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 Problems-with-consecutive-odd-even-integers/492279: the sum of two positive intergers is ------ zero using always,sometimes,or never?1 solutions Answer 334993 by richard1234(5390)   on 2011-09-06 17:16:53 (Show Source): You can put this solution on YOUR website!always greater than 0. Or you can say "never less than or equal to 0."
 Complex_Numbers/492241: Is 4x+12y = 4(x+3y) part of the distributive property. commutative property of addition, commutative property of multiplication, associative property of addition, associative property of multiplication, identity property of addition, identity property of multiplication, inverse property of addition, inverse property of multiplication, or transitive property?1 solutions Answer 334990 by richard1234(5390)   on 2011-09-06 17:15:12 (Show Source): You can put this solution on YOUR website!distributive property.
 Geometry_Word_Problems/491907: The perimeter of a semicircle is doubled when the radius is increased by 0.5. Find the radius of the semicircle.1 solutions Answer 334823 by richard1234(5390)   on 2011-09-06 00:18:33 (Show Source): You can put this solution on YOUR website!Perimeter is a function of the radius, so if the perimeter is doubled then the radius is doubled. Hence the original radius is 0.5, because if it is increased by 0.5, the radius is doubled.
 Functions/491908: Please explain why this is a function. "A rule that associates, to a given time, the distance from a swinging pendulum to its lowest point"1 solutions Answer 334821 by richard1234(5390)   on 2011-09-06 00:16:38 (Show Source): You can put this solution on YOUR website!For some given time, the distance from the pendulum to its lowest point is uniquely defined, i.e. there is one "output" for each input (time). Hence we can say that this is a function.
 test/491872: Your question goes here. Write clearly! We are not mind readers, so be sure to ask a question that we can understand.1 solutions Answer 334818 by richard1234(5390)   on 2011-09-06 00:11:59 (Show Source): You can put this solution on YOUR website!I can ask a question that we can understand...Can you prove that all non-trivial zeros of the Riemann zeta function have a real part of 1/2?
 Permutations/491882: Show that (m+n)Ck = mCk * nC0 + mC(k-1) * nC1 + mC(k-2) * nC2 + ... + mC0 * nCk For k <= (m+n)1 solutions Answer 334815 by richard1234(5390)   on 2011-09-06 00:08:22 (Show Source): You can put this solution on YOUR website!Suppose Committee A has m people and Committee B has n people, and we want to choose a total of k people out of the total m+n. We can choose all k people from Committee A and none from Committee B, for mCk*nC0 ways. Or we can choose k-1 people from A and 1 person from B, and so on, hence the given statement is true. However, this only works for k <= m and k <= n, unless we define xCy = 0, if x < y.
 Angles/491905: 2 angles are complementary if their sum is 90 degrees. If one angle measures x degrees, express the measure of its complement in terms of x.1 solutions Answer 334811 by richard1234(5390)   on 2011-09-06 00:00:23 (Show Source): You can put this solution on YOUR website!90-x. What is x + (90-x)?
 test/491896: Write the equation of the line below: (0,5);m=3/41 solutions Answer 334809 by richard1234(5390)   on 2011-09-05 23:56:24 (Show Source): You can put this solution on YOUR website!y = (3/4)x + 5 Here, 3/4 is the slope and (0,5) is the y-intercept.
 Graphs/491812: write a rule for the function inputx 1,3,5,7 output,y 1,2,3,41 solutions Answer 334772 by richard1234(5390)   on 2011-09-05 21:04:44 (Show Source): You can put this solution on YOUR website!One possible function is y = (x+1)/2.
 test/491792: Help me with my math problem1 solutions Answer 334771 by richard1234(5390)   on 2011-09-05 20:37:12 (Show Source): You can put this solution on YOUR website!Post it here first.
 Linear-equations/491489: If each engineer needs to meet with each other individually, how many engineers would equal 66 meetings? I cannot come up with this number in my son's homework question. I get 8 engineers at 56 meetings, or 9 engineers at 72 meetings. Please help!1 solutions Answer 334730 by richard1234(5390)   on 2011-09-05 18:20:12 (Show Source): You can put this solution on YOUR website!We want nC2 = 66 because the number of ways to choose two engineers to meet out of a pool of n is 66. Hence, n = 12 engineers
 Rational-functions/491615: f(1)=1,f(2n)=f(n),and f(2n+1)=f(2n)+1 Find max of f(n) when n is greater than or equal to 1 and less than or equal to 1994.1 solutions Answer 334727 by richard1234(5390)   on 2011-09-05 18:17:33 (Show Source): You can put this solution on YOUR website!Assuming f is only defined on {1,2,...,1994}, we have for all valid n. Hence, . . . There is a slick algorithm that can be used to find the maximum value of f(n). First, assume that n is odd (this is because f(2n) = f(n), so f(n*2^k) = f(n)). We can now "increment" by 1 because f(3) = f(1)+1 = 2, then we use a recursive definition to obtain f(7) = f(3)+1 = 3, and so on. We have . . . The largest k we can allow is 11, because 2^12 is too large for our domain. Hence, the maximum value of f(n) is 11.
 Problems-with-consecutive-odd-even-integers/491579: If n represents an even integer, what represents the previous smaller even integer? 1 solutions Answer 334702 by richard1234(5390)   on 2011-09-05 17:09:35 (Show Source): You can put this solution on YOUR website!Even integers increment by 2. n-2
 Functions/491263: If f(n) = n + √n, where n is a positive integer, which of the following would be a value of f(n) I) 5 II) 10 III) 121 solutions Answer 334559 by richard1234(5390)   on 2011-09-05 01:00:19 (Show Source): You can put this solution on YOUR website!n could equal 9, in which f(9) = 12.
 Expressions-with-variables/491130: cellular phone company offers a contract for which it costs c in dollars t of telephoning is given by C=0.25 (t-400)+50.95 1 solutions Answer 334558 by richard1234(5390)   on 2011-09-05 00:57:07 (Show Source): You can put this solution on YOUR website!Is there a question?
 Graphs/491271: determine whether (4,-2) is a solution of 9x+3y=171 solutions Answer 334557 by richard1234(5390)   on 2011-09-05 00:50:12 (Show Source): You can put this solution on YOUR website!No, because 9(4) + 3(-2) is not equal to 17.
 Functions/491272: Solve using the multiplication method -2x>1/91 solutions Answer 334556 by richard1234(5390)   on 2011-09-05 00:49:25 (Show Source): You can put this solution on YOUR website!Simply multiply both sides by -1/2. Note that you have to reverse the inequality sign. x < -1/18
 test/490977: Let a and b be relatively prime intergers and let k be any integer. Show that b and a+bk are relatively prime1 solutions Answer 334555 by richard1234(5390)   on 2011-09-05 00:04:10 (Show Source): You can put this solution on YOUR website!One way to show this is to show that the fraction (a+bk)/b is irreducible. This fraction splits to (a/b)+k, which is obviously irreducible because a/b is irreducible. Hence, b and a+bk are relatively prime.
 Quadratic_Equations/491071: Find the power function that the graph of f resembles for large values of [x] f(x)= -x^2(x+4)^3(x^2-1) 1 solutions Answer 334554 by richard1234(5390)   on 2011-09-04 23:59:58 (Show Source): You can put this solution on YOUR website!As x gets really large, I chose -x^7 because that is the polynomial term with the highest degree. The function resembles y = -x^7.
 Geometry_proofs/490853: If D , E and F are the midpoints of sides AB , BC , and CA respectively of an equilateral triangle ABC , prove that triangle DEF is itself an equilateral triangle.1 solutions Answer 334553 by richard1234(5390)   on 2011-09-04 23:56:53 (Show Source): You can put this solution on YOUR website!You will see that, upon drawing D,E,F and forming DEF, that there are three "outer" triangles, and triangle DEF. Each of these "outer" triangles has a 60 degree angle, and its two adjacent sides are 1/2 the length of a side length of ABC; hence the outer three triangles are equilateral. This implies DEF is also equilateral, because the side lengths of DEF are the side lengths of the other three triangles.
 Linear-equations/491253: (5, 9)b = (3, 1) b= {(1,2) (2, 3)} how do i solve that to get (2, -2) ?? can i get a step-by-step explanation to getting the answer.1 solutions Answer 334552 by richard1234(5390)   on 2011-09-04 23:52:56 (Show Source): You can put this solution on YOUR website!You will need to post your entire question. Right now all I see is a bunch of ordered pairs which hardly mean anything. Are those ordered pairs points? Or perhaps rows of a matrix?
 test/491110: How do I find the complex zeros for f(x) = x^3 - 1 And then how do I write that in factored form?1 solutions Answer 334551 by richard1234(5390)   on 2011-09-04 23:51:21 (Show Source): You can put this solution on YOUR website!If you know about roots of unity we can say that These are just three evenly spaced points on a circle of radius 1 in the complex plane.
 Probability-and-statistics/490801: Based on your experience thus far in this class, what is the probability that you will receive an "A" grade? Explain the factors you have used in arriving at this probability assessment. 1 solutions Answer 334550 by richard1234(5390)   on 2011-09-04 23:48:08 (Show Source): You can put this solution on YOUR website!What experience, what class?
 Probability-and-statistics/491187: what is the Probability of rolling an even number on the die? Since a die has 6 numbers with 1 to 6 on each face, there will be just 3 even numbers on it.1 solutions Answer 334544 by richard1234(5390)   on 2011-09-04 22:59:46 (Show Source): You can put this solution on YOUR website!3 even numbers out of 6 total, so P(even) = 3/6 = 1/2.
 Linear-systems/491238: I dont understand the process, 2x-y=32 y-5x=131 solutions Answer 334543 by richard1234(5390)   on 2011-09-04 22:57:35 (Show Source): You can put this solution on YOUR website!Add both equations (y's will cancel) to get 2x + (-5x) = 32 + 13 --> -3x = 45 --> x = -15 Replace x with -15 in either equation (I will use the first one) to get 2(-15) - y = 32 --> -30 - y = 32 --> y = -62 The solution is (x,y) = (-15,-62).
 Average/490509: Short Answer: Convert this number to scientific notation: 64,000,0001 solutions Answer 334364 by richard1234(5390)   on 2011-09-04 09:55:37 (Show Source):
 Percentage-and-ratio-word-problems/490911: how to draw a diagram to show that the fraction 3/4 is the same as the fraction 9/12 1 solutions Answer 334362 by richard1234(5390)   on 2011-09-04 09:54:16 (Show Source): You can put this solution on YOUR website!Draw two circles (or rectangles, whichever), one with four equal parts and one with 12. Shade three parts on the first circle and nine on the second.
 Inequalities/490771: I need to remember how to do this: solve the inequality: [x(x+5)^2]/(x^2-1) answer is(-1,0)U(1,infinity). Just need to know how to solve these things. THANK YOU!!!!1 solutions Answer 334298 by richard1234(5390)   on 2011-09-03 20:57:22 (Show Source): You can put this solution on YOUR website!What inequality? There is no inequality sign anywhere.
 Proofs/490733: Theroem: If a is even and b is odd, then ab is even?? Proof:???1 solutions Answer 334297 by richard1234(5390)   on 2011-09-03 20:56:14 (Show Source): You can put this solution on YOUR website!Let a = 2m, b = 2n+1 where m and n are integers. Then ab = (2m)(2n+1) = 2(2mn+m). 2mn+m is an integer, so 2(2mn+m) is even; ab is even.
 test/490184: I have a question it's from pre algebra ( What is a tangle table? Actually how do I solve a tangle table?)1 solutions Answer 334243 by richard1234(5390)   on 2011-09-03 17:38:11 (Show Source): You can put this solution on YOUR website!What is a tangle table? I have taken pre-algebra, algebra, geometry, and calculus and have never heard of a tangle table; Google doesn't even list "tangle table." Did you spell it correctly?