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# Recent problems solved by 'josmiceli'

josmiceli answered: 10610 problems
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 Travel_Word_Problems/415536: A walker travels 3.6 miles in the same time that a jogger travels 6 miles. If the walkers speed is 2 miles per hour less then the joggers, find the speed of the walker and the speed of the jogger. I know that its r=t/d and that walker= 3.6, jogger 6 ? -2miles Thank you1 solutions Answer 291299 by josmiceli(10616)   on 2011-02-28 20:21:58 (Show Source): You can put this solution on YOUR website!write 2 equations: Let =speed of jogger walker: (1) jogger: (2) This is 2 equations and 2 unknowns, so it's solvable (2) (2) and (1) (1) (1) (1) (1) (1) and The joggers speed is 5 mi/hr The walkers speed is 3 mi/hr
 Square-cubic-other-roots/415526: Simplify (-4- square root of negative 3) (-4+ square root of negative 3)1 solutions Answer 291296 by josmiceli(10616)   on 2011-02-28 20:11:13 (Show Source): You can put this solution on YOUR website! Since answer
 Numbers_Word_Problems/415522: The sum of two numbers is 2. If one number is subtracted from the other, their difference is 8 Thank you, Buffy!1 solutions Answer 291292 by josmiceli(10616)   on 2011-02-28 20:02:48 (Show Source): You can put this solution on YOUR website!call the numbers and given: Add the equations and The numbers are 5 and -3
 Exponents-negative-and-fractional/415237: use the product rule to simplify the expression. y*y^8*y^5= Can you show me how to do this, i dont understand it.1 solutions Answer 291152 by josmiceli(10616)   on 2011-02-28 12:50:25 (Show Source): You can put this solution on YOUR website!Just write this expression without exponents: Now what is this whole thing using exponents? What did you do? (1 y) x (8 y's) x (5 y's) = 14 y's ( 1 + 8 + 5 = 14 ) So, to get the product of y's with exponents, you just add the exponents Give yourself some more examples and practice to drill it in.
 Miscellaneous_Word_Problems/415232: Maple syrup worth \$6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth \$2.36 a gallon. How many gallons of each kind of syrup are needed to make 50 gallons of the mixture?1 solutions Answer 291144 by josmiceli(10616)   on 2011-02-28 12:40:54 (Show Source): You can put this solution on YOUR website!Let = gallons of \$6 syrup needed Let = gallons of \$.80 syrup needed given: (1) (2) ---------------------- (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and (1) 15 gallons of \$6 syrup are needed 35 gallons of \$.80 syrup are needed check answer: (2) (2) OK
 percentage/415231: This yea's salary, \$50,220, is an 8% increase over last year's salary. What was last years salary?1 solutions Answer 291139 by josmiceli(10616)   on 2011-02-28 12:22:53 (Show Source): You can put this solution on YOUR website!Let = last years salary given: Last years salary was \$46,500
 Travel_Word_Problems/415215: A woman can hike 1 mph faster down a trail then she can uphill. It takes her 3 hours to go downhill and 6 hours uphill. What is her speed downhill?1 solutions Answer 291130 by josmiceli(10616)   on 2011-02-28 11:39:04 (Show Source): You can put this solution on YOUR website!Going downhill: Going uphill: (I'm assuming the uphill and downhill trips are the same distance) Her speed downhill is 2 mi/hr check answer: mi and mi OK
 Linear-equations/415206: find the slope if possible of the line passing through each pair of points (2, - 1) and (6, 3) 1 solutions Answer 291129 by josmiceli(10616)   on 2011-02-28 11:33:31 (Show Source): You can put this solution on YOUR website!(2, -1), (6,3) The slope is
 Problems-with-consecutive-odd-even-integers/415210: The sum of two consecutive odd integers is 24. Find the integers. Let n = first integer. (The second let statement is not given. You will have to decide what it should be.)1 solutions Answer 291125 by josmiceli(10616)   on 2011-02-28 11:27:56 (Show Source): You can put this solution on YOUR website!Let = first odd integer Let = the next odd integer (note that would be an even integer) given: The integers are 11 and 13
 Square-cubic-other-roots/415209: find a number between 3/7 and 5/111 solutions Answer 291123 by josmiceli(10616)   on 2011-02-28 11:23:55 (Show Source): You can put this solution on YOUR website!The lowest common denominator (LCD), is I know this for sure because both and have no divisors (they are prime numbers). ----------- Expressing the fractions with LCDs, and -------------------- The number between them is There are many more numbers between them, but that one is the easiest to find.
 Mixture_Word_Problems/414986: How many quarts of pure anitifreeze must be added to 4 quarts of a 20% antifreeze solution to obtain a 50% antifreez solution?1 solutions Answer 291008 by josmiceli(10616)   on 2011-02-27 21:58:42 (Show Source): You can put this solution on YOUR website!Let = quarts of pure antifreeze needed = pure antifreeze in 20% solution 2.4 quarts of pure antifreeze must be added check: OK
 Quadratic_Equations/414895: I am having trouble with a quadratic word problem. The word problem is as follows: The sides of one square have length 3 m more than the sides of a second square. If the area of the larger square is subtracted from 4 times the area of the smaller square, the result is 36 m^2. What are the lengths of the sides of each square?1 solutions Answer 290952 by josmiceli(10616)   on 2011-02-27 19:05:22 (Show Source): You can put this solution on YOUR website!Let the side of the larger square = m The side of the smaller square = m given: m2 (can't use the negative root) and The sides are 5 m and 8 m check answer: OK
 Probability-and-statistics/414878: You compter password has 4 capital letter followed by3 digit.Your friend randomly chooses 4 capital letter and 3 digit.Use caculator to find the probability that your friend chooses your password.Choose answer below 1/3120 1/456976000 3120 4569760001 solutions Answer 290942 by josmiceli(10616)   on 2011-02-27 18:32:23 (Show Source):
 Travel_Word_Problems/414829: two trains leave chicago at the same time traveling in opposite directio. one is going 60 miles per hour and the other is going 65 miles per hour. how long before they are 375 miles a part1 solutions Answer 290940 by josmiceli(10616)   on 2011-02-27 18:26:35 (Show Source): You can put this solution on YOUR website!You can think of one standing still and the other traveling at the sum of their speeds They are 375 mi apart in 3 hrs
 Linear_Algebra/414788: a bus is to be chartered for the senior class trip. the basic fare is \$9.50 per passenger. If more than 20 people go everyone's fare is reduced by \$0.30 for each passenger over this number (20). At least how many people must go to make the fare less than \$7.50 per passenger?1 solutions Answer 290927 by josmiceli(10616)   on 2011-02-27 16:49:56 (Show Source): You can put this solution on YOUR website!Let = number of passengers over 20 who must go in order to make the fare less than \$7.50 per passenger ---------------- The fare /passenger gets reduced by exactly dollars if passengers above 20 go. The total number of passenger is ---------------- (normal cost) - (discount) = (desired cost) (nearest whole number) ----------- If 26 people go, fare is (fare/person)x(number of people) If 27 people go fare is (fare/person)x(number of people) It looks like 27 people must go to make fare less than \$7.50 per person
 Travel_Word_Problems/414764: On a 600-mile trip, the traveler traveled 50 miles per hour for the first 1/3 of the trip and at 40 miles per hour for the rest of the trip. What was the traveled average speed for the entire trip? The answer is supposed to be 300/7 mph, but I don't know how to get that. Can someone please help? 1 solutions Answer 290908 by josmiceli(10616)   on 2011-02-27 15:47:57 (Show Source): You can put this solution on YOUR website!The average speed is always (total distance traveled)/(time to travel that distance) A common mistake is to take an average of 2 averages, which gives the wrong answer. The 1st 1/3 of the trip is mi hrs ------------ The rest of the trip is mi hrs ------------ (total distance traveled)/(time to travel that distance) = mi/hr
 Evaluation_Word_Problems/414660: A plane traveled 756 miles to Shanghai and back. the trip was with wind. it took 9 hours. the trip back was into the air. the trip back took 18 hours. find the speed of the plane in still air and the speed of the wind. so far..i divided 756/9 = 84 (wind) and i divided 756/18 = 42(air) but i don't know how to set the equation up. if you could that would be great! :) 1 solutions Answer 290861 by josmiceli(10616)   on 2011-02-27 11:49:52 (Show Source): You can put this solution on YOUR website!You have 2 trips, each one is 756 mi. Let = the speed of the plane in still air Let = the wind speed Speed with the wind = Speed against the wind = mi ---------------------- given: With the wind: (1) against the wind: (2) ----------------- (1) (1) and (2) (2) ---------------- Add equations (1) and (2) and (2) (2) (2) The speed of the plane in still air is 63 mi/hr The wind speed is 21 mi/hr check answers: (1) (1) (1) (1) and (2) (2) (2) (2) OK In practical terms, I don't think an airplane could stay in the air doing only 63 mi/hr, but I think my method is good.
 Polynomials-and-rational-expressions/414527: Hello! I was absent from my algebra lesson, and I have a queston on my homework.It asks that I solve the equasion. The equasion is -2h^2-28h-98 . I know so far that I need to put it in two different sets of parenthasees. So far, all I have written down is (-h ) (h ). Please help me, because I am very confused. Thank you!1 solutions Answer 290762 by josmiceli(10616)   on 2011-02-26 21:54:44 (Show Source): You can put this solution on YOUR website!What you missed is the factoring of the equation. In order to factor it, you need to find the roots. the roots are where the graph of the equation intersects the x-axis. That is also where , so I can say Now set Divide through by One way to factor this is with the quadratic formula Use this formula when the equation is in the form Plug in these values: and also In this case you have a double root, both are I can write them as: and Multiplying out, So, I have found the 2 factors. The graph of the equation is:
 Travel_Word_Problems/414524: a motorboat took 2 hours to make a downstream trip witha 5 mph current. the return trip against the same current too 4 hours. find the speed of the boat in still water.1 solutions Answer 290755 by josmiceli(10616)   on 2011-02-26 21:30:54 (Show Source): You can put this solution on YOUR website!Let = the speed of the boat in still water in mi/hr Let = the one-way trip in miles Going downstream, speed = mi/hr Going upstream, speed = mi/hr given: downstream: upstream: -------------- is the same in both equations The speed of the boat in still water is 15 mi/hr check: upstream: OK
 Evaluation_Word_Problems/414521: If 4, 5, and 7 are factors of a number, list 4 other numbers that would also be factors of the number.1 solutions Answer 290751 by josmiceli(10616)   on 2011-02-26 21:14:35 (Show Source): You can put this solution on YOUR website!The smallest number that can have both 4 and 7 as factors is 28, so 14 and 28 must also be factors of the number. --------------- The smallest number that can have both 5 and 7 as factors is 35, so 35 must also be a factor of the number. --------------- The smallest number that can have both 4 and 5 as factors is 20, so 10 must also be a factor of the number. --------------- 10,14,28,35
 Linear_Equations_And_Systems_Word_Problems/414458: A \$3.00 toll is charged to cross the bridge from Sanibel Island to mainland Florida. A six-month pass, costing \$15.00, reduces the toll to \$.50. A one-year pass, costing \$150, allows for free crossings. How many crossings per year does it take, on average, for two six-months passes to be the most economical choice? Assume a constant number of trips per month, Show work and explain answer. I am not sure what formula to use for this problem. Please Help! :/1 solutions Answer 290723 by josmiceli(10616)   on 2011-02-26 19:42:38 (Show Source): You can put this solution on YOUR website!Let = crossings per year it takes, on average, for two six-months passes to be the most economical choice. Let = cost per year to make crossings Assume a constant number of trips per month ------------------------------------- Without buying any passes: Buying 2 6-month passes: Buying a 1-year pass: ----------------- First I'll set to find intersection 12 crossings per year make One more crossing, , make and So, becomes more economical on the 13th crossing by \$2.50 and it still cost less than the 1-year pass for \$150
 Human-and-algebraic-language/414453: Hello I was wondering can you help me solve this problem. Not for sure what my next step would be. Problem :A basketball court is a rectangle with a perimeter of 80 meters . The length is 13 meters more than the width. Find the width and length of basketball court. My attempt: Let x be width Let Y be length X+13=width x+13= 80 meters -13=-13 x= 67 meters. 1 solutions Answer 290691 by josmiceli(10616)   on 2011-02-26 17:56:44 (Show Source): You can put this solution on YOUR website!The perimeter of any rectangle is given: Width = Length = ---------- and The width is 13.5 m and the length is 26.5 m check answer: OK
 logarithm/414454: Rewrite the expression 3 ln(2) - 2 ( ln(10) - ln(4) ) in the form ln(x), a single logarithm I rewrote it as ln(2)^3+ln(4)^2 /ln(10)^2 thus getting the the answer ln(8)+ln(16)/ln(100)=ln(24/100) I am told, however, that the correct answer is ln(128/100) Can you please explain how? 1 solutions Answer 290684 by josmiceli(10616)   on 2011-02-26 17:43:25 (Show Source): You can put this solution on YOUR website! ---------- Just look at the sign change carefully I think this is OK
 Exponential-and-logarithmic-functions/414431: Hi could you please show me the steps to evaluate log base 2? thanks so much1 solutions Answer 290679 by josmiceli(10616)   on 2011-02-26 17:29:29 (Show Source): You can put this solution on YOUR website! etc. these are saying, for instance: , so the log is 3 The inverse relations are: ---------- I have also seen expressions like this: These are saying: , which is exactly the same as ---------- Hope this helps
 Word_Problems_With_Coins/414430: A vending machine accepts any combination of nickels, dimes, and quarters equaling 50 cents. How many combinations of coins are possible?1 solutions Answer 290661 by josmiceli(10616)   on 2011-02-26 16:22:43 (Show Source): You can put this solution on YOUR website!1) 2Q 2) 1Q 2D 1N 3) 1Q 1D 3N 4) 1Q 5N 5) 5D 6) 4D 2N 7) 3D 4N 8) 2D 6N 9) 1D 8N 10) 10N
 Money_Word_Problems/414427: Sally's two student loans totaled \$11,500. One of her loans was for 5% simple interest and the other at 7.5%. After one year Sally owed \$712.50 in interest. What was the amount of each loan?1 solutions Answer 290660 by josmiceli(10616)   on 2011-02-26 16:11:28 (Show Source): You can put this solution on YOUR website!Let the amount of the 5% loan = The amount of the 7.5% loan is ----------- The amount of the 5% loan is \$6,000 The amount of the 7.5% loan is \$5,500
 Numbers_Word_Problems/414406: Which number is not real? 1.) -8 2.) sqrt(-64) 3.) - sqrt(64) 4.) 3 times sqrt(-64) I already eliminated -8 and - sqrt(64) beacause I know they are real, I just don't understand the other two. Please help, Thank you!1 solutions Answer 290659 by josmiceli(10616)   on 2011-02-26 15:59:44 (Show Source): You can put this solution on YOUR website!2) and 4) are not real because they both have in the expressions ---------- 2) ---------- 4)
 Numbers_Word_Problems/414342: A wealthy man died and left an estate of \$975, 240 to be divided among 5 friends, 4 charitable organizations, and his university. His will directed that each friend should receive 3 times as much as all the charities combined, and that each charity should receive twice as much as the the university. How much did they all receive?1 solutions Answer 290630 by josmiceli(10616)   on 2011-02-26 11:24:26 (Show Source): You can put this solution on YOUR website!Let = amount received by each friend Let = amount received by each charity Let = amount received by the University given: (1) (2) (3) This is 3 equations and 3 unknowns, so it's solvable ---------------- Substitute (3) into (1) (3) (1) Substitute (2) into (1) (1) and (3) and (2) The 5 friends each got \$181,440 The 4 charities each got \$15,120 The University got \$7,560 check answer: (1) (1) (1) (1) OK
 Equations/414284: Aki's Bicycle Designs has determined that when x hundred bicycles are buiklt ,the average cost per bicycle is given by C(x)=0.1x^2-0.2x+3.511,where C(x) is in hundreds of dollars. How many bicycles should the shop build to minimize the average cost per bicycle?1 solutions Answer 290597 by josmiceli(10616)   on 2011-02-26 09:24:17 (Show Source): You can put this solution on YOUR website! You want to find the vertex of this curve It's in the form The vertex is at V(x,y) where and They should build 100 bicycles to minimize cost, which would be \$341.10 per bicycle Here's a plot (in hundreds of dollars and hundreds of bicycles)
 Rational-functions/414288: a machine can make 6405 screws in 3 hours. How many screws can it make in 8 hours?1 solutions Answer 290589 by josmiceli(10616)   on 2011-02-26 09:07:36 (Show Source): You can put this solution on YOUR website!Call the rate of making screws screws/hr screws/hr screws/hr x hrs = screws It can make 17080 screws in 8 hrs
 Rational-functions/414292: A farmer wants to have a rectangular garden which is 350m^2 in area. a. How do we find the area of a rectangle? b. Make a table of some possible lengths and widths which the garden can ahve. Describe how the length and width are related to one another. c. Explain why the relationship is is one of inverse variation? What is the ratio of proportionality?1 solutions Answer 290587 by josmiceli(10616)   on 2011-02-26 09:02:44 (Show Source): You can put this solution on YOUR website!(area) =(length)*(width) ---------- ------------ The area is the result of multiplying 2 variables If I'm given , for instance, then I can plot on vertical axis and on horizontal