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# Recent problems solved by 'josmiceli'

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 Age_Word_Problems/474228: The sum of a man's age and his grandmother's age is 102. Eighteen years age his grandmother was 10 times as old as he was then. Find their present ages. 1 solutions Answer 325279 by josmiceli(9662)   on 2011-07-25 18:04:14 (Show Source): You can put this solution on YOUR website!Let = Man's present age Let = Grandmother's present age = Man's age 18 years ago = Gradmother's age 18 years ago given: (1) (2) ------------------------ (2) (2) (2) Add (2) to (1) (2) (1) And, from (1), The man is 24 and the Grandmother is 78 ------------- check: (2) (2) (2) OK
 Polynomials-and-rational-expressions/474238: Jack usually mows his lawn in 5 hours. Marilyn can mow the same yard in 3 hours. How much time would it take for them to mow the yard together?1 solutions Answer 325277 by josmiceli(9662)   on 2011-07-25 17:51:16 (Show Source): You can put this solution on YOUR website!Let = time to mow 1 lawn working together Add their rates of working Jack's rate: 1 lawn mowed / 5 hours Marilyn's rate: 1 lawn mowed / 3 hours Rate working together = Rate working together = hrs Time - 1 hr + min It takes them 1 hr and 52.5 min working together
 Quadratic_Equations/474242: Foe the following equation, state the value of the discriminant and then describe the nature of the solutions -19x^2-2x+7=0 ^means raising to that power which statement is correct? a) the equation has 2 imaginary solutions b) the equation has 2 real solutions c) the equation has one real solution1 solutions Answer 325259 by josmiceli(9662)   on 2011-07-25 17:16:35 (Show Source): You can put this solution on YOUR website!When the quadratic has the form , the discriminant is Discriminant = 536 The equation has 2 real solutions
 Finance/473924: Trains A and B are traveling in the same direction on parallel lines. Train A is traveling at 100 miles per hour and Train B is traveling 125 miles an hour. Than Train A passes a station at 10:25 AM. If Train B passes the same station at 10:37 AM. What time will B catch up with Train A? When will Train B catch up with Train A? When will Train B catch up to Train A? Time ??? PM or AM? Thanks1 solutions Answer 325082 by josmiceli(9662)   on 2011-07-25 01:21:52 (Show Source): You can put this solution on YOUR website!Train A has a head start of how many miles when train B passes the station? 10:37 - 10:25 = 12 minutes Train A's head start is: mi ------------------- Now start a stopwatch when B passes the station. Both trains will travel for the same amount of time, until they meet. ------------------- Let = the distance that B has to go until they meet Then = the distance that A has to go until they meet ------------------- For B: (1) For A: (2) -------------------- Substitute (1) into (2) hrs They will meet in hrs or minutes after B leaves station 10:37 AM + 48 min = 11:25 AM is the time B passes A --------------- check answer: A's distance from station is A's time from station is hr mi B's distance from station is also mi OK
 Travel_Word_Problems/473957: A biker bikes 2.7 hours to the city. Bikerbikes .9 hrs more coming back at 3 miles per hours slower. What is the total distance biker biked?1 solutions Answer 325081 by josmiceli(9662)   on 2011-07-25 00:49:27 (Show Source): You can put this solution on YOUR website!Let = biker's speed going to city given: Time going to city is hrs --------------- Coming back from city is the same distance, so --------------- Since the distances are equal, Subtract from both sides Add to both sides -------------- Now find -------------- Since the biker went to the city and then back again, you need to find The total distance biked is 64.8 mi check: OK
 Linear-systems/473955: In 1992 the life expectancy of males in a certein country was 64.1 years. In 1996, it was 66.5 years. let E represent the life expectancy in year t and let t represent the number of years sence 1992. The linear function E(t) that fits the data is? 1 solutions Answer 325078 by josmiceli(9662)   on 2011-07-25 00:32:53 (Show Source): You can put this solution on YOUR website!The linear function looks like where = slope and = y-intercept --------------------- For this problem: Replace with Replace with ----------------- Now you have Note that when , and ------------------ Now you have Now you have to find , the slope of the line is the change in divided by the change in Now you have ------------------ check answer: OK
 test/473953: Log base 8 of n=2/31 solutions Answer 325076 by josmiceli(9662)   on 2011-07-25 00:16:59 (Show Source): You can put this solution on YOUR website! The cube root ( 1/3 power) of 8 is 2, since
 Numbers_Word_Problems/473879: a number when divided by 5, gives a remainder 3. Find the remainder when square of that number is divided by 51 solutions Answer 325012 by josmiceli(9662)   on 2011-07-24 20:17:50 (Show Source): You can put this solution on YOUR website!When 13 is divided by 5, the remainder is 3 The remainder is 4 when 13 squared is divided by 5
 Numbers_Word_Problems/473873: how many times should the keyboard of a computer be pressed to type all the numbers from 1 to 500 numbers1 solutions Answer 325010 by josmiceli(9662)   on 2011-07-24 20:05:15 (Show Source): You can put this solution on YOUR website!The numbers 1 - 9 are key presses The numbers 10 - 99 are key presses The numbers 100 - 500 are key presses total key presses
 Miscellaneous_Word_Problems/473003: Alycias piggy bank has dimes and quarters in it. the number of dimes is four less then three times the number of quarters. If the total value of the coins is \$7.85 how many dimes are in the piggy bann?1 solutions Answer 324326 by josmiceli(9662)   on 2011-07-21 23:15:05 (Show Source): You can put this solution on YOUR website!Let = number of dimes Let = number of quarters given: (1) (in cents) (2) ------------------ Substitute (2) into (1) (1) (1) (1) (1) (1) and, since (2) (2) (2) (2) There are 41 dimes check: (1) (1) (1) (1) OK
 Linear-equations/472966: Calculate the distance from the point K(-10, -13) to the line 8x – 5y + 15 = 0. Explain the answer in terms of the relationship between the point and the line 1 solutions Answer 324321 by josmiceli(9662)   on 2011-07-21 23:04:32 (Show Source): You can put this solution on YOUR website!The point K(-10, -13) is on the line 8x – 5y + 15 = 0 so the distance is zero
 Inequalities/472988: the student council is sponsoring a concert as a fund raiser. tickets are \$3 for students and \$5 for adults. the student council wants to raise more than \$1000. if 200 students attend, how many adults must attend?1 solutions Answer 324317 by josmiceli(9662)   on 2011-07-21 22:15:45 (Show Source): You can put this solution on YOUR website!Let = number of adults who must attend to raise \$1,000 To raise \$1,000, At least 81 adults must attend to raise more than \$1,000
 Inequalities/472991: An automatic swing is designed to hold a baby who weighs at least 12 pounds but no more than 20 pounds. If a baby weighs 7.2 pounds at birth and gains 0.2 pounds each week, for what range of weeks will it be safe to put the baby in the swing? Write your answer in interval notation. No spaces! 1 solutions Answer 324315 by josmiceli(9662)   on 2011-07-21 22:09:34 (Show Source): You can put this solution on YOUR website!Let = the week when the baby is 12 pounds The formula would be: Let = the week when the baby is 20 pounds
 Percentage-and-ratio-word-problems/472091: A car dealer tells you that the price of a new car is \$20,000,which is the original price of the car plus a 5% sales tax and a 2% prep fee. Find the original price of the car1 solutions Answer 323759 by josmiceli(9662)   on 2011-07-19 22:36:34 (Show Source): You can put this solution on YOUR website!Let = the original price of the car given:
 Probability-and-statistics/472127: Boxes are stored in a warehouse. The stack is four boxes wide and 20 boxes long at the bottom. Each layer is one box shorter than the previous layer but the same width. How many boxes are there if the top layer is four boxes long? Write an equation with summation notation to find the total number of boxes. If you solve this question without using summation notation, you may not get full marks. 1 solutions Answer 323757 by josmiceli(9662)   on 2011-07-19 22:24:02 (Show Source): You can put this solution on YOUR website!The formula for the sum of digits 1 through n = The sum of the boxes looks like: . . . to If the top layer was , the answer would be Sum = But I want to subtract from this, so Sum = Sum = Sum = Sum = In summation notation, this would look like: 4 x 1/2 x Sum, n from 1 to 20 of n minus 4 x 1/2 x Sum, n from 1 to 3 of n
 Numbers_Word_Problems/472144: one number is 25% of another. the larger number is 12 more than the smaller. What are the numbers? I tried .25 * 12 =x Which would make one of the numbers 3 and if you add 3 to both sides you get 15. i don't think I am making this into a correct algebraic expression or getting the right answer. 1 solutions Answer 323741 by josmiceli(9662)   on 2011-07-19 22:05:00 (Show Source): You can put this solution on YOUR website!Let the numbers be and given: (1) must be the larger number because is only 25% of (2) Substitute (1) into (2) and, since (1) (1) (1) The numbers are 4 and 16
 Probability-and-statistics/472129: A very annoying clock at your house chimes at the beginning of nth hour, 2n times. ( For example, at 8:00A.M. the clock chimes 16 times and at 2:00P.M. the clock chimes 28 times) The clock also chimes three times at half-past every hour. Determine how many times in total the clock chimes in one full day. 1 solutions Answer 323739 by josmiceli(9662)   on 2011-07-19 21:58:56 (Show Source): You can put this solution on YOUR website!I will start the day at 1 AM The clock chimes times The number of on the hour chimes are: . . . to etc. The formula for the sum of digits 1 through n is When Twice the sum = 3 chimes each half hour, from 1:30 AM to 11:30 PM is chimes Total = answer Hope I got it
 Distributive-associative-commutative-properties/472123: What is 3x+25x+50 completely factored. The answer should look like _(x_?)(x_?) From what I understand the formula is ax+bx+c and the outcome should be (ax+c)(ax+c)1 solutions Answer 323735 by josmiceli(9662)   on 2011-07-19 21:40:01 (Show Source): You can put this solution on YOUR website! The direct way is to use the quadratic formula to find the roots The formula is: when the form of the equation is: and The roots are and I can rewrite the solutions as: and And If I multiply these together: Expanding: Multiply both sides by So the factors of the equation are: and
 Linear-systems/471094: rental car costs \$25 per day plus \$0.20 per mile. If someone has \$200 to spend and needs to drive the car 90 miles each day, for how many days can that person rent the car?1 solutions Answer 323130 by josmiceli(9662)   on 2011-07-17 03:29:42 (Show Source): You can put this solution on YOUR website!Let = number of days the person can rent the car The formula to use is: (cost of the rental) = (cost per day)x(number of days) + (cost per mile)x(number of miles) and (number of miles) = (miles per day)x(number of days) given: Cost per day = dollars/day Cost per mile = dollars/mi Miles per day = mi/day The formula must be OK dimensionally, that is it must be dollars = dollars ---------------------------- The fraction of a day would not be allowed, so the person could rent the car for 7 days That means They would spend \$187.60
 Age_Word_Problems/470219: johnny is 6 years older than Alicia, while Anna is 8 years older than Alicia. 5 years from now, Alicia will be 12 years older than Johnny. How old is Johnny?1 solutions Answer 322563 by josmiceli(9662)   on 2011-07-14 07:16:29 (Show Source): You can put this solution on YOUR website!The problem makes no sense to me. If Johnny is older that Alicia now, how can Alicia be older than Johnny 5 years from now?
 Graphs/470220: i) Sketch on the same diagram the graphs of y = |2x + 3| and . ii) Find the values of x for which x + |2x + 3| = 1 *Please answer as soon as possible and also please explain in details how your sketch the graph. :) =)1 solutions Answer 322562 by josmiceli(9662)   on 2011-07-14 07:07:14 (Show Source): You can put this solution on YOUR website!You can think of as the same as , except that whenever is negative, you just ignore the minus sign and make positive. ------------------------------- Note that when , since ----------- When , then becomes negative, but you just ignore the minus sign. Graphically, that amounts to reflecting the line about the y-axis so that ends up positive ----------- Here's the graph so far: and, adding , Now I want all for which Now subtract from both sides This is just the solutions, or intersections of the graphs. --------------------- The reflected part of will have slope = and the y-intercept is so the equation is So I want the solutions to: (1) (2) (3) (3) and (1): and (-2/3, 5/3) is a solution --------------------- (3) and (2): and (-4, 5) is a solution The answer to (II) is and
 Equations/470217: Solve the equation. If it is an identity (all real numbers) or a contradiction (no solution), so state. 8x + 3 + x = 5x + 3 + 4x1 solutions Answer 322559 by josmiceli(9662)   on 2011-07-14 06:10:36 (Show Source): You can put this solution on YOUR website! This is an identity If I subtract from both sides, If I divide both sides by , If I divide both sides by ,
 Probability-and-statistics/470227: In the bowl of candies, the number of strawberry flavored candies exceeds the number of orange flavored ones by a ratio of 3:2. If two strawberry flavored candies were removed, the ratio of red to orange flavored candies would be 1:1.how many number of orange flavored candies in the bowl?1 solutions Answer 322556 by josmiceli(9662)   on 2011-07-14 05:53:47 (Show Source): You can put this solution on YOUR website!Given: ( s.f.c) / ( o.f.c.) = 3/2 and ((s.f.c) - 2)/ (o.f.c.) = 1/1 Let s.f.c = Let o.f.c = so (1) (2) --------------- From (1) (1) Substitute this into (2) (2) (2) (2) (2) And, from (1): (1) (1) There are 4 orange flavored candies in the bowl check: (2) (2) (2) OK (1) (1) (1) OK
 Probability-and-statistics/470231: two standard dice are rolled. what are the odds against rolling a sum of 4 or 11?1 solutions Answer 322554 by josmiceli(9662)   on 2011-07-14 05:34:37 (Show Source): You can put this solution on YOUR website!In other words: What are he odds in favor of rolling any sum EXCEPT 4 or 11? Since there are 6 numbers of each die, there are ways to get a result. ( odds against rolling 4 or 11) = ( odds in favor of getting ANY number) - ( odds in favor of getting 4 or 11 ) ------------------------ Ways to get a 4: 1 and 3 3 and 1 2 and 2 Ways to get an 11: 4 and 7 7 and 4 5 and 6 6 and 5 So, there are 7 results you must avoid Working with probabilities: P(of getting ANY result) = 1 P(of getting 4 or 11) = 7/36 P(against rolling 4 or 11) = 1 - 7/36 1 - 7/36 = 36/36 - 7/36 1 = 7/36 = 29/36 To compute odds, it is (what you want):(what you don't want) 36 - 29 = 7 (what you don't want) The odds against rolling 4 or 11 is 29:7
 logarithm/469773: The "learning curve" describes the rate at which a person learns certain tasks. If a person sets a goal of typing N words per minute (wpm), the length of time t (in days) to achieve this goal is given by the following formula. t=-62.5ln(1-N/80) (a) According to this formula, what is the maximum number of words per minute? (b) Solve for N. I am trying to remedy this question to no end.Can someone please help me? thanks!1 solutions Answer 322270 by josmiceli(9662)   on 2011-07-12 23:52:54 (Show Source): You can put this solution on YOUR website!The answer to (a) hinges on the fact that is impossible. There is no exponent with a positive base that can give you a negative number. Therefore, cannot be negative. This expression becomes negative when , so 80 words per minutes is the maximum possible. ----------------- (b) Note here that MUST be negative in order that come out positive, since (-)x(-) = (+) A log can certainly be negative, and it will give you a result that is less than 1, but never a negative result as I just stated. ------------- Divide both sides by I can rewrite this as: Multiply both sides by
 expressions/469787: If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?1 solutions Answer 322265 by josmiceli(9662)   on 2011-07-12 23:21:26 (Show Source): You can put this solution on YOUR website!Her rate of typing is ( 1 page ) / ( p minutes ) The formula to use is: ( fraction of a page typed ) = ( rate of typing ) x ( time to type it ) ---------------- given: ( fraction of a page typed ) = ( 1/p ) x ( 5 min ) ( fraction of a page typed ) = 5/p She can type 5/p of a page in 5 minutes ---------------- To check this, suppose p = 7 She can type 1 page in 7 minutes She can type 5/p = 5/7 of a page in 5 minutes
 Linear_Equations_And_Systems_Word_Problems/469699: Word problems are so difficult for me to understand! Please help! Thanks. For an engine with a displacement of 2.8L, the function given by the equation d=Cn^-2 can be used to determine the diameter size of the carburetor's opening, d, in millimeters, where n is the number of rpm's at which the engive achieves peak performace and C is a constant. a. solve the equation for n. b. Suppose the carburetor's opening is 84 mm and rpm's are 4480. Find the value of C that makes the equation true. c. use the value of c that you found to determine the rpm's at which the engine produces peak power when the carburetor's opening is 81 mm.1 solutions Answer 322223 by josmiceli(9662)   on 2011-07-12 19:20:02 (Show Source): You can put this solution on YOUR website! (a) Solve for Take the log of both sides using the rule: Now use the above rule in reverse Use the rule: If , then ------------------ (b) Find Let
 Travel_Word_Problems/469349: Train "A" leaves the station going south at a rate of 50 miles per hour. Train "B" leaves the same station one hour later headed north traveling at 60 miles per hour. How long has train "A" been traveling when the two trains are 270 miles apart ?1 solutions Answer 322037 by josmiceli(9662)   on 2011-07-11 21:49:53 (Show Source): You can put this solution on YOUR website!How much of a head start does train A have? mi Start a stopwatch when train B leaves station You can think of this situation as one train being stationary and the other train traveling at the sum of their speeds hrs Train B has been traveling for 2 hrs when A and B are 270 mi apart Train A has been traveling for hrs when A and B are 270 mi apart
 Miscellaneous_Word_Problems/469347: Prices for the movie were \$4.00 for children and \$8.00 for adults. The total amount of ticket sales was \$1,176. There were 172 tickets sold. How many adult tickets were sold?1 solutions Answer 321991 by josmiceli(9662)   on 2011-07-11 19:42:07 (Show Source): You can put this solution on YOUR website!Let = number of children's tickets sold Let = number of adult tickets sold given: (1) (2) -------------- Multiply both sides of (2) by , and subtract (2) from (1) (1) (2) 122 adult tickets were sold check answer: (2) (2) (2) (2) and (1) (1) (1) (1) OK
 Rectangles/468815: The length of a tunnel was 22 1/2 times its width. If the length had been 50 feet less, it would have been 20 times the width. Find its length; its width.1 solutions Answer 321648 by josmiceli(9662)   on 2011-07-10 04:07:35 (Show Source): You can put this solution on YOUR website!Let = the tunnel's width Let = the tunnel's length given: (1) (2) --------------- Substitute in (1) for in (2) (2) Add to both sides (2) Subtract from both sides (2) (2) And, since (1) (1) (1) The tunnel is 20 ft wide and 450 ft long check answer: (2) (2) (2) OK