 

From Bill: How do I work out the volume and weight of water in a fish tank that is 36in x 14in x 12in? Answered by Penny Nom. 





If 1 is neither prime nor composite... 
20031119 

From Joshua: if 1
is neither prime nor composite...what is it called? Answered by Claude Tardif and Penny Nom. 





If 1 is neither prime nor composite... 
20031119 

From Joshua: if 1
is neither prime nor composite...what is it called? Answered by Claude Tardif and Penny Nom. 





Making a square 
20030907 

From A student: if I am given any number (say 80 for example), how may I determine the smallest whole number integer which when multipled by it will yield a square number ? In other words if I express this as: 80İ*İnİ=İsquareİnumber, what is the least value of n which will yield a square. Answered by Penny Nom. 





Positive, negative and zero 
20030904 

From Brian: Can the Value of zero be positive or can it be negative or can it be both. Answered by Penny Nom. 





Density 
20030219 

From Rob: What is the formula for converting cubic feet to pounds? (with any substance) Answered by Penny Nom. 





Three consecutive positive intergers 
20030209 

From Yew: Prove that when we multiply any consecutive positive intergers, the result is always divisible by 6.
ex. (7)(8)(9) = 504 = 6 (84) Answered by Penny Nom. 





Composites, primes, factors and common factors 
20021120 

From Connie: My son can't remember what a composite number is, what a prime number is and the explaination of factors and common factors. Help! Answered by Penny Nom. 





n +1, n+2, n+3, and n+4 are all composite 
20020409 

From Jonathan: Find the small integer n such that n +1, n+2, n+3, and n+4 are all composite Answered by Penny Nom. 





Composition of functions 
20020406 

From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = x^{2}  4 and g(x) = sqrt(x) The range of f(x), x<=4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(x^{2}  4). In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything? Answered by Claude Tardif. 





Baseball and sit ups 
20020131 

From A student: A baseball team won 8 more games than it lost. If it played 56 games, how many games did it win? On the first day of practice, Paul did 3 sit ups. On the second day he did 5, and on the the third day he did 8, and on the fourth day he did 12. If this pattern continued, how many situps did ihe do on the sixth day of practice? Answered by Penny Nom. 





Composition of functions 
20011216 

From Paula:
 if f(x)= 3x1 and g(x)= 1/2x + 3 find fog(2)
 find the values of x for which tanx=0
Answered by Penny Nom. 





Negative times negative is positive 
20011026 

From Mary: I have a question about adding and multiplying positive and negative numbers. When we add two negative numbers the answer is negative BUT when we multiply two negative numbers the answer is positive. I don't understand. Why? Answered by Penny Nom. 





Marginal Propensity to Consume 
20010509 

From Esther: The derivative of the national consumption function C = f(y) is called the ____________________. Answered by Judi McDonald. 





Neither prime nor composite 
20010508 

From Marc: what 2 numbers are neither prime nor combitative? Answered by Penny Nom. 





A sequence of even terms 
20010429 

From A student: A sequence c is defined recursively as follows: c0 = 2 c1 = 4 c2 = 6 ck= 5ck3 for all integers Prove that cn is even for all integers. Answered by Leeanne Boehm and Penny Nom. 





An order relation 
20010212 

From Amy: What is an order relation? Answered by Claude Tardif. 





The city transit system 
20010107 

From Jacky: The city transit system carries an average of 9450 bus riders a day, for a fare of $1.75 each. The city wants to reduce car pollution by increasing ridership and to maximize the transit system's revenue at the same time. A survey indicates that the number of riders will increase by 150 for every $0.05 decrease in fare. Answered by Harley Weston. 





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. 





LOG(LN(x)) = 1 
20000728 

From An algebra student: LET F(x)=LOG X AND G(x)= LN X. SOLVE (f *G)(x)= 1 SHOW COMPOSITION AND USE DEFINITION OF LOGS. Answered by Harley Weston. 





(mn + m + n)/(m^2 + n^2) = 1 
20000724 

From William: Find all pair of positive integers m and n such that mn + m + n divides m^{2} + n^{2} = 1. Answered by Peny Nom. 





Natural numbers 
20000412 

From Sara: What is a natural number??? Answered by Penny Nom. 





Mass of the earth 
20000221 

From Terry Broughton: My name is terry i am 15 my question is how much does our planet earth weigh ? Answered by Chris Fisher and Harley Weston. 





Whole numbers 
19991202 

From Patty: I'm in a 5th grade class, please explaine what whole numbers are..... Answered by Penny Nom. 





Who is right 
19990904 

From rf, k, p and uncle a: Good morning. Could you please, help us resolve and by the way, confirm "who is right"... regarding the solution of this problem:  a piece of metal is 6 in. wide by 2 in. in height and weights 500 pounds...  what is the weight of a piece made of same metal, 5 in. wide by 1 3/4 in in height? Could you please supply the "formula". Regards, rf, k, p and uncle a. Answered by Penny Nom. 





Is zero positive? 
19990903 

From Shah: Is zero a positive integer? Answered by Penny Nom. 





Division by a negative 
19990819 

From Sangeeta B.: 56/8 Answered by Penny Nom. 





Composite Numbers 
19981007 

From Greg Murphy: What type of composite number has an odd number of factors? Answered by Harley Weston. 





How do you find out if a number is a composite or prime? 
19960916 

From Trish Feenstra: Hi my name is Trish Feenstra. In grade 8. How do you find out if a number is a composite or prime if it is big like 37 529? Reply soon got a test on Friday the 13th Answered by Denis Hanson. 

