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# Recent problems solved by 'jrfrunner'

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 Probability-and-statistics/394805: Do students at various universities differ in how sociable they are? Twenty-five students were randomly selected from each of three universities in a region and were asked to report on the amount of time they spent socializing each day with other students. The result for University X was a mean of 5 hours and an estimated population variance of 2 hours; for University Y,M = 4, S^2 = 1.5 ; and for University Z,M = 6, S^2 = 2.5 . What should you conclude? Use the .05 level. (a) Use the steps of hypothesis testing, (b) figure the effect size for the study; and (c) explain your answers to parts (a) and (b) to someone who has never had a course in statistics.1 solutions Answer 280157 by jrfrunner(365)   on 2011-01-14 18:04:03 (Show Source): You can put this solution on YOUR website!Ho: Ux=Uy=Uz Ha: not all are equal - compute the sum squares for between groups x,y,z SSB=sum(ni*(Xi-Xbar)^2) where ni=sample size for group i, Xi=sample average for group i, and Xbar=overall average. ni=25 for each group, Xx=5,Xy=4,Xz=6, Xbar=5 SSB=25*(0^2+(-1)^2+1^2)=50 degrees of freedom= k-1=3-1=2, k=number of groups - Compute the sum squares for the error SSE=sum((ni-1)*Si^2)=24*(2+1.5+2.5)=144 degrees of freedom= k(ni-1)=3(25-1)=3*24=72, k=number of groups -- Compute Mean sum of squares for between groups and error MSB=SSB/dof=50/2=25 MSE=SSE/dof=144/72=2 -- compute F statistic= MSB/MSE=25/2=12.5 -- determine the critical F value for alpha 0.05, num dof=2, denom dof=72 Fcritical= 3.12 -- Since Fstatistic > Fcritical then reject Ho and conclude The universities differ in their average time socializing
 Triangles/394705: 1)The hypothenuse of right triangle is 15cm. the sum of the legs is 21cm. Find the legs of triangle. 2)A lidles box is constructed from a square piece of tin by cutting a 10cm square from each corner and bending up the sides for the box. if the volume of the box is 1200cm^3,find the dimensions to the nearest tenth of centimetre.1 solutions Answer 280114 by jrfrunner(365)   on 2011-01-14 15:31:20 (Show Source): You can put this solution on YOUR website!i've answered this problem already #394674
 Money_Word_Problems/394770: Find the amount owing on a loan of \$7400 at the end of 3 years, with interest at 10.9%/annum, compounded monthly.1 solutions Answer 280113 by jrfrunner(365)   on 2011-01-14 15:27:26 (Show Source): You can put this solution on YOUR website!loan P=7400 annual interest=0.109 term=3years compounded monthly Final =7400*(1-0.109/12)^(3*12)=5328.05
 Subset/394590: Given these sets: A = {3, 4, 5, 6, 7} B = {6, 7, 8, 9} C = {2, 4, 6, 8} List the elements of this set C(A∩B) 1 solutions Answer 280112 by jrfrunner(365)   on 2011-01-14 15:17:23 (Show Source): You can put this solution on YOUR website!A n B = {6,7} -- not sure what you mean by C(AnB) is this CU(AnB) or Cn(AnB)? or something else like the complement
 Linear-equations/394786: How could you tell if two corresponding lines would be parallel by looking at their linear equations? Thank you so much 1 solutions Answer 280104 by jrfrunner(365)   on 2011-01-14 14:55:32 (Show Source): You can put this solution on YOUR website!the simplest way is to put them in standard form: y=b+mx where b=y intercept and m=slope -- if both lines have the same "m" (or slope) they are parallel
 Probability-and-statistics/394742: A computer program is tested by 3 independent tests. When there is an error, these tests will discover it with probabilities 0.2, 0.3, and 0.5, respectively. Suppose that the program contains an error. What is the probability that it will be found by at least one test?1 solutions Answer 280094 by jrfrunner(365)   on 2011-01-14 14:10:01 (Show Source): You can put this solution on YOUR website!let A =error found by test 1 let B=error found by test 2 let C=error found by test 3 - Given P(A)=0.2, P(B)=0.3, P(C)=0.5 therefore P(notA)=0.8, P(notB)=0.7, P(notC)=0.5 - Note: tests are independent P(notA & notB & notC)=P(notA)*P(notB)*P(notC)=0.8*0.7*0.5=0.28 -- P(found by at least one test)= 1- P(not found by any test)=1-P(notA & notB & notC)=1-0.28=0.82
 expressions/394693: In the following example what does the [ mean and why are { } used after the = sign and why is the I between the two x's. [a,oo)= {xIx > a} (there is a line under the greater than sign, I do not know what the symbol means) My name is Dolly and my email is elkm@suddenlink.net1 solutions Answer 280078 by jrfrunner(365)   on 2011-01-14 13:09:37 (Show Source): You can put this solution on YOUR website!In the following example what does the [ mean and why are { } used after the = sign and why is the I between the two x's. [a,oo)= {xIx > a} (there is a line under the greater than sign, I do not know what the symbol means) My name is Dolly and my email is elkm@suddenlink.net -- in mathematics (and many other disciplines), there are short hand or short cuts for saying something. a "[" means that the value is included, a ")" means the value is not included "{}" is a way to say the set of numbers the "I" is really not an I, but a short line to imply the meaning "such that" -- so [a,oo) means all values between a and infinity including a but since we do not know what infinity is it is left unincluded. -- {xIx > a} this means the set of x numbers, such that x is greater than a. of course this statement is wrong since they are trying to define [a,oo) which includes "a". So the statement should look as [a,oo)= {xIx >= a}, its missing teh equal sign to show that it includes "a"
 Square-cubic-other-roots/394734: How do I cube (3 minus square root of 7)?1 solutions Answer 280061 by jrfrunner(365)   on 2011-01-14 12:09:58 (Show Source): You can put this solution on YOUR website!use the binomial expansion = (Cn,n)*+(Cn,1)b+...(Cn,0)* where Cnx= combinations= n!/[x!*(n-x)!] and comes from pascal triangle. Are you familiar with that? - in your case a=3 b= n=3
 Probability-and-statistics/394731: A pizza shop advertises that they have 8 toppings, and they sell large, medium, and small pizzas. On a small pizza, you must choose 3 different toppings. On a medium pizza, you must choose 4 different toppings, and on a large, you must choose 5 different toppings. How many different pizzas can they make? Choose the answer and explain the reason to choose your response 475 219 182 6571 solutions Answer 280059 by jrfrunner(365)   on 2011-01-14 11:56:56 (Show Source): You can put this solution on YOUR website!my mistake I should have used combinations instead of permutations since order does not matter small pizza: 8C3=336/6=56 medium pizza: 8C4=1680/24=70 large pizza: 8C5=6720/120=56 total pizzas= 56+70+56=182 == ignore below these answers do not make sense! -- for the small pizza there are 8P3=8*7*6=336 different types of small pizzas for the medium pizza there are 8P4=8*7*6*5=1680 for the large pizza there are 8P5=8*7*6*5*4=6720 so there should be 336+1680+6720=8736 different pizzas
 Probability-and-statistics/394616: Suppose that after 10 years of service, 40% of computers have problems with motherboards (MB), 30% have problems with hard drive (HD), and 15% have problems with both MB and HD. What is the probability that a 10-year old computer still has fully functioning MB and HD?1 solutions Answer 280057 by jrfrunner(365)   on 2011-01-14 11:47:04 (Show Source): You can put this solution on YOUR website!let MB=prob with motherboards let HD problems with hard drive P(problems with MB or HD)=P(MB U HD)=P(MB)+P(HD)-P(MB n HD)=0.4+.3-.15=.7-.15=.55 -- This means that P(no MB or HD)= 1-0.55=0.45
 Probability-and-statistics/394723: Sandy and Claude are playing a game in which there are 5 tiles in a bag, numbered 1 through 5. The game is played by the players taking turns pulling out a tile without replacing it. A player wins if they pull out the tile numbered "3". If Sandy goes first, what is the probability that she will win? choose the answer and explain the reason to choose your response 50% 45% 75% 60%1 solutions Answer 280056 by jrfrunner(365)   on 2011-01-14 11:36:46 (Show Source): You can put this solution on YOUR website!p(sandy wins/she goes first)=0.6 -- reasoning on her first try, she has 1/5 chance of getting the "3" tile and wins if she does not get the "3" tile, then clause has 3/4 of not getting the "3" tile since there are only 4 tles left and the game can continue. - On Sandy's second try, there are only 3 tiles left and for Sandy to get a second chance to win, she must of failed the first time 4/5 chance and Claude must of failed 3/4 chance and for Sandy to win in the second try she has 1/3 chance so Sandy can win on the second try with 4/5*3/4*1/3=1/5 -- If Sandy does not win of the second, she gets a third try if she failed on the first and Claude failed oh his first and sandy failed on her second and cluade failed on his second and finally Sandy tries a 3rd time. This can happen by Sandy failing on first 4/5 chance, Claude failing first 3/4 chance, sandy failing on second 2/3 chance and claude failing on his second with 1/2 chance or 4/5*3/4*2/3*1/2=1/5 after this there are no more tiles - So sandy wins by going first if she wins on the first try, or second try or 3rd try = 1/5+1/5+1/5=3/5=0.6
 Square-cubic-other-roots/394720: find the inverse of the function given. f(x)=3x+51 solutions Answer 280051 by jrfrunner(365)   on 2011-01-14 11:21:24 (Show Source): You can put this solution on YOUR website!switch x and y and solve for y -- y=3x+5 then the inverse is found by switching variables x=3y'+5 and solving for y' y'=(x-5)/3 this is the inverse
 Probability-and-statistics/394618: 3.Among employees of a certain firm, 70% know C/C++, 60% know Java, and 50% know both languages. What portion of programmers a. does not know Java? b. does not know Java and C/C++? c. knows C/C++ but not Java? d. knows Java but not C++? e. If someone knows Java, what is the probability that he/she knows C/C++? f. If someone knows C/C++, what is the probability that he/she knows Java? 1 solutions Answer 280050 by jrfrunner(365)   on 2011-01-14 11:18:18 (Show Source): You can put this solution on YOUR website!3.Among employees of a certain firm, 70% know C/C++, 60% know Java, and 50% know both languages. What portion of programmers a. does not know Java? =1-0.6=0.4 b. does not know Java and C/C++? know only C/C++=.7-.5=.2, know only java=.6-.5=0.1, know both=0.5 knows java or C/C++=.2+.5+.1=0.8 neither=1-.8=0.2 c. knows C/C++ but not Java? .7-.5=0.2 d. knows Java but not C++? .6-.5=0.1 e. If someone knows Java, what is the probability that he/she knows C/C++? P(C/java)=P(both)/P(java)=0.5/.6=5/6 f. If someone knows C/C++, what is the probability that he/she knows Java? P(java/C)=P(both)/P(C)=0.5/.7=5/7
 Probability-and-statistics/394621: 5.Three computer viruses arrive as an email attachment. Virus A damages the system with probability 0.4. Independently of it, virus B damages the system with probability 0.5. Independently of A and B, virus C damages the system with probability 0.2. What is the probability that the system gets damaged?1 solutions Answer 280049 by jrfrunner(365)   on 2011-01-14 11:08:17 (Show Source): You can put this solution on YOUR website!if the viruses are truly independent then probability that the system gets damaged= P(AUBUC)=P(A)+P(B)+P(C)-P(AnB)-P(anc)-P(bnc)+P(AnBnC)= 0.4+0.5+0.2-0.4*0.5-0.4*0.2-0.5*0.2+0.4*0.5*0.2=1.1-0.2-0.08-0.1+0.04 =0.76
 Linear_Equations_And_Systems_Word_Problems/394633: Explain how you know when a system has no solution or infinite solutions.1 solutions Answer 280046 by jrfrunner(365)   on 2011-01-14 10:58:10 (Show Source): You can put this solution on YOUR website!a system has no solution when the equations never meet or have no points of interception. - a system has infinite solutions when the equations are one and the same, they just look different
 absolute-value/394652: -3|x+5|=-91 solutions Answer 280042 by jrfrunner(365)   on 2011-01-14 10:52:17 (Show Source): You can put this solution on YOUR website!-3|x+5|=-9 == first isolate the absolute expression |x+5|=3 divide by -3 eliminate the absolute signs x+5=3 or x+5=-3 solve for x x=-2 or x=-8
 Geometry_Word_Problems/394674: 1)The hypothenuse of right triangle is 15cm. the sum of the legs is 21cm. Find the legs of triangle. 2)A lidles box is constructed from a square piece of tin by cutting a 10cm square from each corner and bending up the sides for the box. if the volume of the box is 1200cm^3,find the dimensions to the nearest tenth of centimetre.1 solutions Answer 280036 by jrfrunner(365)   on 2011-01-14 10:37:04 (Show Source): You can put this solution on YOUR website!1)The hypothenuse of right triangle is 15cm. the sum of the legs is 21cm. Find the legs of triangle. -- Given: c=15, a+b=21 thus a=21-b Pythagoream theorem: c^2=a^2+b^2 b=18/2=9 or b=24/2=12 Thus the legs of the triangle are a=21-b=21-9=12, b=9,c=15 === 2)A lidles box is constructed from a square piece of tin by cutting a 10cm square from each corner and bending up the sides for the box. if the volume of the box is 1200cm^3,find the dimensions to the nearest tenth of centimetre - The base of the box will be square and measure x-2*(10)=x-20 The volume of the box: length*width*height= (x-20)*(x-20)*10=1200 therefore (x-20)^2=120 x^2-40x+400=120 x^2-40x+280=0 use the quadratic formula x=(40-21.9)/2=9.05 or x=(40+21.9)/2=30.95 since the base has dimensions x-20 and x-20, x has to be greater than 20 so x=9.05 cannot be one of the answers. - Dimensions of the box length*width*height=30.95-20, 30.95-20,10 or 10.95,10.95,10
 Miscellaneous_Word_Problems/394690: Aki's Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by , where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle? The shop should build ___ bicycles.1 solutions Answer 280029 by jrfrunner(365)   on 2011-01-14 10:15:38 (Show Source): You can put this solution on YOUR website!Avg Cost/bike = -- This is a parabola with its "a" coefficient 0.1 being positive so the curve opens upward indicating that the vertex is a minimum. vertex is located at x=-b/(2a)= -(-0.4)/(2*0.1)=2, so the shop should build 200 bikes to minimize average cost - Another way to do this is to take the first derivative of the avg cost function this gives the instantenous slope and we want to find the extremas which occur when the instantenous slope=0 (also known as critical points) 0.2x-0.4=0 x=2 or 200 bikes since x is in hundreds of bikes. to determine if this is a minimum or maximum extrema, take the second derivative C"(x)=0.2 since this is positive at the critical point (and all points in this case) this means that it curves upward and the critical point is a minimum
 Graphs/394688: Find the x-intercepts and y-intercepts. 1 solutions Answer 280024 by jrfrunner(365)   on 2011-01-14 10:05:34 (Show Source): You can put this solution on YOUR website!Find the x-intercepts and y-intercepts. -- x intercepts occur when y=0 0=(x+6)*(x-8); x=-6 or x=8 (-6,0), (8,0) -- Y intercepts occur when x=0 =48 (0,48)
 Rate-of-work-word-problems/394478: A piece of work can be done in 48 days by 40 men. After 15 days, 16 men were transferred. In how many days can the remaining men finish the work?1 solutions Answer 280022 by jrfrunner(365)   on 2011-01-14 09:57:14 (Show Source): You can put this solution on YOUR website!A piece of work can be done in 48 days by 40 men. After 15 days, 16 men were transferred. In how many days can the remaining men finish the work? == 40 men can do the job in 48 days, this means that 40 men can do 1/48 of the job each hour - after 15 hours: 15/48 of the job is completed and 33/48=11/16 of the job incomplete - 16 men are transferred. That leaves 24 men to complete the job. each man worked at a rate of 1/(48*40) (assuming they all work at the same rate). So the remaining 24 men work at the rate of 24/(48*40)=1/80 - 11/16 of the job needs to be done by a crew of 24 working at a rate of 1/80 per hour. Job=rate *time or time =job/rate=(11/16)/1/80)=80*11/16=55hours
 Polygons/394503: The measure of an interior angle of a regular polygon is given which is 90. find the number of sides in each polygon1 solutions Answer 279917 by jrfrunner(365)   on 2011-01-13 21:25:45 (Show Source): You can put this solution on YOUR website!It is known that The sum of the interior angles of a "n" sided polygon is =(n-2)*180 -- assuming that all the interior angles are equal, then a single interior angle will measure (n-2)*180/n == Since you state that the interior angle is 90 then (n-2)*180/n=90 180n-360=90n 90n=360 n=4
 Travel_Word_Problems/389208: The police car is chasing the getaway car of bank robbers 7 1/2 km ahead. If the speed of the police car is 5 kph more than that of the getaway car, how long will it take the police car to overtake the getaway car?1 solutions Answer 275769 by jrfrunner(365)   on 2010-12-29 11:03:46 (Show Source): You can put this solution on YOUR website!d-distance to make up= 7.5 km r=speed differential= 5kph -- d=r*t or t=d/r == t=7.5/5=1.5 hours or 90 minutes
 Travel_Word_Problems/389044: a and b are two station 300 km apert.Two train start simultaneously from a and b, each to the opposite station .The train from a reaches b 9 hours , the train from b reaches a 4 hours after they meet, Find the rate at which each train travels? slove the problem. 1 solutions Answer 275555 by jrfrunner(365)   on 2010-12-28 10:51:24 (Show Source): You can put this solution on YOUR website!The trains meet somewhere between station a and station b -- let train 1 "from" station a let train 2 "from" station b let d1=distance train 1 travels after meeting train 2 let d2=distance train 2 travels after meeting train 1 let r1=rate of train 1 let r2=rate of train 2 let t=time when trains meet distance =rate * time or d=r*t == from meeting point to station a: train 1 has travelled r1*t and train 2 will travel 4 hours to get to station a or r2*4 so... r1*t = r2*4 -- likewise r2*t=r1*9 -- solving for t: r2*4/r1=t and r1*9/r2=t 4*r2/r1=9*r1/r2 4r2^2=9*r1^2 (cross multiply) 2*r2=3*r1 2*r2/3=r1 -- we also know that the total distance is 300, so d1+d2=300 4*r2+9*r1=300 4*r2+9*(2*r2/3)=300 4*r2+6r*2=300 10*r2=300 r2=30 r1=2*r2/3=20
 Geometry_Word_Problems/388891: With something along this line for a picture A capacitor is a basic component of televisions, radios, electronic toys, computers, and almost all electric devices. Many old radios use an adjustable capacitor to tune in different stations. 8. What do you need to know about the front upper plate and the front lower plate in order to show that any upper plate and any lower plate lie in parallel planes? Explain your reasoning.1 solutions Answer 275332 by jrfrunner(365)   on 2010-12-27 11:10:03 (Show Source): You can put this solution on YOUR website!8. What do you need to know about the front upper plate and the front lower plate in order to show that any upper plate and any lower plate lie in parallel planes? Explain your reasoning. == I suppose you need to know that the distances in all places between the front upper plate and the front lower plate are always the same, this would insure that they lie in parallel plates.
 Linear-systems/388892: A tank can be fully filled with water using a pipe that fills 20 litres in a minute. A bigger pipe that can fill 25 litres in a minute will take one minute less to fill the same tank. How many minutes does the smaller pipe take to fill the tank?1 solutions Answer 275330 by jrfrunner(365)   on 2010-12-27 11:04:57 (Show Source): You can put this solution on YOUR website!let t=time for smaller pipe to fill tank let t-1 =time for larger pipe to fill tank let c=tank capacity == Given small pipe rate = 20 liters per minute large pipe rate=25 liters per minute == use formula: tank capacity=rate * time -- small pipe; tank capacity c=20*t large pipe: tank capacity c=25*(t-1) -- since tank capacity is the same for both pipes 20*t=25*(t-1) 20*t=25*t-25 25=5*t 5=t -- answer: it takes the small pipe 5 minutes to fill the tank
 Probability-and-statistics/388907: You select at random 2 numbers from 1 to 8. What is the probability that the sum of two numbers selected is 3? Answer should be as a common fraction.1 solutions Answer 275326 by jrfrunner(365)   on 2010-12-27 10:27:04 (Show Source): You can put this solution on YOUR website!The answer depends on whether you are selecting with replacement of the selected numbers or without replacement of the selected numbers. === In order for the two numbers to sum to 3, the numbers selected must be 1 and 2. -- Without replacement: Probability of selecting 1 and 2=P(1,2)+P(2,1)=1/8*(1/7)+1/8*(1/7)=2/56=1/28 -- with replacement: P(1,2)+P(2,1)=1/8*(1/8)+1/8*(1/8)=2/64=1/32
 Travel_Word_Problems/387876: A bicyclist leaves Bay Shore traveling at an average speed of 12 miles per hour. Three hours later, a car leaves Bay Shore, on the same route, traveling at an average speed of 30 miles per hour. How many hours after the car leaves Bay Shore will the car catch up to the cyclist?1 solutions Answer 274228 by jrfrunner(365)   on 2010-12-19 19:56:15 (Show Source): You can put this solution on YOUR website!car will catch up to the bike when the distance for the car = distance for the bike -- distance =rate * time -- distance bike= head start distance + distance after car leaves = 12mph*3 hours + 12mph*t = 36+12t distance car=30mph * t -- set distance bike=distance car 36+12t=30t 36=18t 36/18=2=t -- answer: the car will catch the bike in 2 hours after the cars leaves.
 Surface-area/386631: what is the surface area of cylinder with a radius of 3in and a height of 5in in terms of pi1 solutions Answer 273330 by jrfrunner(365)   on 2010-12-15 16:35:21 (Show Source): You can put this solution on YOUR website!Surface area for cylinder: bottom+side+top Bottom area=pi*r^2 Top area=pi*r^2 side area= 2*pi*r*h -- if r=3in, h=5in then surface area= bottom+top+side =pi*(3)^2+pi*(3)^2+2*pi*(3)*(5) =18*pi+30*pi=48*pi
 Problems-with-consecutive-odd-even-integers/386642: the greater of two consecutive odd integers is 7 greater than twice the lesser. Find the integers.1 solutions Answer 273327 by jrfrunner(365)   on 2010-12-15 16:28:44 (Show Source): You can put this solution on YOUR website!the greater of two consecutive odd integers is 7 greater than twice the lesser. Find the integers -- Let the two integers be X and (X+2) -- Given: greater odd=7+2lesser X+2=7+2X 2-7=2X-X -5=X -- answer: Lesser: X=-5 Greater: X+2=-5+2=-3 -- verify -3=7+2*(-5)
 Sequences-and-series/371414: Find the sum of the first twenty terms of the sequence 3,5,7,........1 solutions Answer 264616 by jrfrunner(365)   on 2010-11-15 16:40:35 (Show Source): You can put this solution on YOUR website!In the sequence you provide each number changes by an "constant" value. This is known as an arithmetic sequence -- The change, or is the difference between any two values, so in this case =2 -- For an arithmetic sequence, the nth term = and for an arithmetic series, its sum is defined as the average value times the number of terms or Sum= == in the sequence you provide, =3 and the last term -- The sum = average value * n =