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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209, >>Next

 Radicals/274702: how to write an equivalent expression using radical notation for (16a^6)^3/41 solutions Answer 200430 by stanbon(57277)   on 2010-02-26 18:07:55 (Show Source): You can put this solution on YOUR website!how to write an equivalent expression using radical notation for (16a^6)^3/4 ----------------- 4th root of (16a^6)^3 ============================== Cheers, Stan H.
 expressions/274703: Evaluate the factorial expression (n+5)!/n+51 solutions Answer 200428 by stanbon(57277)   on 2010-02-26 18:05:59 (Show Source): You can put this solution on YOUR website!Evaluate the factorial expression (n+5)!/(n+5) --- = [(n+5)(n+4)!]/(n+5) --- = (n+4)! ============== Cheers, Stan H.
 Mixture_Word_Problems/274616: A pharmacist is to prepare a 50 fluid ounce solution that contains 54% glucose. The pharmacy has a 30% solution and a 90% solution on hand. How many ounces of each solution should be mixed to prepare the desired prescription? Thank You1 solutions Answer 200427 by stanbon(57277)   on 2010-02-26 18:03:12 (Show Source): You can put this solution on YOUR website!A pharmacist is to prepare a 50 fluid ounce solution that contains 54% glucose. The pharmacy has a 30% solution and a 90% solution on hand. How many ounces of each solution should be mixed to prepare the desired prescription? -------------------------------- Equation: glucose + glucose = glucose 0.30x + 0.90(50-x) = 0.54*50 Multiply thru by 100 to get: 30x + 90*50 - 90x = 54*50 -60x = -36*50 --- x = (5/6)(36) x = 30 fluid ounces (amt. of 30% solution needed for the mixture) --- 50-x = 20 fluid ounces (amt. of 90% solution needed for the mixture) =========================================== Cheers, Stan H.
 Length-and-distance/274698: Two ships leave port at the same time. One sails south at 15mph and the other sails east at 2o mph. Find a function that models the distance (D) between the ships in terms of the time (T) in hours elasped since thier departure. I have solved in the followinf way and don't understand where I've gone wrong. I'm coming up with a different answer than what's in my textbook. (By Pathagorean Therom) D= 15(t) squared + 20(t) squared. D(T) = 35(t) squared. My textbook says that the answer is D(T) = 25T. How are they getting this solution? Where am I going wrong? Please help!1 solutions Answer 200425 by stanbon(57277)   on 2010-02-26 17:47:26 (Show Source): You can put this solution on YOUR website!Two ships leave port at the same time. One sails south at 15mph and the other sails east at 2o mph. Find a function that models the distance (D) between the ships in terms of the time (T) in hours elasped since thier departure. -------------------- Draw the picture. East distance = 20t South distance = 15t ------------------------------- Using Pythagoras: D^2 = (20t)^2 + (15t)^2 --- D^2 = 400t^2 + 225t^2 --- D^2 = 625t^2 ---- D = 25t ========================== Cheers, Stan H.
 Rectangles/274692: Two 45 degree angles in a rectangle and we have to solve for x 1 solutions Answer 200423 by stanbon(57277)   on 2010-02-26 17:35:11 (Show Source): You can put this solution on YOUR website!Two 45 degree angles in a rectangle and we have to solve for x --------------- Is the "x" a label for an angle or a side or the hypotenuse. ======================================== Cheers, Stan H.
 Average/274693: during the first 4 wks of summer vacation, danny worked at a camp earning \$50 per wk. during the remaining 6 wks of vacation, he worked as a stock boy earning \$100 per wk. what was his average wkly wage for the summer?1 solutions Answer 200422 by stanbon(57277)   on 2010-02-26 17:29:19 (Show Source): You can put this solution on YOUR website!during the first 4 wks of summer vacation, danny worked at a camp earning \$50 per wk. Total earnings = 4*50 = 200 ------------------------------- during the remaining 6 wks of vacation, he worked as a stock boy earning \$100 per wk. Total earnings = 6*100 = 600 ---------------------------------- what was his average wkly wage for the summer? Equation: Average = total earned / total weeks = 800/10 = \$80.00 per week ================================================================= Cheers, Stan H.
 Equations/274652: 7y-x=32 x=3y Solve by using the substitution method. Please help me with this if you can. Thank you.1 solutions Answer 200412 by stanbon(57277)   on 2010-02-26 14:47:19 (Show Source): You can put this solution on YOUR website!7y-x=32 x=3y Solve by using the substitution method. ------------------- Substitute for "x" and solve for "y": 7y -3y = 32 4y = 32 y = 8 ---- substitute and solve for "x": x = 3(8) x = 24 ================================ Cheers, Stan H.
 Travel_Word_Problems/274651: Ken wants to swim 20 yards out into the ocean. He swims out 5 yards in 4 seconds but then in one second a wave pushes him back 2 yards. If this cycle continues, how long will it take Ken to get 20 yards out for first time, even if only for an instant?1 solutions Answer 200410 by stanbon(57277)   on 2010-02-26 14:42:58 (Show Source): You can put this solution on YOUR website!Ken wants to swim 20 yards out into the ocean. He swims out 5 yards in 4 seconds but then in one second a wave pushes him back 2 yards. If this cycle continues, how long will it take Ken to get 20 yards out for first time, even if only for an instant?
 Probability-and-statistics/274643: a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair?1 solutions Answer 200409 by stanbon(57277)   on 2010-02-26 14:41:28 (Show Source): You can put this solution on YOUR website!a case game consist of one card out of 52. If you get a king or a queen you win 5 dollars. If you select any hearts you win 2 dollars. How much should you pay to keep the game fair? ------------------------------ Let the cost to play be "x" dollars. ------------------------------- Random gain values: 5-x ; 2-x ; -x Probabilities::::: 8/52 ; 13/52 ; 31/52 --------------------------------------------- Note: If the game is fair expected gain should be zero. --------------------------------------------- Equation: E(x) = (8/52)(5-x) + (13/52)(2-x) + (31/52)x = 0 ---------- Multiply thru by 52 to get: [40 - 8x + 26 - 13x + 31x) = 0 10x - 66 = 0 x = \$6.60 (amount you should pay to play the game) ===================================== Cheers, Stan H.
 Probability-and-statistics/274633: among com[anies doing highway or brige construction , 80% test employees for substance abuse . A study oinvolves the randam selection of 10 such companies. FIND the probability that exactly 5 of the 10 companies test for substance abuse.(b) find the probability at least half of the companies test for substance abuse.(c) For such groups of 10 companies , find the mean and standard for the number(among) that test for substance abuse.1 solutions Answer 200400 by stanbon(57277)   on 2010-02-26 13:48:55 (Show Source): You can put this solution on YOUR website!among companies doing highway or brige construction , 80% test employees for substance abuse. A study involves the random selection of 10 such companies. a)FIND the probability that exactly 5 of the 10 companies test for substance abuse --- P(x = 5) = 10C5(0.8)^5*(0.2)^5 = binompdf(10,0.8,5) = 0.0264 ----------------------------------------- (b) Find the probability at least half of the companies test for substance abuse. P(5<= x <=10) = 1 - binomcdf(10,0.8,4) = 0.9936 ------------------------------------------ c) For such groups of 10 companies , find the mean and standard deviation for the number(among 10) that test for substance abuse. ------------- mean = np = 10*0.8 = 8 --- std = sqrt(npq) = sqrt(8*0.2) = sqrt(1.6) = 1.2649 ======== Cheers, Stan H.
 Equations/274630: Solve by the elimination method: 5x+6y=17 5x-y=38 I appreciate any help that you can give me for this. And please try to explain it to me the best you can. Thank you!1 solutions Answer 200396 by stanbon(57277)   on 2010-02-26 13:37:35 (Show Source): You can put this solution on YOUR website! Solve by the elimination method: 5x+6y=17 5x-y=38 ------------------- Subtract the 2nd equation from the 1st to get: 7y = -21 Then, y = -3 ------- Substitute that into 5x-y = 38 and solve for "x": 5x +3 = 38 5x = 35 x = 7 ------- Solution: (7,-3) ======================== Cheers, Stan H.
 Square-cubic-other-roots/274632: how do you solve without a calculator the logarithm lncubed root of t would changing it to lnt^1/3 mean the same thing? to where you could change that to 1/3lnt and that would be your answer? thnx 1 solutions Answer 200395 by stanbon(57277)   on 2010-02-26 13:34:12 (Show Source): You can put this solution on YOUR website!how do you solve without a calculator the logarithm ln cubed root of t would changing it to ln t^1/3 mean the same thing? to where you could change that to 1/3ln t and that would be your answer? thnx ------ Yes, Yes, Yes Cheers, Stan H.
 Probability-and-statistics/274526: in the past no shows were 20% of the people registered in a race. there are 225 registered this year. what is the probability of a. 220 no-shows? B. 50 or less no-shows?1 solutions Answer 200394 by stanbon(57277)   on 2010-02-26 13:31:13 (Show Source): You can put this solution on YOUR website!in the past no shows were 20% of the people registered in a race. there are 225 registered this year. ======= Binomial problem with n = 225 ; p = 0.2 ----- what is the probability of ---- a. 220 no-shows? P(x = 220) = 225C220(0.2)^220(0.8)^5 = binompdf(225,0.2,220) My calculator says the answer is zero to 8 decimal places. ------ B. 50 or less no-shows? P(0<= x <=50) = binomcdf(225,0.2,50) = 0.8211 ==================================================== Cheers, Stan H.
 logarithm/274564: I have been asked to take some figures from a 'yield table' of trees. Specifically the trees per ha/ and the diameters. I have then been asked to take the log base 10 of these figures, prior to plotting them on a graph. So in the first line (of many) I have 2309 trees with a diameter of 11 - what should I be doing with these figures. Am I to just move the decimal place? Thanks Kenton1 solutions Answer 200370 by stanbon(57277)   on 2010-02-26 10:51:39 (Show Source): You can put this solution on YOUR website!I have been asked to take some figures from a 'yield table' of trees. Specifically the trees per ha/ and the diameters. I have then been asked to take the log base 10 of these figures, prior to plotting them on a graph. So in the first line (of many) I have 2309 trees with a diameter of 11 - what should I be doing with these figures. Am I to just move the decimal place? ---- The log(base 10) of a number is the power of 10 required to express the number. For example log(base 10) of 10 = 1 because 10^1 = 10 log(base 10) of 100 = 2 because 10^2 = 100 -------------------------------------- Your Problem requires a calculator (which you can find online). log(base 10) 2309 = 3.3634.. log(base 10) 11 = 1.0414.. ================================= Cheers, Stan H.
 Probability-and-statistics/274477: The average mpg usage for a 2004 Ford Expedition 2WD for a sample of 10 tanks of gas was 17.0 with a standard deviation of 0.8. For a Ford Explorer 2WD, the average mpg usage for a sample of 10 tanks of gas was 18.5 with a standard deviation of 1.0. (a) Assuming equal variances, at α = .01, is the true mean mpg lower for the Ford Expedition? (b) Calculate the p-value using Excel.1 solutions Answer 200297 by stanbon(57277)   on 2010-02-25 23:09:20 (Show Source): You can put this solution on YOUR website!The average mpg usage for a 2004 Ford Expedition 2WD for a sample of 10 tanks of gas was 17.0 with a standard deviation of 0.8. --- For a Ford Explorer 2WD, the average mpg usage for a sample of 10 tanks of gas was 18.5 with a standard deviation of 1.0. (a) Assuming equal variances, at α = .01, is the true mean mpg lower for the Ford Expedition? Ho: u(Explor)-u(Exped) = 0 Ha: u(Explor)-u(Exped) > 0 --- I ran a 2-Sample T test and got test statistic: t = 3.704 p-value = 0.0008685 df = 20-2 = 18 ----------------------- Conclusion Reject Ho. ; Exped < Explo ========================================== Cheers, stan H. ======================================
 Probability-and-statistics/274417: Two dates are selected at random from the 365 days of the year. Determine the number of possible outcomes if the dates are selected (a) with replacement (i.e. we CAN pick the same date twice). (b) without replacement (i.e. we CANNOT pick the same date twice). Bonus: If I randomly pick 2 people off of the street, what is the probability that they have the same birthday? (I mean the day, not the year). 1 solutions Answer 200291 by stanbon(57277)   on 2010-02-25 22:46:01 (Show Source): You can put this solution on YOUR website!Two dates are selected at random from the 365 days of the year. Determine the number of possible outcomes if the dates are selected (a) with replacement (i.e. we CAN pick the same date twice). Ans: (1/365)^2 ------------------------------- (b) without replacement (i.e. we CANNOT pick the same date twice). Ans: (1/365)(1/364) ---------------------------- Bonus: If I randomly pick 2 people off of the street, what is the probability that they have the same birthday? (I mean the day, not the year). Ans: (1/365)^2 =============================================================================== Cheers, Stan H.
 Quadratic-relations-and-conic-sections/274415: Find x and y: x+y=7 and x*y=111 solutions Answer 200290 by stanbon(57277)   on 2010-02-25 22:19:50 (Show Source): You can put this solution on YOUR website!Find x and y: x+y=7 and x*y=11 -------------------- Substitute for "y" to get: x(7-x) = 11 -x^2+7x = 11 --- -x^2 + 7x - 11 = 0 --- x^2 - 7x + 11 = 0 --- x = [7 +- sqrt(49 -4*11)]/2 --- x = [7 +- sqrt(5)]/2 x = [7+sqrt(5)]/2 or x = [7-sqrt(5)]/2 x = (7/2) + (1/2)sqrt(5) or x = (7/2) - (1/2)sqrt(5) ----------------- Since y = 7-x y = (7/2)-(1/2)(sqrt)5 or y = (7/2) + (1/2)sqrt(5) ===================================================== Cheers, Stan H. y = 7 -
 Probability-and-statistics/274423: . A couple plans to have two children. Assume that on any given birth, having a boy and having a girl are equally likely. (a) What is the probability that exactly one of the children is a boy? (b) What is the probability that at least one of the children is a boy? 1 solutions Answer 200289 by stanbon(57277)   on 2010-02-25 21:59:16 (Show Source): You can put this solution on YOUR website!A couple plans to have two children. Assume that on any given birth, having a boy and having a girl are equally likely. --- Binomial with n=2 ; p = 1/2 ; q = 1/2 ---------------------------------------------------- (a) What is the probability that exactly one of the children is a boy? P(one boy) = P(boy first then girl) + P(girl first then boy) = (1/2)(1/2) + (1/2)(1/2) = 1/4 + 1/4 = 1/2 --------------------- (b) What is the probability that at least one of the children is a boy? P(one boy) + P(2 boys) = 1/2 + (1/2)(1/2) = 3/4 ==================================================== Cheers, stan H.
 Linear-systems/274439: Here is my problem. The perimeter of the rectangle is 24 and the perimeter of the triangle is 23 Here are the sides of the rectangle: side 1- x side 2- 3y side 3- x side 4- 3y here are the sides of the isosoles triangle: side 1- x+1 side 2- x+y side 3- y+6 Write a system of linear equations to represent this problem. How would I do that? 1 solutions Answer 200283 by stanbon(57277)   on 2010-02-25 21:33:38 (Show Source): You can put this solution on YOUR website!Here is my problem. The perimeter of the rectangle is 24 and the perimeter of the triangle is 23 Here are the sides of the rectangle: side 1- x side 2- 3y side 3- x side 4- 3y ------------------- Equation: 1-x + 2-3y+3-x + 4-3y = 24 -2x -6y + 10 = 24 -2x - 6y = 14 x + 3y = -7 -------------------- here are the sides of the isosoles triangle: side 1- x+1 side 2- x+y side 3- y+6 Equation: x+1 + x+y + y+6 = 23 2x + 2y + 7 = 23 2x + 2y = 16 x + y = 8 ---------------------------- Write a system of linear equations to represent this problem. x + 3y = -7 x + y = 8 ---- Subtract the 2nd equation from the 1st: 2y = -15 y = -15/2 ------ Since x + y = 8, substitute and solve for "x": x -15/2 = 16/2 x = 31/2 ------------------- Cheers, Stan H.
 Radicals/274443: explain the first condition that must be met for a simplified radical. Explain why 5/sqrt2 is not simplified and demonstrate the steps we must take to simplify it1 solutions Answer 200281 by stanbon(57277)   on 2010-02-25 21:21:58 (Show Source): You can put this solution on YOUR website! explain the first condition that must be met for a simplified radical. Explain why 5/sqrt2 is not simplified and demonstrate the steps we must take to simplify it -------------------------------- Multiply numerator and denominator by sqrt(2) to get: [5sqrt(2)]/2 = (5/2)sqrt(2) ================================= Cheers, Stan H.
 Probability-and-statistics/274424: Suppose that each question of a three-question multiple choice quiz has 5 choices. If you randomly choose an answer to each of the questions, what is the probability that none of the answers are correct? 1 solutions Answer 200280 by stanbon(57277)   on 2010-02-25 21:19:11 (Show Source): You can put this solution on YOUR website!Suppose that each question of a three-question multiple choice quiz has 5 choices. If you randomly choose an answer to each of the questions, what is the probability that none of the answers are correct? ---------------------------- Binomial Problem with n = 3 ; p = 1/5 ------ P(none of 3 are correct) = (4/5)^3 = 64/125 ================================================= Cheers, Stan H.
 Graphs/274441: I have a test on this tomarrow. I am having a very hard time understanding the questions and how to do them. I have to solve the linear system by using elimination. The problem is 3x=y-20 -7x-y=40 how do I do this kind of problem?1 solutions Answer 200278 by stanbon(57277)   on 2010-02-25 21:10:41 (Show Source): You can put this solution on YOUR website!solve the linear system by using elimination. The problem is 3x=y-20 -7x-y=40 ------------------------- Rearrange the equations: 3x - y = -20 -7x -y = 40 ------------------------ Subtract the 2nd equation from the 1st and solve for "x": 4x = -60 x = -15 ----- Substitute into 3x-y = -20 and solve for "y": 3(-15) - y = -20 -45 -y = -20 y = -45+20 y = -25 ======================= Cheers, Stan H.
 Numbers_Word_Problems/274437: The sum of two numbers is 20. What is their greatest possible product?1 solutions Answer 200276 by stanbon(57277)   on 2010-02-25 20:57:49 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 20. What is their greatest possible product? --- Equations: x + y = 20 Product = xy ------------- P = x(20-x) P = -x^2 + 20x ---- You have a quadratic with a = -1, b = 20 --- Maximum occurs when x = -b/2a = -20/-2 = 10 -------- Greatest product = xy = 10*10 = 100 ==================================== Cheers, Stan H.
 expressions/274433: 16d > -641 solutions Answer 200272 by stanbon(57277)   on 2010-02-25 20:49:10 (Show Source): You can put this solution on YOUR website!16d > -64 --- Divide both sides by 16 to get: d > -4 ============ Cheers, Stan H.
 Exponential-and-logarithmic-functions/274430: how to solve each of these questions a.) 2x=1/32 b.) 120x=25 c.) (4/9)^x= 81/16 thank you.......:) 1 solutions Answer 200270 by stanbon(57277)   on 2010-02-25 20:47:40 (Show Source): You can put this solution on YOUR website!how to solve each of these questions a.) 2x=1/32 Multiply both sides by (1/2) x = (1/2)(1/32) x = 1/64 -------------------------------- b.) 120x=25 Divide both sides by 120 to get: x = 25/120 x = 5/24 ---------------- c.) (4/9)^x= 81/16 Invert the left side: (9/4)^-x = (9/4)^2 ---- -x = 2 x = -2 =============== Cheers, Stan H.
 Probability-and-statistics/274425: Your home's security system has a component which is 90% reliable with a back-up component that is 70% reliable. Assume that the reliabilities of the two components are independent. If someone burglarizes your home, what is the probability that (a) both components fail? (b) at least one component functions properly? 1 solutions Answer 200267 by stanbon(57277)   on 2010-02-25 20:41:47 (Show Source): You can put this solution on YOUR website!Your home's security system has a component which is 90% reliable with a back-up component that is 70% reliable. Assume that the reliabilities of the two components are independent. If someone burglarizes your home, what is the probability that (a) both components fail?: 0.9*0.7 = 0.63 ----------------------------------------------- (b) at least one component functions properly? P(at least one) = 1 - P(both fail) = 1-0.63 = 0.37 ================================================= Cheers, Stan H.
 Linear-equations/274421: How do you interpret the slope and y-intercept in a real-world case?1 solutions Answer 200265 by stanbon(57277)   on 2010-02-25 20:35:25 (Show Source): You can put this solution on YOUR website!If "x" is the time when something happens, the y-intercept tells you what happened at the very beginning of the time period. --- Ex: If A(t) = 3t + 10 where A(t) is the amount of money you have at time t, then A(0) = 10 is the amount you started with. ------------------ Cheers, Stan H.
 Polynomials-and-rational-expressions/274414: what are the steps to solving zero-product property ?1 solutions Answer 200261 by stanbon(57277)   on 2010-02-25 20:30:48 (Show Source): You can put this solution on YOUR website!what are the steps to solving zero-product property ? ------------------- Example: x^2 + 5x + 6 = 0 Factor: (x+3)(x+2) = 0 --- Comment: Since the product is zero, one of the factors must be zero: ---- Solve x+3 = 0 or x+2 = 0 --- x = -3 or x = -2 ======================== Cheers, stan H.
 Polynomials-and-rational-expressions/274403: Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve. Include units with your answer. I have chosen the 2010 Jaguar XK-Series XK, 16 MPG city / 22 MPG highway1 solutions Answer 200260 by stanbon(57277)   on 2010-02-25 20:26:35 (Show Source): You can put this solution on YOUR website! Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve. Include units with your answer. ----- I have chosen the 2010 Jaguar XK-Series XK, 16 MPG city / 22 MPG highway --------------------------------------------- In general: x miles/60 gallons = (? miles /gallon) --- Your car: x miles/60 gallons = 22 miles/1 gallon ============== Cheers, Stan H.
 Polynomials-and-rational-expressions/274402: Here's my problem... The difference of the squares of two consecutive negative integers is 9. Find the integers. Here's what I have so far... -x and (-x+1) -x^2 and (-x+1)^2 -x^2 - (-x+1)^2 = 9 -x^2 - (x + 1x + 1) = 9 -x^2 - x - 1x = 8 That's as far as I got and I'm not sure if that's correct. Thanks again!!! 1 solutions Answer 200258 by stanbon(57277)   on 2010-02-25 20:10:53 (Show Source): You can put this solution on YOUR website! Here's my problem... The difference of the squares of two consecutive negative integers is 9. Find the integers. --------------------- 1st: x 2nd: x+1 -------------------- Equation: (x+1)^2-x^2 = 9 x^2 + 2x + 1 - x^2 = 9 2x + 1 = 9 2x = 8 x = 4 x+1 = 5 =============== Cheers, stan H.
 Mixture_Word_Problems/274400: how many ounces of a 35% alcohol solution must be mixed with 17 ounces of a 40% alcohol solution to make 36% alcohol solution? I just a formula to calculate this please! Thank you for ur help! 1 solutions Answer 200257 by stanbon(57277)   on 2010-02-25 20:07:53 (Show Source): You can put this solution on YOUR website!how many ounces of a 35% alcohol solution must be mixed with 17 ounces of a 40% alcohol solution to make 36% alcohol solution? ----------------- Equation: alcohol + alcohol = alcohol 0.40*17 + 0.35x = 0.36(17+x) ----- Multiply thru by 100 to get: 40*17 + 35x = 36*17 + 36x x = 4*17 --- x = 68 ounces (amt. of 35% solution needed for the mixture) ============================================================== Cheers, Stan H.