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Recent problems solved by 'stanbon'

stanbon answered: 57894 problems
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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Rectangles/253602: The length of a rectangle is 5cm, and its perimeter 14 cm. What is the area of the rectangle in square centimeters? 1 solutions Answer 185944 by stanbon(57967)   on 2010-01-04 17:43:38 (Show Source): You can put this solution on YOUR website! The length of a rectangle is 5cm, and its perimeter 14 cm. What is the area of the rectangle in square centimeters? --------------------------------------- Perimeter = 2(L + W) 14 = 2(5 + W) 7 = 5+W W = 2 cm (width) --------------- Area = LW Area = 5*2 = 10 cm^2 ========================= Cheers, Stan H.

Equations/253585: How do I solve this? Sally can paint a house in 4 hours. It takes John 6 hours to paint the same house. How long does it take them together? I am not sure how to set this up. Thanks! Lisa Comer 1 solutions Answer 185924 by stanbon(57967)   on 2010-01-04 17:11:44 (Show Source): You can put this solution on YOUR website! How do I solve this? Sally can paint a house in 4 hours. It takes John 6 hours to paint the same house. How long does it take them together? ------------------------------------ Sally's rate: 1/4 job/hr John's rate: 1/6 job/hr Together rate: 1/x job/hr ---------------------------- Equation: rate + rate = together rate 1/4 + 1/6 = 1/x Multiply thru by 12x 3x + 2x = 12 5x = 12 x = 12/5 = 2.4 hrs (time to do the job if Sally and John work together. =============== Cheers, Stan H.

Equations/253587: 7(c-7)+4c=-2(c+5) 1 solutions Answer 185919 by stanbon(57967)   on 2010-01-04 17:05:38 (Show Source): You can put this solution on YOUR website! 7(c-7)+4c=-2(c+5) --- 7c-49 + 4c = -2c - 10 11c - 49 = -2c - 10 13c = 59 c = 59/13 ================= Cheers, Stan H.

Probability-and-statistics/249314: . A telephone survey gives 96 consumers two choices: Do they prefer Coke or Pepsi? Exactly 32 of those surveyed state that they prefer Coke. Assuming that “a” = 0.01, test the hypothesis that the proportion of the population that prefers Coke is 30%. 1 solutions Answer 185917 by stanbon(57967)   on 2010-01-04 16:58:56 (Show Source): You can put this solution on YOUR website! A telephone survey gives 96 consumers two choices: Do they prefer Coke or Pepsi? Exactly 32 of those surveyed state that they prefer Coke. Assuming that “a” = 0.01, test the hypothesis that the proportion of the population that prefers Coke is 30%. --------------------------- Ho: p = 0.30 H1: p is not 0.30 ------------- sample proportion: 32/96 = 1/3 sample std: sqrt(0.3*0.7/96) = 0.0468 --- critical value for 2-tail test with alpha = 1% = +/-2.2758 Test stat: z(1/3) = (1/3 - 0.3)/0.0468 = 0.7127 --------- Conclusion: Since the test statistic is not in the rejection interval, fail to reject Ho. Conclude that p=0.30 ======================================================== Cheers, Stan H.

Length-and-distance/253576: Hi :o) I hope you guys can help me with this. I think I now understand how to work out a resultant vector using the coordinate system, but this question has stumped me a little. I can't get a picture of it - it seems to be 3D, is that right? Please help... A mine shaft goes due west 75 m from the opening at an angle of 25° below the horizontal surface. It then becomes horizontal and turns 30° north of west and continues for another 45 m. What is the displacement of the end of the tunnel from the opening. Thanks SOOOOO much :o) (Happy New Year) 1 solutions Answer 185916 by stanbon(57967)   on 2010-01-04 16:48:46 (Show Source): You can put this solution on YOUR website! A mine shaft goes due west 75 m from the opening at an angle of 25° below the horizontal surface. It then becomes horizontal and turns 30° north of west and continues for another 45 m. What is the displacement of the end of the tunnel from the opening. ------------- If you know how to graph in 3D, the start point is (0,0,0) the turning point is (-75cos(25), 0 ,-75sin(25)) the final position is (-75cos(25) ,-45,-75sin(25)) ------------------------------- Distance from start to finish: d = sqrt((75cos(25))^2 + (45)^2 + (75sin(25))^2) d = sqrt(5526.47+2025+98.53) d = 87.46 meters ========================== Cheers, Stan H.

Polygons/253575: What is the measure of an exterior angle of an equiangular pentagon? 1 solutions Answer 185910 by stanbon(57967)   on 2010-01-04 16:31:51 (Show Source): You can put this solution on YOUR website! What is the measure of an exterior angle of an equiangular pentagon? --- The pentagon has 5 sides so it has 5 exterior angles. --- The sum of the exterior angles of ANY regular polygon is 360. ---- Equation: measure of each exterior angle = 360/5 = 72 degrees ================= Cheers, Stan H.

Inequalities/253574: Here is an inequality to solve. 4+12x<24x+10 1 solutions Answer 185908 by stanbon(57967)   on 2010-01-04 16:29:12 (Show Source): You can put this solution on YOUR website! Here is an inequality to solve. 4+12x<24x+10 ----------- Subtract 12x from both sides to get: 4 < 12x + 10 Subtract 10 from both sides: 12x > -6 Divide both sides by 12 to get: x > -1/2 ============== Cheers, Stan H.

Travel_Word_Problems/253573: An air plane traveled 3300 miles in 6 hours. How fast did the airplane travel per hour? 1 solutions Answer 185906 by stanbon(57967)   on 2010-01-04 16:26:55 (Show Source): You can put this solution on YOUR website! An air plane traveled 3300 miles in 6 hours. How fast did the airplane travel per hour? ------ rate = distance/time rate = 3300/6 = 550 mph =========================== Cheers, Stan H.

Probability-and-statistics/253558: 1.two men and three women are each waiting for a job interview there is only enough time to interview two people before lunch two people are chosen at random what is the probability that both people are women? what is the probability that at least one person is a women? which is more likely, one of people is a woman and the other is a man or both people are either men or women? 1 solutions Answer 185905 by stanbon(57967)   on 2010-01-04 16:24:59 (Show Source): You can put this solution on YOUR website! 1.two men and three women are each waiting for a job interview there is only enough time to interview two people before lunch two people are chosen at random what is the probability that both people are women? P(2 women) = 3C2/5C2 = 3/10 ------------------------------------ what is the probability that at least one person is a women? P(x>=1) = 1 - P(x=0) P(at least one woman) = 1 - P(no women) P(at least one woman) = 1 - 2C2/5C2 = 1 - 1/10 = 9/10 ------------------------------------------------------ which is more likely, one of people is a woman and the other is a man or both people are either men or women? P(2 men) = 1/10 P(2 women) = 3/10 ----- P(one man and one woman) = 1 - [P(no man) + P(no woman)= 1 - [3/10 + 1/10] = 1 - [4/10] = 6/10 --- Ans: "one of the people is a woman and other is a man" has the higher prob. =========================================================================== Cheers, Stan H.

Rational-functions/253393: Which of the following is a horizontal asymtote of f(x)= 1/x^2-16? A. x=-4 B. y=4 C. x=1 D. y=0 1 solutions Answer 185685 by stanbon(57967)   on 2010-01-03 22:37:56 (Show Source): You can put this solution on YOUR website! As x gets larger and larger that denominator gets hugh and the fraction gets closer and closer to zero. ---- Horizontal asymptote: y = 0 ================================= Cheers, Stan H.

Rectangles/253415: 4. If the perimeter of a rectangle is 8√2 cm, what is the smallest possible value of the length of one of its diagonals in cm? I've tried: let length be l, width be w, and diagonal be d let l be x, then w will be: (8√2-2x)/2 = 4√2-x d^2=l^2+w^2 =x^2+(4√2-x)^2 =x^2+(32-8√2x-x^2) =32-8√2x... 1 solutions Answer 185684 by stanbon(57967)   on 2010-01-03 22:31:43 (Show Source): You can put this solution on YOUR website! If the perimeter of a rectangle is 8√2 cm, what is the smallest possible value of the length of one of its diagonals in cm? ----------------------------------------------------- Perimeter = 2(L + W) = 8sqrt(2) cm L+W = 4sqrt(2) cm Note: W = 4sqrt(2)-L ------------------------ Diagonal = sqrt(L^2 + W^2) Substitute for W: D(L) = sqrt(L^2 + (4sqrt(2)-L)^2) D(L) = sqrt(L^2 + [L^2 - 8sqrt(2)L +32] D(L) = sqrt(2L^2 -8sqrt(2)L + 32) ------ You have a quadratic with a = 2 ; b = -8sqrt(2) Minimum occurs when L = -b/2a = 8sqrt(2)/(4) = 2sqrt(2) W = 4sqrt(2)-2sqrt(2) = 2sqrt(2) ------------------------ Minimum Diagonal: D^2 = L^2 + W^2 D^2 = (2sqrt(2))^2 + (2sqrt(2))^2 D^2 = 8 + 8 D = 4 cm ================ Cheers, Stan H.

Linear-systems/253413: solve the linear system: 2x = 3y x+3y = 9 1 solutions Answer 185680 by stanbon(57967)   on 2010-01-03 22:17:50 (Show Source): You can put this solution on YOUR website! solve the linear system: 2x = 3y x+3y = 9 -------------- Modify: x = (3/2)y --- Substitute for "x" and solve for "Y": (3/2)y + 3y = 9 (9/2)y = 9 (1/2)y = 1 y = 2 ----- Since x = (3/2)y, x = (3/2)2 = 3 ------------------------------------ Solution: x=3;y=2 ====================== Cheers, Stan H.

Probability-and-statistics/253367: A True-False test has 10 questions with each having 2 possible answers with one correct. Assume a student randomly guesses the answers to every question. A. What is the probability of getting exactly 5 correct answers? B. What is the probability of getting less than 6 correct answers? This is what I have come up with so far n=10 p=2 =.05 for p p(5) + P(10) =.000+ P(6) + P(10) =.000+ 1 solutions Answer 185679 by stanbon(57967)   on 2010-01-03 22:14:03 (Show Source): You can put this solution on YOUR website! A True-False test has 10 questions with each having 2 possible answers with one correct. Assume a student randomly guesses the answers to every question. ---------- P(correct) = 1/2 ; P(wrong) = 1/2 ------------------------------------ A. What is the probability of getting exactly 5 correct answers? Binomial Problem with n = 10, p = 1/2 , x = 5 P(x=5) = 10C5*(1/2)^5*(1/2)^5 = 252*0.00097656 = 0.2461 ------------------------------------------------------------------ B. What is the probability of getting less than 6 correct answers? P(0<= x <=5) = binomcdf(10,1/2,5) = 0.6230.. ---------------------------------------------------------- Cheers, Stan H.

Equations/253366: What is the solution to the equation 5.6x - 1.2 = 1x + 26.4 1 solutions Answer 185652 by stanbon(57967)   on 2010-01-03 20:31:21 (Show Source): You can put this solution on YOUR website! What is the solution to the equation 5.6x - 1.2 = 1x + 26.4 ----------------- 4.6x = 26.4+1.2 4.6x = 27.6 --- x = 6 ============ Cheers, Stan H.

Inequalities/253364: there is a question on my paper that i dont understand how to do. its 10+y>12. Can you explain to me how to solve this problem 1 solutions Answer 185650 by stanbon(57967)   on 2010-01-03 20:25:56 (Show Source): You can put this solution on YOUR website! 10+y>12 Subtract 10 from each side to solve for "y": y > 2 ============ Cheers, Stan H.

Inequalities/253358: x2-4x-5<0 1 solutions Answer 185646 by stanbon(57967)   on 2010-01-03 20:14:51 (Show Source): You can put this solution on YOUR website! x^2-4x-5<0 Factor: (x-5)(x+1) < 0 --- x cannot be 5; x cannot be -1 ------------------------ Draw a number line and plot x = -1 and x = 5 -------------------- Note: The number line is broken into 3 intervals. Test a check point from each interval in the inequality to determine where the solutions are. -------- Test x = -2; you get (-)(-) < 0 ; that is false ----- Test x = 4 ; you get (-)(+) < 0 ; true so solutions in (-1,5) ----- Test x = 6 ; you get (+)(+)<0 ; that is false ================ Ans: All x in (-1,5) ============================== Cheers, Stan H.

Exponential-and-logarithmic-functions/253359: what is the solution of the equation e^xe^2x=4? 1 solutions Answer 185644 by stanbon(57967)   on 2010-01-03 20:05:04 (Show Source): You can put this solution on YOUR website! what is the solution of the equation e^xe^2x=4? --------------------------- e^(3x) = 4 Take the natural log to get: 3x = ln(4) x = (1/3)ln(4) x = 0.4621... Cheers, Stan H.

logarithm/253356: If log(base8) 3=p and log(base3) 5=q, express log(base 10) 5 in terms of p and q. 1 solutions Answer 185642 by stanbon(57967)   on 2010-01-03 20:01:59 (Show Source): You can put this solution on YOUR website! If log(base8)3=p 8^p = 3 --- and log(base3) 5=q 3^q = 5 --- express log(base10) 5 in terms of p and q. ----------------------------------------------------------------------- Let log(base 10)5 = x 10^x = 5 Then 10^x = 3^q Then 10^x = (8^p)^q Then 10^x = 8^(pq) Then x = log[8^pq] Then x = (pq)log(base 10)8 ---- So, log(base 10)5 = (pq)log(base 10)8 =========================================== Cheers, Stan H.

Rational-functions/253354: at what x-coordinate does f(x)=|-2x+3|-2 have its minimum value? a. -2 b. -2/3 c. 3/2 d. 3 1 solutions Answer 185638 by stanbon(57967)   on 2010-01-03 19:44:25 (Show Source): You can put this solution on YOUR website! at what x-coordinate does f(x)=|-2x+3|-2 have its minimum value? --------------------- y is minimum when |-2x+3| = 0 --- Solve -2x+3 = 0 -2x = -3 x = 3/2 ---------------- y is at a minimum when x = 3/2 ---------------- Cheers, Stan H.

Rational-functions/253353: if f(x)=x^2-x and g(x)=x-1, what is f(g(x))? 1 solutions Answer 185636 by stanbon(57967)   on 2010-01-03 19:39:03 (Show Source): You can put this solution on YOUR website! if f(x)=x^2-x and g(x)=x-1, what is f(g(x))? ----------------- f[g(x)] = f[x-1] = (x-1)^2-(x-1) --- = x^2-2x+1 -x+1 --- = x^2 - 3x + 2 ================================ Cheers, Stan H.

Angles/253352: the endpoints of PQ are P(-3,1) and Q(4,25). Find the length of PQ 1 solutions Answer 185635 by stanbon(57967)   on 2010-01-03 19:34:05 (Show Source): You can put this solution on YOUR website! the endpoints of PQ are P(-3,1) and Q(4,25). Find the length of PQ ------------------ distance = sqrt[(change in x)^2 + (change in y)^2] ------- d = sqrt[7^2 + 24^2] d = sqrt[625] --- d = 25 =============== Cheers, Stan H.

Linear-equations/253346: Assume 300 students attend a dance. Which band would you choose and the cost per ticket you need to cover your expenses. Band A charges $600 to play for the entire evening Band B charges $350 plus $1.25 for each ticket sold 1 solutions Answer 185633 by stanbon(57967)   on 2010-01-03 19:28:33 (Show Source): You can put this solution on YOUR website! Assume 300 students attend a dance. Which band would you choose and the cost per ticket you need to cover your expenses. Band A charges $600 to play for the entire evening Flat Rate for any number of students: $600 with 300 students the charge will be $600 Cost per ticket to cover expenses would be 600/300 = $2.00 ---------------------------------------------------------- Band B charges $350 plus $1.25 for each ticket sold Band B charges $(350+1.25x) for "x" students with 300 students the charge will be 350+1.25*300 = $725 Cost per ticket to cover expenses would be 725/300 = $2.43 ---------------------------------------------------------- Cheers, Stan H.

logarithm/253332: log(36)=a and log(125)=b. Find (1/12) in terms of a and b. 1 solutions Answer 185631 by stanbon(57967)   on 2010-01-03 19:11:33 (Show Source): You can put this solution on YOUR website! log(36)=a 10^a = 36 10^a = 6^2 10^(a/2) = 6 log(6) = a/2 ------------------- and log(125)=b. 10^b = 125 10^b = 5^3 10^(b/3) = 5 log(5) = b/3 --------- Find (1/12) in terms of a and b. 1/12 = 5/60 = 5/(6*10) -------- log(1/12) = log(5/(6*10)) = log(5)-log(6)-log(10) = (b/3) - (a/2) - 1 ================================ Cheers, Stan H.

Inverses/253238: A certain kind of animal weighs about 77 pounds at birth and gains about two pounds per day for the first few weeks. Determine the days for which the animal's weight is more than 129 pounds. 1 solutions Answer 185514 by stanbon(57967)   on 2010-01-03 13:47:02 (Show Source): You can put this solution on YOUR website! A certain kind of animal weighs about 77 pounds at birth and gains about two pounds per day for the first few weeks. Determine the days for which the animal's weight is more than 129 pounds. ------ W(t) = W(0)+2t ----- 129 < 77 + 2t --- 2t > 129-77 2t > 52 t > 26 days ==================== Cheers, Stan H.

Probability-and-statistics/250032: 37. In this exercise we study the connection between sets (from Chapter 7) and combinations (from Chapter 8). a. Given a set with n elements, what is the number of subsets of size 0? of size 1? of size 2? of size n? b. Using your answer from part a, give an expression for the total number of subsets of a set with n elements. c. Using your answer from part b and a result from Chapter 7, explain why the following equation must be true: (n) + (n) + (n) + ... + (n) =2n (0) (1) (2) (n) d. Verify the equation in part c for n=4 and n=5 e. Explain what the equation in part c tells you about Pascal’s triangle 1 solutions Answer 185510 by stanbon(57967)   on 2010-01-03 13:42:50 (Show Source): You can put this solution on YOUR website! a. Given a set with n elements, what is the number of subsets of size 0?---------nC0 = 1 of size 1? of------nC1 = n size 2?------------nC2= (n(n-1))/2 of size n?---------nCn = 1 ---------------------------------------------- b. Using your answer from part a, give an expression for the total number of subsets of a set with n elements.-------------- Total number of subsets = nC0 + nC1 + nC2 + ... + nCn = 2^n ---------------------------------------- c. Using your answer from part b and a result from Chapter 7, explain why the following equation must be true: nC0 + nC1 + nC2 + ... + nCn = 2^n Ans: Every element in the set of "n" is either chosen or not chosen in each subset. So the number of possible subsets is 2^n (a choice with 2 possible outcomes made n times) ------------------------------------------------------------------ d. Verify the equation in part c for n=4 and n=5 4C0 + 4C1 + 4C2 + 4C3 + 4C4 = 1 + 4 + 6 + 4 + 1 = 16 = 2^4 --------------------------------- Note: I'll leave n = 5 to you --------------------------------- e. Explain what the equation in part c tells you about Pascal’s triangle The sum of the elements in the kth row is 2^(k-1) ==================================================== Cheers, Stan H. ---------------------------------

Exponential-and-logarithmic-functions/253188: Finding zeros - i dont get how Function - f(x) = log 5x Function - f(x) = 6^x Can someone explain how to find the zeros please 1 solutions Answer 185428 by stanbon(57967)   on 2010-01-03 09:25:44 (Show Source): You can put this solution on YOUR website! Finding zeros - i dont get how Function - f(x) = log 5x --- x-intercept: Let y = 0 and solve for "x": log(5x) = 0 5x = 10^0 5x = 1 x = 1/5 ------ y-intercept: Let x = 0 and solve for "y": y = log(5*0) y = log(0) Exponential form: 10^y = 0 Ans: y does not exist. No solution. No y-intercept ============================= Function - f(x) = 6^x --- x-intercept: Let y = 0 and solve for "x": 6^x = 0 Ans: x does not exist No solution No x-intercept ----- y-intercept: Let x = 0 and solve for "y": y = 6^0 y = 1 is the y-intercept ------------------------------- Cheers, Stan H.

Percentage-and-ratio-word-problems/253194: What is the value of n after it has been decreased by 16 2/3% ? a 1/6 n b 1/3 n c 5/6 n d 6/7 n e 7/6 n 1 solutions Answer 185424 by stanbon(57967)   on 2010-01-03 09:19:34 (Show Source): You can put this solution on YOUR website! What is the value of n after it has been decreased by 16 2/3% ? ---------- Equation: n - [(16 2/3)/100]n --- = [(83 1/3)/100]n --- = 0.833333..n --- = (5/6)n ================ Cheers, Stan H. ================ a 1/6 n b 1/3 n c 5/6 n d 6/7 n e 7/6 n

Miscellaneous_Word_Problems/253195: In a group of 80 high school student, 30 study Spanish, 40 study French, and 25 study neither Spanish nor French. How many of 80 students study both Spanish and French? (A) 18 (B) 15 (C) 20 (D) 16 (E) 13 1 solutions Answer 185419 by stanbon(57967)   on 2010-01-03 09:12:54 (Show Source): You can put this solution on YOUR website! In a group of 80 high school student, 30 study Spanish, 40 study French, and 25 study neither Spanish nor French. How many of 80 students study both Spanish and French? (s and f) = s + f - (s or f) --- Note: (s or f) = 80-(s or f)' = 80 - 25 = 55 -------- Therefore: s and f = 30 + 40 - 55 --- s and f = 15 ======================== Cheers, Stan H. ======================== (A) 18 (B) 15 (C) 20 (D) 16 (E) 13

Miscellaneous_Word_Problems/253196: By how much does r - s exceed s - r ? a (r-s)/(s-r) b 2(r-s) c -2 d 2(s-r) e -1 1 solutions Answer 185418 by stanbon(57967)   on 2010-01-03 09:08:27 (Show Source): You can put this solution on YOUR website! By how much does r - s exceed s - r ? a (r-s)/(s-r) b 2(r-s) c -2 d 2(s-r) e -1 -------------------------------- Your Problem: (r-s)-(s-r) = r-s-s+r = 2r-2s = 2(r-s) ==================== Cheers, Stan H.

Probability-and-statistics/253189: a bag has 9 tickets marked with the number 1,2,3,4,5,6,7,8,9.two tickets are drawn at random from the bag.find the probability that both numbers drawn are A)even B)odd 1 solutions Answer 185416 by stanbon(57967)   on 2010-01-03 09:04:28 (Show Source): You can put this solution on YOUR website! a bag has 9 tickets marked with the number 1,2,3,4,5,6,7,8,9.two tickets are drawn at random from the bag.find the probability that both numbers drawn are A)even There are 4 even digits. P(even) = 4C2/9C2 = 6/36 = 1/6 -------- B)odd There are 5 odd digits. P(odd) = 5C2/9C2 = 10/36 = 5/18 ============================= Cheers, Stan H.

expressions/253126: honestly, i don't know if i classified this right. i don't remember how to do problems with a ration in the bottom and top of a fraction. the problem is 8/10-x/2. do i need to multiply the whole fraction by two, or just the bottom 1 solutions Answer 185360 by stanbon(57967)   on 2010-01-02 20:37:05 (Show Source): You can put this solution on YOUR website! the problem is 8/10-x/2. do i need to multiply the whole fraction by two, or just the bottom ----- Yours is a subtraction problem. To add or subtract fractions you need to have a common denominator on the fractions. It's like adding apple and oranges. They only add if you call them both "fruit". ------- The common denominator for your problem is 10. Rewrite each fraction with 10 as its denominator: (8/10)-(5x/10) ---- Combine the numerators over the common denominator: (8-5x)/10 ---- That is the best answer you can get. ---- It's like 3 oranges + 5 apples = 8 fruit ============================================== Cheers, Stan H.