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# Recent problems solved by 'stanbon'

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/343963: 3X=4(mod7)1 solutions Answer 246079 by stanbon(57377)   on 2010-09-16 11:36:03 (Show Source): You can put this solution on YOUR website!3X=4(mod7) Since 4 is -3(mod 7) 3x = -3 x = -1(mod7) x = 6(mod 7) ================= Cheers, Stan H. =================
 Numbers_Word_Problems/343943: which is the 2-digit number that is 3 times its first digit plus 5 times its second digit?1 solutions Answer 246064 by stanbon(57377)   on 2010-09-16 10:42:50 (Show Source): You can put this solution on YOUR website! which is the 2-digit number that is 3 times its first digit plus 5 times its second digit? --- Let the number be 10t+u. ---------------- Equation: 10t+u = 3t+5u 7t = 4u t = (4/7)(u) ---- Since both t and u are singel digits, u must be 7. Then t must be 4 ------------------------ The number is 47 --- Check: 47 = 3*4+5*7 = 12 + 35 = 47 ======================================= cheers, Stan H.
 Money_Word_Problems/343960: how much is 779.87 times 30 and devide by 21 solutions Answer 246062 by stanbon(57377)   on 2010-09-16 10:36:15 (Show Source): You can put this solution on YOUR website! how much is 779.87 times 30 and divide by 2 ----- = 779.87*15 = 11698.05 ============================ Cheers, Stan H.
 Sequences-and-series/343949: use s=n^2 to find the sum of 1+3+5+....+501. ------ 1 solutions Answer 246061 by stanbon(57377)   on 2010-09-16 10:33:41 (Show Source): You can put this solution on YOUR website!find the sum of 1+3+5+....+501 ----------------- 1st find "n" if a(1) = 1 and d = 2 ---- Using a(n) = a(1) + (n-1)d you get: 501 = 1 + (n-1)2 500 = 2(n-1) 250 = n-1 n = 251 ---------------------- Find the sum using S(n)=(n/2)(1 + 501) --- S(251) = 251/2(502) = 251*251 = 63001 ========================================= cheers, Stan H.
 Quadratic_Equations/343953: Solve by factoring and using the principle of zero products 9x^2 + 6x - 8 = 0 Thanks!1 solutions Answer 246060 by stanbon(57377)   on 2010-09-16 10:28:21 (Show Source): You can put this solution on YOUR website!Solve by factoring and using the principle of zero products 9x^2 + 6x - 8 = 0 ------------- 9x^2+12x-6x-8 = 0 ---------------------- 3x(3x+4)-2(3x+4) = 0 (3x+4)(3x-2) = 0 x = -4/3 or x = 2/3 ================================ Cheers, Stan H.
 Quadratic_Equations/343957: Factor completely: 7x^3 - 42x^2 - 112x Really appreciate your help!1 solutions Answer 246058 by stanbon(57377)   on 2010-09-16 10:25:01 (Show Source): You can put this solution on YOUR website!Factor completely: 7x^3 - 42x^2 - 112x ---- Common Factor: 7x --- = 7x[x^2 - 6x - 16] --- = 7x(x-8)(x+2) ==================== cheers, Stan H. ===============
 Quadratic_Equations/343955: Sove for F: r = sqrt kq1q2/ sqrt F Thank you so much!1 solutions Answer 246057 by stanbon(57377)   on 2010-09-16 10:22:32 (Show Source): You can put this solution on YOUR website!Solve for F: r = sqrt kq1q2/ sqrt F -------------------- Interchange r and sqrt(F) to get: sqrt(F) = [sqrt(kq1q2)]/r --- F = {[sqrt(kq1q2)]/r}^2 ================================ cheers, Stan H.
 Linear_Algebra/343954: -X/5+2y/3 is greater than or equal to 0 1 solutions Answer 246056 by stanbon(57377)   on 2010-09-16 10:19:45 (Show Source): You can put this solution on YOUR website!-X/5+2y/3 is greater than or equal to 0 ========================================= What is the question? Cheers, Stan H.
 Quadratic_Equations/343952: Solve the system: 2x + 3y = 6, x - 3y = 8 Thank you!1 solutions Answer 246054 by stanbon(57377)   on 2010-09-16 10:18:18 (Show Source): You can put this solution on YOUR website!Solve the system: 2x + 3y = 6 x - 3y = 8 --------------- Add the two equations to get: 3x = 14 x = 14/3 ---- Sustitute for "x" and solve for "y": (14/3) - 3y = 8 3y = (14/3)-(24/3) 3y = -10/3 y = -10/9 ================ solution: (14/3 , -10/9) ============================ Cheers, Stan H.
 Money_Word_Problems/343951: 100 item for 16.99 each how much is that1 solutions Answer 246053 by stanbon(57377)   on 2010-09-16 10:15:01 (Show Source): You can put this solution on YOUR website!100 items for 16.99 each. How much is that? ----- 100*16.99 = \$1699.00 ========================= Cheers, Stan H. ------
 Probability-and-statistics/343941: A study conducted at a certain college shows that 55% of the school's graduates find a job in their field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.1 solutions Answer 246051 by stanbon(57377)   on 2010-09-16 10:12:59 (Show Source): You can put this solution on YOUR website!A study conducted at a certain college shows that 55% of the school's graduates find a job in their field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. ----- P(at least one) = 1 - P(none of the seven find a job) ---- = 1 - (0.45)^7 = 1 - 0.0037 = 0.963 ============== Cheers, Stan H.
 Circles/343933: a square is inscribed in a circle the area of the square is 120 square mm. what is the area of the circle?1 solutions Answer 246038 by stanbon(57377)   on 2010-09-16 09:11:57 (Show Source): You can put this solution on YOUR website!a square is inscribed in a circle the area of the square is 120 square mm. what is the area of the circle? ------------------------------ Draw the picture. Notice that the diagonal of the square is the diameter of the circle. ------------------- Area of square = s^2 = 120 sq mm ----- Diagonal^2 = side^2 + side^2 d^2 = 120 + 120 d^2 = 240 diagonal of the square = 4sqrt(15) mm ------------------------------------------- Area of the circle = (pi)r^2 radius = 2sqrt(15) ------------------------------- Area of the circle = (pi)(2sqrt(15))^2 = 60pi mm^2 ================================================= Cheers, Stan H.
 Linear-systems/343930: Susan has a number of dimes and quarters in her pocket. She has a total of 84 coins, and the total dollar value of all dimes and quarters is \$15. Write two equations, using variables “d” and “q” to represent the number of dimes and quarters Susan has. Solve those two equations using either the substitution or elimination method to find how many dimes and how many quarters she has.1 solutions Answer 246035 by stanbon(57377)   on 2010-09-16 09:06:08 (Show Source): You can put this solution on YOUR website!She has a total of 84 coins, and the total dollar value of all dimes and quarters is \$15. Write two equations, using variables “d” and “q” to represent the number of dimes and quarters Susan has. Solve those two equations using either the substitution or elimination method to find how many dimes and how many quarters she has. ------------------ Quantity Eq.:::: d + q = 84 Value Eq::::::: 10d+25q = 1500 cents ------------------------------------------ Multiply thru the 1st by 10. 10d + 10q = 10*84 10d + 25q = 1500 ------------------ Subtract 1st from 2nd and solve for "q": 15q = 660 q = 44 (# of quarters) -------------------------------- Since d+q = 84, d = 40 (# of dimes) ====================================== Cheers, Stan H. ========
 Probability-and-statistics/343878: Question 5 (15 marks) Marking criteria Marks will be awarded for the correct inference technique and will include such aspects as appropriate detailed working, diagrams, correct calculations and conclusions, correct use of Excel. a. Eleven percent of the products produced by an industrial process over the past several months fail to conform to the specifications. The company modifies the process in an attempt to reduce the number of non-conformities. In a trial run, the modified process produces 16 nonconforming items out of a total of 300 produced. Do these results demonstrate that the modification is effective? (Test at a = 0.01) (8 marks) b. Use the appropriate Excel macro from the set of workbooks Test Statistics.xls to verify your answer to Part a. Include the resulting Excel output. With reference to the appropriate cells show how the output provided verifies your answer to Part a. (3 marks) c. Find the p-value of the test from the output generated in Part b. Explain how this value can be used to test the hypothesis in Part a.1 solutions Answer 246032 by stanbon(57377)   on 2010-09-16 09:01:58 (Show Source): You can put this solution on YOUR website!a. Eleven percent of the products produced by an industrial process over the past several months fail to conform to the specifications. The company modifies the process in an attempt to reduce the number of non-conformities. In a trial run, the modified process produces 16 nonconforming items out of a total of 300 produced. Do these results demonstrate that the modification is effective? (Test at a = 0.01) ----- Ho: p = 0.11 Ha: p < 0.11 -------------------- p-hat = 16/300 = 0.0533 --- Test Statistic: t(0.0533) = (0.0533-0.11)/sqrt[0.11*0.89/300] = -3.1369 ------------------ p-value: P(z<-3.1369) = 0.00085387.. ----- Conclusion: Since the p-value is less than 1%, reject Ho. =================== Cheers, Stan H. (8 marks) b. Use the appropriate Excel macro from the set of workbooks Test Statistics.xls to verify your answer to Part a. Include the resulting Excel output. With reference to the appropriate cells show how the output provided verifies your answer to Part a. (3 marks) c. Find the p-value of the test from the output generated in Part b. Explain how this value can be used to test the hypothesis in Part a.
 Probability-and-statistics/343885: q-1 The average percentage of failure of in a exam is 40 .What is the probability that out of a group of 6 candidates at least 4 passed in the exam q-2 X registered contractor with the govt .Recently x has submitted his tender for two contracts a&b THE PROBABILITY OF GETTING THE CONTRACT A is 1/2 the contract A&B IS 1/8 .Find the probability that x get contract a&b1 solutions Answer 246028 by stanbon(57377)   on 2010-09-16 08:51:34 (Show Source): You can put this solution on YOUR website! q-1 The average percentage of failure of in a exam is 40 . Percentage of success is 60. ----------------------------- What is the probability that out of a group of 6 candidates at least 4 passed in the exam P(4<= x <=6) = 1 - binomcdf(6,0.6,3) = 1 - 0.4557 = 0.5443 ----------------------------- q-2 X registered contractor with the govt . Recently x has submitted his tender for two contracts a&b THE PROBABILITY OF GETTING THE CONTRACT A is 1/2 the contract A&B IS 1/8 .Find the probability that x get contract a&b ----- Please use the words "AND" and "OR" instead of the symbol "&". ---- Cheers, Stan H.
 Probability-and-statistics/343569: Find the median of the data shown in the frequency distribution below. Cost Frequency \$18-24 8 \$12-18 12 \$6-12 36 \$0-6 28 Teacher said corrct answer was \$6-\$12, Why?1 solutions Answer 246022 by stanbon(57377)   on 2010-09-16 08:38:19 (Show Source): You can put this solution on YOUR website!Find the median of the data shown in the frequency distribution below. Cost Frequency \$18-24 8 \$12-18 12 \$6-12 36 \$0-6 28 Teacher said corrct answer was \$6-\$12, Why? =================== The median is the middle score. You have total frequency = 84 The middle score will be the 42 score or the average of the 42nd and 43rd. ---- Count from the top till you get to 42 and you will find yourself in the \$6-\$12 category. ---------------------------- Cheers, Stan H.
 Probability-and-statistics/343914: Please, I need help with this. I can find information where they are different but not a relationship between them.. I need one example of the relationship between descriptive and inferential Statistics and why? Thank you for your time.1 solutions Answer 246017 by stanbon(57377)   on 2010-09-16 08:30:34 (Show Source): You can put this solution on YOUR website!Using Google is a good way to get general information of any statistic topic. Please see the following site: --- http://writing.colostate.edu/guides/research/stats/pop2b.cfm ============== Cheers, Stan H.
 Mixture_Word_Problems/343789: i really need youre help with this problem how many ounces of a 50% acetic solution should a photographer add to 32 ounces of a 5% acetic acid solution to obtain a 10% acetic acid solution? 1 solutions Answer 245944 by stanbon(57377)   on 2010-09-15 21:44:24 (Show Source): You can put this solution on YOUR website!how many ounces of a 50% acetic solution should a photographer add to 32 ounces of a 5% acetic acid solution to obtain a 10% acetic acid solution? ------------------- Equation: acid + acid = acid ------- 0.50x + 0.05*32 = 0.10*(32+x) Multiply thru by 100 to get: 50x + 5*32 = 10*32 + 10x 40x = 5*32 x = 4 ounces (amt. of 50% solution needed in the mixture) ====================================== Cheers, Stan H.
 Probability-and-statistics/343781: Mobile phone subscribers in millions between 1995 and 2006 can be modeled by S(x)=18.12x+20.19, when x is the number of yrs after 1995, what yr was it 291,990,00 ?Rounding to nearest year1 solutions Answer 245942 by stanbon(57377)   on 2010-09-15 21:38:30 (Show Source): You can put this solution on YOUR website!Mobile phone subscribers in millions between 1995 and 2006 can be modeled by S(x)=18.12x+20.19, when x is the number of yrs after 1995, what yr was it 291,990,000 ?Rounding to nearest year ---------- 18.12x+20.19 = 291,990,000 ?Are the 18.12 and the 20.19 in millions? ==================== Cheers, Stan H.
 Probability-and-statistics/343732: Here is the probability question: a class tossed coins and recorded 161 heads and 179 tails. what is the probability of heads? tails. i am not sure how to start the problem but what i think you do is divide the 161 heads by the 179 tails to get the percent. or add both number then divde by the total with each of the numbers seperately. 1 solutions Answer 245938 by stanbon(57377)   on 2010-09-15 21:30:16 (Show Source): You can put this solution on YOUR website!Here is the probability question: a class tossed coins and recorded 161 heads and 179 tails. what is the probability of heads? 161/340 ---- What is the probability of tails? 179/340 ------------------------------------------------------- Cheers, Stan H.
 Equations/343751: I am trying to figure the following problem out for work. x-7.70/x=.47 i would like to know how the solution will work. Can you help with this?1 solutions Answer 245930 by stanbon(57377)   on 2010-09-15 21:12:50 (Show Source): You can put this solution on YOUR website!x-7.70/x=.47 ---- Multiply thru by x to get: x^2-7.70 = 0.47x --- Rearrange: x^2-0.47x - 7.70 = 0 ---- Solve using the Quadratic formula: x = [0.47 +- sqrt(0.47^2 -4*1*-7.4)]/2 ---- x = [0.47 +- sqrt(29.8209)]/2 ---- x = [0.47 + 5.4609]/2 or x = [0.47-5.4609]/2 ---- x = 2.9654 or x = -2.4955 =================================== Cheers, Stan H.
 Word_Problems_With_Coins/343749: I have a word problem that goes like this. There are 4 dimes. There are also half as many nickels as dimes and 3x as many quarters. How much money do you have in total ? 1 solutions Answer 245925 by stanbon(57377)   on 2010-09-15 21:02:14 (Show Source): You can put this solution on YOUR website!There are 4 dimes = 40 cents. There are also half as many nickels as dimes: 2*5 = 10 cents And 3x as many quarters.: = 3*25 = 75 cents -------------------------------------------------------- How much money do you have in total ? 40 + 10 + 75 = 125 cents = \$1.25 ====================================== Cheers, Stan H.
 Human-and-algebraic-language/343744: What does "the product of -7 and a number us no more than 50" mean1 solutions Answer 245923 by stanbon(57377)   on 2010-09-15 20:55:38 (Show Source): You can put this solution on YOUR website!What does "the product of -7 and a number is no more than 50" mean --------------------------- Let the number be "x". ------------------ -7x <= 50 ============== Cheers, Stan H.
 Numbers_Word_Problems/343734: how do I find 4 integers whose sum is greater than zero and whose product is less than zero1 solutions Answer 245922 by stanbon(57377)   on 2010-09-15 20:51:03 (Show Source): You can put this solution on YOUR website!how do I find 4 integers whose sum is greater than zero and whose product is less than zero --------- 1 + 2 + 5 + (-3) = 5 --- 1*2*5*(-3) = -30 =============================== Cheers, Stan H.
 Human-and-algebraic-language/343714: In your job selling knives, you have two different sets available. The better set sells for \$35.00 and the cheaper set for \$20.00. Last week you sold more of the cheaper set, in fact twice as many as the better sets. Your receipts for the week totaled \$525.00. How many of the better sets did you sell? Question: What is the equation. 1 solutions Answer 245919 by stanbon(57377)   on 2010-09-15 20:42:36 (Show Source): You can put this solution on YOUR website!In your job selling knives, you have two different sets available. The better set sells for \$35.00 and the cheaper set for \$20.00. Last week you sold more of the cheaper set, in fact twice as many as the better sets. Your receipts for the week totaled \$525.00. How many of the better sets did you sell? Question: What is the equation. Equations: c = 2b ---- 20(2b)+35b = 525 75b = 525 better = 7 (# of better sets sold) ================================= Cheers, Stan H. -------------------
 Exponents/343713: How do you slove 4+2(5-2)1 solutions Answer 245905 by stanbon(57377)   on 2010-09-15 20:20:06 (Show Source): You can put this solution on YOUR website!How do you solve 4+2(5-2) ---------------------- = 4 + 2(3) ---- = 4+6 ----- = 10 ======================= Cheers, Stan H.
 Number-Line/343711: Where would you put 2/5 and -4.9 on a number line1 solutions Answer 245902 by stanbon(57377)   on 2010-09-15 20:17:01 (Show Source): You can put this solution on YOUR website! Where would you put 2/5 and -4.9 on a number line --- Put 2/5 between 0 and 1 ------------------------------- Put -4.9 between -5 and -4 ================================= Cheers, Stan H.
 Miscellaneous_Word_Problems/343704: The length of a rectangular field is 45 ft greater than its width. How much fencing is needed to enclose the field and divide it into two parts?1 solutions Answer 245901 by stanbon(57377)   on 2010-09-15 20:13:44 (Show Source): You can put this solution on YOUR website!The length of a rectangular field is 45 ft greater than its width. How much fencing is needed to enclose the field and divide it into two parts? ------------------------ Let the width be "W". Then Length = W+45 --------------------------------- Draw a picture and label the line segments. Two Solutions: 3(W+45)+ 2w = 3W+135+2W = 5W+135 ft ---- OR 3(W)+2(W+45) = 3W+2W+90 = 5W+90 ft ======================================= The anwer depends on where you put the dividing side. ========================================= Cheers, Stan H.
 Problems-with-consecutive-odd-even-integers/343697: find four consecutive odd integers, if the sum of the third and fourth is 681 solutions Answer 245899 by stanbon(57377)   on 2010-09-15 20:02:04 (Show Source): You can put this solution on YOUR website!find four consecutive odd integers, if the sum of the third and fourth is 68 ----- 1st: 2x-3 2nd: 2x-1 3rd: 2x+1 4th: 2x+3 ----------- Equation: 2x+1 + 2x+3 = 68 4x+4 = 68 x+1 = 17 x = 16 -------- 1st: 2x-3 = 32-3 = 29 2nd: 2x-1 = 31 3rd: 2x+1 = 33 4th: 2x+3 = 35 ---------------- Cheers, Stan H.
 Graphs/343693: Compare the graph of the given quadriatic function fwith the graph of y = x squared. f(x)=(x-5) squared (the squared is because I dont know how to put the coefficient on there.1 solutions Answer 245897 by stanbon(57377)   on 2010-09-15 19:56:58 (Show Source): You can put this solution on YOUR website!Compare the graph of the given quadriatic function fwith the graph of y = x squared. f(x)=(x-5) squared ------------------------------------ f(x)=(x-5)^2 is y = x^2 moved 5 units to the right. ---------------------- ===================================================== Cheers, Stan H.
 Travel_Word_Problems/343538: how long the granite took to travel from los angeles to bodega bay? given 10 cm per year formula speed=distance/time1 solutions Answer 245833 by stanbon(57377)   on 2010-09-15 16:05:09 (Show Source): You can put this solution on YOUR website!What distance are you using for LA to B-bay? Cheers, Stan H.