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# Recent problems solved by 'stanbon'

stanbon answered: 57904 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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329 , 57330..57359 , 57360..57389 , 57390..57419 , 57420..57449 , 57450..57479 , 57480..57509 , 57510..57539 , 57540..57569 , 57570..57599 , 57600..57629 , 57630..57659 , 57660..57689 , 57690..57719 , 57720..57749 , 57750..57779 , 57780..57809 , 57810..57839 , 57840..57869 , 57870..57899 , 57900..57929, >>Next

 real-numbers/461897: The cardinal number in the set yellow blue red green indigo orange violet is __?1 solutions Answer 316685 by stanbon(57977)   on 2011-06-16 21:13:19 (Show Source): You can put this solution on YOUR website!The cardinal number in the set yellow blue red green indigo orange violet is __? Use Google to find out what "cardinal number" means. ---- Answer: 7 ============== Cheers, Stan H. ==============
 Probability-and-statistics/461785: Three coins are tossed. A)determine the number of points in the sample space. B)Construct a tree diagram and list the sample space. Determine the probabiltiy that: C)No heads are tossed. D) Exactly one head is tossed. E)Three heads are tossed.1 solutions Answer 316684 by stanbon(57977)   on 2011-06-16 21:11:42 (Show Source): You can put this solution on YOUR website!Three coins are tossed. Sample Space: 3 heads::hhh 2 heads::hht;hth;thh 1 head:::htt;tht;tth 0 heads::ttt --------------------------------------------------- A)determine the number of points in the sample space: 2^3 = 8 -------- B)Construct a tree diagram and list the sample space. Determine the probabiltiy that: C)No heads are tossed::: 1/8 -------------------- D) Exactly one head is tossed::: 3/8 -------------------- E)Three heads are tossed::: 1/8 =================================== Cheers, Stan H. ===================================
 Probability-and-statistics/461817: The probability of winning a certain lottery is 1/54,535. For people who play 949 times, find the standard deviation for the random variable X, the number of wins.1 solutions Answer 316681 by stanbon(57977)   on 2011-06-16 21:06:26 (Show Source): You can put this solution on YOUR website!The probability of winning a certain lottery is 1/54,535. For people who play 949 times, find the standard deviation for the random variable X, the number of wins. --- std = sqrt(npq) = sqrt(949*(1/54535)(54534/54535) --- = 0.1319 ============== Cheers, Stan H. ==============
 Probability-and-statistics/461898: what is the probability that two out of three cards drawn from a deck of 52 without replacement are red? 1 solutions Answer 316677 by stanbon(57977)   on 2011-06-16 21:01:26 (Show Source): You can put this solution on YOUR website!what is the probability that two out of three cards drawn from a deck of 52 without replacement are red? ======== # of ways to pick 2 red = 26C2 # of ways to pick 1 black = 26 ======== # of ways to randomly pick 3 cards + 52C3 ----- P(2red and 1 black) = [26C2*26]/52C3 = 0.3824 =============== Cheers, Stan H. ===============
 Rational-functions/461900: I need help with this one, please.Find the LCM of 10z^2 +40z and 5z^2 +45z + 100. Can anyone help me solve this.1 solutions Answer 316676 by stanbon(57977)   on 2011-06-16 20:57:20 (Show Source): You can put this solution on YOUR website!Find the LCM of 10z^2 +40z and 5z^2 +45z + 100 ---- Factor each expression: 10z^2+40z = 10z(z+4) = 2*5(z+4) --- 5z^2+45z+100 = 5(z^2+9z+20) = 5(z+4)(z+5) ----------------- The LCM must contain each of the different factors: LCM = 2*5*(z+4)(z+5) --- LCM = 10[z^2+9z+20] = 10z^2+90z+200 ====================================== Cheers, Stan H. ============
 Radicals/461901: Subtract. Simplify by collecting like radical terms if possible, assuming that all expressions under radicals represent nonnegative numbers. ∛54x-∛(2x^4 ) Thank you very much.1 solutions Answer 316673 by stanbon(57977)   on 2011-06-16 20:52:45 (Show Source): You can put this solution on YOUR website!Subtract. Simplify by collecting like radical terms if possible, assuming that all expressions under radicals represent nonnegative numbers. ∛54x-∛(2x^4 ) ---- = cbrt(27)*cbrt(2x) - cbrt(x^3)*cbrt(2x) ---- = 3*cbrt(2x) - x*cbrt(2x) ---- = (3-x)*cbrt(2x) =================== Cheers, Stan H. ===================
 Radicals/461902: Subtract. Simplify by collecting like radical terms, if possible. 6∛5-2∛5 Thank you sooo much.1 solutions Answer 316672 by stanbon(57977)   on 2011-06-16 20:50:04 (Show Source): You can put this solution on YOUR website!Subtract. Simplify by collecting like radical terms, if possible. 6∛5-2∛5 ---- = 4*cbrt(5) =============== Cheers, Stan H. ===============
 Polygons/461903: how many sides does a polygon have if the sum of it angles measures is 2700 degrees?1 solutions Answer 316671 by stanbon(57977)   on 2011-06-16 20:48:26 (Show Source): You can put this solution on YOUR website!how many sides does a polygon have if the sum of it angles measures is 2700 degrees? ---- If n is the number of sides, (n-2)*180 = 2700 --- n-2 = 15 --- # of sides = n = 17 ======================= Cheers, Stan H.
 Square-cubic-other-roots/461506: what is the answer to the equation 1/3x+1/4x=x-1/6? 1 solutions Answer 316477 by stanbon(57977)   on 2011-06-15 20:48:14 (Show Source): You can put this solution on YOUR website!what is the answer to the equation 1/3x+1/4x=(x-1)/6? ---- Multiply thru by 12 to get: ------ 4x + 3x = 2(x-1) 7x = 2x-2 5x = -2 x = -2/5 ----------------------------- Cheers, Stan H. ====================
 Miscellaneous_Word_Problems/461487: at 9:45 am Maggie threw a ball upwards while standing on a platform 55 ft off of the ground. The trajectory after t seconds follows the equation: h(t)=-0.6t^2 + 72t + 55 what will be the maximum height of the ball how long will it take the ball to reach its maximum height at what time will the ball hit the ground1 solutions Answer 316476 by stanbon(57977)   on 2011-06-15 20:39:12 (Show Source): You can put this solution on YOUR website!at 9:45 am Maggie threw a ball upwards while standing on a platform 55 ft off of the ground. The trajectory after t seconds follows the equation: h(t) = -0.6t^2 + 72t + 55 --------------------- What will be the maximum height of the ball? max occurs when t = -b/(2a) = -72/(2*-0.6) = -72/(-1.2) = 6 seconds -------------------- how long will it take the ball to reach its maximum height? 6 seconds -------------------- at what time will the ball hit the ground Solve -0.6t^2+72t+55 = 0 Use the quadratic formula: t = [-72 +- sqrt(72^2 - 4*-0.6*55)]/(2*-0.6) ----- Positive solution: t = 120.76 seconds ~ 2 min ------------------- the ball will hit the ground at 9:47
 Polynomials-and-rational-expressions/461485: jenna has a total of 23 coins, made up of dimes and nickels. if she has a \$1.90, how many nickels and dimes does she have?1 solutions Answer 316471 by stanbon(57977)   on 2011-06-15 20:01:53 (Show Source): You can put this solution on YOUR website!jenna has a total of 23 coins, made up of dimes and nickels. if she has a \$1.90, how many nickels and dimes does she have? ----- Equations: d + n = 23 coins 10d+5n=190 cents ----------------------- Divide thru the lower equation by 5: ------ d + n = 23 2d + n = 38 ---- Subtract and solve for "d": d = 15 (# of dimes) ---- Solve for "n": --- d + n = 23 15 + n = 23 n = 8 (# of nickels) ------------------------ Cheers, Stan H. =================
 Linear-equations/461474: Hi, could someone please help me with this problem? You want a fence in a rectangular area,but first you must determine the dimensions of the area. 2) Define the shape of the rectangular area by establishing a relationship between the length and the width of the rectangular,for example, L=2w+5 or w=3L-4, be sure to include the appropriate units(inches, feet, yards, miles or meters).Using the fact that A=LW,together with the relationship in stept 2, eliminate one of the variables to set up a quadratic equation1 solutions Answer 316470 by stanbon(57977)   on 2011-06-15 19:56:23 (Show Source): You can put this solution on YOUR website!You want a fence in a rectangular area,but first you must determine the dimensions of the area. 2) Define the shape of the rectangular area by establishing a relationship between the length and the width of the rectangular,for example, L=2w+5 or w=3L-4, be sure to include the appropriate units(inches, feet, yards, miles or meters). Using the fact that A=LW,together with the relationship in stept 2, eliminate one of the variables to set up a quadratic equation ----- Area = LW Area = (2w+5)(3L-4) --- Substitute for "w" to get: Area = (2(3L-4)+5)(3L-4) --- Area = (6L-3)(3L-4) ---- Area = 18L^2-24L-9L+24 ---- Area = (18L^2-33L+24) sq.ft =========================== Cheers, Stan H.
 Polynomials-and-rational-expressions/461459: Essay: Show all work. A gardener wants to create a triangular garden in the shape of a right triangle with shortest side length x – 8y ft. and the middle length side x + 6y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out and express in simplest correct mathematical form, including units. 1 solutions Answer 316466 by stanbon(57977)   on 2011-06-15 19:35:24 (Show Source): You can put this solution on YOUR website!Essay: Show all work. A gardener wants to create a triangular garden in the shape of a right triangle with shortest side length x – 8y ft. and the middle length side x + 6y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out and express in simplest correct mathematical form, including units. ------------------------------------ The given sides are the legs of the right triangle. Area = leg1*leg2 ---- Area = (x-8y)(x+6y) sq. ft --- Area = x^2-8xy+6xy-48y^2 ---- Area = x^2-2xy-48y^2 ======================= Cheers, Stan H.
 Radicals/461462: Multiply. √3(2√2-8√9) Thank you very much.1 solutions Answer 316457 by stanbon(57977)   on 2011-06-15 18:57:20 (Show Source): You can put this solution on YOUR website!Multiply. √3(2√2-8√9) --- = 2sqrt(6) - 8*3*sqrt(3) ----- = 2sqrt(6) - 24sqrt(3) =========================== Cheers, Stan H. =============
 Probability-and-statistics/460450: Discrete probability distribution: Basic Fill in the values in the table below to give a legitimate probability distribution for the discrete random variable , whose possible values are , , , , and . The numbers are -2,1,3,4, and 6. 1 solutions Answer 316349 by stanbon(57977)   on 2011-06-15 09:26:27 (Show Source): You can put this solution on YOUR website!Fill in the values in the table below to give a legitimate probability distribution for the discrete random variable , whose possible values are , , , , and . The numbers are -2,1,3,4, and 6. ---- 1/5;1/5;1/5;1/5;/1/5 would do it. ================= Cheers, Stan H.
 Probability-and-statistics/460790: with a sample size of 20 what is the result using a one tailed test1 solutions Answer 316348 by stanbon(57977)   on 2011-06-15 09:23:50 (Show Source): You can put this solution on YOUR website!with a sample size of 20 what is the result using a one tailed test --- What result? You need more information than just sample size to get a "result". Cheers, Stan H. ========
 Probability-and-statistics/461190: A confidence interval estimate for the population mean is given to be (46.66, 54.74). If the standard deviation is 11.822 and the sample size is 57, answer each of the following (show all work): (A) Determine the maximum error of the estimate, E. (B) Determine the confidence level used for the given confidence interval 1 solutions Answer 316347 by stanbon(57977)   on 2011-06-15 09:21:27 (Show Source): You can put this solution on YOUR website!A confidence interval estimate for the population mean is given to be (46.66, 54.74). ---------------------------------- If the standard deviation is 11.822 and the sample size is 57, answer each of the following (show all work): (A) Determine the maximum error of the estimate, E. --- Fact: The width of the Confidence interval is ALWAYS 2*ME 2*ME = (54.74-46.66) = 8.08 ME = 4.04 ---------------------- (B) Determine the confidence level used for the given confidence interval ME = zs/Sqrt(n) 4.04 = z*11.822/sqrt(57) --- z = 2.5 ---- Confidence level = 1 - 2*P(z > 2.5) = 1 - 1.24% = 98.76% ============================================ Cheers, Stan H.
 Graphs/461217: Hello - please solve this non-function and explain why it is not a function: solve y2 + 4x = 8 thanks!1 solutions Answer 316346 by stanbon(57977)   on 2011-06-15 09:02:18 (Show Source): You can put this solution on YOUR website!please solve this non-function and explain why it is not a function: solve y2 + 4x = 8 ----- y^2 = -4x+8 --- y = +/-sqrt[-4x+8] --- For every x-value there are 2 y-values. That is why it is not a function. =========== Cheers, Stan H. ===========
 Linear-equations/461208: I am having a hard time finding the solution of this set using the graphing method x-2y=-2 x+2y=61 solutions Answer 316345 by stanbon(57977)   on 2011-06-15 08:59:56 (Show Source): You can put this solution on YOUR website!solution of this set using the graphing method: x-2y=-2 x+2y=6 ----- Solve for "y": y = (1/2)x +1 Plotting Points: (0,1) and (2,2) ------------------------------------- y = (-1/2)x + 3 Plotting Points: (0,3) and (2,2) -------------------------------------- Solution: (2,2) ==================== Graph: ============ Cheers, Stan H. -------------------------
 absolute-value/461216: What is the absolute value of 4 1/61 solutions Answer 316344 by stanbon(57977)   on 2011-06-15 08:55:33 (Show Source): You can put this solution on YOUR website!Absolute value of any non-negative number is the number. |4 1/6| = 4 1/6
 Pythagorean-theorem/461214: given endpoint (-6,2) and the midpoint (5,2 ) find the other endpoint1 solutions Answer 316343 by stanbon(57977)   on 2011-06-15 08:53:53 (Show Source): You can put this solution on YOUR website!given endpoint (-6,2) and the midpoint (5,2) find the other endpoint ----- Fact: The mid-point coordinates are the average of the corresponding end-point coordinates. ---------- Solve: Let the end-point be (x,y) (x+-6)/2 = 5 (y+2)/2 = 2 ----- x-6 = 10 y+2 = 4 --- x = 16 y = 2 ------------- Cheers, Stan H.
 Probability-and-statistics/460843: The time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site has a Normal distribution with a mean of 15 seconds and a standard deviation of 3 seconds. On 90% of the occasions, the computer link is made in less than ___1 solutions Answer 316342 by stanbon(57977)   on 2011-06-15 06:30:43 (Show Source): You can put this solution on YOUR website!The time taken for a computer link to be made between the terminal in an executive's office and the computer at a remote factory site has a Normal distribution with a mean of 15 seconds and a standard deviation of 3 seconds. On 90% of the occasions, the computer link is made in less than ___ -------------- Find the z-value with a 90% left tail: invNorm(0.90) = 1.2816 ----- Find the corresponding x-value: x = zs+u x = 1.2816*3 + 15 = 18.84 seconds ================ Cheers, Stan H.
 Probability-and-statistics/460876: It has been reported that 83% of federal government employees use eamil. If a sample of 200 federal governmnet employees is selected, find the mean, variance, and standard deviation of the number who use email. 1 solutions Answer 316341 by stanbon(57977)   on 2011-06-15 06:27:22 (Show Source): You can put this solution on YOUR website!It has been reported that 83% of federal government employees use eamil. If a sample of 200 federal governmnet employees is selected, find the mean, variance, and standard deviation of the number who use email. ---- n = 200 ; p = 0.83 mean = np variance = npq std = sqrt(npq) ==================== Cheers, Stan H.
 Probability-and-statistics/460931: Nine guests are invited for dinner. If there are 2 "ends" to the table, how many different pairs can be seated on the ends? Assume the seating is random (a "couple" can be split up) and the same pair at either end is still only one pair.1 solutions Answer 316340 by stanbon(57977)   on 2011-06-15 06:25:54 (Show Source): You can put this solution on YOUR website!Nine guests are invited for dinner. If there are 2 "ends" to the table, how many different pairs can be seated on the ends? Assume the seating is random (a "couple" can be split up) and the same pair at either end is still only one pair. ---- # of ways to pick a "pair": 9C2 = 36 # of ways to pick an "end": 2 ---- # of different "pairs" on the "ends" = 2*36 = 72 =================================================== Cheers, Stan H.
 Probability-and-statistics/461188: Assume that a sample is drawn and z(α/2) = 1.65 and σ = 30. Answer the following questions: (A)If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size? (B)Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate? (C)What happens to the Maximum Error of Estimate as the sample size gets larger? (D) What effect does the answer to C above have to the size of the confidence interval?1 solutions Answer 316339 by stanbon(57977)   on 2011-06-15 06:21:28 (Show Source): You can put this solution on YOUR website!Assume that a sample is drawn and z(α/2) = 1.65 and σ = 30. Answer the following questions: ---- Note: n = [zs/E]^2 or E = zs/sqrt(n) ========================= (A)If the Maximum Error of Estimate is 0.05 for this sample, what would be the sample size? n = [1.65*30/0.05]^2 =========================== (B)Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate? E = 1.65*30/sqrt(400) =========================== (C)What happens to the Maximum Error of Estimate as the sample size gets larger? ME and n are inversely related so the ME would get smaller =========================== (D) What effect does the answer to C above have to the size of the confidence interval? The confidence interval is ALWAYS 2*ME so the confidence interval would get smaller. ========================== Cheers, Stan H.
 Probability-and-statistics/461062: Six hundred chances are sold at \$7 apiece for a raffle. There is a grand prize of \$500 dollars, two second prizes of \$250, and five third prizes of \$100. First calculate the expected value of the lottery. Determine if the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair. The expected value of the game is \$______ If the game is not fair, determine a price for playing the game would make the game fair. \$_______1 solutions Answer 316338 by stanbon(57977)   on 2011-06-15 06:13:58 (Show Source): You can put this solution on YOUR website!Six hundred chances are sold at \$7 apiece for a raffle. There is a grand prize of \$500 dollars, two second prizes of \$250, and five third prizes of \$100. ----------------------- First calculate the expected value of the lottery. Determine if the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair. ------ Random gain values: 493, 243, 93, -7 ---- Corresponding Probs: 1/600 , 2/600, 5/600, 592/600 ---- E(x) = [493+2*243+5*93+592*-7]/600 E(x) = -\$4.50 The expected value of the game is \$-\$4.50 -------------------------------------------------- If the game is not fair, determine a price for playing the game would make the game fair. \$7-4.5 = \$2.50 ================================ Cheers, Stan H.
 Probability-and-statistics/461065: a manufacturing process has a 70% yield, meaning that 70% of the porducts are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable.1 solutions Answer 316337 by stanbon(57977)   on 2011-06-15 06:03:43 (Show Source): You can put this solution on YOUR website!a manufacturing process has a 70% yield, meaning that 70% of the porducts are acceptable and 30% are defective. If three of the products are randomly selected, find the probability that all of them are acceptable. --- Ans: 0.7^3 = 0.3430 ======================= Cheers, Stan H.
 Polynomials-and-rational-expressions/461138: solve for the variable in each equation below. show all work please. check the answer. if solution is undefined, state that in the answer. thank you for your help. (5a-3/2)-(3a-9/8)=61 solutions Answer 316336 by stanbon(57977)   on 2011-06-15 06:01:49 (Show Source): You can put this solution on YOUR website!(5a-3)/2 -(3a-9)/8 = 6 ---- The least common multiple of 2 and 8 is 8. Multiply thru by 8 to get: 4(5a-3) - (3a-9) = 8*6 --- 20a-12-3a+9 = 48 --- 17a - 3 = 48 --- 17a = 51 --- a = 3 =========== Cheers, Stan H.
 Quadratic_Equations/461169: Breifly discuss the effect of the sign of the coefficient a on the graph of y=ax^2+bx+c. Please include two example of graph to support your thoughts one where a<0 and one where a>0. If you do not include the actual graph, please describe your examples in detail with words.1 solutions Answer 316335 by stanbon(57977)   on 2011-06-15 05:57:09 (Show Source): You can put this solution on YOUR website!If "a" is positive the graph (parabola) opens up and has a minimum point at its vertex. Examples: y = x^2 ; y = 2x^2-4 ========================= If "a" is negative the graph (parabola) opens down and has a maximum point at its vertex. Examples: y = -x^2 ; y = -2x^2+4 ---- Cheers, Stan H.
 Percentage-and-ratio-word-problems/461178: This year, 7 students tried out for the soccer team than last year. This is a 14% decline. How many student’s tried out last year? This year?1 solutions Answer 316334 by stanbon(57977)   on 2011-06-15 05:51:03 (Show Source): You can put this solution on YOUR website!This year, 7 fewer students tried out for the soccer team than last year. This is a 14% decline. How many student’s tried out last year? This year? ----- Let "x" be number that tried out last year. --- Equation: 7 = 0.14x x = 50 (# that tried out last year) --- Then # that tried out this year is 43 ============ Cheers, Stan H.
 logarithm/461179: log5log5log2x=0, x=? 1 solutions Answer 316333 by stanbon(57977)   on 2011-06-15 05:47:31 (Show Source): You can put this solution on YOUR website!You need to separate the base from the anti-log. Example log5(2x) tells me the base is 5 and the anti-log is 2x. Cheers, Stan H.