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# Recent problems solved by 'josmiceli'

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 logarithm/347762: How do I express this expression as a single logarithm? 5log U-(1/3)logU^61 solutions Answer 248656 by josmiceli(9674)   on 2010-09-24 21:26:12 (Show Source):
 Miscellaneous_Word_Problems/347781: Jack usually mows his lawn in 5 hours, Marilyn can mow the same lawn in 4 hours. How much time would it take for them to mow the lawn together. They could mow the lawn in _?_ hours if they worked together.1 solutions Answer 248653 by josmiceli(9674)   on 2010-09-24 21:19:53 (Show Source): You can put this solution on YOUR website!Add their rates of mowing to get the rate mowing together Jack's rate: 1 lawn/5 hrs Marilyn's rate: 1 lawn/4 hrs Rate working together = 1 lawn/x hrs multiply both sides by hrs This is about 2 hrs and 13 min
 logarithm/347768: How do I solve for X? log (small x) (1/9) = -11 solutions Answer 248649 by josmiceli(9674)   on 2010-09-24 21:14:02 (Show Source): You can put this solution on YOUR website! logs are exponents. This equation says that the exponent with the base gives me I can write it this way:
 Systems-of-equations/347738: The Sheng family had dinner at their favorite restaurant. A 10% sales tax was added to their bill. amy paid the bill with a \$20 gift certificate plus \$23.5. How much did the family's dinner cost before tax? Round your answer to the nearest penny.1 solutions Answer 248615 by josmiceli(9674)   on 2010-09-24 18:39:44 (Show Source): You can put this solution on YOUR website!Let = bill before tax is the cost before tax
 Length-and-distance/347617: What is the area of a quadrilateral with vertices at (-3,-1), (-1,4) ,(7,4), and (5,-1) ? A 50 units^2 B 45 units^2 C 8sqrt(29) units^2 D 40 units^2 1 solutions Answer 248614 by josmiceli(9674)   on 2010-09-24 18:36:18 (Show Source): You can put this solution on YOUR website!The area, is the length x height The line connecting (-3,-1) and (5,-1) is a horizontal line segment with length and is unit below the x-axis The other pair, (-1,4) and (7,4) also has a length and also is horizontal with a height above the x-axis of The total distance between the horizontal line segments is square units
 Travel_Word_Problems/347693: Hillary is driving North on Route 15 with her cruise control set on 55 mph. Her car is 15 feet long. If it takes 0.2 seconds to pass the same type of car in the opposite direction, how fast is the other car traveling? (r1+r2)t=d1 solutions Answer 248611 by josmiceli(9674)   on 2010-09-24 18:25:38 (Show Source): You can put this solution on YOUR website!Let = the speed of the other car. Since they travel in opposite directions, I can consider Hillary's car to be stationary and the other car to be traveling at the sum of their speeds, which is First the nose of the other car has to travel 15 ft to get side-by-side, and another 15 ft to get past Hillary's car. (there are 3600 sec /hour and 5280 ft/mile) The other car's speed is 42.6 mi/hr
 expressions/347720: Showing my work and rounding to the nearest whole number, how do I evaluate 280ft/1s x 1mi/5280ft x 3600s/1hr ?1 solutions Answer 248603 by josmiceli(9674)   on 2010-09-24 18:07:01 (Show Source): You can put this solution on YOUR website!Regrouping the units, I have (ft/ft) x (s/s) , leaving mi/hr Doing the calculation:
 Quadratic_Equations/347665: A wire 60 inches long is cut into two pieces whose lengths have a ratio of 3 to 1. To find the length of each piece, let x be the length of the shorter piece. Since the wire is 60 inches long, and since the shorter piece is x inches long, what is the length of the longer piece?1 solutions Answer 248537 by josmiceli(9674)   on 2010-09-24 15:39:22 (Show Source): You can put this solution on YOUR website!If the ratio of the lengths is 3 to 1, the ratios of the lengths to the total length is 3 to 4 and 1 to 4 given: total length = in shorter piece = in ------------------- multiply both sides by Since the total length is , the longer piece is in
 Miscellaneous_Word_Problems/347676: LaToya Smith is a buyer for a large manufacturing company . She can purchase 200 pounds of chemicals for \$95. She can also purchase mixing vats for \$400 each. Sales tax on all products is 6% of the total cost of the order. Shipping costs for her order will be a flat \$30. This month she doesn’t know yet how many mixing vats she will need to order. Let y = number of mixing vats required. Write an equation using y that she can use to determine the total amount of her order. 1 solutions Answer 248534 by josmiceli(9674)   on 2010-09-24 15:32:57 (Show Source): You can put this solution on YOUR website!Let = number of 200 lb orders for chemicals Let = total dollar amount of order
 Linear_Equations_And_Systems_Word_Problems/347682: in 1994, the life expectancy of males in a certain country was 62.6 years. In 2001, it was 65.2 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994. Could someone help me solve this question by step by step? Thank you!!!1 solutions Answer 248530 by josmiceli(9674)   on 2010-09-24 15:24:22 (Show Source): You can put this solution on YOUR website!There must be a little more information. Is this problem part of exercises on linear equations? If so, given: Let t represent the number of years since 1994. (1994) (2001) Assuming this is a linear relation between and , The formula to use is: plugging in data: With this equation, you can find for any
 percentage/347387: an alloy of metals is 25% copper. another alloy is 50% copper. how much of each should be used to make 1000 grams of an alloy that is 45% copper?1 solutions Answer 248416 by josmiceli(9674)   on 2010-09-23 21:34:42 (Show Source): You can put this solution on YOUR website!given: By subtraction: 200 grams of the 25% copper and 800 grams of the 50% copper should be used
 Travel_Word_Problems/347407: A boat travels 12 miles up the Mississippi River and 12 miles back down river in a total of eight hours. The rate of the boat in still water is four miles per hour. Find the speed of the current.1 solutions Answer 248415 by josmiceli(9674)   on 2010-09-23 21:27:54 (Show Source): You can put this solution on YOUR website!given: mi/hr mi hrs Going upstream: Going downstream: By substitution: The speed of the current is 2 mi/hr check answer: Going upstream: hrs Going downstream: hrs hrs total OK
 Travel_Word_Problems/347413: Two cyclists, 108 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other. If they meet 3 hours later, what is the speed (in mi/h) of the faster cyclist? 1 solutions Answer 248399 by josmiceli(9674)   on 2010-09-23 20:57:43 (Show Source): You can put this solution on YOUR website!If they are cycling towards each other, you can think of one as being stationary, and the other as moving at the sum of their speeds. Thinking of the faster one as the one in motion, the equation is The faster cyclist's speed is 27 mi/hr check: The slower cyclist: mi The faster cyclist: mi
 Inequalities/347414: i don't understand inequalities1 solutions Answer 248383 by josmiceli(9674)   on 2010-09-23 20:23:26 (Show Source): You can put this solution on YOUR website!">" means "greater than" You know this is true Just like an equaliy, you can add or subtract the same number from both sides, and it's still true. I can rewrite this as: You have to picture this on the number line. I can rewrite again as: (with many, many more 6's) This is still true if you plot it on the number line. Always make use of the number line whenever you are confused by inequalities.
 Proportions/347412: I cant figure out the proportion for: How many minutes are equal to 2 1/3 hours? I'm stuck on how to turn fractions into whole numbers, unfortunately.1 solutions Answer 248380 by josmiceli(9674)   on 2010-09-23 20:15:22 (Show Source): You can put this solution on YOUR website!You can break up 2 1/3 into a whole number, 2 and a fraction, 1/3. Since there are 60 min in an hour, there are 120 min in 2 hrs And 1/3 of an hour is 1/3 of 60 min, and that is 20 min so the answer is 120 + 20 = 140 min in 2 1/3 hrs
 Travel_Word_Problems/345517: A car enters the freeway traveling at 60 miles per hour. A second car enters the freeway 11 minutes later traveling at 65 miles per hour. How long will it take for the second car to catch up to the first car?1 solutions Answer 247106 by josmiceli(9674)   on 2010-09-20 09:49:42 (Show Source): You can put this solution on YOUR website!In min, the 1st car travels mi Assume you have a stopwatch and you start it when the 2nd car enters the freeway. Write equations for both cars that show as the distance that the 2nd car goes in order to catch the 1st car. 1st car: (1) (1) 2nd car: (2) Note that the time is when you stop the stopwatch Set (1) = (2) hr It will take 2 hrs and 12 min for 2nd to catch 1st check: (1) (1) mi and (2) (2) mi OK
 Miscellaneous_Word_Problems/345479: There are k gallons of gasoline available to fill a tank. after d gallons have been pumped, what percent of gasoline , in terms of k and d has been pumped ?1 solutions Answer 247099 by josmiceli(9674)   on 2010-09-20 09:34:45 (Show Source): You can put this solution on YOUR website!After gallons have been pumped from the available gallons, this is per cent of available gasoline
 Geometry_Word_Problems/345480: The hands of a clock form the same angle at various times of the day . for example , the angle formed at 2:00 is congruent to the angle formed at 10:00. if a clock has a diameter of 1 foot , what is the distance along the edge of the clock from the minute hand the hour hand at 2:00 ?1 solutions Answer 247098 by josmiceli(9674)   on 2010-09-20 09:29:29 (Show Source): You can put this solution on YOUR website!The circumference, C, = given: ft ft The angle formed at 2 o'clock is of a whole circle- this is (10 min)/(60 min) This is about 3.14159/6 feet
 Mixture_Word_Problems/345458: How many liters of pure acid must be mixed with 20 liters of a 15% acid solution to get a 20% mixture?1 solutions Answer 247056 by josmiceli(9674)   on 2010-09-20 01:57:53 (Show Source): You can put this solution on YOUR website!Let = liters of pure acid needed In words: (total liters of acid)/(total liters of solution) = 20% given: acid already in solution: liters ------------- liters 1.25 liters of acid are needed check: OK
 Mixture_Word_Problems/345459: A 36-foot pipe is divided into three pieces. One piece is twice as long the shortest piece, and the third piece is 1 foot longer than four times the shortest piece. Find the Length of the shortest piece.1 solutions Answer 247055 by josmiceli(9674)   on 2010-09-20 01:48:32 (Show Source): You can put this solution on YOUR website!Let = length of shortest piece given: The shortest piece is 5 ft long
 Equations/345461: A ball falls from the top of a roof 320 feet above the ground. The formula h = -16t2 + 16t + 320 described the height of the ball above the ground, h, in feet, t seconds after the fall begins. How long will it take the ball to strike the ground?1 solutions Answer 247054 by josmiceli(9674)   on 2010-09-20 01:44:27 (Show Source): You can put this solution on YOUR website!When the ball hits the ground, , so Divide both sies by Use quadratic equation to find Take the negative square root in order to get a positive answer: sec The ball will hit the ground in 5 sec check answer: OK
 Mixture_Word_Problems/345429: You have 3 mL of 0.9% salt solution and you add 2 mL of pure water to it. What is the percentage of the salt solution now?1 solutions Answer 247051 by josmiceli(9674)   on 2010-09-20 00:09:40 (Show Source): You can put this solution on YOUR website!In words: (ml of salt)/(total ml of solution) = % salt given: Total ml of solution: ml Salt in solution: ml = .54%
 Mixture_Word_Problems/344406: We have 171 kg rice custing 7 rs/kg.we have rice at 11 rs/kg and 2 rs/kg .then after mixing 11 rs/kg and 2 rs/kg rice. What is quantity of 11 rs/kg rice ..1 solutions Answer 246335 by josmiceli(9674)   on 2010-09-17 01:53:55 (Show Source): You can put this solution on YOUR website!Let = kg of 11 rs/kg rice needed Let = kg of 2 rs/kg rice needed = cost of 11 rs/kg rice = cost of 2 rs/kg rice = cost of 7 rs/kg rice given: (1) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) The quantity of 11 rs/kg rice needed is 95 kg And, from (1): check answer: (2) (2) OK
 test/344403: Sandy held garage sale during w/c she charged a dime for everything but accepted a nickel if a buyer bargained well. At the end she had sold 12 items and had a total of 95 cents. She only had nickels & dimes. How many of each did she have? Pls I need the equation1 solutions Answer 246333 by josmiceli(9674)   on 2010-09-17 01:33:05 (Show Source): You can put this solution on YOUR website!Let =number of items that she sold for a nickel Then = number of items that she sold for a dime given: She sold 5 items for a nickel and 7 items for a dime check: OK