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# Recent problems solved by 'jrfrunner'

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 Probability-and-statistics/395679: Two girls, Anna and Cathy, attempt independently to solve a problem. The probability of Anna solving it is 0.60 and the probability of Cathy solving it is 0.30. Find the probability that only one of them will be able to solve it.1 solutions Answer 280800 by jrfrunner(365)   on 2011-01-17 11:41:48 (Show Source): You can put this solution on YOUR website!let p(A)=prob Anna solves the problem let p(C)=prob Cathy solves the problem let p(nA)=prob Anna does not solve the problem let p(nC)=prob Cathy does not solve the problem -- Given P(A)=0.6, P(C)=0.3 and P(A), P(C) are independent -- P(nA)=1-P(A)=0.4 and P(nC)=0.7 -- Find the probability that only one of them will be able to solve it. =P(A and nC)+P(nA + C) =P(A)P(nC)+P(nA)P(C) by independence =0.6*0.7+0.4*0.3=0.42+0.12=0.54
 Linear-systems/395672: What does the y-intercept represent in a linear equation and a word problem?1 solutions Answer 280781 by jrfrunner(365)   on 2011-01-17 11:19:22 (Show Source): You can put this solution on YOUR website!y intercept represent the value of y when the independent x=0. If a word problem deals with a variable x such that it begins with 0, such as money or time and it cannot be negative, the y intercept represent the y value at the start or beginning when x=0.
 Probability-and-statistics/395670: In normal distributions, if P(X < k) = 0.50, then k is the median of the distribution. True False 1 solutions Answer 280780 by jrfrunner(365)   on 2011-01-17 11:15:57 (Show Source): You can put this solution on YOUR website!true this is true whether the distribution is normal or not, the median is the point where 50% of the distribution is below it.
 Polynomials-and-rational-expressions/395665: i need help with this word problem. It deals with Multiplying a Polynomial by a Monomial. LaTanya's modulat office is square. her office in th company's new building will be 2 feet shorter in one direction and 4 feet longer in the other. a. write expression for the dimenstions of LaTanya's new office b. Write a polynomial expression for the area of her new office. c.suppose her office is presently 9 feet by 9 feet. will her new office be bigger or smaller then her old office and by how much? explain.1 solutions Answer 280778 by jrfrunner(365)   on 2011-01-17 11:11:43 (Show Source): You can put this solution on YOUR website!Given: Her office is square let s=one side of her square office -- Given: new office is s-2 by s+4 a. write expression for the dimenstions of LaTanya's new office (s-2) by (s+4) b. Write a polynomial expression for the area of her new office. Area=(s-2)*(s+4)=s^2+2s-8 c.suppose her office is presently 9 feet by 9 feet. will her new office be bigger or smaller then her old office and by how much? explain. Current office: area=9x9=81 sq ft new office: area=9^2+2*9-8=91 sq ft new office is 10 sq ft bigger
 Radicals/395654: What is the solution set of the equation ? [Show work.]1 solutions Answer 280774 by jrfrunner(365)   on 2011-01-17 10:59:33 (Show Source): You can put this solution on YOUR website!square both sides x+1=(x-1)^2=x^2-2x+1 0=x^2-3x=x(x-3) x=0 or x=3 -- validate by checking each value on orginal equation x=0: 1=-1 this is not true so x=0 is not a solution - x=3 2=3-1=2 check - so x=3 is the solution
 Numbers_Word_Problems/395635: A boy said I have as many brothers as i have sisters.Then his sister said i have double the number of brothers as i have sistes.Find the number of brothers and sisters.1 solutions Answer 280771 by jrfrunner(365)   on 2011-01-17 10:49:05 (Show Source): You can put this solution on YOUR website!let B=total boys, G=total girls boy's criteria: equal number of brothers and sisters girl's criteria: twice as many brothers as sisters - if B=1 and G=1, this does not satify the conditions if B=2 and G=1 satisfies boy's criteria but not sister's if B=2 and G=2 does not satify the boy's criteria but satisfies sister's if B=3 and G=2 satisfies boy's criteria but not sister's if B=3 and G=3 niether condition satisfied if B=4 and G=2 neither condition satisfied if B=4 and G=3 satisfies both conditions
 Miscellaneous_Word_Problems/395556: Apples are collected in a basket for six people. One third, one fourth, one eighth, and one fifth are given to four people. The fifth Person gets ten apples, leaving one for the sixt. Find the original number of apples in the basket.1 solutions Answer 280767 by jrfrunner(365)   on 2011-01-17 10:31:17 (Show Source): You can put this solution on YOUR website!Apples are collected in a basket for six people. One third, one fourth, one eighth, and one fifth are given to four people. The fifth Person gets ten apples, leaving one for the sixt. Find the original number of apples in the basket. -- let x=number of apples x=x/3+x/4+x/8+x/5+10+1 x-x/3-x/4-x/8-x/5=11 120x-40x-30x-15x-24x=11*120 11x=11*120 x=120
 Quadratic_Equations/395572: Aki's bicycle designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by C(x) = 0.1x^2 - 1.6x + 8.78, where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bucycle? The shop should build ___ bicycles? 1 solutions Answer 280760 by jrfrunner(365)   on 2011-01-17 10:20:29 (Show Source): You can put this solution on YOUR website!Problem was solved already 394690
 Permutations/395385: Sarah decided to try telemarketing. She calls people from 3pm to 9pm. Marley has a 15% chance of being called during this time. If Marley eats dinner from 6:6:30, how likely is it that she'll have a conversation with Sarah during this time? 1 solutions Answer 280624 by jrfrunner(365)   on 2011-01-16 18:14:53 (Show Source): You can put this solution on YOUR website!let A=Marley is called during 3pm to 9pm let B=Sarah calls someone during 6pm to 6:30pm -- Given P(A)=0.15 --- P(B)=30/360 =1/12 since there are 30 minutes during the 6hours that he can be called. - Need to know P(AnB) if we assume A & B are independent then P(AnB)=P(A)*P(B)=0.15*1/12=0.0125
 Quadratic_Equations/395421: If the numerical value of the area of a rectangle is 19 more than 2 times the perimeter, and the length is 2 more than the width, what is the width? Area = L * W 2x + 19 w = X l = X + 2 X(X + 2) = 2x + 19 ? x^2 + 2x = 2x + 19 + x + 2 1 solutions Answer 280616 by jrfrunner(365)   on 2011-01-16 17:51:42 (Show Source): You can put this solution on YOUR website!known: Area=L*W Perimeter =2*(L+W) -- given : A=2P+19 or A=4*(L+W)+19 and L=2+W -- set both expression of area equal to each other L*W=4L+4W+19 (2+W)*W=4*(2+W)+4W+19 substitute L=2+W 2W+W^2=8+8W+19 W^2-6W-27=0 (W-9)(W+3)=0 so W=9 or W=-3 measurements must be positive so eliminatte W=-3 solution, W=9 -- L=2+W=2+9+11 == validate the answer by substituting back into Area equations A=L*W=11*9=99 A=4*(11+9)+19=80+19=99 check
 Travel_Word_Problems/395422: a salesperson purchased a car that avg 25mpg in the city and 40 mpg on highway. A recent sales trip that covered 1800 miles required 51 gal of gas. Assuming the advertised mileage estimates were correct, how many miles were driven in the city?1 solutions Answer 280615 by jrfrunner(365)   on 2011-01-16 17:40:02 (Show Source): You can put this solution on YOUR website!you have two unknowns: C=gallons used in city driving and H=gallons used in highway driving so you will need two equations to solve the two unknowns -- eq1 gallons used: C+H=51 eq2 miles driven: 25*C+40*H=1800 - solve eq1 for H: H=51-C and substitute in eq2 25*C+40*(51-C)=1800 solve for C 25C-40C+2040=1800 2040-1800=15C C=240/15=16gallons used -- they want to know how many miles were driven in the city 25*C=25*16=400 miles
 Miscellaneous_Word_Problems/395291: betty has \$2.20 in dimes and quarters. If the number of dimes is 1/4 the number of quarters, how many dimes does she have.1 solutions Answer 280551 by jrfrunner(365)   on 2011-01-16 13:01:27 (Show Source): You can put this solution on YOUR website!you have two unknowns d=number of dimes and q=number of quarters so you need two equations to find the two unknowns -- given eq1: d=1/4q or 4d=q eq2: 0.1d+0.25d=2.20 - multiply eq2 by 100 to eliminate decimals 10d+25d=220 10d+25(4d)=220 substitute 4d=q 110d=220 d=220/110=2 or 2 dimes since q=4d then 8 quarters
 Linear-equations/395324: what is the domain of p(x)=x^2+2 thank you1 solutions Answer 280550 by jrfrunner(365)   on 2011-01-16 12:52:58 (Show Source): You can put this solution on YOUR website!the domain = all possible input values of x - Any values of x that make the function, p(x) undefined are not allowed. for instance if p(x)=1/(x-3) then x=3 is not allowed because x=3 makes P(3) undefined. - since no values of x, makes the function. p(x) undefined, then all real values of x are allowed as the domain.
 Polynomials-and-rational-expressions/395322: A long distance trucker traveled 80 miles in one direction during a snow storm. The return trip in rainy whether was accomplished at double the speed and took 2 hours less time. Find the speed going?1 solutions Answer 280549 by jrfrunner(365)   on 2011-01-16 12:50:33 (Show Source): You can put this solution on YOUR website!remember the relationship distance=rate*time or d=rt - going: 80 miles at speed r and time t 80=rt coming: 80 miles at speed 2r and time t-2 80=2r*(t-2) or 40=r(t-2)=rt-2r -- 80=rt and 40=rt-2r 40=80-2r 2r=40 r=20 this is the going speed 20mph
 Radicals/395243: $\sqrt[4]{7}\cdot \sqrt[2]{6}$ Use radical exponents to write $\sqrt[4]{7}\cdot \sqrt[2]{6}$ as a single radical expression.1 solutions Answer 280546 by jrfrunner(365)   on 2011-01-16 12:39:12 (Show Source): You can put this solution on YOUR website!already answered 395247
 Trigonometry-basics/395311: Please help me solve this equation: (cos^2 Alpha / csc^2 Alpha) + cos^4 Alpha = cos^2 Alpha Thanks1 solutions Answer 280544 by jrfrunner(365)   on 2011-01-16 12:37:12 (Show Source): You can put this solution on YOUR website!understand that csc(a)=1/sin(a) -- work with the left hand of the equation to get the right hand side = substitute csc(a)=1/sin(a) = invert = factor out a cos^2(a) = indetity
 Trigonometry-basics/395282: I couldn't find the proper place to submit this question, because you do not have a pre-calculus section on your website. Hopefully you can still answer this question. (9x^2-24x-57)/(x+1)(x+3)(x-5) It's a partial fraction decomposition problem. I haven't done any of these in a while, so I can't remember what to do with (9x^2-24x-57). Thanks1 solutions Answer 280539 by jrfrunner(365)   on 2011-01-16 12:14:23 (Show Source): You can put this solution on YOUR website!set up the following equation - next multiply both sides by the common denominator (x+1)(x+3)(x-5) - - at this point you can expand out all terms, then combined common terms and set correponding parts equal yielding a system of equation to solve for A,B and C but another alternative is to select "convenient values of x and solve -- x=-1: 9+24-57=-12A or A=-24/-12=2 x=-3: 81+72-57=72B or B=96/72=4/3 x=5: 225-120-57=48C or C=48/48=1 == if I did my math correctly
 Quadratic_Equations/395287: A football is kicked in the air and lands on the ground 32m from where it was kicked. If the maximum height reached by the ball is 14m, determine the transformational form of the quadratic function representing the path of the football while it is in the air.1 solutions Answer 280536 by jrfrunner(365)   on 2011-01-16 11:52:28 (Show Source): You can put this solution on YOUR website!You need to put the formula in standard form y=a(x-h)^2+k (h,k) is the vertex - you have three points. the origion (0,0) the end (32,0) and its middle (16,14) which is the vertex - let's use input the vertex in the standard formula y=a(x-16)^2+14 - lets use the origin (0,0) to solve for "a" 0=a(-16)^2+14 0=256a+14 a=-14/256= - 7/128 -- substitute a into formula y=-7/128*(x-16)^2+14
 Trigonometry-basics/395283: Hopefully you can answer this, I didn't seem to be able to locate a pre-calculus section on your website. The question is: Find the 6 trig ratios for the angle whose terminal side contains the point (-2,5). Then find the angle measure. I'm basically clueless on this problem, so any help would be appreciated. Thanks1 solutions Answer 280531 by jrfrunner(365)   on 2011-01-16 11:36:57 (Show Source): You can put this solution on YOUR website!the point (-2,5) makes a right triangle whose hypotenus is -- the six trig ratios are; cos t = adjacent/hypotenus=-2/sqrt(29) sin t = opposite/hypotenus = 5/sqrt(29) tan t = opposite/adjacent= 5/-2 cot t = adjacent/opposite = -2/5 sec t = hypotenus/adjacent=sqrt(29)/2 csc t = hypotenus /opposite = sqrt(29)/5 The angle is using anyone of these and finding the arc value, for simplicity i'll use tan t=-2.5 t=arc tan(-2.5)=180-arc tan(2.5)=180-68.2=111.8
 Radicals/395247: $\sqrt[4]{7}\cdot \sqrt[2]{6}$ Use radical exponents to write $\sqrt[4]{7}\cdot \sqrt[2]{6}$ as a single radical expression.1 solutions Answer 280529 by jrfrunner(365)   on 2011-01-16 11:22:17 (Show Source):
 Probability-and-statistics/395259: A chemical company produces a substance composed of 98% cracked corn particles and 2% zinc phosphide for use in controlling rat population in sugarcane field. Production must be carefully controlled to maintain the 2% zinc phosphide because too much zinc phosphide will cause damage to the sugarcane and too little will be ineffective in controlling the rate population. Records from past production indicate that the distribution of the actual percentage of zinc phosphide present in the substance is approximately mound-shaped with a mean of 2.0% and standard deviation o 0.08%. a) If the production line is operating correctly, approximately what proportion of batches from a days' production will contain less than 1.84% of zinc phosphid? b) Suppose one batch chosen randomly actually contains 1.80% zinc phosphide. Does this indicate that there is too little zinc phosphide in today's production? Explain your reasoning.1 solutions Answer 280526 by jrfrunner(365)   on 2011-01-16 11:10:49 (Show Source): You can put this solution on YOUR website!I presume that by distribution being mound-shaped that implies that its normally distributed. == a) If the production line is operating correctly, approximately what proportion of batches from a days' production will contain less than 1.84% of zinc phosphid? -- let x=% of zinc phosphid Assuming Normally distribution with mean=2.0 and standard deviation=0.08 P(x<1.84)=P(z<(1.84-2)/.08)=P(z<-2.0)=0.02275 or 2.3% of batches == b) Suppose one batch chosen randomly actually contains 1.80% zinc phosphide. Does this indicate that there is too little zinc phosphide in today's production? Explain your reasoning. P(x<1.80)=p(z<-2.5)=0.00621 or 0.62% This is highly unlikely from a normal distribution centered at 2.0 and std dev=0.08. This implies that the sample was obtained from a distribution centered lower than 2.0
 Probability-and-statistics/395262: Looking for help with the following: Provide the p-value for a left-tailed one sample hypothesis test (z test) where the test statistic is -2.6. You must show your work or provide the Excel formula that you used. Thanks!1 solutions Answer 280523 by jrfrunner(365)   on 2011-01-16 10:53:43 (Show Source): You can put this solution on YOUR website!this was answered already using excel =NORMSDIST(-2.6)
 Probability-and-statistics/395263: Looking for help with the following: Using the p-value from Question #1, would you accept or reject the null hypothesis at the 95% confidence level? Why or why not? Note: Question #1 is: Provide the p-value for a left-tailed one sample hypothesis test (z test) where the test statistic is -2.6. You must show your work or provide the Excel formula that you used. Thanks!1 solutions Answer 280521 by jrfrunner(365)   on 2011-01-16 10:43:31 (Show Source): You can put this solution on YOUR website!the pvalue for z test statistic of -2.6 is 0.00047 -- Since the pvalue is less than the significance level 0.05, then reject Ho. -- The pvalue represent the probability that the test statistic, assuming Ho is true deviated from Ho by pure chance. Since this probablity is small, you conclude that it is evidence that it does not come from Ho.
 Probability-and-statistics/395264: If you are performing a one sample hypothesis test of the mean and the standard deviation of the population is unknown, do you use a t-test or a z-test? 1 solutions Answer 280520 by jrfrunner(365)   on 2011-01-16 10:37:10 (Show Source): You can put this solution on YOUR website!the appropriate test "always" when the population variance is unknown is to use a t-test. although as the samples sizes get larger and larger, the t-test and Z-test will converge but this does not happen (based on my experience) until the sample size is greater than 100. -- The other wrinkle is that if the sample size is small, and the population variance is unknown, you can only use the t-test if the sample comes from a normal distribution as the central limit theorem can't help you with small samples.
 Probability-and-statistics/395265: Choose the correct decision rule for a “right-tailed” t-test where the critical value is 2.05. a. Reject H0 if t < 2.05 b. Reject H0 if z >2.05 c. Reject H0 if t > 2.05 d. Reject H0 if t < .05 1 solutions Answer 280518 by jrfrunner(365)   on 2011-01-16 10:30:11 (Show Source): You can put this solution on YOUR website!the right tail test implies that you want to reject Ho the null, if your test statistic exceeds the critical value -- c. Reject H0 if t > 2.05
 Equations/395095: how to write 4/d without a fraction bar1 solutions Answer 280402 by jrfrunner(365)   on 2011-01-15 18:38:40 (Show Source):
 Rational-functions/395080: how do you solve? 1 solutions Answer 280401 by jrfrunner(365)   on 2011-01-15 18:37:37 (Show Source): You can put this solution on YOUR website!first, isolate the radical -- next square both sides to eliminate the radical multiply both sides by 4 gather terms on one side 0=(x-5)*(x+3) factor x=5, or x=-3 -- verify by substituting the answers into original equation x=5: 2*3-1=5 check x=-3: 2-1=1 does not equal -3 so x=-3 is not a solution -- the answer is x=5
 Miscellaneous_Word_Problems/395086: A car dealership interviewed every driver who came onto their lot on Tuesday. This produced the following results: there were 34 people who owned trucks and 54 people who owned cars. If 12 people owned both a truck and a car and 8 people owned neither, how many people were interviewed? 1 solutions Answer 280395 by jrfrunner(365)   on 2011-01-15 18:17:29 (Show Source): You can put this solution on YOUR website!let T = number truck owners let C=number of car owners let B=number who own both let N=number who own neither === given T=34, C=54, B=12, N=8 Total interviewed =34+54-12+8=84 -- subtract B=12 because in counting T and C the B is counted twice.
 Unit_Conversion_Word_Problems/394819: the latent heat of fusion for ice is 79.8 cal/gram. how much ice can we melt with 1000 calories? what are the key pieces to solve. im lost on thermodynamics !!!! PLEASE HELP!!!!1 solutions Answer 280160 by jrfrunner(365)   on 2011-01-14 18:17:03 (Show Source): You can put this solution on YOUR website!when solving these types of equations, look at what you have and what you need. -- you have an identiy 79.8 calories/1gram , this identity can be written as 1gram/79.8calories. It can be used either way depending on what you need. -- you have 1000 calories and want to find grams so set up your expression notice that I used this form of the identity so I could cross cancel the units and leave me with grams. -- =12.53 grams
 Radicals/394679: Simplify, assuming that all variables are positive numbers: sqrt(8a^9/b^3 ), Thank you so much in advance!1 solutions Answer 280159 by jrfrunner(365)   on 2011-01-14 18:10:19 (Show Source): You can put this solution on YOUR website! -- break the inside of the square root expression into perfect squares -- factor out the perfect squares
 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