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Answers by John M.

Cashlin, these kind of problems involve converting the ratio or percentage into a number of people.  Check your numbers though, my math is giving me fractional people, which is always suspect in these kinds of problems).  There are often faster ways to do these kinds of problems for standardized...

Edward,   1st, recognize that csc=1/sin and sec=1/cos.  So we can simplify the equation to sin(6b+pi/8)=cos(2b-pi/8).  Generally trig problems are easier if you convert everything to sines and cosines.   2nd, sin & cos are 90 degrees out of phase or pi/2...

Brenda, the key is to recognize that you need to convert the percentages into amounts.   You start with 2 quarts of liquid that is 25% antifreeze, or you have 2 x .25 = .5 quarts of antifreeze to start with.   You are going to add another amount of liquid that is 100% antifreeze...

Todd, the key is to translate the sentences into equations. Let's define L=Length of the rectangle and W=Width of the rectangle   The word "is" tells you where the equals sign is.   Your first sentence translates: (a rectangles length) [is] 8 cm more than...

Emily, the key is to turn this geometry problem into a 2-equation / 2-unknown algebra problem. A = Angle S = Supplement   A + S = 180 degrees (definition of supplementary angles) S = A - 78 (The supplement (S) has a measure (=) of the angle (A) less 78)   Substituting...

Statistics (answer)

Anna,   There is a good explanation of the model I'm using below at http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCsQFjAA&url=http%3A%2F%2Fwww.csus.edu%2Findiv%2Fb%2Fblakeh%2Fmgmt%2Fdocuments%2FOPM101SupplC...

Jeff, I think you have an error in your transcription   Take a look at this link   http://www.numberempire.com/graphingcalculator.php?functions=%281%2Bsin%282*x%29%29%2F%281-sin%282*x%29%29%2C%28cot%282*x%29^2%29&xmin=-3&xmax=3&ymin=-3&ymax=3&var=x   I've...

Heather,   Drexel has a good webpage describing the calculations using matrix algebra at https://www.math.drexel.edu/~jwd25/LM_SPRING_07/lectures/Markov.html   If its a little to technical, I'll summarize as needed for your problem   Given a transition...

can someone help (answer)

Heather,   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   Confidence...

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...

Vivian,   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...