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

 Probability-and-statistics/749079: A survey is being planned to estimate, with a 98% confidence interval, the mean amount of time per week that seniors spend watching television. The population standard deviation is known to be 5.2 hours. What sample size will be required to obtain an estimate that is within 0.5 hours of the population mean?1 solutions Answer 455796 by stanbon(57219)   on 2013-05-15 16:50:27 (Show Source): You can put this solution on YOUR website!A survey is being planned to estimate, with a 98% confidence interval, the mean amount of time per week that seniors spend watching television. The population standard deviation is known to be 5.2 hours. What sample size will be required to obtain an estimate that is within 0.5 hours of the population mean? ----- Since E = z, n = [z*s/E]^2 ---- n = [2.3263*5.2/(1/2)]^2 --- n = 586 when rounded up Cheers, Stan H. =============
 Probability-and-statistics/749084: A survey was conducted to determine the percentage of students at a post secondary institution who prefer the new alpha-grading system. The responses from a random sample of 30 students are shown below. YES-18, NO-12 Construct a 98.5% confidence interval for a population proportion who prefer the new alpha-grading system.1 solutions Answer 455795 by stanbon(57219)   on 2013-05-15 16:44:53 (Show Source): You can put this solution on YOUR website!A survey was conducted to determine the percentage of students at a post secondary institution who prefer the new alpha-grading system. The responses from a random sample of 30 students are shown below. YES-18, NO-12 Construct a 98.5% confidence interval for a population proportion who prefer the new alpha-grading system. ------ Note: 0.985-1 = 0.015 (1/2)0.015 = 0.0075 invNorm(0.0075) = 2.4324 ------------------------------- p-hat = 18/30 = 0.6 ME = 2.4324*sqrt[0.6*0.4/30] = 0.2176 ---------------------- 98.5% CI: 0.6-0.2176 < P < 0.6+0.2176 ========================================== Cheers, Stan H. =============
 Probability-and-statistics/749085: Grade point averages of math majors at a large distance education university are normally distributed with a mean of u= 2.85 and a standard deviation of σ=0.30. If a random sample of 25 math majors is selected from that university, what is the probability that the sample mean grade point averages will be a) either less than 2.709 or more then 2.955? b) at least 2.757?1 solutions Answer 455793 by stanbon(57219)   on 2013-05-15 16:37:17 (Show Source): You can put this solution on YOUR website!Grade point averages of math majors at a large distance education university are normally distributed with a mean of u= 2.85 and a standard deviation of σ=0.30. If a random sample of 25 math majors is selected from that university, what is the probability that the sample mean grade point averages will be a) either less than 2.709 or more then 2.955? t(2.709) = (2.709-2.85)/[0.3/sqrt(25)] = -2.35 P(x < 2.709) = P(t < -2.35) = tcdf(-100,-2.35,24) = 0.0137 -------------- t(2.9557) = (2.9557-2.85)/[0.3/sqrt(25)] = 1.7617 P(x > 2.9557) = P(z > 1.7617) = tcdf(1.7617,100,24) = 0.0454 --- Add those probabilities to get your answer. ======================================================== b) at least 2.757? Use the same procedure. ============================= Cheers, Stan H. =========================
 Probability-and-statistics/749111: Determine the area of the largest rectangle that can be inscibed in the circle x^2 + y^2=a^21 solutions Answer 455784 by stanbon(57219)   on 2013-05-15 16:20:53 (Show Source): You can put this solution on YOUR website!Determine the area of the largest rectangle that can be inscibed in the circle x^2 + y^2=a^2 ---- By "largest" I assume you mean "has the greatest area". ----- That rectangle would be a square. ---- If the square fits inside, it's diagonal must be the diameter of the circle. ----- The diameter = 2*radius = 2*a ------- Letting the sides be "x" you get: x^2 + x^2 = (2a)^2 2x ^2 = 4a^2 x = a*sqrt(2) ===== So the area is x*x = (a*sqrt(2))^2 = 2a^2 sq. units ==================================================== Cheers, Stan H.
 Probability-and-statistics/749123: I need to find the z-score and the r for the data of x=4,5,6,8 and y=9,11,13,17 I need the zx and zy I have tried to come up with the mean and the standard of deviation for the formula and am still getting my answers wrong. I got the mean for x as 5.75 and y as 12.5 and then the standrd deviation is x=1.7078 and y =3.4157 I am so lost.1 solutions Answer 455783 by stanbon(57219)   on 2013-05-15 16:16:24 (Show Source): You can put this solution on YOUR website!I need to find the z-score and the r for the data of x=4,5,6,8 and y=9,11,13,17 ------ I'm not sure what you mean by all that. But here's the equation relating x to y: y = 2x+1 ------------------------ Cheers, Stan H. =================== I need the zx and zy I have tried to come up with the mean and the standard of deviation for the formula and am still getting my answers wrong. I got the mean for x as 5.75 and y as 12.5 and then the standrd deviation is x=1.7078 and y =3.4157 I am so lost.
 percentage/748947: The average cost of a wedding today is \$19,104 which is 26% more then the average cost of weeding in the last 5 years ago. Find the average cost of a wedding 5 years ago. Round to the nearest cent.1 solutions Answer 455700 by stanbon(57219)   on 2013-05-15 07:16:38 (Show Source): You can put this solution on YOUR website!The average cost of a wedding today is \$19,104 which is 26% more then the average cost of weeding in the last 5 years ago. Find the average cost of a wedding 5 years ago. Round to the nearest cent. ---- Let "x" be the price 5 years ago. Equation: x + 0.26x = 19,104 ---- 1.25x = 19,104 x = \$15,283.20 ============= cheers, Stan H. =============
 Inverses/748950: if n/5=17, which inverse operation will find n?1 solutions Answer 455698 by stanbon(57219)   on 2013-05-15 07:13:24 (Show Source): You can put this solution on YOUR website!if n/5=17, which inverse operation will find n? ------- The n is being divided by 5. The inverse of division is multiplication. ---- Multiply both sides by 5 to get: 5(n/5) = 5*17 n = 85 ============ Cheers, Stan H. ============
 Percentage-and-ratio-word-problems/748954: At a recent health fair 32% of the people tesred were found to have high blood cholesterol levels. If 350 people were texted, find the number haveing high blood cholesterol.1 solutions Answer 455696 by stanbon(57219)   on 2013-05-15 07:10:48 (Show Source): You can put this solution on YOUR website! At a recent health fair 32% of the people tesred were found to have high blood cholesterol levels. If 350 people were texted, find the number haveing high blood cholesterol. --- Use a Proportion: x/350 = 32/100 ---- x = 350(32/100) ---- x = 112 ============== Cheers, Stan H. ===========
 Angles/748937: One angle is thrice another. What are their measures, if they are supplementary, what are the angles?1 solutions Answer 455695 by stanbon(57219)   on 2013-05-15 07:08:36 (Show Source): You can put this solution on YOUR website!One angle is thrice another. What are their measures, if they are supplementary, what are the angles? ---- Equation: x = 3y x + y = 180 ----- 3y + y = 180 4y = 180 y = 45 ---- Solve for "x": x = 3y = 3*45 = 135 ---- The angles are 45 and 135 ----- Cheers, Stan H. =================
 percentage/748944: New home sales this year in the Sacramento area were 14% fewer than last year. If the number of new homes sold this year was 5645, find the number of new homes sold last year. Round to the nearest whole number.1 solutions Answer 455694 by stanbon(57219)   on 2013-05-15 06:41:38 (Show Source): You can put this solution on YOUR website!New home sales this year in the Sacramento area were 14% fewer than last year. If the number of new homes sold this year was 5645, find the number of new homes sold last year. Round to the nearest whole number. ----- Let x be # sold last year. --- Equation: x = 5645-0.14*5645 = 0.86*5645 = 4855 ================= Cheers, Stan H. =================
 percentage/748943: A mortgage lender made 52% more loans to minorities this year than last year. If the number of loans to minorities this year is 2660, find the number of loans made to minorities last year.1 solutions Answer 455693 by stanbon(57219)   on 2013-05-15 06:39:02 (Show Source): You can put this solution on YOUR website!A mortgage lender made 52% more loans to minorities this year than last year. If the number of loans to minorities this year is 2660, find the number of loans made to minorities last year. ----- Let # last year be "x": Equation: x = 1.52*2660 --- x = 4043 ============== Cheers, Stan H. ==============
 Permutations/748941: In what proportion should water & wine be mixed to reduce price of wine from Rs. 150 to Rs.120/litre ?1 solutions Answer 455692 by stanbon(57219)   on 2013-05-15 06:36:31 (Show Source): You can put this solution on YOUR website!In what proportion should water & wine be mixed to reduce price of wine from Rs. 150 to Rs.120/litre ? ------ (new wine/old wine) = 120/150 --- new wine = old wing(4/5) ----- New Mix: 4/5 th wine to 1/5 th water ================== Cheers, Stan H.
 Numbers_Word_Problems/748822: In two digit number,the product of its digits is 18.if the places of the digits are interchanged,the number so formed is greater than the original number by 27,find the original number.1 solutions Answer 455653 by stanbon(57219)   on 2013-05-14 21:30:42 (Show Source): You can put this solution on YOUR website!In two digit number,the product of its digits is 18.if the places of the digits are interchanged,the number so formed is greater than the original number by 27,find the original number. ---- Let the number be 10t+u ---- Equations: t*u = 18 10u+t - (10t+u) = 27 ----- Simplify: t*u = 18 9u - 9t = 27 ----- t*u = 18 u - t = 3 ---- t*u = 18 u = t+3 ----- t(t+3) = 18 t^2 + 3t -18 = 0 (t-6)(t+3) = 0 Positive solution: t = 6 ===== solve for "u": u = t + 3 u = 9 ------- Ans: 10t+u = 10*6+9 = 69 =============================== Cheers, Stan H.
 Average/748801: Andrew has a mean score of 18 points per game in his four basketball games of the season. How many points must he score in his next game to raise his mean score to 20 points per game? 1 solutions Answer 455645 by stanbon(57219)   on 2013-05-14 20:46:08 (Show Source): You can put this solution on YOUR website!Andrew has a mean score of 18 points per game in his four basketball games of the season. Total points = 4*18 = 72 ------------------------------- How many points must he score in his next game to raise his mean score to 20 points per game? Total points needed = (72+x)/5 = 20 72+x = 100 x = 28 (# of points needed on the 5th test) ========================== Cheers, Stan H. ----------
 Average/748798: I don't understand how to find the mixed number for the fraction 46/30 could someone help me please?1 solutions Answer 455643 by stanbon(57219)   on 2013-05-14 20:31:49 (Show Source): You can put this solution on YOUR website!I don't understand how to find the mixed number for the fraction 46/30 ----- 46/30 = (30+16)/30 = (30/30)+(16/30) = 1 + 8/15 = 1 8/15 ============================== Cheers, Stan H.
 test/748795: -2/(-5+3i)1 solutions Answer 455642 by stanbon(57219)   on 2013-05-14 20:23:40 (Show Source): You can put this solution on YOUR website!-2/(-5+3i) Multiply numerator and denominator by -5-3i to get: ----- = [-2(-5-3i)]/[25+9] ------ = [10+6i]/34 =================== Cheers, Stan H. ===================
 Rate-of-work-word-problems/748790: An experienced worker can unload a truck in one hour forty minutes. When he works together with a trainee, they can unload the truck in one hour. How long would the trainee need to unload the truck if he works alone?1 solutions Answer 455641 by stanbon(57219)   on 2013-05-14 20:09:24 (Show Source): You can put this solution on YOUR website!An experienced worker can unload a truck in one hour forty minutes. When he works together with a trainee, they can unload the truck in one hour. How long would the trainee need to unload the truck if he works alone? ----- exp worker rate = 1/100 job/min together worker rate = 1/60 job/min trainee worker rate = 1/x job/min =============================================== Equation: rate + rate = together rate 1/100 + 1/x = 1/60 ----- Multiply thru by 100*60x to get: ----------------------------------- 60x + (100*60) = 100x ------- 40x = 6000 x = 150 minutes (time for the trainee to do the job alone) ================ Cheers, Stan H. ==================
 Probability-and-statistics/748773: What is the mean for a single binomial trial, where S(ucess) is scored as 1 and F(ailure) is scored as 0?1 solutions Answer 455638 by stanbon(57219)   on 2013-05-14 19:57:38 (Show Source): You can put this solution on YOUR website!What is the mean for a single binomial trial, where S(ucess) is scored as 1 and F(ailure) is scored as 0? ------- mean = np ============== Cheers, Stan H. ====================
 Probability-and-statistics/748776: Verify the mean for the binomial distribution with n trials, where S(uccess) is scored as 1 and F(ailure) is scored as 0, is np.1 solutions Answer 455636 by stanbon(57219)   on 2013-05-14 19:53:22 (Show Source): You can put this solution on YOUR website!Verify the mean for the binomial distribution with n trials, where S(uccess) is scored as 1 and F(ailure) is scored as 0, is np. ---- That is a tricky proof. Please Google "binomial distribution proof of mean". ----- Cheers, Stan H.
 Probability-and-statistics/748684: Suppose A and B are events where P(A)=0.4, P(B)=0.5, and P(A and B)=0.1. So, P(B|A)=? P(A|B)=? P(A or B)=? (if A and B are independent) And why?1 solutions Answer 455635 by stanbon(57219)   on 2013-05-14 19:31:09 (Show Source): You can put this solution on YOUR website!Suppose A and B are events where P(A)=0.4, P(B)=0.5, and P(A and B)=0.1. So, P(B|A)= P(A and B)/P(A) = 0.1/0.4 = 1/4 --------------------------------------------- P(A|B)= P(A and B)/P(B) = 0.1/0.5 = 1/5 --------------------------------------------- P(A or B)= P(A)*P(B) (if A and B are independent) ----------------------- Cheers, Stan H.
 Probability-and-statistics/748698: P(B)=9/10,P(A and B)=3/5.Find P(A).1 solutions Answer 455631 by stanbon(57219)   on 2013-05-14 19:24:28 (Show Source): You can put this solution on YOUR website!P(B)=9/10, P(A and B)=3/5. Find P(A). ------- P(A or B) = P(A) + P(B) - P(A and B) ----- Your post has insufficient information to solve for P(A) unless P(A and B) = 0 ----------- Cheers, Stan H.
 Probability-and-statistics/748730: Can you please help me out? I dont understand how to solve this question! Five cards are drawn from a standard deck of cards. How many hands consist of three clubs and two diamonds? Thanks so much!!!!1 solutions Answer 455627 by stanbon(57219)   on 2013-05-14 19:14:16 (Show Source): You can put this solution on YOUR website!Five cards are drawn from a standard deck of cards. How many hands consist of three clubs and two diamonds? ---- # of ways to get 3 clubs: 4C3 = 4 # of ways to get 2 diamonds: 4C2 = 6 ---- # of hands with 3 clubs and 2 diamonds: 4*6 = 24 ===================== Cheers, Stan H. ===================
 Probability-and-statistics/748752: The psychology club conducted a lottery and sold 150 tickets. You bought 1 ticket, and your friend bought 3 tickets. There will be a first-place winner and a second-place winner. What is the probability that you will win first place?1 solutions Answer 455625 by stanbon(57219)   on 2013-05-14 18:47:57 (Show Source): You can put this solution on YOUR website!The psychology club conducted a lottery and sold 150 tickets. You bought 1 ticket, and your friend bought 3 tickets. There will be a first-place winner and a second-place winner. What is the probability that you will win first place? ----- # of ways to succeed: 1 # of possible outcomes: 150 --- P(win) = 1/150 ====================== Cheers, Stan H. ======================
 Functions/748754: Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms. f(x) = (3x-5)(3x + 2)1 solutions Answer 455624 by stanbon(57219)   on 2013-05-14 18:45:20 (Show Source): You can put this solution on YOUR website!Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms. f(x) = (3x-5)(3x + 2) ----- f(x) = 9x^2 + 6x -15x -10 ----- Quadratic: f(x) = 9x^2 - 9x - 10 -------------------------- Quad term: 9x^2 linear term: -9x constant term: -10 ============ Cheers, Stan H. =========
 Graphs/748741: Normal body temperature is 98.6 Fahrenheit. Write and inequality that describes the temperature t of people with below normal temperatures.1 solutions Answer 455623 by stanbon(57219)   on 2013-05-14 18:41:56 (Show Source): You can put this solution on YOUR website!Normal body temperature is 98.6 Fahrenheit. Write an inequality that describes the temperature t of people with below normal temperatures. ---------------------------------- t < 98.6 ------------ Cheers, Stan H. ============
 expressions/748750: (6^-7)^31 solutions Answer 455618 by stanbon(57219)   on 2013-05-14 18:36:22 (Show Source): You can put this solution on YOUR website!(6^-7)^3 ------ = 6^(-21) ---- = 1/[6^21] =============== Cheers, Stan H. =====================
 Expressions-with-variables/748747: Been a while since ive done algebra :) instructions: Solve each equation. The letter a b and c are constants. the problem is 1-ax=b and a DOESNT equal 0.1 solutions Answer 455616 by stanbon(57219)   on 2013-05-14 18:32:52 (Show Source): You can put this solution on YOUR website!1-ax=b ----- 1 = ax+b ---- ax = 1-b ---- x = (1-b)a ============== Cheers, Stan H.
 Expressions-with-variables/748746: Simplifying Rational Expressions The problem below is difficult for me to understand. I am having trouble soving it. I Have written it three ways. Please Help! 1. 5 or 5/10x-60 or Five divided by ten(x) minus sixty --- 10x-601 solutions Answer 455615 by stanbon(57219)   on 2013-05-14 18:28:16 (Show Source): You can put this solution on YOUR website!5/(10x-60) ----- = 5/[10(x-6)] ----- = 1/[2(x-6)] ----- = 1/(2x-12) =============== Cheers, Stan H. ===============
 test/748743: 5power of3÷(10+15)+9power2+331 solutions Answer 455614 by stanbon(57219)   on 2013-05-14 18:24:26 (Show Source): You can put this solution on YOUR website!5power of3÷(10+15)+9power2+33 ---- = 5^3 119/ [25] + 9^2 + 33 ---- = 125/25 + 81 + 33 ---- = 5 + 81 + 33 ---- = 119 =========== Cheers, Stan H. ===========
 Mixture_Word_Problems/748736: What quantity of 64% acetic acid solution must be mixed with a 29% acetic acid solution to produce 595 mL of 52% solution?1 solutions Answer 455613 by stanbon(57219)   on 2013-05-14 18:17:15 (Show Source): You can put this solution on YOUR website!What quantity of 64% acetic acid solution must be mixed with a 29% acetic acid solution to produce 595 mL of 52% solution? ------------------ Equation: acid + acid = acid 0.64x + 0.29(595-x) = 0.52*595 ----- 64x + 29*595 - 29x = 52*595 ------ 35x = 21*595 x = 17*21 x = 357 mL (amt. of 64% solution needed) --- 595-357 = 238 mL (amt of 29% solution needed) ========================================= Cheers, Stan H. ==============
 Circles/748722: what are the coordinates of the center of the circle whose equation is (x-3)^2+(y+7)^2=36?1 solutions Answer 455604 by stanbon(57219)   on 2013-05-14 17:39:11 (Show Source): You can put this solution on YOUR website!what are the coordinates of the center of the circle whose equation is (x-3)^2+(y+7)^2=36? --- Ans: (3,-7) ============== Cheers, Stan H. =============