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# Recent problems solved by 'richard1234'

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 Permutations/570859: minimum number of individual shoes to be picked up from a dark room(containing 10 pair of shoes). if we have to get at least one proper pair1 solutions Answer 368011 by richard1234(5390)   on 2012-02-11 10:37:43 (Show Source): You can put this solution on YOUR website!By Pigeonhole principle, if we have ten boxes corresponding to ten pairs of shoes and we have 11 shoes, two shoes must go into the same box (and hence, make a match).
 Subset/570704: Let A = {1, 2, 3, 4, 5, 6, 7}. How many TWO element subsets does A have?1 solutions Answer 368006 by richard1234(5390)   on 2012-02-11 10:12:37 (Show Source): You can put this solution on YOUR website!Assume order of the elements doesn't matter, i.e. {3,4} is equivalent to {4,3}. Then the number of subsets of size 2 is 7C2 = 7*6/2! = 21.
 Functions/571211: A little help and understanding with this one is greatly appreciated... Find f(x) and g(x) such that h(x) = (f o g)(x). h(x) = |6x + 9| 1 solutions Answer 368005 by richard1234(5390)   on 2012-02-11 10:09:37 (Show Source): You can put this solution on YOUR website!Let f(x) = |x| g(x) = 6x+9 Then, f(g(x)) = |6x+9|
 Functions/571210: The point (6,-3) is on the graph of y=f(x). Find the corresponding point on the graph of g(x)=f(3x) Big troubles on this one for some reason...any help is greatly appreciated.1 solutions Answer 368004 by richard1234(5390)   on 2012-02-11 10:08:45 (Show Source): You can put this solution on YOUR website!All we know is f(6) = -3 and g(x) = f(3x). The only point on g(x) that we can find occurs when x = 2. This is because g(2) = f(3*2) = f(6) (in other words, I basically set 3x = 6). Since we know f(6) = -3, g(2) must also be -3, so (2,-3) is the corresponding point.
 Numbers_Word_Problems/570798: I am less than 20. I am more than 13. I am less than 17. I am 4 more than 12. What number am I?1 solutions Answer 368003 by richard1234(5390)   on 2012-02-11 10:06:16 (Show Source): You can put this solution on YOUR website!"I am 4 more than 12" --> 16 That wasn't too hard, was it?
 Probability-and-statistics/570867: A company brings a new product to market: The probability of loosing $1,000,000 is 10% The probability of loosing$500,000 is 20% The probability of breaking even is 20% The probability of making $500,000 profit is 20% The probability of making$2,000,000 profit is 30% what is the expected profit? I can calculate this ((2,000,000*.3)+(500000*.2)) - ((1,000,000*.1)+(500,000*.2)) yields 700,000-200000 = $500,000 expected profit. but im not sure how to handle the 20% probability of breaking even, 0 * 20% = 0? how is this factored in to my calculations?1 solutions Answer 368002 by richard1234(5390) on 2012-02-11 10:00:31 (Show Source): You can put this solution on YOUR website!Do it just like you did with the other numbers. Expected value for this problem is defined as the sum of (profit)*(probability of that profit), so with the case of zero profit, you would add 0*.2, or 0. Since your other numbers are correct, you can just add everything and obtain$500,000.
 Functions/571039: If f(x)= x^2 + 3, g(x)=4x, the value of g(f(6)) is ?1 solutions Answer 367979 by richard1234(5390)   on 2012-02-11 00:32:33 (Show Source): You can put this solution on YOUR website!g(f(6)) means "g of f(6)," so find f(6). f(6) = 6^2 + 3 = 39 So g(f(6)) = g(39) = 4*39 = 156
 Volume/571149: I need to know how to estimate the volume of a box (approximately 100 - 500 cm3) in cubic centimeters.1 solutions Answer 367978 by richard1234(5390)   on 2012-02-11 00:26:10 (Show Source): You can put this solution on YOUR website!Volume of a box = length*width*height. Also, I would think that "approximately 100 - 500 cm3" is an estimate for the volume of a box in cubic centimeters.
 Probability-and-statistics/570976: Suppose k identical boxes contained n balls numbered one through n. One ball is drawn from each box. What is the probability that m is the largest number drawn? 1 solutions Answer 367974 by richard1234(5390)   on 2012-02-11 00:09:21 (Show Source): You can put this solution on YOUR website!For this problem we will assume that . The best way is probably to try small cases (for m). Let P(m) be the probability that m is the largest number drawn. If m = 1, then every number drawn must be a 1, and If m = 2, every number must be a 1 or a 2, and we would try to claim something like However, this is incorrect, because this includes the case where every number is a 1 (which violates the constraint that at least one number must be a 2). To fix this, we subtract P(1): Finding P(3) is similar to finding P(2), except that we subtract P(2): This generalizes to , or where the plus/minus of (1/n)^k depends on the parity of m (i.e. if m is odd, +; if m is even, -).
 Pythagorean-theorem/571129: The measures of the legs of angle ABC are 5 and 8. Find the length of the hypotenuse. Show diagram and calculation. Simplify your answer.1 solutions Answer 367972 by richard1234(5390)   on 2012-02-10 23:40:57 (Show Source): You can put this solution on YOUR website!Pythagorean theorem
 Triangles/571081: Leg XY of right triangle XYZ shown below is 3 inches long. The sise of Z is about how long?1 solutions Answer 367969 by richard1234(5390)   on 2012-02-10 23:26:07 (Show Source): You can put this solution on YOUR website!"shown below," there's a key phrase. You didn't show any triangle.
 test/570673: I need the answers to each problem1 solutions Answer 367808 by richard1234(5390)   on 2012-02-10 08:43:35 (Show Source): You can put this solution on YOUR website!Why don't you post the actual problems instead. Also, you won't learn much from the answers unless you know the solution to them.
 Sequences-and-series/570772: In the figure below, line m is parallel to line n, and line t is a transversal crossing both m and n. Which of the following lists has 3 angles that are all equal in measure? A. ∠a, ∠b, ∠d B. ∠a, ∠c, ∠d C. ∠a, ∠c, ∠e D. ∠b, ∠c, ∠d E. ∠b, ∠c, ∠e1 solutions Answer 367807 by richard1234(5390)   on 2012-02-10 08:39:14 (Show Source): You can put this solution on YOUR website!How are we supposed to know where angles a,b,..,e are if you didn't provide a diagram?
 test/570709: The points on a scatterplot lie very close to the line: y = 6x - 1 The correlation between x and y is closest to which of the following values? 1. 6 2. 0 3. -6 4. 1 5. -1 1 solutions Answer 367775 by richard1234(5390)   on 2012-02-10 00:55:52 (Show Source): You can put this solution on YOUR website!Correlation is defined to be between -1 and 1, so 6 and -6 are impossible. The correlation is 1 if the (x,y) points all lie on a line of positive slope (-1 for negative slope). Since y = 6x - 1 has positive slope, the correlation is roughly 1.
 Geometric_formulas/570478: hi how would u be able to figure out the distance formula passing through the points (3,-2) and (6,4) step by step!!! please1 solutions Answer 367774 by richard1234(5390)   on 2012-02-10 00:54:09 (Show Source): You can put this solution on YOUR website!Just apply the distance formula, which is literally applied Pythagorean theorem.
 Graphs/570690: A number greater than 1 is called a ______ ________.1 solutions Answer 367773 by richard1234(5390)   on 2012-02-10 00:51:48 (Show Source): You can put this solution on YOUR website!I'm pretty sure there's no name for an arbitrary number greater than 1. I would just say it is "a number greater than 1."
 Triangles/570511: How do you find the area of a triangle?1 solutions Answer 367772 by richard1234(5390)   on 2012-02-10 00:50:03 (Show Source): You can put this solution on YOUR website!Many different ways. The most common one is (b = base, h = height) For the next several formulas, denote a,b,c = side lengths A,B,C = angles opposite from sides a,b,c s = semiperimeter (=(a+b+c)/2) r = inradius R = circumradius Other area formulas you'll see are (Heron's formula) where AB and AC are the vectors from A to B and A to C respectively (excuse my sloppy notation of using A twice...treat them as different variables)
 Angles/570409: if C and D are supplementary , and the measure of D is 45 , what is the measure of D 1 solutions Answer 367770 by richard1234(5390)   on 2012-02-10 00:38:43 (Show Source): You can put this solution on YOUR website!Reread your question...you stated that the measure of D is 45, and you asked for the measure of D. You probably want the measure of C, which is 180-45 or 135.
 Trigonometry-basics/570725: Explain why sin(7 degrees)+ sin(353 degrees)= 01 solutions Answer 367769 by richard1234(5390)   on 2012-02-10 00:36:11 (Show Source): You can put this solution on YOUR website!Look on a unit circle. The sine of an angle is the y-coordinate of the point determined by that angle. The point on the unit circle corresponding to 7 degrees will have some y-coordinate y1, so sin 7 = y1. Similarly, the point corresponding to 353 degrees is "reflected" over the x-axis and will have the y-coordinate -y1, so sin 353 = -y1. y1 + (-y1) = 0, so the statement is true.
 Geometry_proofs/570537: given a||b and c||d prove angle 1 is supplementary1 solutions Answer 367767 by richard1234(5390)   on 2012-02-10 00:25:47 (Show Source): You can put this solution on YOUR website!Where are a,b,c,d and angle 1? Also, one angle (angle 1) cannot be supplementary; you need two angles that add up to 180 for them to be supplementary.
 Probability-and-statistics/570661: what is the probability of a person is between the ages of 40 and 49?1 solutions Answer 367766 by richard1234(5390)   on 2012-02-10 00:24:37 (Show Source): You can put this solution on YOUR website!Depends on the distribution of ages in your population.
 Linear-equations/570770: How would I solve this problem? p(x)=x^2-2x+7... I have to find the domain of P1 solutions Answer 367765 by richard1234(5390)   on 2012-02-10 00:22:12 (Show Source): You can put this solution on YOUR website!Polynomials are defined everywhere, so the domain of P is (-infinity, infinity).
 Trigonometry-basics/570729: Explain why there are no solutions to logbcos(theta)=.01 for any base b>1 (b is not an exponent but the thing that goes down instead of up, don't know the name for it)1 solutions Answer 367764 by richard1234(5390)   on 2012-02-10 00:21:16 (Show Source): You can put this solution on YOUR website!b is called a subscript. The log equation is equivalent to However, (because b^{.01} is greater than b^0 or 1). This implies that cos theta > 1, which cannot occur. Therefore there are no solutions.
 Trigonometry-basics/570773: If A + B + C = 180°,Prove that Cos²A + Cos²B + Cos²C = 1-2cosAcosBcosC1 solutions Answer 367763 by richard1234(5390)   on 2012-02-10 00:17:56 (Show Source): You can put this solution on YOUR website!A,B,C can form a triangle so use law of cosines, where a,b,c are the sides opposite A,B,C respectively. Similarly, Replace this into your equation and you (should) obtain an identity. However, this part is awfully long so a more elegant solution would be nice. A similar solution would be to use the law of sines: where R is the circumradius. Therefore . Also another long solution.
 Linear-equations/570745: Why should we clear fractions when solving linear equations and inequalities? Demonstrate how this is done with an example. Why should we clear decimals when solving linear equations and inequalities? Demonstrate how this is done with an example.1 solutions Answer 367761 by richard1234(5390)   on 2012-02-09 23:59:23 (Show Source): You can put this solution on YOUR website!Because it makes solving them easier, that's the main reason. For example, Clear fractions by cross-multiplying to get Same reasoning applies to decimals.
 Probability-and-statistics/570761: Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.1 solutions Answer 367759 by richard1234(5390)   on 2012-02-09 23:47:41 (Show Source): You can put this solution on YOUR website!, where z = 1.645, E = .03, assume p = .5 because this maximizes p(1-p) and we want a safe estimate. Plugging in everything, we obtain A sample size of 752 would work.
 Linear-equations/570763: Are the graphs of these two equations perpindicular? x+2y=5 2x+4y=7 Thanks1 solutions Answer 367756 by richard1234(5390)   on 2012-02-09 23:22:53 (Show Source): You can put this solution on YOUR website!No, if you rearrange and put in y = mx + b form, you will see that the slopes are the same, and that the graphs of the two lines are parallel.
 Matrices-and-determiminant/570183: Can't solve this determinant 2 5 0 4 1 -2 0 2 3 -1 1 6 4 0 3 -21 solutions Answer 367592 by richard1234(5390)   on 2012-02-09 08:34:43 (Show Source): You can put this solution on YOUR website!For this square matrix, the determinant is equal to 2 det A - 5 det B + 0 det C - 4 det D where A,B,C,D are the 3x3 matrices whose entries are neither in a row or column of the top entry (e.g. matrix A would contain -2 0 2/-1 1 6/0 3 -2). Additionally, you would have to find the determinant of 3x3 matrices, which reduces to a several 2x2 matrices. Since this problem requires a lot of "bashing" (not the correct word usage, but math people use it all the time), you could use a calculator. Most graphing calculators can evaluate determinants of square matrices.