Posts by Reiny

Total # Posts: 40,239

  1. Math

    Just think it through. He bought 30 dozen, or 360 eggs So the cost price was 1800/360 RS or Rs 5 per egg But he can only sell 330 eggs. According to the wording of the question, he wants to make a profit of 1 rupe per egg, but it doesn't say if that profit is based on the ...
  2. math

    ((3^n)^n*(3^n)^-1) / 81 = 1 3^(2n) * 3^-n = 81 3^n = 81 3^n = 3^4 n = 4 testing the n = -1 solution Left Side = ( (3^-1)^(-1) * (3^-1)^-1 )/81 = (3^1 * 3^1 )/81 = 9/81 ? 1 So according to the way you typed it, the book is wrong, the only solution is n = 4
  3. math

    5x?y = 625 -----> y = 5x-625 sub into the 2nd equation: 32x × 3y = 243 ----- divide both sides by 3 32xy = 81 32x(5x-625) = 81 160x^2 - 20000x - 81 = 0 yuk this is not going nicely ... use your calculator and the quadratic formula to find x, then y let's work on ...
  4. CAlculuss

    I don't like to show you by just plugging into some formula, since that way you really don't learn much So I will do it by using the actual definition of the parabola let P(x,y) be any point on our parabola. P must be equidistant from (3,5) and the line x = -1 so x...
  5. Algebra

    Your 1.01^6 represents an increase of 1%, not 10% try 1.1^6
  6. Maths

    original number: let the unit digit be x let the tens digit be y the number is 10y + x new number: unit digit ---- y tens digit ---- x new number is 10x+y new number < twice original number by 12 10x+y = 2(10y+x) - 12 10x+y = 20y + 2x - 12 8x - 19y = -12 but x+y=12 ---->...
  7. math

    The way I understand it ... so we are buying 3 articles for 2160 so each one costs 720 This represents a decrease of 12% or .88x = 720 x = 818.18 check: after taking 12% off of 818.18 we have 720.00 cost of 3 of those = 3(720) = 2160 my answer is correct
  8. math

    amount sold of each kind : x , x, and 3x total cost = x(24) + x(30) + 3x(42) = 180x avg cost = 180x/(5x) = 36
  9. Algebra

    Why do you think Scott told you to check your arithmetic?
  10. statistics

    E(rolls 12) = 5(1/36) E(rolls 9,10,11) = 1(9/36) E(rolls any other ) = 1(26/36) add them up for your expected win What do they charge to play the game? multiply your expected win by 100
  11. Math

    Your table has a length 2.25 m and a width of 1.20 m area = length x width = ....... m^2
  12. Maths

    I appears that you have a triangle PQR , with PQ = 15 km, and angle P = 50°, angle Q = 80° A quick mental calculation gives us angle R = 50° , making the triangle isosceles. So without any work, QR = 15 km by the sine law: PR/sin80 = 15/sin50 PR = 15sin80/sin50...
  13. help[

    No, you have 2 apples, not 2 1 apple + 1 apple = 2 apples ? + ? = 2? ? + ? = 2? so a+a = 2a
  14. help[

    If you have an apple and an apple, what do you have ?
  15. math

    width --- x m length --- 2x m height ---- 5 m total surface area of the 4 walls = (5)(2x) + (5)(x) + (5)(2x) + (5)(x) = 30x But in your un-punctuated sentence you say that this is 210 m^2 30x = 210 x = 7 so the room is 7m by 14m by 5 m for a volume of 490 m^3 "Find its ...
  16. Math

    Ahhh, the pitfalls of auto-correct. let the "hypo tennis" be x x^2 = 9^2+ 12^2 ----> you should know this formula = 81 + 144 = 225 x = ?225 = 15
  17. math

    Keep in mind that I calculated your cost for you, not how much you saved. You will still have to do that calculation.
  18. math

    after a 20% discount, you would be paying 80% or .8 two ways: 1. .8(2.50+4.95+6.00) = .8(13.45) = 10.76 2. .8(2.5) + .8(4.95) + .8(6.00) = 2.00 + 3.96 + 4.8 = 10.76
  19. math

    original speed ---- x km/h slower speed ----- x-15 km/h 6(x-15) = 5x solve for x Once you have the speed x, multiply that by 5 to get the distance
  20. algebra

    total height of first 5 students = 5(1.65) Add the new girl's height and take the average of the 6 students.
  21. algebra

    Peter has ---- x cards Jane has ---- 3x cards (x+3x)/2 = 64 continue ....
  22. Math

    x = 3?x square both sides x^2= 9x x^2 - 9x = 0 x(x-9) = 0 x = 0 or x = 9
  23. algebra

    let e^x = y then you have 2y^2 - 7y - 15 = 0 (y - 5)(2y + 3) = 0 y = 5 or y = -3/2 e^x = 5 then x = ln5 or e^x = -3/2 no solution, look at a graph of y = e^x, it is never negative
  24. Math

    In what way does this question differ from your other one? /display.cgi?id=1511142923 What simple adjustment do you think you should make?
  25. Math

    This one is even easier than the one I just did for you.
  26. Math

    Assuming you count 5 vowels, and no repetition , prob(4 vowels in 4 tries) = (5/26)(4/25)(3/24)(2/23) = .....
  27. calculus

    I can see it. from your link, v(t) = 6sin(t/2) , we must integrate to get x(t), where x(t) is the distance on the x-axis x(t) = -12cos(t/2) + c given: when t = 0 , x(0) = 1 1 = -12cos(0) +c c =-12 so x(t) = -12cos(t/2) - 12 when x = ? x(?) = -12cos(?/2) - 12 = 0 - 12 = -12
  28. Math helppp

    Avator--- a Titanic --- t Harry Potter -- p let's just reduce all monies to millions a+t+p = 5900 ** a = t+p-300 ---> a-t-p = -300 *** a+t= 4p - 600 --- a+t-4p = -600 **** add** and *** 2a = 5600 a = 2800 add *** and **** 2a - 5p = -900 5900 - 5p = -900 -5p = -6500 p = ...
  29. Advanced Algebra

    correct
  30. Math

    "in which each number is 17 more than its predecessor " I hope you realize that is a great hint. so a = 11, d = 17 of an arithmetic sequence use your formula for the 100th term to find it
  31. geometric progression

    given: a= x^-4 ar^7 = x^52 use substitution: (x^-4)r^7 = x^52 r^7 = x^59 r = x^(59/7) 2nd term = ar = (x^-4)(x^59/7) = x^(31/7) matching it with x^t ---> t = 31/7
  32. Math

    or: if right angled, then two lines must be perpendicular slope between 1st point and 2nd = 2/3 slope between 1st and third = -1/5 slope between 2nd and 3rd = -3/2 notice that 2/3 and -3/2 are negative reciprocals of each other, thus , yes we have a right-angled triangle
  33. Math - Im soooo lost need help fast

    if you have two points (x1, y1) and (x2, y2) the slope = (y2 - y1)/(x2 - x1) OR (y1 - y2)/(x1- x2) so for your first one: (6,5) (3,1) slope = (1-5)/(3-6) = -4/-3= 4/3 OR slope = (5-1)/(6-3) = 4/3 , same result Do the same for #5, be careful with the subtraction of negatives. I...
  34. math

    a) is correct b) banks do not lend out money for 4 years at simple interest, they use compound interest. You will have to answer c) first, that is , find the monthly payment c) i = .09/12 = .0075 n = 4(12) = 48 paym = ? 4600 = paym( 1 - 1.0075^-48)/.0075 you should get $114.47...
  35. Math

    This is a quadratic. It can only factor over the rational numbers if the discriminant is a perfect square. What do you think?
  36. math

    To be a perfect square, the number must be factorable into pairs of equal factors e.g. 144 = 2x2 x 2x2 x 3x3 10 = 2x5 15 = 3x5 20 = 2x2x5 30 = 2x3x5 So the LCM would be 2x2 x 3 x 5 So to pair them up, we will need another 3x5 So the least square divisible by 10,15,20, and 30...
  37. math

    smaller number ---- x larger number ----- 2x product means we multiply them, so x(2x) = 98 2x^2 = 98 x^2 = 49 etc
  38. Math

    I will guess we are just evaluating these. I will do the first one, you show me how you did the rest 8q + 6 for q = 2 = 8(2) + 6 = 16 + 6 = 22
  39. Business Math

    only difference would be in the time fraction for I = PRT 220/365 in the first case, and 220/360 in the second. (I assume my Canadian and the US methods are the same)
  40. math?

    You didn't tell us how long he is paying for the trip.
  41. Algebra 2

    consider 8^x = 25 take logs of both sides and use your log rules xlog8 = log 25 x = log25/log8 = appr 1.55 so x ? 1.55 test some values: x = 0, 8^0 = 1 which is ? 25 x = -5 , 8^-5 = .0000305.. which is ? 25 we can easily see that all negative values of x will work let's ...
  42. correction = Math

    wrong! your answer's ratio would be 5 : 17 which is not 2:5 number of males --- 2x number of females --- 5x 5x - 2x = 12 3x = 12 etc ....
  43. APY-math

    let the equivalent annual rate be i daily rate = .031/365 = .000084931 1.000084931^365 = 1+i 1+i = 1.031484143 i = annual = .03148 annual rate = .03148 or appr 3.15% Scott's answer would be the instantaneous rate at .0314855 which of course would be very close to the daily...
  44. Liberal are maths

    prob(red, red) = (20/36)(19/35) = ....
  45. Math

    10 4/17 ÷ 4 5/9 = (174/17) ÷ (41/9) use your rule for division of fractions to continue
  46. Math helppp

    The angle between their flight paths is 110° I sketched the triangle and used the cosine law. x^2 = 450^2 + 380^2 - 2(4500)(380)cos110° = 463870.889 x = ?463870.889 = appr 681 km or using vectors and the actual angles let v = (450cos320, 450sin320) = (344.72,-289.25) ...
  47. math 7/8 grd

    let d = -6.9, valid for d > -7 -6.9+s > -3 s > 3.9 which is NOT s > 4 Yup, Steve is right, we have one exception which rules out my entire solution.
  48. math 7/8 grd

    subtract them, (valid since both inequality signs are the same) d+s - d > -3 - (-7) s > 4
  49. Math

    I agree http://www.wolframalpha.com/input/?i=pattern+%7B0,6,15,27%7D
  50. algebra

    replace x with 1 f(1) = 5(1) + 4 = .....
  51. Algebra

    dimensions of a rectangular prism , (a box), consist of 3 constants, the length, the width and the height "dimensions 11 by 9 by 3. 23 in 297 in 318in 159in" makes no sense to me "I think the answer is c 318 in". What does that mean? Volume would be measure...
  52. Quantitative Aptitude

    I have no idea what this is supposed to mean. Looks like a series of random statements.
  53. Math

    total number of students ---- x number of girls = (2/7)x number of boys = (5/7)x number of girls with glasses = (1/2)(2/7)x = (1/7)x number of boys with glasses = (1/3)(5/7)x = (5/21)x given: (5/21)x = 10 solve for x, and sub into my definition
  54. Trigonometry

    N45W ---> an angle of 135° using trig notation. So we are de-composing your vector into its vertical and horizontal displacement. horizontal: 99cos 135 = 99(-?2/2) = appr - 70 metres vertical : 99 sin 135° = appr 70 metres notice if you construct a right-angled ...
  55. Math/calculus

    165 = 180-15 or = 120+45 or = 90+75 I will pick 120+45 tan 165 = tan(120+45) = (tan120 + tan 45)/(1 - tan120tan45) ** 2 we know tan 45=1 tan120 = -tan60 , by the CAST rule = -?3 , from the 30-60-90 triangle so back in ** tan165 = (-?3 + 1)/(1 - (-?3)(1)) = (1 - ?3)/(1 + ?3)
  56. Math

    to be a multiple of 3, the sum of the digits must be a multiple of 3 For 74A52B1, 7+4+A+5+2+B+1 must divide evenly by 3 19 + A+B must divide by 3 then 18 +A+B+1 must divide by 3 A+B+1 must divide by 3 So A+B could be 2, 5, 8, 11, 14, 17, no more in the second: 326AB4C the same...
  57. Math/calculus

    f (x) = 3cos (4pix -pi/2) -2 = 3cos (4?(x - 1/8) ) - 2 <---- a horizontal shift of 1/8 to right period = 2?/(4?) = 1/2 On the x-axis mark off 0, 1/8, 2/8, 3/8 and 4/8 the magnitude of your cosine curve is 3, so on the y-axis, mark off 5 or 6 units above and below Knowing ...
  58. Math/calculus

    Using the standard "compass heading" http://www.allstar.fiu.edu/aero/fltmidcomp.htm that would be 120° based on standard trig notation. what If I told you the plane ends up at (125(1.5)cos120°, 125(1.5)sin125°) ??
  59. Math

    let the smaller be x then the larger is x+4 so x + x+4 = 90 2x = 86 x = 43 so how about 43 and 47. Did you skip that pair ? You knew the were only 4 apart, so just about equal and half of 90 is 45 , so ....
  60. Math

    For linear equations, - if in your solution, the variable drops out, and you end up with a true statement, there will be an infinite number of solutions. e.g. 3x - 9 = 3(x-3) solving you get 0 = 0, which is true, so infinite number - if in your solution, the variable drops out...
  61. Algebra 2

    all good except #8 8. it asked for the actual solutions. x^2 - (-x^2 - 6)^2 = 36 x^2 - (x^4 + 12x^2 + 36) = 36 x^2 - x^4 - 12x^2 - 36 = 36 x^4 + 11x^2 + 72 = 0 no real roots, the discriminant is negative. http://www.wolframalpha.com/input/?i=plot+x%5E2+-+(y+-+6)%5E2+%3D+36+,+y...
  62. Math Posttest Connexus 09:Posttest 9:Solving Two-

    Are you even reading the question?? Your reply to Ms Sue suggests that you are merely looking for the answer. You want an average of 200 Your first day sales were good, there were 6 over your goal your second day not so good, you were 15 short of the goal. take it from there
  63. Math

    See the post I answered for you
  64. Math

    look back at your post that was answered
  65. Math

    /display.cgi?id=1510589905
  66. No to Pizza - Math

    dividing 754 by 13 will give you the distance per hour you then have to multiply by 8 or use a simple ratio: x/8 = 754/13 x = 8*754/13 =...... notice I performed the same steps as above
  67. math

    first step is correct: 2075 – 1195 = $880 now you want the percentage based on the original amount, so 880/1195 = ... now change that to a percentage You have to learn to get a "feel" for numbers 1195 is almost 1200 the increase is 880 or about 3/4 so 8.8% is a ...
  68. Math

    All 3 are wrong. Are you just guessing, hoping that somebody will just give you the answer. Show me what you did to get your answers, that is the only way I can help you.
  69. @ Kira

    Don't just yell out answers, no learning takes place by doing that.
  70. Math

    You could visualize it by looking at the face of a clock and imagining a circle around the face. There would be 12 markings on it (the knots of your string) the first marking could be 1:00 , the second at 4:00 and the third at 8:00 now count the number of hours between the ...
  71. Algebra

    Your function would be: f(x) = (x-1)(x-2)(x+2)(x+3) = (x^2 - 4)(x-1)(x+3) expand it further to see which one matches. That way you will not have to "guess" what the correct version is.
  72. Math

    Well, in a parallelogram, opposite angles are equal and adjacent angles add up to 180° Take it from there.
  73. Algebra

    F(x)=x^2+8x+15 complete the square, you must know this procedure! = (x^2 + 8x + 16 - 16) + 15 = ( (x+4)^2 - 16) + 15 = (x+4)^2 - 1
  74. Algebra

    not enough data
  75. Algebra I

    so the new line must be y = (-1/5)x + b which automatically rules out a) and d) plug in the point (-10,3) and find b to decide which of the remaining choices is it.
  76. Math

    The number ---- x the reciprocal of the number --- 1/x "The reciprocal of a number decreased by the reciprocal of twice the number" ---- 1/x - 1/(2x) 1/x - 1/(2x) ? 2 2/2x - 1/2x ? 2 1/x ? 2 1 ? 2x 2x ? 1 x ? 1/2 test: let x = 1/4 reciprocal --- 4 twice the number...
  77. Math

    1(1/2)^(t/5730) = .921 .5^(t/5730) = .921 take log of both sides and use log rules ... (t/5730) log .5 = log .921 take over
  78. Math

    let the rate be r 101(1 + r)^10 = 160 (1+r)^10 = 160/101 = 1.58418... take 10th root of both sides to get 1+r subtract 1 from that, then change to a percent
  79. Math

    So each square has an area of 16 units^2, so each side is 4 units. the circle on each square will have a radius of 2 units, for an area of ?(2^2) or 4? so the left over from each square is 16 - 4? units or 4(4 - ?) Now, how many squares did you have ?
  80. Calculus

    looking at your answer for y' I will assume you meant: y = x^2/(x^2 + 3) your first derivative is correct, I suspect you used the quotient rule. So why not use it also to get y'' y'' = ( (x^2 + 3)^2 (6) - 6x(2)(x^2 + 3) (2x) )/(x^2 + 3)^4 = ( 6(x^2+3)^2 - ...
  81. Math - Accounting

    Assumption on 9% I will assume that the rate is 9% per annum, compounded monthly, so ... i = .09/12 = .0075 n = 30(12) = 360 Paym= ? 125000 = paym( 1 - 1.0075^-360)/.0075 find paym. "The total payment over the term of the loan is" I suppose they want you to multiply ...
  82. Mathematics

    First bottle: unit price .... £55/80 ml = 68.75 cents/ml 2nd bottle: 50 ml at £45 plus 50 ml at £22.50 or 100 ml for £67.50 unit price = £67.50/100 = 67.50 cents/ml so what do you think?
  83. Math

    with distribution: 6( 1/2 + 2/3) + 3/4) = 3 + 4 + 9/2 =7 9/2 or 11 1/2 or 23/9 without distribution: add up the 3 fractions in the bracket, first obtaining a common denominator, then multiply that by 6 , reduce your fraction answer to lowest terms You MUST get the same answer.
  84. Math

    Yes, there would be no solution. If your variable disappears and you end up with a FALSE statement, there is no solution e.g. x +8 = x - 6 if your variable disappears and you end up with a TRUE statement, there will be an infinite number of solutions. That is, every possible ...
  85. Math

    no, what you typed makes no sense to me notice in 5^3, 5 is the base and 3 is the exponent so your ^3 has no base what does 8+^7 mean? did you mean 8^7 ??
  86. Math

    retype using the convention ^ to show exponents e.g. 5^3 means "5 to the third" or (5)(5)(5)
  87. Math

    #3 x/-10 > 6 , we are going to multiply by -10 so the inequality sign must reverse ... x < -60, so ------ C all others are correct
  88. Pre-Calc

    "bearings" to indicate direction is often misunderstood so you should stick with the conventional method used in trigonometry I will use vectors, so ... (400cos10° , 400sin10°) = R + (50cos90° , 50sin90°) where R is the required vector (393.923, 69....
  89. algebra

    If Karen deposits $x in the 2.5% account, how much does she deposit in the other account ?? if her interest from the first account is .025x , what is ther interest from the 2nd account ?? (sum of the two interests) = 850 take over
  90. Algebra

    I had assumed you found the new perimeter to be 4(x+3) = 4x + 12 so 4x + 12 = 2x+40 I had formed that equation for you, no solve it.
  91. Algebra

    Side of original square ---- x cm perimeter = 4x side of new square = x+3 New perimeter = ..... translate: "the perimeter of the new square is 40 more than twice the length of each side of the original square" ---> new perimeter you found above = 2x + 40 solve for x
  92. Pre-Calc

    According to my diagram, they ploughed at an angle of 135° to each other, one went .5 miles , the other 2.5 miles area = (1/2)(side1)(side2)(sin(angle between them)) = (1/2)((.5)(2.5)sin 135° = .... square miles
  93. Maths

    let each of the base angles be x then the vertical angle = 2(x+x) =4x solve for x: x + x + 4x = 180
  94. Trigonometry

    let the diameter be D ft in one rotation the belt moves D? ft. The wheel rotates at 360 rpm, or at 60 rotations per second In that 1 second the belt covers 40 ft. so 60(D?) = 40 D? = 2/3 D = 2/(3?) ft = appr .2122 ft or appr 2.546 inches
  95. Calculus

    If typed fully , this is one of the standard optimization problems, and it probably asked for a minimum sum of the areas. I will define my variables different from Steve's, mainly to avoid fractions let each side of the square be x let each side of the equilateral triangle...
  96. Calculus

    Ok, I did that, no what ?
  97. Math

    We have four possible outcomes: 1 ww ** 2 wb 3 bw 4 bb we want the cases marked by ** #1: ww, prob(first w) = 6/11 so the white gets transferred to B and prob(2nd w) = 4/8 = 1/2 prob(ww) = (6/11)(1/2) = 6/22 = 3/11
  98. Math

    Identical post to this /display.cgi?id=1510190947 which I had answered yesterday. Why are you reposting it ?
  99. algebra

    JoJo you were right -5(5) + 4 = -25 + 4 = -21 D
  100. Maths

    9:12:18 ---> a:b:12 9:12:18 = 3:4:6 = 6:8:12 state your conclusion
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