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# Recent problems solved by 'stanbon'

stanbon answered: 57288 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 , 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 Probability-and-statistics/620528: If the period of a tangent function is 7π, what is the frequency of the function?1 solutions Answer 390208 by stanbon(57361)   on 2012-06-13 14:44:18 (Show Source): You can put this solution on YOUR website!If the period of a tangent function is 7π, what is the frequency of the function? ------ time = 7(pi) seconds/cycle freq = [1/(7pi)] cycles/second =================================== Cheers, Stan H. ==============
 Probability-and-statistics/620534: 14% of what number is 0.31 solutions Answer 390205 by stanbon(57361)   on 2012-06-13 14:36:45 (Show Source): You can put this solution on YOUR website!14% of what number is 0.3 ---- Equation: 0.14x = 0.3 x = 0.3/0.14 x = 2.1429 ============= Cheers, Stan H.
 Probability-and-statistics/620301: what is the 6th term of (2x-1/3y)^71 solutions Answer 390068 by stanbon(57361)   on 2012-06-12 21:32:24 (Show Source): You can put this solution on YOUR website!what is the 6th term of [(2x-(1/3)y)]^7 ---- 6th term: 7C2*(2x)^2*(-(1/3)y)^5) = 21*4x^2*(-1/243)y^5 --- = (-28/81)x^2y^5 ====================== Cheers, Stan H.
 Probability-and-statistics/619963: Hi, I've been stuck on this question all day! Hoping I could get some help: Whats the height of college hockey players? The avg height has been 68.3 inches. A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with std dev of 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use 5% level of significance and this one as well please: A random sample of 83 investment portfolios managed by Kendra showed that 62 of them met the targeted annual percent growth. A random sample of 112 portfolios managed by Lisa showed that 87 met the targeted annual percent growth. Find a 99% confidence interval for the difference in the proportion of the portfolios meeting target goals managed by Kendra compared with those managed by Lisa. Is there a difference in the proportions at the 99% confidence level?1 solutions Answer 390067 by stanbon(57361)   on 2012-06-12 21:27:43 (Show Source): You can put this solution on YOUR website!What is the height of college hockey players? The avg height has been 68.3 inches. A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with std dev of 0.9 inch. Does this indicate that the population mean height is different from 68.3 inches? Use 5% level of significance Ho: u = 68.3 (claim) Ha: u # 68.3 ----- t(69.1) = (69.1-68.3)/[0.9/sqrt(14)] = 0.2138 p-value = 2*p(0.2138< = t <= 100 when df = 13) = 2*tcdp(0.2138,100,13) = 0.4170 ---- Since the p-value is greater than 5%, fail to reject Ho. The mean height is 68.3. ================================= A random sample of 83 investment portfolios managed by Kendra showed that 62 of them met the targeted annual percent growth. A random sample of 112 portfolios managed by Lisa showed that 87 met the targeted annual percent growth. -------- Find a 99% confidence interval for the difference in the proportion of the portfolios meeting target goals managed by Kendra compared with those managed by Lisa. -------- Is there a difference in the proportions at the 99% confidence level? --- Kendra DATA: sample proportion = phat2 = 62/83 = 0.75 Lisa DATA: sample proportion = phat1 = 87/112 = 0.78 ------ Ho: p1 - p2 = 0 Ha: p1 - p2 # 0 --------------------------------- std of proportion differences: sqrt[(p1q1/n1) + (p2q2/n2)] = sqrt[(.75*0.25/83)+(0.78*0.22/112)] = 0.0616 --------------------------------------------------- z(difference) = (0.78-0.75)/0.0616 = 0.4872 ---- sample proportion difference = 0.03 std of sample difference: sqrt[(0.75*0.25/83)+(0.78*0.22/112)] = 0.0616 ----- Margin of error: 2.5758*0.0616 = 0.1586 ------ 99% CI: 0.03-0.1586 < p1-p2 < 0.03+0.1586 (-0.1286 , +0.1886) =========== Conclusion: Since zero is in the 99% CI, fail to reject Ho. =============================== Cheers, Stan H. =============================================
 Mixture_Word_Problems/620192: How many gallons of an 80% antifreeze solution must be mixed with 100 gallons of 30% antifreeze to get a mixture that is 70% antifreeze?1 solutions Answer 389979 by stanbon(57361)   on 2012-06-12 14:45:40 (Show Source): You can put this solution on YOUR website!How many gallons of an 80% antifreeze solution must be mixed with 100 gallons of 30% antifreeze to get a mixture that is 70% antifreeze? ------ Equation: anti + anti = anti 0.80x + 0.30*100 = 0.70*(x+100) ------- 80x + 30*100 = 70x + 70*100 10x = 40*100 x = 400 gallons (amt. of 80% solution to add) ================== Cheers, Stan H.
 Mixture_Word_Problems/620188: If I have a 80ml solution that is 20% acid by volume, how many mL should I remove and replace with pure 100% acid to obtain a final solution of 80ml that is 40% acid by volume? What is the equation?1 solutions Answer 389973 by stanbon(57361)   on 2012-06-12 14:34:57 (Show Source): You can put this solution on YOUR website!If I have a 80ml solution that is 20% acid by volume, how many mL should I remove and replace with pure 100% acid to obtain a final solution of 80ml that is 40% acid by volume? What is the equation? ----- Equation: acid - acid + acid = acid 0.20*80 - 0.20x + x = 0.40*80 --- Multiply thru by 100 to get: 20*80 - 20x + 100x = 40*80 80x = 20*80 x = 20 ml (amt. to remove and replace) ================ Cheers, Stan H.
 Money_Word_Problems/620156: If a new car costs \$18,000.00 and depreciates at a rate of 12% per year, what will be the value of the car in four years?1 solutions Answer 389937 by stanbon(57361)   on 2012-06-12 12:00:46 (Show Source): You can put this solution on YOUR website!If a new car costs \$18,000.00 and depreciates at a rate of 12% per year, what will be the value of the car in four years? --- Each year the car is worth 88% of last year's value. --- Equation: 18000*0.88^4 = \$10794.52 ================= Cheers, Stan H.
 Average/620154: hi my averages where 69.33 72 62 and 53 how do get an average for 4 terms 1 solutions Answer 389935 by stanbon(57361)   on 2012-06-12 11:58:29 (Show Source): You can put this solution on YOUR website!69.33 72 62 and 53 how do get an average for 4 terms Add the numbers and divide the sum by 4 to get the average: sum = 256.33 average = 64.0825 ================= Cheers, Stan H. ===========
 Square-cubic-other-roots/620150: please help on this Essay question: show all work. Suzie’s flower shop estimates that supplies costs for one month will be given by the polynomial 2x2 – 3x – 2. She estimates that utilities costs for one month is given by 4x – 6. Find and simplify an expression that would estimate Suzie’s total costs for one month.1 solutions Answer 389933 by stanbon(57361)   on 2012-06-12 11:56:02 (Show Source): You can put this solution on YOUR website!answered
 Equations/620149: I did the work for this one, it basically came down to me getting a LCD of 60 and the answer I ended up with was x=-5/2. I just want to check to make sure this is correct. 1 solutions Answer 389932 by stanbon(57361)   on 2012-06-12 11:55:05 (Show Source): You can put this solution on YOUR website!I ended up with was x=-5/2. I just want to check to make sure this is correct. {x/5)+(1/12) = (x/6} ---- An LCD is used if you are adding or subtracting fractions. --- Use an LCM (least common multiple) when you have an equation. --- LCM = 60 --- Multiply thru by the LCM to get: 12x + 5 = 10x 2x = -5 x = -5/2 ================ Cheers, Stan H. =====================
 Quadratic-relations-and-conic-sections/620148: does y value also increase towards infinity along with x value towards positive infinity if so does y value increase faster or slower than x value 1 solutions Answer 389930 by stanbon(57361)   on 2012-06-12 11:49:22 (Show Source): You can put this solution on YOUR website!Insufficient information
 Square-cubic-other-roots/620131: please help it says Essay question: show all work. Suzie’s flower shop estimates that supplies costs for one month will be given by the polynomial 2x2 – 3x – 2. She estimates that utilities costs for one month is given by 4x – 6. Find and simplify an expression that would estimate Suzie’s total costs for one month.1 solutions Answer 389928 by stanbon(57361)   on 2012-06-12 11:48:03 (Show Source): You can put this solution on YOUR website!Essay question: show all work. Suzie’s flower shop estimates that supplies costs for one month will be given by the polynomial 2x2 – 3x – 2. She estimates that utilities costs for one month is given by 4x – 6. Find and simplify an expression that would estimate Suzie’s total costs for one month. ------ supply costa: 2x^2-3x-2 utility costs: 4x-6 ---- Total cost: 2x^2 + x - 8 ============================= Cheers, Stan H.
 Percentage-and-ratio-word-problems/620100: (A) Find the binomial probability P(x = 6), where n = 15 and p = 0.30. (B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation. (C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations. 1 solutions Answer 389910 by stanbon(57361)   on 2012-06-12 10:08:14 (Show Source): You can put this solution on YOUR website!(A) Find the binomial probability P(x = 6), where n = 15 and p = 0.30. P(x=6) = 15C6*0.3^6*0.7^9 = binompdf(15,0.3,6) = 0.1472 ----------------------------------- (B) Set up, without solving, the binomial probability P(x is at most 6) using probability notation. P(0<= x <=6) = binomcdf(15,0.3,6) = 0.8689 ====================== (C) How would you find the normal approximation to the binomial probability P(x = 6) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations. mean = np = 15*0.3 = 4.5 std = sqrt(npq) = sqrt(4.5*0.7) = 1.7748 --- P(x = 6) = P(5.5<= x <= 6.5) z(5.5) = (5.5-4.5)/1.7748 = 0.5634 Z(6.5) = (6.5-4.5)/1.7748 = 1.1269 --- Then approx P(x = 6) = P(0.5634< z < 1.1269) = 0.1567 =========== Cheers, Stan H. ==================
 Word_Problems_With_Coins/620082: Please Help i'd greatly appreciate it! Bob has a coin jar containing nickels, quarters, and one dollar coins. He has a total of 44 coins totaling \$9.75. And, he has five times as many nickels as he has one dollar coins. How many of each coin does he have? Write a system of equations that can be used to solve this problem. Define what your variables represent. (Nickel \$.05, Quarter \$.25) Thanks you!1 solutions Answer 389899 by stanbon(57361)   on 2012-06-12 08:59:38 (Show Source): You can put this solution on YOUR website!Bob has a coin jar containing nickels, quarters, and one dollar coins. He has a total of 44 coins totaling \$9.75. And, he has five times as many nickels as he has one dollar coins. How many of each coin does he have? ---- Quantity Eq::: n + q + d = 44 coins Value Eq::::: 5n +25q +100d= 975 cents Quantity Eq:: n + 0 - 5d = 0 ----------------------- Solve the system anyway you can to get: n = 25 q = 14 d = 5 =========== Cheers, Stan H. ===========
 Travel_Word_Problems/620087: One pipe can fill a tank in 36 minutes, a second can fill it in 9 minutes, and a third can fill it in 12 minutes. If the tank is empty, how long will the three pipes, operating together, take to fill it? 1 solutions Answer 389898 by stanbon(57361)   on 2012-06-12 08:53:31 (Show Source): You can put this solution on YOUR website! One pipe can fill a tank in 36 minutes, a second can fill it in 9 minutes, and a third can fill it in 12 minutes. If the tank is empty, how long will the three pipes, operating together, take to fill it? --- The rates are 1/36 ; 1/9 ; 1/12 Together rate is 1/x --- Equation: (1/36) + (1/9) + (1/12) = 1/x --- Multiply thru by 36x to get: x + 4x + 3x = 36 8x = 36 x = 4.5 minutes (time to do the job together) =============== Cheers, Stan H.
 real-numbers/620088: what is the set of counring number less than 10?1 solutions Answer 389897 by stanbon(57361)   on 2012-06-12 08:49:57 (Show Source): You can put this solution on YOUR website!answered
 real-numbers/620089: what is the set of counting number less than 10?1 solutions Answer 389896 by stanbon(57361)   on 2012-06-12 08:49:14 (Show Source): You can put this solution on YOUR website!what is the set of counting number less than 10? --- Answer: 1,2,3,4,5,6,7,8,9 0 is sometimes included, but not always. ====================== Cheers, Stan H. =============
 Finance/620084: I am having trouble with a word problem. The question is: Runyon Co. sells T-shirts for \$4 and shorts for \$5. If total sales were \$850 and people bought three times as many T-shirts as shorts, what would be the number of T-shirts and shorts sold? I think that shorts should be X and shirts should be 3X, but I'm not sure how to figure the rest. Thank you for your help, Lance1 solutions Answer 389895 by stanbon(57361)   on 2012-06-12 08:45:59 (Show Source): You can put this solution on YOUR website!Runyon Co. sells T-shirts for \$4 and shorts for \$5. If total sales were \$850 and people bought three times as many T-shirts as shorts, what would be the number of T-shirts and shorts sold? I think that shorts should be X and shirts should be 3X, but I'm not sure how to figure the rest. --- Equations: Quantity Eq::: T = 3S Value Eq::::; 4T + 5S = 850 ------ Substitute for "T" and solve for "S": 4(3S) + 5S = 850 17S = 850 S = 50 (# of shorts sold) ----- Solve for "T": T = 3S T = 3*50 = 150 (# of T-shirts sold) ======================================== Cheers, Stan H. ==============
 Probability-and-statistics/619946: Hi, I was wondering if I could get some help understanding how to do this question: How long do new batteries last on a camping trip? n1 = 42 random small camp flashlights were fitted with brand 1 batteries and left on until the batteries failed. The sample mean lifetime was x = 9.8 hours. Another n2 = 38 random small flashlights of the same model were fitted with brand II batteries and left on until the batteries failed. The sample mean for lifetimes was x = 8.1 hours. Historical data suggests that σ1 = 2.2 hours and σ2 = 3.5 hours. Find a 90% confidence interval for the population difference of lifetimes for these batteries.1 solutions Answer 389866 by stanbon(57361)   on 2012-06-11 21:39:15 (Show Source): You can put this solution on YOUR website!How long do new batteries last on a camping trip? n1 = 42 random small camp flashlights were fitted with brand 1 batteries and left on until the batteries failed. The sample mean lifetime was x = 9.8 hours. ===================================================== Another n2 = 38 random small flashlights of the same model were fitted with brand II batteries and left on until the batteries failed. The sample mean forlifetimes was x = 8.1 hours. Historical data suggests that σ1 = 2.2 hours and σ2 = 3.5 hours. ----------------------------------------------------------------------- Find a 90% confidence interval for the population difference of lifetimes for these batteries. --- I used the 2-SampleZInterval function on my TI-84 to get this 90% conf. int.: (0.6119 , 2.7881) ======================= Cheers, Stan H. =======================
 Geometry_Word_Problems/619947: one leg of a triangle is three times bigger than the other leg , the hypotenuse is 12 feet . how long is the shorter leg ?1 solutions Answer 389865 by stanbon(57361)   on 2012-06-11 21:30:36 (Show Source): You can put this solution on YOUR website!one leg of a triangle is three times bigger than the other leg , the hypotenuse is 12 feet . how long is the shorter leg ? ------- Let the shorter leg be "x". Then the longer leg is "3x". -------- Equation: x^2 + (3x)^2 = 12^2 10x^2 = 144 x^2 = 14.4 x = 3.79 feet (shorter leg length) ================================== Cheers, Stan H. ===============
 Mixture_Word_Problems/619949: If you mixed a \$0.49 lb. of candy with a \$0.65 lb. of candy, what will be the new price of new mixture of candy?1 solutions Answer 389864 by stanbon(57361)   on 2012-06-11 21:26:27 (Show Source): You can put this solution on YOUR website!If you mixed a \$0.49 lb. of candy with a \$0.65 lb. of candy, what will be the new price of new mixture of candy? ---- That depends on the quantity of each of those candies are in the mix. ---------- Cheers, Stan H.
 Miscellaneous_Word_Problems/619934: on monday harold picked five donuts and six large coffees he paid \$8.65 on tuesday he picked three donuts and five coffees he paid \$6.38. what's the cost of one donut and the cost of one large coffee1 solutions Answer 389863 by stanbon(57361)   on 2012-06-11 20:53:36 (Show Source): You can put this solution on YOUR website!on monday harold picked five donuts and six large coffees he paid \$8.65 on tuesday he picked three donuts and five coffees he paid \$6.38. what's the cost of one donut and the cost of one large coffee ------ Equation: 5d + 6c = 865 cents 3d + 5c = 638 cents ------------------------ Multiply thru 1st by 3: Multiply thru 2nd by 5: 15d + 18c = 3*865 15d + 25c = 5*638 --- Subtract and solve for "c": 7c = 595 c = 75 cents (cost on one large coffee) ---- solve for "d": 3d + 5c = 638 cents 3d + 5*75 = 638 3d = 263 d = 87 2/3 cents (cost of one donut) =============== Cheers, Stan H. ===============
 Angles/619924: What is the difference between supplementary angles and complementary angles? Solve: If I have one angle that measures 450 less than twice the measure of its supplement, what is the measure of each angle?1 solutions Answer 389861 by stanbon(57361)   on 2012-06-11 20:45:55 (Show Source): You can put this solution on YOUR website!What is the difference between supplementary angles and complementary angles? Solve: If I have one angle that measures 450 less than twice the measure of its supplement, what is the measure of each angle? ------ The sum of 2 supplementary angles is 180 degrees. --- The sum of 2 complementary angles is 90 degrees. ---- If I have one angle that measures 450 less than twice the measure of its supplement, what is the measure of each angle? --------------------------------------------- Let the 1st angle be "x": Then 2nd angle 2(180-x)-450 ---- Equation: 1st + 2nd = 180 x + 2(180-x)-450 = 180 x + 360-2x-450 = 180 -x - 90 = 180 x = -270 (1st angle) 2nd angle: 2(180-x)-450 = 360 -2x-450 = 360 -2(-270)-450 = 450 ================ Cheers, Stan H. ================
 Rate-of-work-word-problems/619929: Two pumps of different sizes, working together can empty a tank in five hours. The larger pump can empty this tank in four hours less than the smaller. If the larger pump is out of order, how long will it take the smaller one to do the job alone? 1 solutions Answer 389860 by stanbon(57361)   on 2012-06-11 20:34:53 (Show Source): You can put this solution on YOUR website!Two pumps of different sizes, working together can empty a tank in five hours. The larger pump can empty this tank in four hours less than the smaller. If the larger pump is out of order, how long will it take the smaller one to do the job alone? --------------------------------- Together rate: 1/5 job/hr -------- Larger pump rate: 1/x job/hr -------- Smaller pump rate: 1/(x+4) job/hr ======================================= Equation: rate + rate = together rate 1/x + 1/(x+4) = 1/5 -------- Multiply thru by 5x(x+4) to get: 5(x+4) + 5x = x(x+4) 10x + 20 = x^2 + 4x x^2 - 6x - 20 = 0 x = 8.3852 hrs x+4 = 12.3852 hrs (time for the smaller pipe) Cheers, Stan H. =================
 Percentage-and-ratio-word-problems/619914: describe the relationship between the standard error (of the mean) and maximum error. 1 solutions Answer 389853 by stanbon(57361)   on 2012-06-11 19:51:48 (Show Source): You can put this solution on YOUR website!standard error is the standard deviation maximum error is the product of the std and the z or t value associated with the degree of confidence. ============================== Cheers, Stan H. ====================
 Quadratic_Equations/619902: Y=-2xsquared-2x-7 write in vertext form and tell me the vertex please1 solutions Answer 389851 by stanbon(57361)   on 2012-06-11 19:42:48 (Show Source): You can put this solution on YOUR website!Y=-2xsquared-2x-7 write in vertext form and tell me the vertex please ---- y = -2(x^2 +x + ?) -7 - (-2*?) --- y = -2(x^2 + x + (1/4)) - 7 - (-2(1/4)) --- y = -2(x+1/2)^2-7 + 1/2 --- y = -2(x+(1/2))^2 - (13/2) ---- Vertex: (-1/2 , -13/2) ------ --------------------- Cheers, Stan H. ========================
 Probability-and-statistics/619722: Sarah has a deck of 52 cards and ramdomly selects 2. What is the probability that she will pick the same cards?1 solutions Answer 389843 by stanbon(57361)   on 2012-06-11 18:14:52 (Show Source): You can put this solution on YOUR website!Sarah has a deck of 52 cards and ramdomly selects 2. What is the probability that she will pick the same cards? --- # of ways to succeed: 1st: pick a card type: 13 ways 2nd: pick 2 of that card: 4C2 = 6 ways ----- # of random results: Pick 2 cards from the deck: 52C2 ===== P(2 of the same card type) = (13*6)/52C2 = 78/1326 = 1/17 ================================= Cheers, Stan H. ================
 Probability-and-statistics/619788: Mobile homes are tightly constructed for energy conservation. This can lead to a buildup of indoor pollutants. The paper "A Survey of Nitrogen Dioxide Levels Inside Mobile Homes" discussed various aspects of NO2 concentration in these structures. (a) In one sample of mobile homes in the Los Angeles area, the mean NO2 concentration in kitchens during the summer was 36.66 ppb, and the standard deviation was 11.44. Making no assumptions about the shape of the NO2 distribution, what can be said about the percentage of observations between 13.78 and 59.54? (Round the answer to the nearest whole number. (b) Inside what interval is it guaranteed that at least 89% of the concentration observations will lie? 1 solutions Answer 389842 by stanbon(57361)   on 2012-06-11 18:10:32 (Show Source): You can put this solution on YOUR website!(a) In one sample of mobile homes in the Los Angeles area, the mean NO2 concentration in kitchens during the summer was 36.66 ppb, and the standard deviation was 11.44. Making no assumptions about the shape of the NO2 distribution, what can be said about the percentage of observations between 13.78 and 59.54? (Round the answer to the nearest whole number. --- That interval is 2 std to the left and 2 std to the right of the mean. Chebyshev says there will be at least (1-(1/2)^2) = 75% of the data in that interval. =============================== (b) Inside what interval is it guaranteed that at least 89% of the concentration observations will lie? Chebyshev says (1-(1/3)^2)% = 89% of the data lies within 3 std of the mean. Lower limit: 36.66-3*11.44 = 2.34 Upper limit: 36.66+3*11.44 = 70.98 ==================================== cheers, Stan H. ============
 Probability-and-statistics/619850: A box contains 25% black balls and 75% white balls. The same number of black balls as were in the box are added (so new number of black balls is twice the original number). A ball is now drawn from the box at random. What is the probability that it is black?1 solutions Answer 389841 by stanbon(57361)   on 2012-06-11 18:03:00 (Show Source): You can put this solution on YOUR website!A box contains 25% black balls and 75% white balls. The same number of black balls as were in the box are added (so new number of black balls is twice the original number). A ball is now drawn from the box at random. What is the probability that it is black? ----- Converting the problem to numbers: Original mix: 25 black and 75 white. -- New mix: 50 black and 75 white --- P(black) = 50/125 = 2/5 = 40% ==================================== Cheers, Stan H.