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# Recent problems solved by 'richard1234'

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 Probability-and-statistics/527157: HELP!!!!!!!! Suppose you earned 100 points on an exam. Under which of the following conditions did you earn the best grade? When: a. μ = 80 and σ = 10 b. μ = 80 and σ = 5 c. μ = 105 and σ = 10 d. μ = 105 and σ = 5 Make sure to justify your response with one to two sentences. 1 solutions Answer 348860 by richard1234(5390)   on 2011-11-06 22:57:01 (Show Source): You can put this solution on YOUR website!B, because you are four standard deviations above the mean score (as opposed to two with A).
 Proofs/527290: Prove : If m is an odd integer, then 4 divides m^2 +2m+5 I have gotten this so far but i dont know if its right and how to finish working it out! Proof: Let m be an odd integer there is an integer such that m=2k+1 then m^2 +2m +5 = (2k+1)^2 + 2(2k+1) +5 then m^2 + 2m +5= (4k^2 +4k +1) + (4k+2) +5 then m^2 +2m +5= (4k^2 +4k+4k) +1+2+5 then m^2 +2m +5 = 4(k^2 +k+k) + 81 solutions Answer 348858 by richard1234(5390)   on 2011-11-06 22:53:48 (Show Source): You can put this solution on YOUR website!You're correct. All you need to do now is factor it to 4(k^2 + 2k + 8). Since k^2 + 2k + 8 is an integer, the expression is divisible by 4. Another way to prove it is to use modular arithmetic, or arithmetic dealing with remainders. If m is an odd integer, then m ≡ 1 mod 2 (i.e. m divided by 2 leaves a remainder 1. The ≡ sign means "equivalent"). Then m^2 ≡ 1 (mod) 4, 2m ≡ 2 (mod 4), and 5 ≡ 1 (mod 4). We can add modulos or residues the same way we add numbers; in this case, m^2 + 2m + 5 ≡ 1 + 2 + 1 ≡ 4 ≡ 0 (mod 4). Note that if a number is m mod n, we can subtract any multiple of n and still obtain an equivalent result. Since the expression is 0 mod 4, it is divisible by 4 (since it leaves remainder 0).
 Proofs/527300: Disprove: If a, b, and c are integers such that a does not divide b and c does not divide d, then a+c does not divide b+d1 solutions Answer 348856 by richard1234(5390)   on 2011-11-06 22:46:09 (Show Source): You can put this solution on YOUR website!Counterexample: Let a = 2, b = 7, c = 3, d = 13. Here, the conditions are met, but a+c divides b+d (5 divides 20).
 Surface-area/525777: how do you find the surface area of a triangular pyramid? 1 solutions Answer 348502 by richard1234(5390)   on 2011-11-04 21:47:22 (Show Source): You can put this solution on YOUR website!Find the areas of all the faces, and add them up.
 Geometry_proofs/526246: Can someone help me with this I don't understand proofs at all. Here is the link to what I do not understand. Can you explain how to do this right! http://www.flickr.com/photos/68627030@N06/6312732786/ 1 solutions Answer 348501 by richard1234(5390)   on 2011-11-04 21:44:39 (Show Source): You can put this solution on YOUR website!Since angle 1 and angle 2 are equal, name each angle "x." The sum of angle 1 and angle 2 is 2x, which is equal to 180 degrees (since BD is a straight line). Hence 2x = 180, x = 90, so the angles are right angles. This implies that AC and BD are perpendicular. Use this to write out your proof.
 Complex_Numbers/526130: if x = y^2 and y = x^2, what is the least possible real value of x^2 + x + 1, where x and y are complex numbers ?1 solutions Answer 348500 by richard1234(5390)   on 2011-11-04 21:42:21 (Show Source): You can put this solution on YOUR website!We have (if x is not equal to 0). Hence the three possible values of x (roots of unity) are: , and . Hence, replacing each of these values into the expression x^2 + x + 1 and simplifying yields 3, 0, and 0 respectively, so the minimum value is 0.
 Graphs/526137: what are tables,graph and equations good for? when can i use them in another real life scenerio. what are the disadvantages and advantages of them?1 solutions Answer 348495 by richard1234(5390)   on 2011-11-04 21:34:15 (Show Source): You can put this solution on YOUR website!They're used in virtually every field of science, as well as economics, business, engineering, systems design, engineering, and so on.
 Geometry_proofs/526359: What are some good proofs and what are some good strategies to solving them?1 solutions Answer 348474 by richard1234(5390)   on 2011-11-04 20:24:00 (Show Source): You can put this solution on YOUR website!Proofs are very broad, and are found in an extremely wide range of mathematics. The questions found in the prestigious USAMO and IMO competitions contain lots of good proofs, if you want to check into them. Here are some websites containing useful information about proofs: http://www.artofproblemsolving.com/Resources/articles.php?page=howtowrite& http://www.artofproblemsolving.com/Resources/articles.php?page=gallery
 Probability-and-statistics/526066: the probability the sum of the numbers shown on the dice is a 7 0r 8 ?1 solutions Answer 348315 by richard1234(5390)   on 2011-11-03 23:49:04 (Show Source): You can put this solution on YOUR website!How many dice are there?
 Rational-functions/525392: f(5) if f(x) = x+6 1 solutions Answer 348107 by richard1234(5390)   on 2011-11-02 22:14:02 (Show Source): You can put this solution on YOUR website!Replace "x" with "5" f(5) = 5+6 = 11
 Linear-equations/525173: I don't get linear equations, slopes, rate. Or whatever x = y, or m=, b=. Like these problems: 3x-y=8. I don't know how to do them, I'm in Pre-Alegbra. I want to be in Algebra 1, but my teacher is Asian! I can not understand her, therefore, I do not know how to do this. Please, help! I really want to pass 8th grade, and be in Algebra 1.1 solutions Answer 348106 by richard1234(5390)   on 2011-11-02 22:11:01 (Show Source): You can put this solution on YOUR website!The nationality of your teacher shouldn't affect your ability to learn; you'll have to learn to cope with it. The high school I go to has teachers that are mostly Turkish or Russian. The equation "y = mx + b" is simply a *general* form of a line. For example, 3x - y = 8 becomes y = 3x - 8 (after some algebraic manipulation), in which m = 3 (i.e. the slope is 3) and the y-intercept is -8 (i.e. the graph crosses the y-axis at (0,-8)).
 Graphs/525398: I am having a hard time understanding standard normal distribution: how would you figure this from a problem such as: P(1.22 < Z < 2.15) 1 solutions Answer 348105 by richard1234(5390)   on 2011-11-02 22:05:54 (Show Source): You can put this solution on YOUR website!That question is asking, for a normal curve with and , what is the probability that the z-score is between 1.22 and 2.15. Use your calculator and the normal cdf (cumulative distribution function) to evaluate it. On a TI calculator, it might look something like normcdf(1.22, 2.15, 0, 1) The syntax might be slightly different on other calculators.
 Geometry_proofs/524477: are there any tricks when doing proofs?1 solutions Answer 347925 by richard1234(5390)   on 2011-11-02 01:19:27 (Show Source): You can put this solution on YOUR website!It really depends on the what you are supposed to prove.
 Geometry_proofs/524825: How do you solve proofs? 1 solutions Answer 347924 by richard1234(5390)   on 2011-11-02 01:13:26 (Show Source): You can put this solution on YOUR website!Just prove what the question is asking for (note that "prove" means to justify or demonstrate the truth of a statement -- it does not mean to check only one case and claim it works, except for some existence proofs). Then once you're familiar with various proof techniques such as induction, proof by contradiction, direct proof, etc., you can move onto more challenging proofs. The annual USAMO competition, for example, is a prestigious contest that has six proof questions to be completed in nine hours, spread over two days (yes, 1 1/2 hrs per question). The Art of Problem Solving website contains all of the past USAMO questions, if you're interested (note that some of the problems can be extremely difficult).
 Probability-and-statistics/524828: Out of a group of 100 US residents, how many would you expect to have travelled no more than 386.9 miles in any given year?1 solutions Answer 347921 by richard1234(5390)   on 2011-11-02 00:56:22 (Show Source): You can put this solution on YOUR website!What is the significance of 386.9 miles? And you didn't provide any data to work with.
 Inequalities/524507: What is the five step problem solving strategy for a problem similare to this A 72-in.board is cut into two pieces one piece is 2in.Longer than the other find the lengths of the pieces USING five-step problem solving. Thank you Kia1 solutions Answer 347920 by richard1234(5390)   on 2011-11-02 00:55:45 (Show Source): You can put this solution on YOUR website!Let L be the length of the shorter piece. The longer piece is 2 in longer so we can say the length of that piece is L+2. Hence, L + (L+2) = 72 --> 2L + 2 = 72 --> 2L = 70 --> L = 35. Therefore L+2 = 37, so the lengths of the two pieces are 35 and 37 inches.
 test/524807: I need help with all the math1 solutions Answer 347910 by richard1234(5390)   on 2011-11-01 23:36:12 (Show Source): You can put this solution on YOUR website!"All the math" is quite a bit of math. Please ask a more specific question.
 Parallelograms/524288: does diagonals of a trapezoid bisect each other at 90 degree? 1 solutions Answer 347897 by richard1234(5390)   on 2011-11-01 22:20:51 (Show Source): You can put this solution on YOUR website!Not necessarily.
 Sequences-and-series/524497: Hi, Could you help me find the 7th, 8th, and 9th terms of the following sequence (1, 2, 3, 6, 11, 20, ...)? As the sequence progresses, each number equals the sum of the previous three numbers (ie 20 = 11 + 6 +3), but I can't figure out how they got 1 and 2. Another idea is that every even term equals the previous term plus 3 to increasing powers (3 to the zero is 1, 3 to the first is 3, etc-- sorry no exponents or superscript in the text box!)and every odd term is simply a summation. I'd really appreciate any help you can give. Thanks very much, Amy1 solutions Answer 347784 by richard1234(5390)   on 2011-11-01 18:09:01 (Show Source): You can put this solution on YOUR website!Each number after the third number equals the sum of the previous three numbers. The first three are completely arbitrary. Use these facts to find the 7th, 8th and 9th terms.
 Numeric_Fractions/522723: What is 5/9 divided by 5 1 solutions Answer 347774 by richard1234(5390)   on 2011-11-01 17:36:19 (Show Source): You can put this solution on YOUR website!Five ninths divided into five parts yields one ninth per part, so (5/9)/5 = 1/9.
 Average/524393: find the infinite sum series. 1024+512+256+12... i put 64 i was told was the next term in series so what is the sum1 solutions Answer 347769 by richard1234(5390)   on 2011-11-01 17:17:46 (Show Source):
 Miscellaneous_Word_Problems/524520: I am planning to spend no less than $6,000 and no more than$10,000 on my landscaping project. Write an inequality that demonstrates how much money I am willing to spend on the project.1 solutions Answer 347767 by richard1234(5390)   on 2011-11-01 17:14:06 (Show Source): You can put this solution on YOUR website! where c is the amount spent.
 test/524297: in this question- 18-2m=0 m=0 well, we moved 18 to the right of the expression. Can you tell me why did we did that??1 solutions Answer 347765 by richard1234(5390)   on 2011-11-01 17:08:53 (Show Source): You can put this solution on YOUR website!Presuming 18 - 2m = 0 We can subtract both sides by 18 (it will almost look like "moving" 18 to the right) to get -2m = -18 Divide both sides by -2. m = 9.
 Polynomials-and-rational-expressions/524264: Why is determining whether or not a polynomial is the difference of two squares useful when factoring?? Why is determining whether or not a polynomial is the difference of two squares useful when factoring?1 solutions Answer 347697 by richard1234(5390)   on 2011-11-01 09:35:00 (Show Source): You can put this solution on YOUR website!You just asked the same question twice. It's useful since we can write a difference of squares as a product of two factors.
 Length-and-distance/524163: Find the coordinates of the centroid, orthocenter, and circumcenter of a triangle with vertices A(4, -1), B(2, 6), and C(9, -5). 1 solutions Answer 347653 by richard1234(5390)   on 2011-11-01 00:40:51 (Show Source): You can put this solution on YOUR website!The easiest way to find the centroid is to take the average of the x-coordinates and the average of the y-coordinates (this corresponds to a "center of mass" encountered in physics). To find the orthocenter and circumcenter, use the methods that the other tutor suggested.
 Pythagorean-theorem/523564: Can you determine the relationship between the areas of the three squares?1 solutions Answer 347652 by richard1234(5390)   on 2011-11-01 00:35:26 (Show Source): You can put this solution on YOUR website!No, because I don't know what the three squares are. Since you noted the topic as "Pythagorean theorem" you are probably referring to the squares of the lengths of the sides of a right triangle, in which the sum of the areas of the smaller two squares equals the area of the larger square.
 Human-and-algebraic-language/523815: There is a hopscotch board. It has alot of squares with different numbers inside of it . The width of the squares is t and the length is ( t-3). What is the area? By the way I am learnig about polynomials in Algebra, so the answer is likely to turn as a polynomial. Thank you for your help. -James1 solutions Answer 347651 by richard1234(5390)   on 2011-11-01 00:33:43 (Show Source): You can put this solution on YOUR website!Area = length*width = (t-3)(t) = t^2 - 3t
 Numbers_Word_Problems/523643: Two numbers have a sum of 50. If one number is p, express the other number in terms of p.1 solutions Answer 347650 by richard1234(5390)   on 2011-11-01 00:32:19 (Show Source): You can put this solution on YOUR website!50-p
 Geometry_proofs/523833: I need examples of proofs and how to solve them. I also need help in solving paragraph proofs with trinagles whether they are isoceles, equilateral, or both. Please reply as soon as possible. Thank You1 solutions Answer 347649 by richard1234(5390)   on 2011-11-01 00:31:35 (Show Source): You can put this solution on YOUR website!Here are some for you to try on your own: 1 (easy). In triangle ABC, the altitude from A onto BC bisects BC. Show that triangle ABC is isosceles. 2 (medium). Prove that the incenter and circumcenter of a triangle are the same point if and only if the triangle is equilateral. 3 (hard). Prove that for any triangle, the circumcenter, orthocenter, and centroid all lie on a line.
 test/523313: ∫5x^4/x^5+1 The answer is In(x^5+1)+c. I know how to integrate but I don't know how to get to this answer. Can you show me the working to get to this answer? Many Thanks Andrew1 solutions Answer 347391 by richard1234(5390)   on 2011-10-31 00:45:47 (Show Source): You can put this solution on YOUR website!Just use a simple substitution and that is all. By letting u = x^5 + 1 and, du/dx = 5x^4, du = 5x^4 dx, This is equal to where C is a constant.