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 Rate-of-work-word-problems/329354: Anne, Lucy, and Phoebe can do a piece of work in 2 2/3 days when they work together. If Anne and Phoebe work for 3 days and Lucy for 2 days, they will finish the work. If Anne works for 2 days and Lucy and Phoebe each 1 day, the work will be only 13/24 finished. In how many days can each do the work alone?1 solutions Answer 236049 by josmiceli(9686)   on 2010-08-06 03:00:40 (Show Source): You can put this solution on YOUR website!In these kind of problems, you add the RATES that each works to get their rates working together. (portion of job completed by #1)/(time to complete that portion) + (portion of job completed by #2)/(time to complete that portion) + (portion of job completed by #3)/(time to complete that portion) = (portion of job completed by all working together)/(time to complete that portion) Let r[a] = Anne's rate of working in (portion of job)/(days to do that portion) Let r[l] = Lucy's rate of working in (portion of job)/(days to do that portion) Let r[p] = Phoebe's rate of working in (portion of job)/(days to do that portion) given: (1) (note that 1 means the whole job) I can also say: equals Anne's rate x days worked = portion of job done by her equals Lucy's rate y days worked = portion of job done by her equals Phoebe's rate z days worked = portion of job done by her given: (2) (1 means whole job) (3) ------------------------------- The problem wants to find rate for each = (1 job)/(time to do 1 job) There are 3 equations and 3 unknowns, so it's solvable First, I divide both sides of (2) by (2) (2) Now, I subtract this from (1) (1) (2) ---------------------------------------------- Now I put this value back into (1) (1) (1) (1) Now I subtract this from (3) (3) (1) --------------------------------- Now I put and back into (2) (2) (2) (2) Anne can do the job in 6 days working alone Lucy can do the job in 8 days working alone Phoebe can do the job in 12 days working alone check answer: (3) (3) OK
 Complex_Numbers/329362: how do you begin this... Express the answer in the form a + bi, where a and b are real numbers. I know you use the foil method (3 + 3i) (4 – i) 1 solutions Answer 236043 by josmiceli(9686)   on 2010-08-06 01:42:04 (Show Source): You can put this solution on YOUR website! Note that answer
 Word_Problems_With_Coins/329235: Linda has six more quarters than nickles . If she has n nickles, what is the total value in cents of her quarter and nickles?1 solutions Answer 235994 by josmiceli(9686)   on 2010-08-05 19:27:04 (Show Source): You can put this solution on YOUR website!Let = number of quarters she has Let = number of nickels she has given: (1) ------------------ = value of quarters in cents = value of nickels in cents From (1): The total value in cents of the nickels and quarters is 30 times the number of nickels plus 150 cents
 Evaluation_Word_Problems/329189: A chef has containers of heavy cream that are 40% butterfat and light cream that are 20% butterfat. How much heavy cream must be added to a 1000 ml container of light cream to produce a mixture that is 36% butterfat? Briefly explain your answer. 1 solutions Answer 235890 by josmiceli(9686)   on 2010-08-05 13:23:02 (Show Source): You can put this solution on YOUR website!Let = ml of heavy cream that needs to b added given: Butterfat in heavy cream = ml Amount of 20% light cream = ml Butterfat in ml of light cream= ml -------------------- In words: (total ml of butterfat I end up with)/(total ml of mixture) = .36 4000 ml or 4 liters of heavy cream must be added check answer: OK
 Linear_Equations_And_Systems_Word_Problems/329182: Solve each system by addition: 4x+3= -3y -x/7 + 4y/21= 1 / are fractions I know the answer is (-3,3) can you show me how to do that?1 solutions Answer 235879 by josmiceli(9686)   on 2010-08-05 12:45:32 (Show Source): You can put this solution on YOUR website!(1) (2) first, I will get (1) into the same form as (2) (1) Then I multiply both sides of (2) by (2) Now I multiply both sides of (1) by (1) Now I multiply both sides of (2) by (2) Now I add (1) and (2) Then I substitute this result back into (1) (1) The answer is (-3,3)
 Travel_Word_Problems/329025: An airplane can travel 450 miles into the wind in 2 hours and 25 minutes. This plane takes the same time to travel 630 miles with the wind. Find the speed of the airplane without any wind.1 solutions Answer 235746 by josmiceli(9686)   on 2010-08-05 00:12:45 (Show Source): You can put this solution on YOUR website!Let = wind speed Let = speed of plane without wind = speed of plane flying into wind = speed of plane flying with the wind given: This is 2 equations with 2 unknowns so it's solvable ------------------- Divide both sides of each by add the equations ------------------- mi/hr and, since mi/hr The speed of the plane without wind is 223.445 mi/hr check: close enough and OK
 Miscellaneous_Word_Problems/328726: A student opens a mathematics book to two facing pages. The product of the page numbers is 2352. Find the page numbers. The first page is? and The second page is?1 solutions Answer 235510 by josmiceli(9686)   on 2010-08-04 08:36:24 (Show Source): You can put this solution on YOUR website!Call the first page The 2nd page will be given: Complete the square: Take the square root of both sides The pages are 48 and 49 check: OK
 Linear-systems/328606: This is the question that is on my homework... Select the graph from the choices below that is a solution to the following system of equations: -3x +4y = 12 6x - 8y =16 I Cant put graphs up on here so can you please tell me how to solve this question and give somewhat of an algorithem on how you do these steps? Thank you for your Time.1 solutions Answer 235413 by josmiceli(9686)   on 2010-08-03 20:51:41 (Show Source): You can put this solution on YOUR website!Locate the x and y intercepts for both equations x-intercept: solve for ----------- y-intercept: solve for The intercepts are at (-4,0) and (0,3) drw a straight line through these points ------------- Now repeat the process for and draw a straight line through the points
 Polynomials-and-rational-expressions/328438: The speed of train A is 8mph slower than the speed of train B. Train A travels 230 miles in the same time it takes train B to travel 270 miles. Find the speed of both trains. Thank you1 solutions Answer 235411 by josmiceli(9686)   on 2010-08-03 20:42:28 (Show Source): You can put this solution on YOUR website!You need 2 equations: and You are given that , so Multiply both sides by and, since The speed of train A is 46 mi/hr The speed of train B is 54 mi/hr check answers: hrs and hrs OK
 Radicals/328577: Does anyone know how to set this equation up ans simplify in the end? I am lost!1 solutions Answer 235397 by josmiceli(9686)   on 2010-08-03 19:51:49 (Show Source): You can put this solution on YOUR website! answer Since square roots can be either (+) or (-), there are other valid solutions also: 2nd solution and 3rd solution and 4th soution
 Radicals/328580: Stumped once again!!! 2x^2-5x-2 =0 How is the quadratic formula used to solve this equation? Anyone know?1 solutions Answer 235391 by josmiceli(9686)   on 2010-08-03 19:32:01 (Show Source): You can put this solution on YOUR website!The quadratic formula for finding roots is You need to know what a, b, and c refer to This formula assumes that the equation is in the form Your equation is already in this form: plugging in the numbers: I'm guessing that should be and not . That would make the solution and These are the 2 roots. If for real, then stick with
 Equations/328525: write the equation of the line that is perpendicular to the line y = 2/3x - 7 and passes through the point (4,1) the answer i got is 3x+2y=14 i want to see if this is right1 solutions Answer 235313 by josmiceli(9686)   on 2010-08-03 15:48:28 (Show Source): You can put this solution on YOUR website!The slope would be -(1/slope of line) OK
 Sequences-and-series/328501: I need to find the sum of the first n terms of the g.p. 4,12,36... and find the least value of n for which the sum is greater than 500,000. I know that r = 3 and a = 4 but then I am stuck.1 solutions Answer 235309 by josmiceli(9686)   on 2010-08-03 15:41:29 (Show Source): You can put this solution on YOUR website!the formula is: I'll find out when the sum is greater than 500000 Multiply both sides by I can take the log of both sides If , the left side is close to , so Putting this back into formula, The next whole number for is I think that would put over seems to be too small
 Money_Word_Problems/328397: Mrs. Goodman invested half of her money at 7% interest in a bank and the other half at 8% interest per year. Her annual income from the two investments was \$7,500.00. How much did she invested in each?1 solutions Answer 235249 by josmiceli(9686)   on 2010-08-03 11:16:55 (Show Source): You can put this solution on YOUR website!Let = amount invested in each bank She invested \$50,000 in each
 Percentage-and-ratio-word-problems/328420: out of 561 children, 98 live in a single family home. what percentage is that? thank you1 solutions Answer 235246 by josmiceli(9686)   on 2010-08-03 11:11:46 (Show Source): You can put this solution on YOUR website!percentage means "per one hundred" Let In this equation is the percent that is of Solve for Use calculator
 test/328422: chad drove three times as fast as katy pedaled. In fact chad drove 90 miles in 2 hrs less than it took katy to pedal 40 miles how fast did each of them travel? How long did they travel? 1 solutions Answer 235245 by josmiceli(9686)   on 2010-08-03 11:05:21 (Show Source): You can put this solution on YOUR website!given: Katy: Chad: By substitution: mi/hr and mi/hr How long did they travel? hrs and hrs Katy traveled for 8 hrs Chad traveled for 6 hrs
 Travel_Word_Problems/328411: An airplane took 2.5 hours to fly 625 miles with the wind. It took 4 hours and 10 minutes to make the return trip against the same wind. Find the wind speed and the speed of the plane in still air. (Show all work) 1 solutions Answer 235244 by josmiceli(9686)   on 2010-08-03 10:55:53 (Show Source): You can put this solution on YOUR website!You need 2 equations, one going with the wind and one going against the wind Let = wind speed Let = speed of plane in still air given: with the wind: hrs mi against the wind: mi -------------- This is 2 equations with 2 unknowns, so it's solvable (1) (2) Multiply both sides of (1) by and add (1) and (2) I can't find my calculator, so you can do it
 logarithm/328312: antilog(8.4)=I waht is the answer to this one 1 solutions Answer 235150 by josmiceli(9686)   on 2010-08-03 03:44:35 (Show Source): You can put this solution on YOUR website! You can look up on calculator
 Travel_Word_Problems/328336: Two planes leave Newark Airport at the same time. The rate of speed of the northbound plane is 100 mils per faster than that of the Southbound plane. At the end of 5 hrs, the planes are 2000 mils apart. Find the rate of each.1 solutions Answer 235149 by josmiceli(9686)   on 2010-08-03 03:37:15 (Show Source): You can put this solution on YOUR website!Let = speed of southbound plane in mi/hr = speed of northbound plane in mi/hr The are separating at the rate of After 5 hrs The speeds of the planes are: southbound: 150 mi/hr northbound: 250 mi/hr
 Miscellaneous_Word_Problems/328324: A reduction of 25% in the price per dozen apples enables a purchaser to get 2 dozen more for \$20. What is the reduced price per dozen apples?1 solutions Answer 235148 by josmiceli(9686)   on 2010-08-03 03:28:12 (Show Source): You can put this solution on YOUR website!Let = the original price/dozen of apples given: = purchaser's savings after reduction -------------------- (savings)*(dozens bought) = amount spent The reduced price/dozen is The reduced price/dozen is \$30
 logarithm/328052: Need Help Please! I am failing this class.. 5. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. logx (log3 9) = 2 1 solutions Answer 234951 by josmiceli(9686)   on 2010-08-02 12:55:59 (Show Source): You can put this solution on YOUR website!Wow, this looks so confusing, I'm not sure what it says. The is where to start, since it looks simple. It says "I am an exponent to the base that gives I know that , so Now I have This is saying "An exponent which is , with a base that is gives me I'll rewrite it as: Now take the square root of both sides answer and not answer Only the positive result would work here, because what would the answer to this be? Can't solve it
 logarithm/328048: Need help please! I am failing this class and just can't seem to grasp it.. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this. log9x = -3 9 is base( i believe)1 solutions Answer 234947 by josmiceli(9686)   on 2010-08-02 12:40:20 (Show Source): You can put this solution on YOUR website!You have to be able to read this. First you must know that **logs are exponents**. If you have , then is a log to the base says the log to the base which gives me is . You know is the exponent because log(something) = If is the exponent, and is the base, I can write Now you have to know what to do with a negative exponent The rule is: , so , and So far, I have , so Remember, also, that there is no way you could have something like This is saying There is no possible that can give you a minus result Good luck - just pound away at this stuff- It's like cement- It will crumble after a while
 Linear-equations/328045: (2,-1),m=-2/3 I can get most of the problem but get lost when with the end1 solutions Answer 234938 by josmiceli(9686)   on 2010-08-02 12:04:11 (Show Source): You can put this solution on YOUR website!The formula is: where( x[1],y[1]) = (2,-1) plugging in numbers: Multiply both sides by Here's the plot:
 Miscellaneous_Word_Problems/328016: A company profit was \$75,000 in 1972, in 1992, its profit was \$450,000 the profit in 1992 was how many times as great as the profit in 1972 ? A 2 B 4 c 6 D 10 E 601 solutions Answer 234890 by josmiceli(9686)   on 2010-08-02 10:00:56 (Show Source): You can put this solution on YOUR website! c)6 is the answer
 Probability-and-statistics/328001: A population of small town is 250. Out of 250, 150 are adults and one of those is a millionaire who makes \$ 8 million per year. The average salary of that town is \$100,020 per year. What is the average salary for remaining 149 adults in that town? Answer A) \$ 52000 B) \$47000 C) \$ 51000 D) \$ 490001 solutions Answer 234888 by josmiceli(9686)   on 2010-08-02 09:59:14 (Show Source): You can put this solution on YOUR website!The average salary for the 149 adults is (their total income)/149 = given: This is the total salary for 149 people (not including millionaire) the average salary for the remaining 149 adults in that town is \$47000
 Travel_Word_Problems/327862: Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by S(t)=-16t^2-32t+1281 solutions Answer 234785 by josmiceli(9686)   on 2010-08-01 20:42:57 (Show Source): You can put this solution on YOUR website! When the wrench hits the ground, since the height is zero. The minus in front of the squared term tells me the parabola solution has a maximum peak Divide both sides by Complete the square sec The wrench will hit the ground in 2 seconds
 logarithm/327864: log4(4096)1 solutions Answer 234780 by josmiceli(9686)   on 2010-08-01 20:24:42 (Show Source): You can put this solution on YOUR website!First, write
 Mixture_Word_Problems/327711: How much 20% acid solution and 80% acid solution should be combined to obtain 100 liters of 62% acid solution?1 solutions Answer 234717 by josmiceli(9686)   on 2010-08-01 14:08:44 (Show Source): You can put this solution on YOUR website!Let = liters of 20% acid solution needed Let = liters of 80% acid solution needed given: liters liters -------------------------- acid in final solution: subtract liters and, since liters 30 liters of 20% solution and 70 liters of 80% solution are needed check: OK
 Exponents-negative-and-fractional/327719: 100=C(3963)^-2 Solve for C1 solutions Answer 234715 by josmiceli(9686)   on 2010-08-01 13:59:01 (Show Source): You can put this solution on YOUR website! Multiply both sides by
 Numbers_Word_Problems/327590: A garden table and a bench cost \$858 combined. The garden table costs \$42 less than the bench. What is the cost of the bench? So far I have 858=(x-42)+x1 solutions Answer 234634 by josmiceli(9686)   on 2010-07-31 22:19:44 (Show Source): You can put this solution on YOUR website!Let = cost of garden table Let = cost of bench given: By substitution: and, since The bench costs \$450
 Linear_Equations_And_Systems_Word_Problems/323799: The cost of a new math textbook was \$80 in 2005. It went up to \$120 in 2010. Assuming the cost increases linearly, write an equation representing the cost as a function of time.1 solutions Answer 231758 by josmiceli(9686)   on 2010-07-19 20:35:13 (Show Source): You can put this solution on YOUR website!You need a linear equation, which has the form = cost of a textbook during a particular year is a particular year, calling etc. All you have to do is find and in the equation is the slope, or rate of increase When increases from to (2005- 2010), increases from to The slope is (change in C)/(change in y) So far the equation is Now to find , Use , and (a point on the line) So, the equation is The plot of this equation is: