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John M.'s Resources

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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...

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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...

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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...

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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...

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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. ...

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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...

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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...

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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...

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Kx^2-16x+32=0 (answer)

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 equations:   a^2=k, 2ab=-16,...

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Moe, take a look at this page   http://hotmath.com/hotmath_help/topics/law-of-sines.html   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 a=3, b=4...

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L,   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    

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Moe,   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)   So...

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Dalia,   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 and 18, C, 8   The...

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