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Recent problems solved by 'stanbon'

stanbon answered: 57883 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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Probability-and-statistics/245523: Two percent of the parts produced by a machine are defective. Twenty parts are selected at random. What is the probability that the number of defective parts will be more than 2 but fewer than 6? 1 solutions Answer 179325 by stanbon(57956)   on 2009-12-03 16:24:36 (Show Source): You can put this solution on YOUR website! Two percent of the parts produced by a machine are defective. Twenty parts are selected at random. What is the probability that the number of defective parts will be more than 2 but fewer than 6? --- It's binomial with n=20 ; p = 0.02 ; 2< x < 6 --- binomcdf(20,0.02,5)-binomcdf(20,0.02,2) = 0.007 =================================================== Cheers, Stan H.

Triangles/245415: Triangle ABC has an exterior angle, please help me solve this, i have been working on this for two days and all i have been getting is decimals for my measurements 1 solutions Answer 179267 by stanbon(57956)   on 2009-12-03 10:43:41 (Show Source): You can put this solution on YOUR website! Triangle ABC has an exterior angle, ---------------------- The exterior angle is DAB and it has measure 11x+13 It sounds like the corresponding interior angle is angle B and it has measure 7x-7 --- If that is true, 11x+13 + 7x-7 = 180 degrees 18x + 6 = 180 18x = 174 x = 9 2/3 ------------------ Then measure of angle B is 7(29/3)-7 = 60 2/3 degrees And 9x = 87 degrees. ======================= Cheers, Stan H.

Graphs/245417: Solving Systems by Graphing could some one show me how to do this 3x-y=3 and 6x+y=5 I have looked in my textbook,looked online i would like to know how to go about sovling these and how to get the plot points so i can graph them. Thank you 1 solutions Answer 179261 by stanbon(57956)   on 2009-12-03 10:08:25 (Show Source): You can put this solution on YOUR website! Solving Systems by Graphing could some one show me how to do this 3x-y=3 Solve for y: y = 3x-3 Plot two or more points: If x = 0, y = 3*0-3 = -3, giving you point (0,-3) If x = 2, y = 3*2-3 = 3, giving you point (2,3) Plot those two points and draw a line thru them to see the graph. ============================================= and 6x+y=5 Solve for y: y = -6x+5 Plot two or more points: If x = 0, y = -6*0+5 = 5, giving you point (0,5) If x = 1, y = -6*1+5 = -1, giving you point (1,-1) Plot those two points and draw a line thru them to see the graph. ============================================= To "solve" the system by graphing you have to put both of those lines on the same coordinate system and try to determine where the lines intersect. ============================================= Comment: Most problems of this type have a whole-number solution pair, like (2,3). Your problem does not so it is virtually impossible to "solve" the system using the graphing technique. Try to not let that fact frustrate your effors. The real solution to the system is best found using substitution or elimination. Using substitution you would get: 3x-3 = -6x+5 9x = 8 x = 8/9 ------------- y = 3x-3 y = 3(8/9)-3 = 8/3 - 9/3 = -1/3 ------------- So the point of intersection of the two lines is (8/9 , - 1/3) ==================================================== Cheers, Stan H. Hope that helps. Cheers, Stan H. -----

Volume/245416: The formula A =3.14 r2 is used to find the area of a circle. If the radius is tripled, by what factor will the new area increase? 1 solutions Answer 179260 by stanbon(57956)   on 2009-12-03 09:53:30 (Show Source): You can put this solution on YOUR website! The formula A =3.14 r2 is used to find the area of a circle. If the radius is tripled, by what factor will the new area increase? ----------- Original Area: (pi)r^2 ---------------- New Area: (pi)(3r)^2 = (pi)(9r^2) = 9[(pi)r^2 = 9 times the original area =============================== Cheers, Stan H.

Probability-and-statistics/245397: mean of a set of number given below is 6 with mode . find the median. 9, 7, x, 5, y, z, 7, 20 1 solutions Answer 179259 by stanbon(57956)   on 2009-12-03 09:51:04 (Show Source): You can put this solution on YOUR website! You did not post enough information to tackle the problem. Cheers, Stan H.

Miscellaneous_Word_Problems/245401: At the pure water bottling company one machine can produce 180 bottles in 5 hours and a newer machine can produce 180 bottles in three hours. How long would it take the two machines working together to produce 720 bottles of water? 1 solutions Answer 179257 by stanbon(57956)   on 2009-12-03 09:03:31 (Show Source): You can put this solution on YOUR website! At the pure water bottling company one machine can produce 180 bottles in 5 hours and a newer machine can produce 180 bottles in three hours. How long would it take the two machines working together to produce 720 bottles of water? ---------------- rate of the 1st machine: 180/5 = 36 bottles per hour ------------------- rate of the 2nd machine: 180/3 = 60 bottles per hour ------------------- rate of both machines together: (36+60) = 96 bottles per hour -------------------- Time to produce 720 bottles: Let the time be "x" hrs. x(96/hr) = 720 x = 720/96 x = 7.5 hrs. ================== Cheers, Stan H.

Quadratic_Equations/245396: how many solutions does y^2= 4/7 y +2/5 have? f(x)=-2x^2+2x+6 what is the x cordinate of the vertex? the y cordinate of the vertex? the equation of the line of semitry? the minumun/maximun value of f(x)? 1 solutions Answer 179256 by stanbon(57956)   on 2009-12-03 08:58:20 (Show Source): You can put this solution on YOUR website! how many solutions does y^2= 4/7 y +2/5 have? Rearrange: y^2 -(4/7)y - (2/5) = 0 Quadratic with a = 1 ; b = -4/7 ; c = -2/5 Discriminant = b^2-4ac = (16/49) - 4(1)(-2/5) = (16/49)+(8/5) This sum is greater than zero so the quadratic has two unequal Real Number solutions. ===================================== f(x)=-2x^2+2x+6 what is the x cordinate of the vertex? x = -b/2a = -2/(2(-2)) = 1/2 --- the y cordinate of the vertex? f(1/2) = -2(1/2)^2+2(1/2)+6 = -1/2+1+6 = 13/2 or 6.5 --- the equation of the line of symmetry? x = 1/2 --- the minumun/maximun value of f(x)? Max is at the vertex (1/2,13/2) ============================================= ============================================= Cheers, Stan H.

Probability-and-statistics/245189: Assume that the average annual salary for a worker in the United States is $28,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,500. Find the following: (A)What percentage of Americans earn below $24,000? (B)What percentage of Americans earn above $36,000? 1 solutions Answer 179255 by stanbon(57956)   on 2009-12-03 08:47:27 (Show Source): You can put this solution on YOUR website! Assume that the average annual salary for a worker in the United States is $28,000 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,500. Find the following: (A)What percentage of Americans earn below $24,000? Find the z-value of 24000 z(24000) = (24000-28000)/6500 = -4000/6500 = -0.615 P(x < 24000) = P(z < -0.615) = 0.269 --------------------------------- (B)What percentage of Americans earn above $36,000? z(36000) = (36000-28000)/6500 = 1.231 P(x > 36000) = P(z > 1.231) = 0.109 ================================== Cheers, Stan H.

Functions/245326: you invest 209$ to buy shirts and then sell them for 9.50 each write a function rule to determine your profit use your rule to find your profit after selling 24 shirts how many do you need to sell to get back your investment 1 solutions Answer 179237 by stanbon(57956)   on 2009-12-02 23:19:01 (Show Source): You can put this solution on YOUR website! you invest $209 to buy shirts and then sell them for 9.50 each write a function rule to determine your profit --- Profit = Income - Cost P(x) = 9.50x - 209 where x is the number of shirt sold ------------------------------------------------------------ use your rule to find your profit after selling 24 shirts P(24) = 9.50*24 - 209 P(24) = $19 -------------------------------- how many do you need to sell to get back your investment 9.50x = 209 x = 22 shirts must be sold to break even ============================================= Cheers, Stan H.

Functions/245321: how do i write a function rule if it says pens are shipped to the supply office in boxes of 12 each write a function rule to calculate the total number of pens when you know the number fo boxes? calcualate the number of pens in 16boxes? 1 solutions Answer 179234 by stanbon(57956)   on 2009-12-02 23:06:35 (Show Source): You can put this solution on YOUR website! how do i write a function rule if it says pens are shipped to the supply office in boxes of 12 each write a function rule to calculate the total number of pens when you know the number fo boxes? --- N(x) = 12x, where x is the number of boxes. =================================================== calculate the number of pens in 16 boxes? N(16) = 12*16 = 192 pens ========================================= Cheers, Stan H.

Numbers_Word_Problems/245322: translate into an algebraic expression, three less than a product of two numbers, how do i figure this out? 1 solutions Answer 179233 by stanbon(57956)   on 2009-12-02 23:01:29 (Show Source): You can put this solution on YOUR website! translate into an algebraic expression, three less than a product of two numbers, how do i figure this out? ----------------------- Let one of the numbers be "x" Let the other number be "y". ------------------------------------ Expression: xy-3 ======================= Cheers, Stan H.

Functions/245317: what would the function rule be if the table said that X f(x) and is said write the function rule?? -4 9 0 0 1 1 5 25 1 solutions Answer 179232 by stanbon(57956)   on 2009-12-02 22:58:31 (Show Source): You can put this solution on YOUR website! what would the function rule be if the table said that X f(x) and is said write the function rule?? -4 9 0 0 1 1 5 25 ============================= I ran a linear recursion program and got the following: f(x) = 0.825x^2 + 0.943x + 0.384 ============================= Cheers, Stan H.

Travel_Word_Problems/245314: Kay rode his bike from his home to Daniels and walked back home. The total travel time was 45 minutes. If Kay average 20 mph on the bike and 4 mph walking, how far does Daniel live from Kay. 1 solutions Answer 179231 by stanbon(57956)   on 2009-12-02 22:50:46 (Show Source): You can put this solution on YOUR website! Kay rode his bike from his home to Daniels and walked back home. The total travel time was 45 minutes. If Kay average 20 mph on the bike and 4 mph walking, how far does Daniel live from Kay. --------------------------------------- Bike DATA: rate = 20 mph ; distance = x miles ; time = d/r = x/20 hrs. ------------------------ Walking DATA: rate = 4 mph ; distance = x miles ; time = d/r = x/4 hrs. ------------------------ Equation: time + time = 3/4 hr. x/20 + x/4 = 3/4 x + 5x = 15 6x = 15 x = 5/2 = 2.5 miles (distance from Kay's house to Daniel's) ============================================================= Cheers, Stan H.

Probability-and-statistics/245300: There are 100 students that are randomly placed into 4 classrooms. Three students want to be in the same class. Probability they are in the same class? probability they are all P's class? Probability they are all in different classes? 1 solutions Answer 179229 by stanbon(57956)   on 2009-12-02 22:44:22 (Show Source): You can put this solution on YOUR website! There are 100 students that are randomly placed into 4 classrooms. Three students want to be in the same class. ---------------------------------------------- Probability they are in the same class? Pick a classroom: 4 ways Place the 3 randomly: 100*99*98 ways Probability 4/(100*99*98) = 0.000004123 --------------------------------------------- probability they are all in P's class? # of ways to succeed: 1 way # of ways to place randomly: 100*99*98 Probability = 1/970200 ============================================= Probability they are all in different classes? Pick 3 classes: 4C3 = 4 Put the 3 students in the three classes: 3*2*1 = 6 probability (4*6)/970200 = 0.00002474 ======================================== Cheers, Stan H.

Probability-and-statistics/245302: An insurance company has discovered that only about 0.1% of the population is involved in a certain type of accident each year. If its 10000 policy holders were randomly selected from the population, what is the probability that not more than 5 of its clients are involved in such an accident next year? 1 solutions Answer 179227 by stanbon(57956)   on 2009-12-02 22:20:44 (Show Source): You can put this solution on YOUR website! An insurance company has discovered that only about 0.1% of the population is involved in a certain type of accident each year. If its 10000 policy holders were randomly selected from the population, what is the probability that not more than 5 of its clients are involved in such an accident next year? ----------------------------------- It's binomial with n = 10000, p = 0.001 , 0<=x<=5 -------------- binomcdf(10,000,0.001,5) = 0.067 ======================================= Cheers, Stan H.

Probability-and-statistics/245303: A book shelf containing 20 books of which 12 are on circuit theory and 8 are on Mathematics. If three books are taken out at random, find the probability that all the three are on the same subject. 1 solutions Answer 179225 by stanbon(57956)   on 2009-12-02 22:11:00 (Show Source): You can put this solution on YOUR website! A book shelf containing 20 books of which 12 are on circuit theory and 8 are on Mathematics. If three books are taken out at random, find the probability that all the three are on the same subject. -------------------------------- # of ways to get 3 of the same kind: 12C3 + 8C3 = 220 + 56 = 276 ------------------ # of possible sets of 3: 20C3 = 1140 ----------------------- Probability = 276/1140 = 0.242 ===================================== Cheers, Stan H.

Inequalities/245249: Solve the inequality: |x+12/x-12|< or equal to 3 Please help 1 solutions Answer 179220 by stanbon(57956)   on 2009-12-02 21:04:43 (Show Source): You can put this solution on YOUR website! Solve the inequality: |x+12/x-12|<= 3 ------------- Looking you can see that x cannot be 12. --- Solving the EQUALITY you gt: (x+12)/(x-12) = 3 or (x+12)/(x-12) = -3 x+12 = 3x-26 or x+12 = -3x+36 2x = 38 or 4x = 24 x = 19 or x = 6 -------------------------------------- So, draw a number line and plot x = 6, x = 12, x = 19 -------------------------------------- Now find the solutions for the INEQUALITY by checking a value in each of the four resulting intervals of the number line. -------------------------------------- |x+12/x-12| < 3 --- Let x = 0; you get |12/-12| < 3 ; true, so solutions in (-inf,6) --- Let x = 10; you get |22/-2} < 3 ; false, so no solutions in (6,12) --- Let x = 15; you get |27/3| < 3 ; false, so no solutions in (12,19) --- Let x = 25 ; you get |37/13| < 3 ; true, so solutions in (19,+inf) ==================================================================== Combining the solutions for the EQUALITY and the INEQALITY you get: (-inf,6] U [19,+inf) ------------- Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/245246: band a charges $600 to play for the entire evening band b charges $350 plus $1.25 for each ticket sold. write a linear equation for the cost of each band. 1 solutions Answer 179219 by stanbon(57956)   on 2009-12-02 20:49:54 (Show Source): You can put this solution on YOUR website! band a charges $600 to play for the entire evening band b charges $350 plus $1.25 for each ticket sold. write a linear equation for the cost of each band. -------------- A(x) = $600 --- B(x) = $350 + 1.25x, where x is the number of tickets sold. ========================================================== Cheers, Stan H.

Mixture_Word_Problems/245234: Find the x- and y-intercepts (if any) for each line. Show your work. Plot those intercepts, and graph the two lines. Submit your graph through the Dropbox. Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). x + 5y = 2 2x = -10y + 4 1 solutions Answer 179218 by stanbon(57956)   on 2009-12-02 20:45:54 (Show Source): You can put this solution on YOUR website! Apply elimination or substitution to find the coordinates of the point of intersection (if there are no solutions or infinite solutions, state this). x + 5y = 2 2x = -10y + 4 ---------------------- Multiply thru the 1st equation by 2. Rearrange the 2nd equation. 2x + 10y = 4 2x + 10y = 4 --- The two equations are the same so you have an infinite number of solutions. --- Each point is of the form (x , -(x+2)/5) =========================================== Cheers, Stan H.

absolute-value/245233: 2{5x+3}=16 The bracket's stand for absolute value i just started absolute value with equations so i would love to see steps to help me get the picture thanks :) 1 solutions Answer 179215 by stanbon(57956)   on 2009-12-02 20:33:34 (Show Source): You can put this solution on YOUR website! 2|5x+3|=16 --- Divide both sides by 2 to get: |5x+3| = 8 --- Comment: That "5x+3" must be +8 or maybe is it -8. That gives you two equations to solve: --- 5x+3 = 8 or 5x+3 = -8 5x = 5 or 5x = -11 x = 1 or x = -11/5 ===================== Cheers, Stan H. =====================

Graphs/245206: You are running in a marathon. You either run 8 miles per hour or walk 4 miles per hour. Write an equation to show the relationship between time ran and time walked during the 26.2 mile course and then graph the equation. I tried to use 8X + 4Y = 26.2 but it did not work out. If you could just help me get the right equation then I can do the graph and the following couple of problems which are all related to this equation. Thanks in advance for your help! 1 solutions Answer 179213 by stanbon(57956)   on 2009-12-02 20:26:28 (Show Source): You can put this solution on YOUR website! You are running in a marathon. You either run 8 miles per hour or walk 4 miles per hour. Write an equation to show the relationship between time ran and time walked during the 26.2 mile course and then graph the equation. ----------------------------- Run DATA: rate = 8 mph ; time = r hrs. ; distance = 8r miles ----------------------------- Walk DATA: rate = 4 mph ; time = w hrs ; distance = 4w miles ----------------------------- Equation: distance + distance = 26.2 miles 4w + 8r = 26.2 ---- Graphable equation: w = -2r + 6.55 ------------------------- ========================================= Cheers, Stan H.

Probability-and-statistics/245191: X has a normal distribution with a mean of 75.0 and a standard deviation of 3.5. Find the following probabilities: (A) P(x < 73.0) (B) P(72.0 < x < 78.0) (C) P(x>79.0) 1 solutions Answer 179207 by stanbon(57956)   on 2009-12-02 19:59:03 (Show Source): You can put this solution on YOUR website! X has a normal distribution with a mean of 75.0 and a standard deviation of 3.5. Find the following probabilities: (A) P(x < 73.0) z(73) = (73-75)/(3.5) = -2/3.5 = -0.571 P(x < 73) = P(z < -0.571) = 0.284 =============================================== (B) P(72.0 < x < 78.0) z(72) = (72-75)/3.5 = -0.857 z(78) = (78-75)/3.5 = +0.857 --- P(72 < x < 78) = P(-857 < z < 0.857) = 0.609 =============================================== (C) P(x>79.0) z(79) = (79-75)/3.5 = 1.143 P(x > 79) = P(z > 1.143) = 0.127 =============================================== Cheers, Stan H.

Graphs/245177: I am having a lot of trouble with these problems: x=y^2-8y-1 x=(y+2)^2-4 we have to graph them 1 solutions Answer 179201 by stanbon(57956)   on 2009-12-02 19:23:28 (Show Source): You can put this solution on YOUR website! I am having a lot of trouble with these problems: x=y^2-8y-1 x=(y+2)^2-4 we have to graph them ----------------------- They cannot be graphed on this site as they are not functions. Cheers, Stan H.

Mixture_Word_Problems/245174: A 40 mL solution is 80% acid. How much water must be added to produce a solution that is 60% acid? 1 solutions Answer 179200 by stanbon(57956)   on 2009-12-02 19:21:01 (Show Source): You can put this solution on YOUR website! A 40 mL solution is 80% acid. How much water must be added to produce a solution that is 60% ---------------------- Equation: acid + acid = acid 0.80*40 + 0*x = 0.60(40+x) Multiply thru by 100 to get: 80*40 + 0 = 60*40 + 60x 20*40 = 60x x = (1/3)*40 x = 13 1/3 mL (amt. of water needed in the mixture) =========== Cheers, stan H.

Linear-equations/245173: could you show me how to get to the solution pls.[-2x 22 -3z] = [6x -2y 45] 1 solutions Answer 179198 by stanbon(57956)   on 2009-12-02 19:16:25 (Show Source): You can put this solution on YOUR website! [-2x 22 -3z] = [6x -2y 45] ------------ Questions: Are those absolute value symbols? --- Do you mean |44-3z| = |6x-2y^45| --- You seem to have two variables but only one equation. ======================= Cheers, Stan H.

logarithm/245163: John deposits 10000 in a college trust fund in which i=6.4% compounded quarterly. How much $ would be in the account after 18 yrs. #2 In an account which pays 6.5% compounded continuosly, how much $ would need to be deposited in order to rach 50000 in 15 yrs? 1 solutions Answer 179197 by stanbon(57956)   on 2009-12-02 19:10:20 (Show Source): You can put this solution on YOUR website! John deposits 10000 in a college trust fund in which i=6.4% compounded quarterly. How much $ would be in the account after 18 yrs. ----------- A(t) = P(1+(r/n))^(nt) A(18) = 10,000(1+(0.064/4))^(4*18) A(18) = 10,000(1+0.016)^72 A(18) = 10,000*3.136 A(18) = $31,360 =========================== #2 In an account which pays 6.5% compounded continuosly, how much $ would need to be deposited in order to rach 50000 in 15 yrs? --- A(t) = Pe^(rt) 50,000 = Pe^(0.065*15) 50,000 = P(2.651) P = $18,859.62 ===================== Cheers, Stan H.

Graphs/245150: 3/7n<3/49 1 solutions Answer 179196 by stanbon(57956)   on 2009-12-02 18:58:58 (Show Source): You can put this solution on YOUR website! 3/7n<3/49 --- I'm going to assume the "n" is not in the denominator. --- Multiply both sides by 49 to get: 7*3n < 3 --- Divide both sides by 3 to get: 7n < 1 Divide both sides by 7 to get: n < 1/7 ================== Cheers, Stan H.

Mixture_Word_Problems/245152: In a chemistry class, 5 liters of a 4%-saline solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? 1 solutions Answer 179195 by stanbon(57956)   on 2009-12-02 18:53:40 (Show Source): You can put this solution on YOUR website! In a chemistry class, 5 liters of a 4%-saline solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? ----------------------------------- Equation: saline + saline = saline 0.04*5 + 0.10x = 0.06(5+x) Multiply thru by 100 to get: 4*5 + 10x = 6*5+6x 4x = 2*5 x = 2.5 liters (amt. of 10% solution needed in the mix) --- Cheers, Stan H.

Polynomials-and-rational-expressions/245144: Solve: x+4/x^2-x-2=6/x^2-4x-5 I've gotten so far as x^2=32/-7, but I'm pretty sure it's not right. 1 solutions Answer 179194 by stanbon(57956)   on 2009-12-02 18:46:15 (Show Source): You can put this solution on YOUR website! Solve: x+4/(x^2-x-2) = 6/(x^2-4x-5) --- Factor: (x+4)/[(x-2)(x+1)] = 6/[(x-5)(x+1)] --- Multiply both sides by (x+1): --- (x+4)/(x-2) = 6/(x-5) Cross-multiply and solve for "x": x^2-x-20 = 6x-12 x^2-7x-32 = 0 --------------------- Quadratic Formula: x = [7 +- sqrt(49-4*-32)]/2 --- x = [7 +- sqrt(177)]/2 ============================== Cheers, Stan H.

Trigonometry-basics/245135: please help me solve this quadratic equations: Find the center of the following equation x^2-y^2+24+4y+28=0: here are the possible answers: a)(-4,3) b)(4,3) c)(8,-6) 1 solutions Answer 179190 by stanbon(57956)   on 2009-12-02 18:37:02 (Show Source): You can put this solution on YOUR website! solve this quadratic equations: Find the center of the following equation x^2-y^2+24+4y+28=0: --- (x-0)^2 -(y^2-4y+?) = -52 (x-0)^2 -(y^2-4y+4) = -52-4 (x-0)^2 -(y-2)^2 = -56 (y-2)^2 - (x-0)^2 = 56 Center: (0,2) ==================== Note: I think your post of the problem is missing something. You are probably missing an "x" term. ==================== Cheers, Stan H. here are the possible answers: a)(-4,3) b)(4,3) c)(8,-6)

Probability-and-statistics/244807: Please Answer the following Questions and explain how you derived at each of the following answers. · What symbol do we use for representing the mean of a population and what symbol do we use to represent the mean of a sample that you have taken? · What Statements can you make about the density curves? (give at least 2) · By Chebyshev’s Rule: Attendance at a university’s basketball games follows a normal distribution with mean m = 8,000 and standard deviation s = 1,000. Estimate the percentage of games that have between 7,000 to 9,000 people in attendance. 1 solutions Answer 179187 by stanbon(57956)   on 2009-12-02 18:25:57 (Show Source): You can put this solution on YOUR website! Please Answer the following Questions and explain how you derived at each of the following answers. · What symbol do we use for representing the mean of a population and what symbol do we use to represent the mean of a sample that you have taken? --- population mean = mu = u sample mean = x-bar or maybe y-bar ---------------------------------------- · What Statements can you make about the density curves? (give at least 2) 1) the area under the curve is 1 2) The range of the z or t values is approximately 6sigma. ---------------------------------------- · By Chebyshev’s Rule: Attendance at a university’s basketball games follows a normal distribution with mean m = 8,000 and standard deviation s = 1,000. Estimate the percentage of games that have between 7,000 to 9,000 people in attendance. --- 7000 to 9000 covers the interval within 1 standard deviation of the mean. Chebyshev's Rule only states that there will be at least 1-[1/1^2]% = 0% of the population. In other words, Chebyshev's Rule tells us nothing about the amount of population within one standard deviation of the mean. ================================================ Cheers, Stan H.