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# Recent problems solved by 'stanbon'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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 Geometry_proofs/180848: what is a quadrilatral with 2 right angles?1 solutions Answer 135589 by stanbon(57387)   on 2009-02-08 07:38:53 (Show Source): You can put this solution on YOUR website!It's a rectagle. Cheers, Stan H.
 Quadratic_Equations/180849: the diagram shows the a right angled triangle. based on the length of the sides of the triangle form a quadratic equation in term of y. AB=(y+3)cm BC=3y cm AC= (4y-3) cm help me pless...tq for helping me,.... 1 solutions Answer 135587 by stanbon(57387)   on 2009-02-08 07:37:58 (Show Source): You can put this solution on YOUR website!the diagram shows the a right angled triangle. based on the length of the sides of the triangle form a quadratic equation in term of y. AB=(y+3)cm BC=3y cm AC= (4y-3) cm ---------------- The answer depends on which of the lengths is the hypotenuse; I'm going to assume that y+3 is the hypotenuse. ---------------- (y+3)^2 = (3y)^2 + (4y-3)^2 y^2 + 6y + 9 = 9y^2 + 16y^2-24y+9 24y^2 -30y = 0 3y(8y-10) = 0 y = 0 or y = 10/8 = 5/4 ------------------------ If y = 5/4 cm AB = (5/4) + 3 = 5/4 + 12/4 = 17/4 cm BC = 3*(5/4) = 15/4 AC = 4(5/4)-3 = 5-3 = 2 cm ================================ If one of the other sides is really the hypotenuse, use Pythagoras, as I have, and solve for "y". ================================================= Cheers, Stan H.
 Radicals/180847: Ok, I have been working on these two since 4 30 this morning and still can't figure them out. Could somebody help me before I go nuts? One is (z-6)^2-40=0 and 2x^2+7x+2=0 I keep getting some odd ball numbers and have not a clue what to do with them. Thanks in advance, Judy1 solutions Answer 135586 by stanbon(57387)   on 2009-02-08 07:30:21 (Show Source): You can put this solution on YOUR website!(z-6)^2-40=0 z^2-12z+36-40 =0 z^2 - 12z - 4 = 0 Use the quadratic formula to get: z = [12 +- sqrt(12^2 - 4*1*-4)]/2 z = [12 +- sqrt(160)]/2 z = [12 +- 4sqrt(10)]/2 z = 6 +- 2sqrt(10) ========================== 2x^2+7x+2=0 Use the quadratic forula to get: x = [-7 +- sqrt(7^2 -4*2*2)]/4 x = [-7 +- sqrt(33)]/4 x = (-7/4) +- (1/4)sqrt(33) =============================== Cheers, Stan H.
 Functions/180834: find the derivative. 1. x = ln(x+y+1) and 2. F(x) = (square root of quantity 1 + x)- ln(1 + square root of quantity x + 1) 1 solutions Answer 135578 by stanbon(57387)   on 2009-02-07 22:50:07 (Show Source): You can put this solution on YOUR website!find the derivative. 1. x = ln(x+y+1) 1 = [1/(x+y+1)](1 + (y')) y' = [x+y+1] -1 ============================= and 2. F(x) = sqrt(1 + x)- ln[1 + sqrt(x + 1)] F'(x) = (1/2)(1+x)^(-1/2) - [1/(1+sqrt(x+1)] * [(1/2)(x+1)^(-1/2)] ==================================================================== Cheers, Stan H.
 Probability-and-statistics/180823: Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If 5 Colonials games are chosen at random, what is the probability that exactly 4 of those games are won by the Colonials? Round your response to at least three decimal places. 1 solutions Answer 135576 by stanbon(57387)   on 2009-02-07 22:42:18 (Show Source): You can put this solution on YOUR website!Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If 5 Colonials games are chosen at random, what is the probability that exactly 4 of those games are won by the Colonials? Round your response to at least three decimal places. ---------------------------------------------------------- P(win) = 1/2 = P(lose) ------------------------- Your problem is binomial with n=5,p=1/2,x = 4 ----------------- Answer: P(x=4) = 5C4(1/2)^4(1/2) = 5(1/2)^5 = 5/32 ==================================================== Cheers, Stan H.
 Money_Word_Problems/180831: David split his \$25,000 inheritance between Fidelity Short-Term Bond Fund with an annual yield of 5% and T. Rowe Price Tax-Free Short-Intermediate Fund with an annual yield of 4%. If his total income for 1 year on the two investments was \$1140, then how much did he invest in each fund?1 solutions Answer 135573 by stanbon(57387)   on 2009-02-07 22:30:36 (Show Source): You can put this solution on YOUR website!David split his \$25,000 inheritance between Fidelity Short-Term Bond Fund with an annual yield of 5% and T. Rowe Price Tax-Free Short-Intermediate Fund with an annual yield of 4%. If his total income for 1 year on the two investments was \$1140, then how much did he invest in each fund? --------------------------------------- Equation: interest + interest = interest 0.04x + 0.05(25000-x) = 1140 Multiply thru by 100 to get: 4x + 5*25000 - 5x = 114000 x = 125000 - 114000 x = \$11000 (amt invested at 4%) 25000-x = \$14 (amt invested by 5%) --------------------------------------- Cheers, Stan H.
 Quadratic_Equations/180830: 4. Create a real-life situation that fits the equation (x + 3)(x - 5) = 0 and express the situation as the same equation. 1 solutions Answer 135571 by stanbon(57387)   on 2009-02-07 22:24:20 (Show Source): You can put this solution on YOUR website! Create a real-life situation that fits the equation (x + 3)(x - 5) = 0 and express the situation as the same equation. ----------------- balance = (x+3)(x-5) The balance on our savings accout was zero 3 month ago and will be zero 5 monts from now. ---------------------- Cheers, Stan H.
 Functions/180825: Please solve 1. Let m(x) be the slope of the tangent line to the curve y = x^3 - 2x^2 + x at the point (x,y). Find the instantaneous rate of change of m(x) with respect to x at the point (2,2).1 solutions Answer 135570 by stanbon(57387)   on 2009-02-07 22:17:43 (Show Source): You can put this solution on YOUR website!Let m(x) be the slope of the tangent line to the curve y = x^3 - 2x^2 + x at the point (x,y). Find the instantaneous rate of change of m(x) with respect to x at the point (2,2). ------------------ Take the derivative to get: m(x) = 3x^2 - 4x + 1 ---- Then slope at (2,2) = m(2) = 3*4 -4*2+1 = 5 =============================================== Cheers, Stan H.
 Linear-equations/180821: Can you please help me. I am very confuse with this problem. The accompanying table shows the percent of the adult population that married before age 25 in several different years. Using the year as the independent variable, find the linear regression equation. Round the regression coefficients to the nearest hundredth. Using the equation found above, estimate the percent of the adult population in the year 2009 that will marry before age 25, and round to the nearest tenth of a percent Year(x) Percent (Y) 1971 42.4 1976 37.4 1980 37.1 1984 34.1 1989 32.1 1993 28.8 1997 25.7 2000 25.5 thank you very much! 1 solutions Answer 135567 by stanbon(57387)   on 2009-02-07 22:11:20 (Show Source): You can put this solution on YOUR website!The accompanying table shows the percent of the adult population that married before age 25 in several different years. Using the year as the independent variable, find the linear regression equation. Round the regression coefficients to the nearest hundredth. Using the equation found above, Year(x) Percent (Y) 1971 42.4 1976 37.4 1980 37.1 1984 34.1 1989 32.1 1993 28.8 1997 25.7 2000 25.5 ---------------------- You need a calculator or some software to generate the linear regression equation. Enter the data as (71,42.4) (76,37.4) (80,37.1) etc. Run the program to get: f(x) = -0.58x + 82.92 ----------------------- estimate the percent of the adult population in the year 2009 that will marry before age 25, and round to the nearest tenth of a percent --- 2009 means x = 109 f(109) = -0.58*109 + 82.92 = 19.75% =========================================== Cheers, Stan H.
 Functions/180819: Determine whether the equation defines y as a function of x. x^2 + y = 36; |x| - y = 41 solutions Answer 135559 by stanbon(57387)   on 2009-02-07 21:57:03 (Show Source): You can put this solution on YOUR website!Determine whether the equation defines y as a function of x. x^2 + y = 36 Rearrange: y = -x^2 + 36 Ans: y is a function of x. ---------------------------------- |x| - y = 4 Rearrange: y = |x|-4 Ans: y is a function of x ================================== Cheers, Stan H.
 Graphs/180792: This question is from textbook Elementary and Intermediate Graphing a line given a point and slope. Draw /1 through (-4,0) and (0,6).What is the slope of any line parallel to /1? Draw /2 through the orgin andf parallel to /11 solutions Answer 135554 by stanbon(57387)   on 2009-02-07 21:53:51 (Show Source): You can put this solution on YOUR website!Graphing a line given a point and slope. Draw /1 through (-4,0) and (0,6). --- slope = (6-0) / (0--4) = 6/4 = 3/2 ------------------------- Form: y = mx + b (0,6) is the y-intercept Equation: y = (3/2)x + 6 =================== What is the slope of any line parallel to /1? Ans: 3/2 ------------------------------- Draw /2 through the origin and parallel to /1 Thru the origin means the y-intercept is at 0 Equation: y = (3/2)x + 0 y = (3/2)x ==================== Cheers, Stan H. --------------------------------------
 Miscellaneous_Word_Problems/180813: Solve Variation Problem The cost of pipe at Home Depo varies jointly as the length and diameter of the pipe. If 20 feet of 0.5 inch diameter pipe costs \$36.60, then what is the cost of 12 feet of 0.75 inch diameter pipe?1 solutions Answer 135550 by stanbon(57387)   on 2009-02-07 21:45:37 (Show Source): You can put this solution on YOUR website!Solve Variation Problem The cost of pipe at Home Depo varies jointly as the length and diameter of the pipe. --- c = k -- If 20 feet of 0.5 inch diameter pipe costs \$36.60 Solve for "k": 36.60 = k[20*0.5] k = 36.60/10 = 3.66 --- Equation: c = 3.66[Ld] --- , then what is the cost of 12 feet of 0.75 inch diameter pipe? --- c = 3.66[12*0.75] cost = 3.66*9 cost = \$32.94 ===================== Cheers, Stan H.
 Radicals/180806: The owner of a health foods store determines that the demand equation for selling a nutritional supplement is where p is the price in dollars and x is the number of bottles demanded per week. Solve the equation for x. How many bottles are demanded per week if the price of the supplement is \$13.50? 1 solutions Answer 135544 by stanbon(57387)   on 2009-02-07 21:15:34 (Show Source): You can put this solution on YOUR website!The equation is missing and maybe some other narrative. Cheers. Stan H.
 Rate-of-work-word-problems/180803: 1) Find the domain of the following: a) f(t)= 4.5e^t 1 solutions Answer 135542 by stanbon(57387)   on 2009-02-07 21:13:16 (Show Source): You can put this solution on YOUR website!Find the domain of the following: a) f(t)= 4.5e^t Find the domain of the following: a) f(t)= 4.5e^t Domain: All Real Numbers =========================== Cheers, Stan H.
 Trigonometry-basics/180794: This question is from textbook Analytic Trigonometry Standing on the bank of a river, a surveyor measures the angle to the top of a tree on the opposite bank to be 23 degrees. He backs up 45ft and remeasures the angle to the top of the tree at 18 degrees. How wide is the river?1 solutions Answer 135527 by stanbon(57387)   on 2009-02-07 18:58:34 (Show Source): You can put this solution on YOUR website!Standing on the bank of a river, a surveyor measures the angle to the top of a tree on the opposite bank to be 23 degrees. He backs up 45ft and remeasures the angle to the top of the tree at 18 degrees. How wide is the river? ------------------------------------- Let the width of the river be "x". Draw the picture and solve for "x". --------------------------- tan(23) = tree/x tan(18) = tree/(x + 45) ----------------------- tree = x*tan(23) tree = (x+45)*tan(18) ------------------------ Equation: x*tan(23) - (x+45)*tan(18) xtan(23) - x*tan(18) = 45*tan(18) x[tan(23)-tan(18)] = 45*tan(18) Solve for "x" =========================== Cheers, Stan H.
 Miscellaneous_Word_Problems/180795: This question is from textbook During the last hour, a telemarketer dialed 20 numbers and reached 4 busy signals, 3 answering machines, and 13 people. Use this information to determine the empirical probability that the next call will be answered in person. 1 solutions Answer 135525 by stanbon(57387)   on 2009-02-07 18:43:41 (Show Source): You can put this solution on YOUR website!During the last hour, a telemarketer dialed 20 numbers and reached 4 busy signals, 3 answering machines, and 13 people. Use this information to determine the empirical probability that the next call will be answered in person. ------------------------- Ans: 13/20 -------------- Cheers, Stan H.
 Miscellaneous_Word_Problems/180796: This question is from textbook If you roll a die many times, what would you expect to be the relative frequency of rolling a number less than 6? A) 2 out of 3 B) 1 out of 3 C) 1 out of 6 D) 1 out of 2 E) 5 out of 6 1 solutions Answer 135524 by stanbon(57387)   on 2009-02-07 18:40:03 (Show Source): You can put this solution on YOUR website!If you roll a die many times, what would you expect to be the relative frequency of rolling a number less than 6? --- P(<6) = 1 - P(6) P(<6) = 1 - (1/6) P(<6) = 5/6 Ans: 5 out of 6 ================================== Cheers, Stan H. A) 2 out of 3 B) 1 out of 3 C) 1 out of 6 D) 1 out of 2 E) 5 out of 6
 Miscellaneous_Word_Problems/180797: This question is from textbook A jar contains 5 yellow marbles, 16 green marbles, and 8 black marbles. If one marble is selected at random, what is the probability that it is not green? 1 solutions Answer 135522 by stanbon(57387)   on 2009-02-07 18:28:23 (Show Source): You can put this solution on YOUR website!A jar contains 5 yellow marbles, 16 green marbles, and 8 black marbles. If one marble is selected at random, what is the probability that it is not green? ------------------------------------------------------- P(not green) = 1 - P(green) P(not green) = 1 - (16/29) P(not green) = 13/29 ========================== Cheers, Stan H.
 Volume/160357: A cylinder is inscribed in a sphere of radius 1. Express the volume of the sphere as a function of the base radius. PLEASE HELP ME!!!1 solutions Answer 135513 by stanbon(57387)   on 2009-02-07 17:55:17 (Show Source): You can put this solution on YOUR website!A cylinder is inscribed in a sphere of radius 1. Express the volume of the sphere as a function of the base radius. ------------ The volume of every sphere is V = (4/3)pi*r^3 ================================================== Cheers, Stan H.
 Volume/180783: I WANT TO FIND THE LATERAL AREA OF A REGULAR PYRAMID 3,2AND 21 solutions Answer 135510 by stanbon(57387)   on 2009-02-07 17:44:28 (Show Source): You can put this solution on YOUR website!That is not enough information. You have to indicate which numbers are the dimensions of the base and the dimension of the height. =============== Cheers, Stan H.
 Quadratic_Equations/180787: Connect English with Mathematics and Graphing Lines 4. Translate each sentence into an algebraic equation. a) One sixth of a number, increased by 15, is 42. b) Three times a number, decreased by four, is five more than six times the number. c) When tickets to a soccer game cost \$4 each, the revenue at the gate is \$320. d) the total length of the base and height of a triangle 15cm. PLeaseeeeeeeeeeeeeeeeeee thankssssssssssssssss alottttttttttttttttttt1 solutions Answer 135509 by stanbon(57387)   on 2009-02-07 17:40:21 (Show Source): You can put this solution on YOUR website!Connect English with Mathematics and Graphing Lines 4. Translate each sentence into an algebraic equation. a) One sixth of a number, increased by 15, is 42. (1/6)x +15 = 42 ---------------------------- b) Three times a number, decreased by four, is five more than six times the number. 3x - 4 = 6x + 5 ---------------------------- c) When tickets to a soccer game cost \$4 each, the revenue at the gate is \$320. 5x = 320 ------------------------------- d) the total length of the base and height of a triangle 15cm. b + h = 15 =========================================== Cheers, Stan H.
 Graphs/180788: This question is from textbook Elementary and Intermediate Graph a line. The line through (-2,5) with slope -1.1 solutions Answer 135507 by stanbon(57387)   on 2009-02-07 17:36:07 (Show Source): You can put this solution on YOUR website!Graph a line. The line through (-2,5) with slope -1. --------------------- y = mx + b You know y = 5 when x = -2 and m = -1; so solve for "b": 5 = -1*-2 + b b = 3 -------------------------- Equation: y = -x + 3 Graphing: when x = 0, y = 3 giving you point (0,3) Plot (0,3) and (-2,5) and draw a line thru them: =========================================== Cheers, Stan H.
 Rational-functions/180779: This question is from textbook Sullivan Algebra and Trigonometry f(x)= 2x^2/ x^4+1 In regards to 27c, d, e, and f. c>> if f(x)=-1, what is x? what points are on the graph of f? My understanding... -1=2x^2/x^4+1 My confusion is really how to solve for x (due to the fraction with exponents) d>> what is the domain of f? The answer is all real numbers. Why? e>> List the X Intercept. f>> List the Y Intercept. My understanding... both intercepts are zero. My graph comes out to be a short line symmertrical to the y axis where both x and y are intercepting at the orgin (0,0)1 solutions Answer 135500 by stanbon(57387)   on 2009-02-07 15:55:35 (Show Source): You can put this solution on YOUR website!f(x)= 2x^2/(x^4+1) In regards to 27c, d, e, and f. c>> if f(x)=-1, what is x? My understanding... -1=2x^2/x^4+1 Cross-multiply to get: -x^4-1 = 2x^2 Rearrange: x^4 + 2x^2 + 1 = 0 Factor: (x^2+1)(x^2+1) = 0 x = +i or x = -i ----------------------------- what points are on the graph of f? ----------------------------------------- f(x) = 2x^2/(x^4+1) d>> what is the domain of f? The answer is all real numbers. Why? The domain of a function is always "all Real Numbers" unless the equation of the function excludes certain values. The x^4+1 in the denominator is always positive so no x-values are excluded from the Domain. ------------------------------------------- e>> List the X Intercept. f(x) = 2x^2/(x^4+1) y can only be zero if 2x^2 = 0; so the x-intercept is (0,0) -------------------------------------------------------------- f>> List the Y Intercept. If x = 0, y = 0; so the x-intercept is the same as the y-intercept. ================================ Cheers, Stan H.
 Complex_Numbers/180780: 2 + i/ i + 51 solutions Answer 135499 by stanbon(57387)   on 2009-02-07 15:40:39 (Show Source): You can put this solution on YOUR website!(2 + i) / (5+i) = [(2+i)(5-i)] / [(5+i)(5-i)] = [10 + 3i +1] / 25 + 1] = (11+3i) / 26 ================== Cheers, Stan H.
 Trigonometry-basics/180775: Find the exact value of cot(75º). PLEASE HELP ME!!!!! I really dont know what to do!!!1 solutions Answer 135498 by stanbon(57387)   on 2009-02-07 15:36:43 (Show Source): You can put this solution on YOUR website!Find the exact value of cot(75º). ------- cot(x+y) = [cot(x)cot(y)-1] / [cot(x) + cot(y)] Your Problem: cot(30 + 45) = [cot(30)cot(45)-1] / [cot(30) + cot(45)] = [sqrt(3)*sqrt(2)/2 - 1] / [sqrt(3) + sqrt(2)/2] = [(sqrt(3)*sqrt(2) - 2)/2] / [(2sqrt(3) = sqrt(2))/2] = etc. ========================= Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/180776: What is the answer for this problem? Find two consecutive even integers such that the sum of their squares is 52.1 solutions Answer 135495 by stanbon(57387)   on 2009-02-07 15:23:15 (Show Source): You can put this solution on YOUR website!Find two consecutive even integers such that the sum of their squares is 52. ------------- 1st: 2x 2nd: 2(x+1) ---------------- Equation: (2x)^2 + (2(x+1))^2 = 52 4x^2 + 4(x+1)^2 = 52 x^2 + (x+1)^2 = 13 2x^2 + 2x + 1 = 13 2x^2 + 2x - 12 = 0 x^2 + x - 6 = 0 (x+3)(x-2) = 9 Positive solution: x = 2 --------- 1st: 2x = 4 2nd: 2x+2 = 6 --- Checking: 4^2 + 6^2 = 52 16 + 36 = 52 52 = 52 ================== Cheers, Stan H.
 Trigonometry-basics/180777: Simplify to a single trig function: (cos3x-cosx)/ (sin3x-sinx) PLEASE HELP ME I DON'T KNOW WHAT TO DO!!!1 solutions Answer 135493 by stanbon(57387)   on 2009-02-07 15:16:53 (Show Source): You can put this solution on YOUR website!Working with just the cos(3x) you get the following: cos3x = cos(x)cos(2x) - sin(x)sin(2x) =cos(x)[1-2sin^2(x)] - sin(x)[2sin(x)cos(x)] =cos(x)-2cos(x)sin^2(x) - 2sin^2(x)cos(x) =cos(x) - 4sin^2(x)cos(x) ----------------------------- So subtracting cos(x) from this result you would get: = - 4sin^2(x)cos(x) ========================== Cheers, Stan H.
 Probability-and-statistics/180108: Suppose that 48% of the women who gave birth at a certain hospital last year were over 30 years old, and that 46% were unmarried. If 65% of the women were over 30 or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried and over 30 ? 1 solutions Answer 135492 by stanbon(57387)   on 2009-02-07 15:09:33 (Show Source): You can put this solution on YOUR website!Suppose that 48% of the women who gave birth at a certain hospital last year were over 30 years old, and that 46% were unmarried. If 65% of the women were over 30 or unmarried (or both), what is the probability that a woman who gave birth at the hospital was both unmarried and over 30 ? ---------------------------- Formula: P(A and B) = P(A) + P(B) - P(A or B) ----------------------------- Your problem: P(un and >30) = P(un) + P(>30) - P(un or >30) P(un and >30) = 0.46 + 0.48 - 0.65 = 0.29 ========================== Cheers, Stan H.
 Pythagorean-theorem/180768: an isoceles triangle has a hypotenuse 15 cm long. Determine the length of the two equal sides? thnxx1 solutions Answer 135490 by stanbon(57387)   on 2009-02-07 15:02:42 (Show Source): You can put this solution on YOUR website!an isoceles triangle has a hypotenuse 15 cm long. Determine the length of the two equal sides? --------- Let each of the equal sides have length "x" 15^2 = x^2 + x^2 2x^2 = 15^2 x = (15/2)sqrt(2) ====================== Cheers, Stan H.
 Pythagorean-theorem/180767: an apartment building casts a shadow. From the tip of the shadow to the top of the building is 100 m. The tip of the shadow is 72 m from the base of the building? How tall is the building? thnakyou1 solutions Answer 135486 by stanbon(57387)   on 2009-02-07 14:52:01 (Show Source): You can put this solution on YOUR website!an apartment building casts a shadow. From the tip of the shadow to the top of the building is 100 m. The tip of the shadow is 72 m from the base of the building? How tall is the building? -------------------- Draw the picture and label the height of the building "x". ----------------------- Use Pythagoras or use trigonometry if you know it. 100^2 = 72^2 + x^2 x^2 = 10000 - 5184 x^2 = 4816 x = 69.40 meters ======================= Cheers, Stan H.
 Miscellaneous_Word_Problems/180745: This question is from textbook ) One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is not a spade. 1 solutions Answer 135485 by stanbon(57387)   on 2009-02-07 14:46:58 (Show Source): You can put this solution on YOUR website!One card is selected at random from a standard 52-card deck of playing cards. Find the probability that the card selected is not a spade. -------------- There are 13 spades and 39 other cards --- P(spade) = 39/52 = 3/4 =========================== Cheers, Stan H.