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# Recent problems solved by 'josmiceli'

josmiceli answered: 9696 problems
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 Money_Word_Problems/520863: A motorboat traveled 36 miles downstream, with the current, in 1.5 hours. The return trip upstream against the current, covered the same distance, but took two hours. Find the boats rate in still water and the rate of the current. I tried to figure this problem out, but had trouble making it into an equation. What would X and Y stand for in this case? 1 solutions Answer 346254 by josmiceli(9698)   on 2011-10-25 13:51:20 (Show Source): You can put this solution on YOUR website!Let = boat's rate in still water Let = rate of current given: ----------- Going downstream: (1) Going upstream: (2) ----------------- (1) (1) (1) and (2) (2) -------------- Add the equations (1) (2) and, since (1) (1) (1) The boats rate in still water is 21 mi/hr The rate of the current is 3 mi/hr check: (1) (1) (1) (1) OK
 Travel_Word_Problems/520875: ramon and liza found two snails that were trudging along together in the driveway. Having nothing to do, Liza and Ramon decided to figure out how fast they were moving. They determined that one was craling at a page of 15 mm/min and the other one at 10 mm/min. At these rates, how long will it take for the snails to be 10 centimeters apart?1 solutions Answer 346250 by josmiceli(9698)   on 2011-10-25 13:36:33 (Show Source): You can put this solution on YOUR website! cm is mm Let = time in minutes for snails to get mm apart For fast snail: (1) For slow snail: (2) and (3) ----------------- There are 3 equations and 3 unknowns so, it's solvable Subtract (2) from (1) (1) (2) Substituting: It will take 20 min for them to be 10 cm apart
 Rational-functions/520871: Please help!!! I keep getting 0.2123 seconds but not positive that this is correct...could someone show me the steps? Thank you!!! The period of time the pirate ship ride at a carnival takes to complete one cycle swinging to and fro is represented by the formula below for L feet long and T seconds. Find to the nearest hundredth of a second the period of time it takes the ride to swing one cycle if the ride hangs 200 feet. T=3π √(L/940)1 solutions Answer 346247 by josmiceli(9698)   on 2011-10-25 13:25:55 (Show Source): You can put this solution on YOUR website! sec This makes more sense to me if I was watching the actual ride. Hope I got it.
 Average/520874: If I take a test with 150 questions how many answers would have to be correct to get a 70 or above?1 solutions Answer 346241 by josmiceli(9698)   on 2011-10-25 13:14:44 (Show Source): You can put this solution on YOUR website!Let = number of correct answers Must get al least 105 correct answers
 Inequalities/520867: A car rents for \$40 per day plus 20 cents per mile. You are on a daily budget of \$92. What mileage will allow you to stay within your budget?1 solutions Answer 346240 by josmiceli(9698)   on 2011-10-25 13:12:23 (Show Source): You can put this solution on YOUR website!Let = miles driven to stay within budget given: (daily budget) - (daily rental fee) = \$52 is left for milage cost (dollars)/(dollars/mile) A maximum of 260 miles/day driven will allow you to stay within budget
 Travel_Word_Problems/520674: Roberta can drive her car 8.3 miles per dollar of gasoline that she buys. Her and three of her friends go on a road trip to a university that is 100 miles away and they want to split the cost of gasoline evenly. How much money does each have to contribute? 1 solutions Answer 346173 by josmiceli(9698)   on 2011-10-25 02:04:42 (Show Source): You can put this solution on YOUR website! miles x cost of trip Each contributes \$4.02
 Linear_Equations_And_Systems_Word_Problems/520665: Twice last month, Judy Carter rented a car from Enterprise in Fresno, California, and traveled around the southwest on business. Enterprise rents its cars for a daily fee, plus an additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her \$240.50. One her second business trip she drove 200 miles in 3 days, and paid \$146.00 for the rental. Fnd the daily fee and the mileage charge. I get so confused in all these numbers. How do I set up my equation?1 solutions Answer 346171 by josmiceli(9698)   on 2011-10-25 01:56:52 (Show Source): You can put this solution on YOUR website!Let = daily fee in dollars Let = milage charge in dollars In words: ( Cost of rental ) = ( number of days rented )x( daily fee ) + ( miles driven )x( milage fee ) For her first trip: (1) For her 2nd trip: (2) ------------------------- Multiply both sides of (1) by Multiply both sides of (2) by , Then subtract (2) from (1) (1) (2) and, since (2) (2) (2) (2) (2) The rental cost is \$32/day and \$.25/mile check answer: (1) (1) (1) (1) OK
 Linear-systems/520446: Assume that the number of defective basketballs produced is related by a linear equation to the total number produced. Suppose that 10 defective balls are produced in a lot of 325, and 17 defective balls are produced in a lot of 450. Find the number of defective balls produced in a lot of 550 balls.1 solutions Answer 346074 by josmiceli(9698)   on 2011-10-24 19:54:41 (Show Source): You can put this solution on YOUR website!Plot number of defective balls, , on the vertical axis Plot the lot size, , on the horizontal given: 2 points on the straight line ( 325,10 ) ( 450,17 ) Use the point-slope formula check: ( 450,17 ) OK When , Rounding off, there are 23 defective balls
 Numbers_Word_Problems/520437: A portable media player holds up to 9,000 songs. Kylie has 832 songs on her portable media player. Lance has 3 times as many songs. How many fewer songs can Lance add to his player than Kylie can add to hers?1 solutions Answer 346061 by josmiceli(9698)   on 2011-10-24 19:23:25 (Show Source): You can put this solution on YOUR website!Kylie can add to her player Lance has on his player He can add to his player Lance can add 1664 fewer songs to his player than Kylie
 Miscellaneous_Word_Problems/520167: This is a Rational Word Problem but i think it still goes under this category. The word problem is: My dog, Pooba, likes to swim in the river. Pooba can swim 6 miles per hour in still water. He can swim 6 miles upstream in the same time it takes to swim 18 miles downstream. What is the speed of the river's current? Please help me.1 solutions Answer 345951 by josmiceli(9698)   on 2011-10-24 13:07:10 (Show Source): You can put this solution on YOUR website!Let = speed of current in mi/hr Let = dog's swimming speed in still water in mi/hr Let = dog's time swimming both upstream and downstream in hours given: --------- Swimming upstream: (1) (1) Swimming downstream: (2) (2) --------------- (1) (2) Add the equations and, since (1) (1) (1) (1) (1) The speed of the current is 3 mi/hr check answer: (2) (2) (2) (2) and (1) (1) (1) (1) OK
 Numbers_Word_Problems/520170: All the positive integers with an initial digit of 2 are written down in succession. What is the 1978th digit thus written?1 solutions Answer 345948 by josmiceli(9698)   on 2011-10-24 12:45:21 (Show Source): You can put this solution on YOUR website!2 = 1 integer 20 - 29 = 10 integers 200 - 299 = 100 integers 2000 - 2999 = 1000 integers So far: integers 20000 - 20866 = 867 integers The 1978th integer is 20866
 Mixture_Word_Problems/520163: John is going to make 13 pounds of mixed nuts for a party. if keil can spend \$64.50 on nuts and peanuts cost \$2.50 per pound and fancy nuts cost \$6.50 pound, how many pounds of each should he buy?1 solutions Answer 345945 by josmiceli(9698)   on 2011-10-24 12:37:04 (Show Source): You can put this solution on YOUR website!Let = pounds of peanuts Let = pounds of fancy nuts given: (1) (2) ---------------------- (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) 5 pounds of peanuts are needed 8 pounds of fancy nuts are needed
 Probability-and-statistics/520004: if a single card is drawn from a deck of plying cards what is the probability of that is diamond,a face card or a king1 solutions Answer 345908 by josmiceli(9698)   on 2011-10-24 03:04:18 (Show Source): You can put this solution on YOUR website!P(diamond) = P(face card) = P(king) = --------------------- P(diamond) OR P(face card) OR P(king) =
 Travel_Word_Problems/520014: Kevin's plane flew in a direct line from its base at 480 kph and returned over the same route at a rate of 400 kph, requiring 15 minutes longer on the return trip. How far did it fly from its base?1 solutions Answer 345907 by josmiceli(9698)   on 2011-10-24 02:56:41 (Show Source): You can put this solution on YOUR website!Let = distance from base Let = time of flight from base given: km/hr km/hr hrs ------------------------- Flying away from base: (1) Flying back to base: (2) ---------------------------- (2) Substitute (1) into (2) (2) (2) (2) and, since (1) (1) (1) It flew 600 km from its base
 Miscellaneous_Word_Problems/519758: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 10 L of a 40% disinfectant solution? 75% solution ? L 25% solution ? 1 solutions Answer 345775 by josmiceli(9698)   on 2011-10-23 17:41:58 (Show Source): You can put this solution on YOUR website!Let = liters of 75% solution needed Let = liters of 25% solution needed given: = liters of disinfectant in 75% solution = liters of disinfectant in 25% solution --------------- (1) (2) --------------------------- (2) (2) (2) Subtract (1) from (2) (2) (1) and (1) (1) (1) 3 liters of 75% solution are needed 7 liters of 25% solution are needed check: (2) (2) (2) (2) (2) OK
 Functions/519729: I don't understand how to do this: Find the domain of: Thanks in advance :)!1 solutions Answer 345768 by josmiceli(9698)   on 2011-10-23 17:09:04 (Show Source): You can put this solution on YOUR website! In the 1st factor, , x can be any real value + or - ----------------- Of the factor inside the square root, cannot be between and If that is true, the factor , will be negative, and the square root is not a real number. ---------------- As for between and , both of the factors under the square root turn out to be negative, and (-) x (-) = + so that is a real number. The domain is or
 Square-cubic-other-roots/519736: How do you solve 9 divided by parenthesis the square root of 11 plus the square root of 5 end parenthesis?1 solutions Answer 345754 by josmiceli(9698)   on 2011-10-23 16:44:42 (Show Source): You can put this solution on YOUR website! You can do this on a (good) calculator, or, you can simplify it first
 Mixture_Word_Problems/519698: During Chemistry class, Tamika plans to mix a bottle containing 50ml of 10% HCL solution with a bottle containing 25% HCL solution. If she wants a 20% solution. How much 25% HCL must be added?1 solutions Answer 345749 by josmiceli(9698)   on 2011-10-23 16:35:25 (Show Source): You can put this solution on YOUR website!let = ml of 25% HCL solution to be added In words: ( final ml of HCL ) / ( final ml of total solution ) = 20% given: ml of HCL in 10% solution ml of HCL in 25% solution ----------------------------- 100 ml of 25% HCL solution are needed check: OK
 Age_Word_Problems/519498: "you were a quarter of my age when I was twice your present age" said A to B. In five years from now, our ages will add upto 45. how old was I when you were born? {A is asking B}1 solutions Answer 345663 by josmiceli(9698)   on 2011-10-23 03:59:36 (Show Source): You can put this solution on YOUR website!Let = A's age now Let = B's age now given: The difference in their ages is always (assuming a is older) When , then B must have been and and, since When B was born ( age = 0 ) The difference in their ages was so A was answer ----------------- check answer: In 5 years, their ages will add up to OK When A was , B was is 1/4 of OK
 Money_Word_Problems/519460: A woman paid \$21.56 (including sales tax) for a book that was marked 20% off. The sales tax was 8%. What was the cover price of the book?1 solutions Answer 345620 by josmiceli(9698)   on 2011-10-22 22:05:39 (Show Source): You can put this solution on YOUR website!Let = cover price Let = tax included (1) (2) (2) (2) By substitution: (1) (1) (1) cover price is \$24.95 ---------------- check: with 20% off: plus 8% tax: OK
 Finance/519446: Bob collects dimes and quarters. He has \$31.70 total. If he has 5 fewer dimes than quarters, how many of each does he have?1 solutions Answer 345615 by josmiceli(9698)   on 2011-10-22 21:50:59 (Show Source): You can put this solution on YOUR website!Let = number of dimes Let = number of quarters given: (1) (2) ( in cents) ----------------------- (2) and (1) (1) Add the equations (2) (1) and (1) (1) (1) He has 87 dimes and 92 quarters check: (2) (2) (2) OK
 Mixture_Word_Problems/519443: ...A coffee merchant combines coffee costing \$6.00 per pound with coffee costing \$4.50 per pound. How many pounds of each should be used to make 30 lb of a blend costing \$5.30 per pound? \$6.00/lb coffee 1 lb \$4.50/lb coffee 2 lb 1 solutions Answer 345598 by josmiceli(9698)   on 2011-10-22 21:14:55 (Show Source): You can put this solution on YOUR website!Let = pounds of \$6 coffee needed Let = pounds of \$4.50 coffee needed given: (1) (2) ( in dimes) ------------------------- (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) 16 pounds of \$6 coffee are needed 14 pounds of \$4.50 coffee are needed check: (2) (2) (2) (2) OK
 Travel_Word_Problems/519427: How to & steps to solve: Justin drove to his parents 175 miles away. On his way there his speed averaged 24 times faster then on his way back. He drove a total of 5 hours. What was his speed on the way there and on the way back? I've solved it to: 175s+175(5+24)=5s(s+24) But I'm stuck there. I don't know what to do next. 1 solutions Answer 345592 by josmiceli(9698)   on 2011-10-22 20:57:56 (Show Source): You can put this solution on YOUR website!Let = his speed on the way back Let = his time on the way back given: = his speed going = one way distance = his time going ---------------------- Going to parents: (1) Coming back: (2) Substitute (2) into (1) (1) (1) (1) (1) mi/hr mi/hr ----------------------- check: (2) (2) (1) (1) (1) (1) and (2) (2) I think there is something wrong with the data, maybe a miscopy. The speed going can't be 875 mi/hr I rechecked my math- I think it's OK Is the right?
 Miscellaneous_Word_Problems/519124: an "n-gauge" train model is created using a scale of 1:160 feet. if an actual train engine, "K-4", is 45 feet long, what is the length of the "n-gauge" model engine in inches?1 solutions Answer 345399 by josmiceli(9698)   on 2011-10-21 16:59:55 (Show Source): You can put this solution on YOUR website! Multiply both sides by feet The length of the model engine is 3 and 3/8 inches
 Quadratic_Equations/518785: use FOIL method to find the product (9x^2-8)(x^3-2)1 solutions Answer 345256 by josmiceli(9698)   on 2011-10-20 21:07:55 (Show Source):
 Travel_Word_Problems/518777: Rob can deliver papers 4 times as fast as his younger brother. If they work together, it takes them 2 hours. How long would it take each to deliver the papers alone?1 solutions Answer 345255 by josmiceli(9698)   on 2011-10-20 21:04:03 (Show Source): You can put this solution on YOUR website!Call delivering the papers 1 job Let = Rob's time to deliver the papers in hours = younger brother's time Add their rates to get rate working together Multiply both sides by Rob's time working alone is 2.5 hrs Brother's time working alone is 10 hrs
 Graphs/518256: what is the intercepts of x-4y=41 solutions Answer 345111 by josmiceli(9698)   on 2011-10-20 00:06:29 (Show Source): You can put this solution on YOUR website! y-intercept: (0, -1) ------------ x-intercept: (4, 0) ----------
 Travel_Word_Problems/518246: At noon, a car B is 10 km north of another car A. Car A travels to the east at 30 km/h and car B travels south at 40 km/h. When will they be the closest to each other?1 solutions Answer 345108 by josmiceli(9698)   on 2011-10-19 23:45:43 (Show Source): You can put this solution on YOUR website!The position of car B relative to car A's starting point is km The position of car A relative to it's own starting point is The distance between A and B is The minimum value occurs at They will be closest to each other in 9.6 minutes Hope I got it
 Equations/518241: Sarah and Keith Robinson purchased 40 stamps, a mixture of 39 cent and 24 cent stamps. Find the number of each type of stamp if they spent \$14.85 1 solutions Answer 345103 by josmiceli(9698)   on 2011-10-19 23:23:56 (Show Source): You can put this solution on YOUR website!Let = number of 39c stamps Let = number of 24c stamps given: (1) (2) ( in cents ) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) They buy 35 39c stamps They buy 5 24c stamps check: (2) (2) (2) OK
 Travel_Word_Problems/518231: the rate of the boat in still water is 8 mph. At this rate a 30 mile trip downstream takes the same amount of time as an 18 mile trip upstream. What is the rate of the current?1 solutions Answer 345102 by josmiceli(9698)   on 2011-10-19 23:14:21 (Show Source): You can put this solution on YOUR website!Let = rate in still water Let = rate of current going downstream: (1) Going upstream: (2) ----------------- given: mi mi mi/hr --------------- (1) (2) ----------------- (1) (2) Add the equations hrs and, since (1) (1) (1) (1) The rate of the current is 2 mi/hr check: (1) (1) (1) OK
 Linear-equations/518220: Find the vertex, x and y intercepts of the parabola given by the equation y= 3x2-2x+11 solutions Answer 345101 by josmiceli(9698)   on 2011-10-19 22:58:15 (Show Source): You can put this solution on YOUR website!The vertex is at The vertex is at ( 1/3, 2/3 ) ---------------------- y-intercept: ( 0,1) ------------------- x-intercept: Use quadratic formula There is no x-intercept, since both roots are complx numbers Here's a plot: