There is a good explanation of the model I'm using below at
First, the area of a rectangle is length (l) time width (w). Now its not very useful to use l and w as the variables, but recognize that we can always swap l and w, that one will normally be larger and the other smaller. So lets assume for the moment
The consecutive numbers must both be positive (given), so representing the two numbers as (n) and (n+1), if we multiply n by 3 we have 3*n*(n+1)=6, or if we multiply (n+1) by 3 we get n*3*(n+1)=6 and the left hand side is the same for both equations 3n^2+3n=6...
Jeff, I think you have an error in your transcription
Take a look at this link
Drexel has a good webpage describing the calculations using matrix algebra at
If its a little to technical, I'll summarize as needed for your problem
Given a transition...
We need a matrix where the items are each Probabilities (P), P(i,j), where P(1,2) is the probability of going from group 2 to group 1 in one step so P(F,C) is the probability from shifting from a Chevy to a Ford and P(F,F) is the probability of staying
with a ford. ...
Vivian, this involves reverse engineering the solution. In your previous problems you had a known sample size and wanted to compute the confidence interval, now you know the interval, and want to compute the sample size.
Standard Error of the Mean (SEM) = σ/√n
Vivian, the Standard error of the mean (SEM) is the standard deviation (s or σ) divided by the square root of the sample size or in this case σ/√n = 0.001/√8
Since we are given the population standard deviation (σ, rather than s), you can use a z-table value for the 99% confidence...
Generally, margin of error and confidence intervals require knowing not only the mean and the sample size, but the standard deviation (of either the population or the sample).
The formula for standard error of the mean is the standard deviation divided by the...
The simplest approach is to think about what Shawn's hand can look like if he has only blue and yellow cards and five cards in his hand.
He can have
0 blue and 5 yellow
1 blue and 4 yellow
2 blue and 3 yellow
3 blue and 2 yellow
4 blue and...
Caleb, as I read this your second attempt 4x=(12)(6) gives x=18, but x≠OC, x=AC.
The secant formula is that the product of the full length of the secant from A to where it exits the Circle at B times the length of the secant from A to where it enters the circle at D is equal to the...
Mol, for the roots to be equal their factored equations have to be the same, i.e. in the form of (ax+b)^2=0 or a^2x^2 + 2abx + b^2 = 0, so if we replace the numbers in front of the x terms in the given equation with the coefficients above, we'll get 3
Lisa, look at the formula for the variance:
µ is the mean and is a measure of the center of all of the x's (i.e. a measure of the average position of all the xi's), so the numerator is a measure of the relative position of each individual to their collective...
Chani, Given this description
-------- + ----------
We first need a common...
Moe, take a look at this page
We need to use the properties of the law of sines
You've been given a, b and B, but the page uses a, b, and A, so I'm going to swap things around and use
Check this page for the process. http://www.wyzant.com/resources/answers/23935/how_do_you_find_a_in_parabola_equations_using_just_the_vertex_and_the_focus
Its exactly the same, only the numbers are different
The key to solving this problem is to look at the trigonometric definitions and identities.
The sin 1/2 angle identity (http://www.wyzant.com/resources/lessons/math/trigonometry/half-angle-double-angle-formulas) is
sin (x/2) = ±√((1-cos(x))/2)
Since arrangement does not matter (i.e. A, B, C is the same as C, B, A) you have a combination problem, as the total sample space is the total number of possible combinations. In this case you have sample spaces of
15, C, 2
6, C, 4
18, C, 8
So you have 100 gallons at 120 degrees and add x gallons at 40 degrees and you end up with 100+x gallons at 100 degrees when you are finished. The easiest way is to treat this as a weighted average. You have (100 gallons) (120 degrees of heat) + (x gallons)(40...
Grace, for conic sections, the best thing to do is put the equations into standard form. For a circle standard form is (x - h)^2 + (y - k)^2 = r^2
where (h,k) is the center of the circle and r is the radius of the circle.
So, yes, you...