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# Recent problems solved by 'josmiceli'

josmiceli answered: 9683 problems
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 Linear_Equations_And_Systems_Word_Problems/746010: In one week, Fearless Frank drove 100 miles on the freeway and 150 miles in town. His car consumed 18.2 gallons of gasoline. The next week his journeys took him over 180 miles of freeway and 30 miles of local driving, and he used only 10.9 gallons of gas. What were his highway m.p.g. and his local m.p.g.? 1 solutions Answer 454105 by josmiceli(9685)   on 2013-05-07 14:52:34 (Show Source): You can put this solution on YOUR website!The key is to see that ( miles driven ) / ( miles / gallon ) = gallons I can say: Let = mpg on the highway Let = mpg in town (1) (2) ----------------------------- (1) (2) ------------------------------ Multiply both sides of (2) by and subtract (1) from (2) (2) (1) and (2) (2) (2) (2) (2) ----------------- His highway m.p.g. was about 22 and his local m.p.g. was about 11 ----------------- check: (1) (1) (1) close enough
 Reduction-of-unit-multipliers/746011: a water hose can fill a 1 quart bottle with water in 2.2 seconds; I need to buy a pond pump but its flow rates are given in gallons per hour. what size pump should I purchase to the nearest 100 GPH?1 solutions Answer 454103 by josmiceli(9685)   on 2013-05-07 14:32:10 (Show Source): You can put this solution on YOUR website!You want an answer in ( gallons / hr ), so in terms of just units: ( quarts / sec ) x ( gallons / quart ) x ( sec / min ) x ( min / hr ) = ( gallons / hr ) ----------------------- This is easier to see if you pull out all the like units: ( quarts / quarts ) x ( sec/ sec ) x ( min / min ) x ( gallons / hr ) = ( gallons / hr ) ------------- Using your numbers: To the nearest 100 GPH, you need a 400 GPH pump
 Rate-of-work-word-problems/745788: Peter and Paul can do a certaion job in 3 hours. On a given day, they worked together for 1 hour then Paul left and Peter finishes the rest of the work in 8 more hours. How long will it take Peter to do the job alone?1 solutions Answer 454019 by josmiceli(9685)   on 2013-05-06 23:25:05 (Show Source): You can put this solution on YOUR website!If they can do the whole job in 3 hrs working together, then in 1 hour, they can do of the job That means there is 2/3 of the job left to do ----------------- Then, ( Peter's rate of working ) x ( 8 hrs ) = 2/3 Let = Peter's rate of working Peter would take 12 hrs to do the job alone check: ---------- Let = Paul's rate of working In hr, So, of the job is left Peter does OK
 Rate-of-work-word-problems/745794: father and a his son can dig a well if the father works 6 hours and his son works 12 hours or they can do its if the father works 9 hours and the son works 8 hours. How long will it take for the son to dig the well alone?1 solutions Answer 454007 by josmiceli(9685)   on 2013-05-06 22:10:56 (Show Source): You can put this solution on YOUR website!You can add their rates of digging to get their rate working together Let = father's rate of digging Let = Son's rate of digging -------------------------------- In general, I can say that: ( time spent digging ) x ( rate of digging ) = fraction of job done --------------- given: (1) (2) ( note that means entire job done ) ---------------- Multiply both sides of (1) by and both sides of (2) by Then subtract (2) from (1) ---------------------- (1) (2) ----------------- (1) (1) (1) (1) (1) (1) (1) (1) ----------------- The son would take 20 hrs working alone check: (2) (2) (2) (2) (2) OK
 Mixture_Word_Problems/745797: they combine 15lbs of a mix that is 60% peanuts with 10lbs of a second mix that is 30% peanuts. How many pounds of peanuts are in the combined mix? 1 solutions Answer 453996 by josmiceli(9685)   on 2013-05-06 21:32:49 (Show Source): You can put this solution on YOUR website! 12 pounds of peanuts are in the mix
 Travel_Word_Problems/745513: THE HEIGHT OF THE ROCKET AFTER t SECONDS WHEN FIRED STRAIGHT UP WITH AN INITIAL SPEED OF 150FT PER SECOND FROM AN INITIAL HEIGHT OF 2 CAN BE MODELED BY THE FUNCTION: s(t)=-16t^2+150t+2 WHEN WILL THE ROCKET BE 300ft? WHAT IS THE MEANING OF THE Y INTERCEPT WHEN WILL IT REACH THE GROUND? I AM UNSURE OF HOW TO START THE PROBLEM. DO I USE THE QUADRATIC FORMULA? 1 solutions Answer 453866 by josmiceli(9685)   on 2013-05-06 11:01:46 (Show Source): You can put this solution on YOUR website! is the height of the rocket from the ground If you want the height to be ft, then Divide through by Use quadratic wquation sec In 2.858 sec the height of the rocket will be 300 ft ------------------ I have to run now- check my math. The method should be OK
 Money_Word_Problems/745328: In 1980 the average price of a home in Brainerd County was \$95,000. By 1987 the average price of a home was \$123,000. Which of the following is a linear model for the price of a home, P in brainerd County in terms of a year, t? let t=0 correspond to 1980. Answers: A) P=123,000-4000t B) P=4000t+95,000 C) P= 123,000- 28,000t D) P= 28,000t + 95,0001 solutions Answer 453803 by josmiceli(9685)   on 2013-05-05 20:11:51 (Show Source): You can put this solution on YOUR website!Use the point slope formula: is plotted on the vertical axis is plotted on the horizontal axis The answer is B)
 Travel_Word_Problems/745124: When Mr. Gomez drives his car to work, the trip takes 30 minutes. When he rides the bus, it takes 45 minutes. If his average driving speed is 12 mph faster than the average speed of the bus, find the distance he travels to work. 1 solutions Answer 453738 by josmiceli(9685)   on 2013-05-05 13:07:44 (Show Source): You can put this solution on YOUR website!Let = the distance to work Let = the speed of the bus Convert minutes to hours By car: (1) By bus: (2) ------------------ Substitute (2) into (1) (1) Multiply both sides by (1) (1) (1) Substitute this result into (2) (2) (2) (2) The distance to work is 18 miles
 Functions/745110: The height s, in feet, of a rock thrown upward at an initial speed of 64 ft/sec from a cliff 50 ft above an ocean beach is given by the function s(t)=-16t^2+64t+50, where t is the time in seconds. Find the maximum height above the beach that the rock will attain.1 solutions Answer 453737 by josmiceli(9685)   on 2013-05-05 12:56:57 (Show Source): You can put this solution on YOUR website!The maximum height of this parabolic curve is when and the equation has the form: In your equation, , so sec -------------- Now find which is the maximum height ft The maximum height is 114 ft Here's the plot:
 Travel_Word_Problems/745117: Megan is going on a long distance road trip. She drives for 14 miles before being able to travel at a constant speed using cruise control. The equation y = 70x + 14 can be used to find her total distance traveled. If y is the total number of miles driven, and x is the number of hours driven after reaching 14 miles, which statement best describes the rate of change in the distance traveled?1 solutions Answer 453736 by josmiceli(9685)   on 2013-05-05 12:45:08 (Show Source): You can put this solution on YOUR website!The rate of change of the distance traveled is the slope of the equation, which is: ( change in y ) / ( change in x ) = 70 mi/hr
 Mixture_Word_Problems/744992: Wilma went to the local market and bought 3 lemons and 5 oranges for \$2.40.The same day and for the same price ,Fran bought 4 lemons and 7 oranges for \$3.31.What was the prices per lemon and the price per orange? Answer is \$o.25 per lemon and \$.33 per orange1 solutions Answer 453642 by josmiceli(9685)   on 2013-05-04 21:46:45 (Show Source): You can put this solution on YOUR website!Let = price of a lemon Let = price of an orange given: (1) ( in cents ) (2) ( in cents ) -------------------- Multiply both sides of (1) by and both sides of (2) by Then subtract (1) from (2) (2) (1) and (1) (1) (1) (1) 25 cents /lemon and 33 cents/orange
 Miscellaneous_Word_Problems/744942: A herd of 575 deer is introduced onto a small. island. At first the herd increases rapidly, but eventually food resources dwindle and the population declines. suppose that the number of deer after t years is given by the following formula N(t)= -t^4 + 2t^2 + 575 please show a step by step on how you got your answer 1 solutions Answer 453639 by josmiceli(9685)   on 2013-05-04 21:36:21 (Show Source): You can put this solution on YOUR website!You didn't finish the question
 Travel_Word_Problems/744989: 1) At 6 a.m., a passenger train and a freight train leave stations that are 360 miles apart and travel toward each other. The passenger train averages twice the speed of the freight train. At 10 a.m., the trains pass each other. Write and solve an equation to find the average speed of each train1 solutions Answer 453638 by josmiceli(9685)   on 2013-05-04 21:27:44 (Show Source): You can put this solution on YOUR website!Think of one train as standing still and the other approaching at the sum of their speeds ( it doesn't matter which train is moving ) -------------------------------------- Let = the speed of the slower train = the speed of the faster train The time the moving train is traveling is 10 AM minus 6 AM = hrs ---------------------------- The average speed of the freight train is 30 mi/hr The average speed of the passenger train is 60 mi/hr --------------- check: freight train: --------------- passenger train: -------------- mi OK
 Mixture_Word_Problems/744940: three solutions contain a certain acid. the first contains 15% acid, the second 35%, and the third 40%. A chemist wishes to use all three solutions to obtain a 75-liter mixture containing 34% acid. If the chemist wants to use twice as much of the 35% solution as of the 40% solution, how many liters, to the nearest 10th, of each solution should be used?1 solutions Answer 453617 by josmiceli(9685)   on 2013-05-04 16:43:03 (Show Source): You can put this solution on YOUR website!Let = liters of 40% solution needed = liters of 35% solution needed Let = liters of 15% solution needed --------------- = liters of acid in 40% solution = liters of acid in 35% solution = liters of acid in 15% solution ---------------- (1) (2) ---------------- (1) and (2) (2) (2) ---------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) (1) 21.9 liters of 40% solution are needed 43.8 liters of 35% solution needed 9.2 liters of 15% solution are needed -------------- check: (2) (2) (2) (2) OK
 Mixture_Word_Problems/744895: How much pure water must be mixed with 2 pints of 50% developer to produce a mixture that is 31% developer1 solutions Answer 453616 by josmiceli(9685)   on 2013-05-04 16:20:51 (Show Source): You can put this solution on YOUR website!Let = pints of water needed pint of developer in 50% solution -------------- pints -------------------- check: OK
 logarithm/744927: If log(base 3)2 = x simplify each logarithm a) log(base 3)8 b) log(base 3)24 c) log(base 3)√2 d) log(base 3)6√2 Can you please help me out? Thanks so much in advance:) Can you also show all the steps because it would help me understand :)1 solutions Answer 453615 by josmiceli(9685)   on 2013-05-04 16:12:49 (Show Source): You can put this solution on YOUR website!How well do you understand what logs are? If I say , then is the log is the result So I can rewrite this exactly as: ---------------- The general rules are: ( the base can be 10, or anything else ) ( again, the base can be anything ) ---------------- a) b) c) d)
 Travel_Word_Problems/744932: two airplanes start at the same time and fly toward each other from points 200 km apart at rates of 350 km/h and 400km/h when will they meet1 solutions Answer 453614 by josmiceli(9685)   on 2013-05-04 15:49:57 (Show Source): You can put this solution on YOUR website!Think of one plane as standing still and the other approaching at the sum of their speeds. Equation for the moving plane: hrs min They will meet in 16 min
 logarithm/744755: Show that log(base 1/c)x = log(base c)1/x Can you please help me out with this question? Thanks so much in advance:) Can you show all the steps because it will help me understand more thanks1 solutions Answer 453525 by josmiceli(9685)   on 2013-05-03 19:53:51 (Show Source): You can put this solution on YOUR website!Prove: I will say that Now I can say (1) (2) ----------------- (2) Now I can say This is the same as
 Quadratic_Equations/744337: Karens Backyard has a width of 25 meters and a length of 35 meters. SHe wants to put a rectangular flower garden in the middle of the backyard leaving a strip of grass of uniform width around all sides of the flower garden. If she wants to have 324 square meters of grass what will be the width and length of the garden1 solutions Answer 453270 by josmiceli(9685)   on 2013-05-02 15:59:21 (Show Source): You can put this solution on YOUR website!Let = the uniform width of the grass border The dimensions of the rectangular flower garden can be expressed as: width = m length = m ---------------------- She wants to have square meters of grass Her whole backyard has an area of m2 -------------- The area of her garden is Now I can say: ( by inspection ) The width of the border can't be , since that is wider than her backyard, so width = m length = m -------------------------- check answers: OK
 Miscellaneous_Word_Problems/744333: A train ticket has an area of 192 square centimeter and a perimeter of 56 centimeters. What are the dimensions of the tickets.1 solutions Answer 453266 by josmiceli(9685)   on 2013-05-02 15:39:33 (Show Source): You can put this solution on YOUR website! = length in cm = width in cm = area in cm2 = perimeter in cm ---------------- (1) (2) --------------- given: (1) and (2) (2) (2) By substitution: (1) (1) and, also ----------- If I pick the larger answer, then (2) (2) (2) --------------- These are the answers, because if I picked , then I would get for the width ---------- The length is 16 cm The width is 12 cm
 Rate-of-work-word-problems/744074: Billy's pool has a hole and is losing water at a rate of 4/9 gallon per minute. How many hours will it take for Bill to lose 100 gallons? 1 solutions Answer 453185 by josmiceli(9685)   on 2013-05-01 21:48:50 (Show Source): You can put this solution on YOUR website!In terms of units: ( gallons ) / ( gallons / min ) = min This answer is in minutes. To get hours: ( minutes ) x ( hours / minute ) = hours and It will take Bill 3 hrs and 45 min
 Linear_Equations_And_Systems_Word_Problems/744034: If 900 apples cost me 79 dollars how much would 100 apples cost?1 solutions Answer 453155 by josmiceli(9685)   on 2013-05-01 18:48:14 (Show Source): You can put this solution on YOUR website!The rate for the apples is dollars / apple In terms of units: ( dollars / apple ) x ( apples ) = dollars 100 apples cost \$8.78
 Equations/744041: can I get the expression and define the variables for this word problem: The cost of gas is 3.35 per gallon. If you travel 40 miles a day and gas mileage is 25 miles per gallon. How much gas money will be spent in a 5 day work week? 1 solutions Answer 453153 by josmiceli(9685)   on 2013-05-01 18:42:18 (Show Source): You can put this solution on YOUR website!In terms of units: ( dollars / gallon ) x ( ( miles / day ) / ( miles / gallon ) ) x ( days ) After doing the division, you get: ( dollars / gallon ) x ( miles / day ) x ( gallons / mile ) x ( days ) Now I'll do a slight reordering: ( dollars / gallon ) x ( gallons / mile ) x ( miles / day ) x ( days ) Doing the cancellations, I get: ( dollars / mile ) x ( miles ) = dollars Which is what you're after Now, plugging in the numbers: For a 5 day work week, \$26.80 is spent
 test/744036: 10zē+3z-3=0 I need to know what is the discriminant? Is it positive or negative? What kind of solution would you get if the discriminant were negative? Thank You!1 solutions Answer 453150 by josmiceli(9685)   on 2013-05-01 18:26:57 (Show Source): You can put this solution on YOUR website!When the equation has the form , then the roots are found using the quadratic formula: The discriminant is: If the discriminant is positive, both roots are real If the discriminant is negative, both roots are imaginary If the discriminant is zero, there is 1 real root ------------------ Your equation is: and the discriminant is: This result is positive, so there are 2 real roots Here is the plot:
 Rate-of-work-word-problems/744030: one printing machine works twice as fast as another. When both machines are used, they can print a magazine in 3 hrs. How many hours would each machine require to do the job alone? 1 solutions Answer 453146 by josmiceli(9685)   on 2013-05-01 18:11:12 (Show Source): You can put this solution on YOUR website!Add their rates of printing Let = the slower machine's rate of printing = the faster machine's rate of printing When both machines are used, their rate of printing is ( 1 magazine ) / ( 3 hrs ) --------------------- The fast machine can print a magazine in 4.5 hrs The slow machine can print a magazine in 9 hrs
 Percentage-and-ratio-word-problems/743994: if you have 12 quarters and spend 1/3 of them how much did you spend ? how did you get your answer .1 solutions Answer 453127 by josmiceli(9685)   on 2013-05-01 16:54:44 (Show Source): You can put this solution on YOUR website!Divide your quarters into 3 piles ( 4 quarters ) + ( 4 quarters ) + ( 4 quarters ) = 12 quarters You spent one of these piles, which is 4 quarters cents cents = dollar
 Exponential-and-logarithmic-functions/743985: how do you solve log base36(216) without a calculator?1 solutions Answer 453125 by josmiceli(9685)   on 2013-05-01 16:51:18 (Show Source): You can put this solution on YOUR website! answer ----------------- To show this is true, I can say Now I can say and 'OK
 Rational-functions/743970: It take one pipe 3 hours to fill the pool and a second pipe 4 hours to drain a pool. The pool is empty and the first pipe begins to fill it. The second pipe is accidentally left open, so the water is also draining out of the pool. Under these conditions how long will it take to fill the pool?1 solutions Answer 453120 by josmiceli(9685)   on 2013-05-01 16:39:24 (Show Source): You can put this solution on YOUR website!Add the rate of filling and subtract the rate of draining. Let = time in hrs to fill pool with both pipes open ( 1 pool filled ) / ( 3 hrs ) - ( 1 pool emptied ) / ( 4 hrs ) = ( 1 pool filled ) / ( t hrs ) Multiply both sides by It will take 12 hrs to fill the pool
 Travel_Word_Problems/743918: Flying with the wind, a plane traveled 510 miles in 3 hours. Flying against the wind, the plane traveled the same distance in 5 hours. Find the rate of the plane in calm air and the rate of the wind.1 solutions Answer 453099 by josmiceli(9685)   on 2013-05-01 15:10:11 (Show Source): You can put this solution on YOUR website!Let = the speed of the plane in still air in mi/hr Let = the speed of the wind in mi/hr = plane's speed flying with the wind in mi/hr = plane's speed flying against the wind in mi/hr -------------------- Flying with the wind: (1) Flying against the wind: (2) ---------------------- (1) and (2) --------------------- (1) (2) Add the equations and (1) (1) The rate of the plane in calm air is 136 mi/hr The rate of the wind is 34 mi/hr check: (2) (2) OK
 Travel_Word_Problems/743802: The speed of a bayou near Lafayette, Louisiana is 4 miles per hour. A paddle boat travels 48 miles upstream in the same amount of time it takes to travel 72 miles downstream. Find the speed of the boat in still water.1 solutions Answer 453074 by josmiceli(9685)   on 2013-05-01 09:52:57 (Show Source): You can put this solution on YOUR website!Let = the speed of the boat in still water = speed going downstream = speed going upstream Let = time for both trips ------------- Going upstream: (1) Going downstream: (2) --------------------- This is 2 equations and 2 unknowns, so you can solve for and
 Equations/743807: What are the values of x and y when (5−3i)−(x+ yi)=(3−i)?1 solutions Answer 453072 by josmiceli(9685)   on 2013-05-01 09:45:46 (Show Source): You can put this solution on YOUR website! ---------------------------- I have separated the left side into a real part and an imaginary part ---------------------------- and ---------- check: OK