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# Recent problems solved by 'richard1234'

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 Sequences-and-series/475304: Write a formula for the nth term of the infinite sequence. Do not use a recursion formula. 1, 1/4,1/9,1/16/,1/25 show work 1 solutions Answer 325917 by richard1234(5390)   on 2011-07-28 02:06:00 (Show Source): You can put this solution on YOUR website!, this is actually easier than trying to write a recursive formula. The recursive formula might look something like where .
 test/475152: If the lengths of the sides of a right triangle are, in increasing order, a, b, and c. Prove that a^3+b^31 solutions Answer 325916 by richard1234(5390)   on 2011-07-28 02:02:18 (Show Source): You can put this solution on YOUR website!The inequality is true iff The a^6 + b^6 on both side cancel out, so we want to show for positive a,b Divide both sides by (a^2)(b^2) By AM-GM inequality, This implies that , so we're done.
 test/475241: 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 325913 by richard1234(5390)   on 2011-07-28 01:48:12 (Show Source): You can put this solution on YOUR website!I'm wondering if the developer of this site made some program to automatically post this message every several hours or so. Even then, it shouldn't be where the "unsolved problems" are, it should be contained in the instructions for posting problems.
 real-numbers/475301: find three rational between -0.2 and -0.221 solutions Answer 325911 by richard1234(5390)   on 2011-07-28 01:43:50 (Show Source): You can put this solution on YOUR website!-.201 -.204 -.21
 Polygons/475186: A checkered flag used for racing is a square flag containing 64 alternating white and black squares. How many squares on the checkered flag contain an equal number of white and black squares? 1 solutions Answer 325824 by richard1234(5390)   on 2011-07-27 19:21:24 (Show Source): You can put this solution on YOUR website!Any k-by-k square where k is even. This is because we can divide up the k by k square into 2x2 squares, and if k is odd, this cannot possibly be done. Hence, find the number of 2x2, 4x4, 6x6, and 8x8 squares contained within the 8x8 square and add them (there should be a pattern).
 Permutations/475195: Find both the number of combinations and the numbers of permutations of 10 objects taken 4 at a time.1 solutions Answer 325822 by richard1234(5390)   on 2011-07-27 19:18:27 (Show Source): You can put this solution on YOUR website!10P4 = 10*9*8*7 = 5040 10C4 = (10*9*8*7)/(4*3*2*1) = 210
 Divisibility_and_Prime_Numbers/474828: If m is an odd integer, which expression always represents an odd integer? A) 3^m - 1 B) (m - 1)/2 C) (2m - 1)^2 D) (m + 1)^2 E) m^2 + 2m + 1 Please explain how I could approach and solve this, thanks!1 solutions Answer 325798 by richard1234(5390)   on 2011-07-27 16:31:53 (Show Source): You can put this solution on YOUR website!Choice C, because (2m - 1) is odd, so (2m - 1)^2 will always be odd.
 Evaluation_Word_Problems/474955: two sides of a triangle have lengths 5 and 12.what must be true about the lenght of the thrid side 1 solutions Answer 325796 by richard1234(5390)   on 2011-07-27 16:30:35 (Show Source): You can put this solution on YOUR website!The third side must be between 7 and 17. To see why, draw segment AB with length 12. Draw a circle with radius 5 around point B. You can connect vertex A to some point on the circle to obtain the third side.
 Sequences-and-series/475066: what is the next number? 40, 42, 21, 24, 8, 12, 3, ___1 solutions Answer 325795 by richard1234(5390)   on 2011-07-27 16:28:34 (Show Source): You can put this solution on YOUR website!The pattern is: add 2, divide by 2, add 3, divide by 3, add 4, divide by 4. To obtain the next number, we add 5 to the previous number to get 8.
 test/475147: 1.Which of the following is equal to the sum of two consecutive even integers? (A)144 (B)146 (C)147 (D)148 (E)149 2.If x^2+y^2=2xy,then x must equal (A)-1 (B)0 (C)1 (D)-y (E)y Thank you so much for giving your time to answer my questions.1 solutions Answer 325793 by richard1234(5390)   on 2011-07-27 16:26:14 (Show Source): You can put this solution on YOUR website!1. If we let 2x and 2x+2 be two consecutive even integers, then their sum is 4x+2, which is 2 modulo 4. 146 is the only answer choice that is 2 mod 4, so B is correct. 2. We have x^2 - 2xy + y^2 = 0 --> (x - y)^2 = 0, x - y = 0. Hence x = y, answer choice E.
 Polynomials-and-rational-expressions/474833: Find all numbers for which the rational expression is undefined. (s^3-7s)/(s^2-81) The numbers for which the rational expression is undefined are___. (Use a comma to separate answers.)1 solutions Answer 325740 by richard1234(5390)   on 2011-07-27 13:01:27 (Show Source): You can put this solution on YOUR website!The expression is undefined when the denominator is zero and the numerator is nonzero (otherwise it is said to be "indeterminate"). We can set s^2 - 81 = 0, then s = 9 or -9.
 Linear_Algebra/474936: what is the slope-intercept of m= 5, b= -2?1 solutions Answer 325734 by richard1234(5390)   on 2011-07-27 12:15:55 (Show Source): You can put this solution on YOUR website!Presuming you want slope-intercept form, if m is the slope and b is the intercept, it is simply y = 5x - 2. Be careful that when you post questions, that you specify your variables clearly. Most tutors will know what m and b refer to, but there could be others who used different variables for slope and y-intercept when they learned it, e.g. y = ax + b.
 Quadratic_Equations/475020: Finding a quadratic equation of 25 and 36 are the following: (x-25)(x+25) (x-36)(x+36) x-25 x-36 1 solutions Answer 325732 by richard1234(5390)   on 2011-07-27 12:11:30 (Show Source): You can put this solution on YOUR website!Question does not make sense. Maybe if you said "Find a quadratic equation with 25 and 36 as the roots" it would make sense; even then, none of the answer choices are correct.
 Average/474999: a students test scores are 89, 100, and 85. Find what score the student must get on the next test to pass the class with an A average.1 solutions Answer 325731 by richard1234(5390)   on 2011-07-27 12:08:16 (Show Source): You can put this solution on YOUR website!Assuming A is between 90% and 100%, we can set up an inequality (let x be the next test score): Least possible score is 86.
 Miscellaneous_Word_Problems/474905: A stack contains between 70 and 80 \$100 dollar bills. If the bills are taken out of the stack six at a time, two bills will be left in the stack. If the bills are taken out of the stack four at a time, two bills will be left in the stack again. How many bills are in the stack? A) 70 B) 72 C) 74 D) 78 E) 80 Please explain how I could approach and solve this, thanks!1 solutions Answer 325656 by richard1234(5390)   on 2011-07-27 02:18:16 (Show Source): You can put this solution on YOUR website!The number of bills is two more than a multiple of 6, so 74 and 80 are the only possible choices given the first constraint. The second constraint implies that the number of bills is 2 more than a multiple of 4, so 70, 74, 78 are the only ones satisfying this. 74 is the only number satisfying both, so there must be 74 bills.
 Divisibility_and_Prime_Numbers/474908: When a positive integer n is divided by 6, the remainder is 2. What is the remainder when 7n is divided by 3? Please explain how I could approach and solve this, thanks!1 solutions Answer 325654 by richard1234(5390)   on 2011-07-27 02:16:20 (Show Source): You can put this solution on YOUR website!Note that n ≡ 2 (mod 3) because n can equal anything in {2, 8, 14, ...} and all of these numbers are 2 modulo 3. If n ≡ 2 (mod 3) then 7n ≡ 14 ≡ 2 (mod 3) (hence, the remainder is 2). Try this with various values of n and you will see that the remainder is always 2.
 Divisibility_and_Prime_Numbers/474907: How many integers from -8000 to 8000 are divisible by 4? Please explain how I could approach and solve this, thanks!1 solutions Answer 325653 by richard1234(5390)   on 2011-07-27 02:13:19 (Show Source): You can put this solution on YOUR website!Count the numbers in the set {-8000, -7996, -7992, ..., 8000}. Obviously we are not going to do this by hand so what we can do is make transformations to the set by adding 8004 to each element: |{-8000, -7996, ..., 8000}| = |{4, 8, ..., 16004}| (here |S| denotes the number of elements in set S). We can divide everything by 4. |{4, 8, ..., 16004}| = |{1, 2, ..., 4001}| There are 4001 numbers between -8000 and 8000 inclusive that are divisible by 4.
 logarithm/474483: In a scientific calculator the base for a lagarithm equation is 10 by default. How to change the base? Please explain elaborately.1 solutions Answer 325652 by richard1234(5390)   on 2011-07-27 02:08:28 (Show Source): You can put this solution on YOUR website!I don't know if this requires an elaborate explanation (however it could get deep into proving the change-of-base formula then deriving the Taylor series for logarithms, then proving Taylor's theorem in the first place, etc.). Simply put, if you want to convert from base b to base 10 (so you can input it on your calculator), use the change-of-base formula: Then it is easy to input it on a calculator. Also, most graphing calculators can allow logarithms of bases other than 10 or e. They are quite expensive, though, but graphing calculators can do all sorts of functions such as sums/products, derivatives/integrals, limits, determinants of matrices, factorials, defining your own functions, etc.
 Polynomials-and-rational-expressions/474878: State the degree of the given Polynomial: 2x^4+9x^3-6x+7 I am not sure what he is talking about, state the degree1 solutions Answer 325650 by richard1234(5390)   on 2011-07-27 01:55:17 (Show Source): You can put this solution on YOUR website!The degree of a single-variable polynomial is the highest exponent that has a non-zero coefficient. In this case the degree is 4. For multi-variable polynomials, the degree is the largest sum that is obtained by adding the exponents of the corresponding terms. For example, if the degree would be 4+5 = 9.
 Triangles/474904: If the measures of the angles of a triangle are in the ratio of 3:5:7, what is the measure of the largest angle of the triangle? A) 60 B) 72 C) 84 D) 90 E) 144 Please explain how I could approach and solve this, thanks!1 solutions Answer 325649 by richard1234(5390)   on 2011-07-27 01:51:12 (Show Source): You can put this solution on YOUR website!Let the angles be 3x, 5x, 7x. Their sum is 180, so 3x + 5x + 7x = 180 15x = 180 --> x = 12 The largest angle is 7x, which is 7(12) = 84, choice C.
 Problems-with-consecutive-odd-even-integers/474838: the difference of 67 and an integer is 3 more than the product of 8 and 7. what is the integers? 1 solutions Answer 325648 by richard1234(5390)   on 2011-07-27 01:50:19 (Show Source): You can put this solution on YOUR website!"Three more than the product of 8 and 7" is just a cheap, seemingly tricky way of saying "59." So all this problem asks is "The difference of 67 and an integer is 59." If we let x be the integer, either equation could be true, depending on how the question is interpreted: x - 67 = 59 --> x = 126 67 - x = 59 --> x = 8
 Divisibility_and_Prime_Numbers/474844: When k is divided by 7, the remainder is 4; and when k is divided by 3, the remainder is 0. What is a possible value of k? A) 32 B) 30 C) 25 D) 18 E) 15 Please explain how I could approach and solve this, thanks!1 solutions Answer 325647 by richard1234(5390)   on 2011-07-27 01:48:10 (Show Source): You can put this solution on YOUR website!We want a multiple of 3, and one that is 4 more than a multiple of 7. B, D, E are the only multiples of 3, and D is the only one four more than a multiple of 7, so D is correct.
 absolute-value/474857: absolute value of n is less than or equal to n1 solutions Answer 325646 by richard1234(5390)   on 2011-07-27 01:43:39 (Show Source): You can put this solution on YOUR website! If you were to graph y = x and y = |x| on a coordinate plane, they would intersect where x >= 0 and |x| is greater than x for negative x (which does not work here) Hence, the only values of n that satisfy are nonnegative values of n.
 Radicals/474691: Are each of the statements below true or false? Explain your answer. √a + √b = √(a+b). Explain why. The numerator and denominator of the following must be multiplied by √3 to rationalize 3 -----------. Explain why. 3 + √3 1 solutions Answer 325645 by richard1234(5390)   on 2011-07-27 01:41:37 (Show Source): You can put this solution on YOUR website!1. Statement is false because if we square both sides we get which does not hold for all real a,b. 2. It must be multiplied by 3 - sqrt(3), not just sqrt(3). This is because the denominator becomes a rational number (applying difference of two squares).
 Quadratic_Equations/474872: what is the real numbers1 solutions Answer 325644 by richard1234(5390)   on 2011-07-27 01:39:42 (Show Source): You can put this solution on YOUR website!Any number you can locate on a number line, e.g. 5, -3.8, sqrt(2), 0, pi/6, 25749, etc.
 Probability-and-statistics/474901: in 2 successive throws of pair of dice ,determine rhe second card is red queen 1 solutions Answer 325643 by richard1234(5390)   on 2011-07-27 01:38:29 (Show Source): You can put this solution on YOUR website!How does one get a red queen out of two dice rolls?
 Expressions-with-variables/474887: When I Evaluate this expression,(-5x)^2= ? if x=4 , What do I do first, get square root of 4 or the product of 4 and then get square root? Do I get sqrt of the product of -5*4 which is -20? or do sqrt x which is ^4=16. Such as -5*16=-80. I then tried it on the calculator and just entered just as written in book with the parenthesis (-5x)^2 x=4 and came up with 400 for the answer, but if I left out the parenthesis the answer was - 80 . That further confused me and I can not find it in my book with parenthesis. Thank you 1 solutions Answer 325639 by richard1234(5390)   on 2011-07-27 00:22:47 (Show Source): You can put this solution on YOUR website!80 has nothing to do with it; you do not multiply -5*4*2. The ^2 means you square the expression, so if x is 4, then (-5x)^2 = (-5*4)^2 = (-20)^2 (-20)^2 = 400, which is the correct answer.
 Miscellaneous_Word_Problems/474886: The product of two numbers is 8933. If each of the two numbers is doubled the product of these larger numbers is?1 solutions Answer 325637 by richard1234(5390)   on 2011-07-27 00:08:05 (Show Source): You can put this solution on YOUR website!Let a,b be the numbers ab = 8933 (2a)(2b) = 4ab = 4(8933) = 35732
 Average/474817: If a + b = 3, b + c = 5, and a + c = 8, what is the average (arithmetic mean) of a, b, and c? Please explain how to approach and solve this problem. Thanks!1 solutions Answer 325636 by richard1234(5390)   on 2011-07-27 00:05:00 (Show Source): You can put this solution on YOUR website!Add all three equations to get 2a + 2b + 2c = 3 + 5 + 8 = 16 The average of a,b,c is (a+b+c)/3, so if we divide both sides of the equation by 6 we obtain our desired result (2a + 2b + 2c)/6 = 16/6 (a + b + c)/3 = 8/3
 Probability-and-statistics/474724: probability At most 1 queen1 solutions Answer 325634 by richard1234(5390)   on 2011-07-27 00:02:11 (Show Source): You can put this solution on YOUR website!At most one queen, but how many cards are dealt (if they are even dealt)?
 Human-and-algebraic-language/474524: The neighborhood association sent a survey asking families to rank their concerns for the neighborhood. The eight items listed were crime, recycling, speeding, pool safety, noise, parking, graffiti, and trash collection. In how many ways can a family answer this survey?1 solutions Answer 325632 by richard1234(5390)   on 2011-07-26 23:57:41 (Show Source): You can put this solution on YOUR website!Assuming the family must answer all eight categories, there are eight ways to choose the first category. After this, there are only seven ways to choose the second category, since the original one cannot be picked again. Then there are six choices for the third category, and so on. The total number of ways is 8! = 8*7*6*...*1 = 40320.