Dear Easter,
A little interpretation of this question goes a long way. I THINK the intent is, how many ways could three cheeses be selected as a permutation ("in order"). That would be P (6 . 3) or 6!/(6-3)! = 120 ways.
However, the question could ALSO be interpreted as finding...

In addition to Kenneth S's note above, you might note that each side has 2 adjacent, 2 next-adjacent, 2 further-adjacent, and 1 opposite side. And distances could be specified as from the nearest points of each side (i.e. vertex to vertex), or averages of all the points of each side -- since you're...

JT: First, you must appreciate that the graph for this equation is a double spiral, which starts from the origin at .theta. = c , and proceeds outwards from there in 2 interleaved lobes (this assumes that negative values of r are permitted). So the angle at which the spiral(s) originate is c, and...

Not a question.

Michael,
It's difficult to give you guidance on this, because it's not clear (to me, anyway) what your expressions are, exactly. Is the original = 0.5 * (7x+48), or is it = 1 / (14x+96) , if you see what I mean. And so on. There is PEMDAS interpretation, but I'm not sure that's what...

And don't forget that the $0.60 doesn't include any sales tax; thus, you should reduce your answer appropriately if you live in an area which charges such a tax! (in addition to rounding it down to an integer, obviously, unless some other party wants to split a wing with you. Personally, I would...

Whoa, Patrick, you haven't finished entering your problem. "1 is greate"? Really? Without the complete problem, it's useless to speculate what kind of a problem it might be.

Wendy,
You first must strategize how to lay your circles out. Do you want them in a 3x3 square arrangement of centers, or can you possibly do better by staggering them (every other row offset, but "nestled" down into the crevices between circle crests)? This is actually an elegant...

So -- all you need is a line with slope (say) =1 and a non-integer y-intercept (assuming the "lattice points" are the ordered pairs of integers for coordinates). If you consider ALL the possible lines in a plane, the ones that DO go through lattice points are an infinitely small proportion...

There may be several ways of visualizing this problem - the one I'd choose is, set up L L L L L R R ..... as the initial permutation, probability = 0.14^5*0.86^40. Then multiply this by the combinations possible = 45!/(40!5!). This given 0.1576, approximately, which seems reasonable.

Kaylee, there's no problem whatever with this problem!
You start with the complete height (distance) of the 27 story building: -7x^2+8x-4 . From that you subtract the measure (distance) of the top 7 floors (-11x^2+2-14x^2) and then you get the measure (distance) of the remaining...

Hi Emilia,
Looks like you're heating 20 g of water by 6.8C, right? In a styrofoam cup calorimeter?
Your calculations look fine to me. If your value is far away from theory or values of your labmates, check to see what about your data is way off. Is it your temperature rise? If so, consider...

Demane, percentage of 5000 of 7000 IN 2000 of 5000 looks literally like (5000/7000)/(2000/5000)*100, or (5/7)/(2/5)*100 = 25/14*100 ~ 178.57%. But this sounds like a gibberish problem.
But then you say 5000 of 7000 AND 2000 of 5000. Is that what you really want? If so, then 5000/7000*100 and...

Carlos,
In order to solve a problem like this, you need to do the following in order:
1) decide if there are any special conditions likely to apply that would require special solution formats (that's what Mark M. is asking above, i.e. could the second plane run out the end of the cylinder...

Looks like you should try to factor the latter polynomial into a product of 4 terms (x+b)(x+c)(x+d)(x+e) using all the tricks you have learned about signs in the polynomial product, etc. Since it's likely to be integer whole-number roots, the easiest way to do this is to use a graphing...

What an odd problem!
Since the sample is a gas, of course it will expand to fill any available volume. So in a 10L bottle, it fills all 10L.
Perhaps the question was intended to elicit a response about the pressure of the gas sample in the 2 different volumes respectively -- namely,...

Olivia -- where you made your error -- you processed (evaluated) the expression arithmetically from left to right, to simplify it. Evaluation is not at all the same as differentiation. And that's not how expressions are evaluated when they have parenthesised arguments! The parenthesis says, "process...

Gee, Always thought it was the pituitary, read your descriptions again! "Lead" means it controls the others, through hormone signaling.
- S. de Riel

Abigail, you didn't finish the problem statement. Presumably it's "How many mL of a XXM concentrated stock do you need to measure out?" Since it's 500 mL final volume you need, you would simply multiply the desired final volume (500mL) by the ratio of the ending and starting concentrations...

Jason, something's amiss in your translation of types of words into math. [words with 3 e] may therefore have the "other" letter in positions 1, 2, 3, or 4; since there are 6 choices for "other" letter and they are independent for the 4 positions, that's 6+6+6+6 =...