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# Recent problems solved by 'josmiceli'

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 Probability-and-statistics/551256: How many cards must be drawn from a standard 52 card deck to be certain that 4 cards of the same suit are drawn? Thanks in advance!!!1 solutions Answer 359566 by josmiceli(9668)   on 2011-12-31 12:40:34 (Show Source): You can put this solution on YOUR website!The 1st 13 cards you draw could all be the same suit. Not likely, but possible. If you draw 14 cards, there is zero probability that they will all be the same suit, and it is certain you will have at least 2 cards of different suits. If you draw more cards until you have drawn 26, it is still possible you have 13 of one suit and 13 of another suit If you draw one more card to make 27, you know that you are certain to have at least 3 cards of different suits. If you keep drawing until you have 3x13 = 39 cards it is still possible that you have only cards of 3 suits, Drawing one more card makes it 100% certain that you have all 4 suits So, you must draw 40 cards to know that you have cards of all 4 suits
 test/551145: A certain two digit number Is two more than 3 times the units digit. If the digits if the number are interchanged, the resulting number is 24 less than 4 times the original number. Find the original number. Please help me solve this!!!!!!!1 solutions Answer 359451 by josmiceli(9668)   on 2011-12-30 17:22:58 (Show Source): You can put this solution on YOUR website!Let = the 10's digit Let = the 1's digit given: (1) (2) --------------------------- (1) (1) and (2) (2) (2) ------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) (1) (1) (1) The original number is 29 check: (2) (2) (2) (2) (2) OK
 test/551147: The sum of the digits of a certain two digit number is eight. If the original number is subtracted from the number formed by interchanging the digits, the result is -18. What is the original number? Please help!!!1 solutions Answer 359440 by josmiceli(9668)   on 2011-12-30 16:49:45 (Show Source): You can put this solution on YOUR website!Let the 10's digit = Let the 1's digit = given: (1) (2) ------------------------------ (2) (2) Multiply both sides of (1) by and add (1) and (2) (1) (2) and, since (1) (1) (1) The original number is 53 check answer: (2) (2) (2) (2) OK
 Mixture_Word_Problems/551089: How much soil containing 45% sand do you need to add to 1ft.of soil containing 15% sand in order to make a soil containing 35% sand?1 solutions Answer 359392 by josmiceli(9668)   on 2011-12-30 14:08:28 (Show Source): You can put this solution on YOUR website!Let = ft of 45% soil needed = ft of sand in 45% soil = ft of sand in 15% soil -------------------------- 2 ft of soil containing 45% sand is needed check answer: OK
 Mixture_Word_Problems/551101: A chemist has one solution that is 20% acid and a second that is 65% acid. How many gallons of each should be mixed together to get 120 gallons of a solution that is 50% acid?1 solutions Answer 359380 by josmiceli(9668)   on 2011-12-30 13:51:25 (Show Source): You can put this solution on YOUR website!Let = gallons of 20% solution needed Let = gallons of 65% solution needed = gallons of acid in 20% solution = gallons of acid in 65% solution given: (1) (2) ------------------------- (2) (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) (1) 40 gallons of 20% solution are needed 80 gallons of 65% solution are needed check answer: (2) (2) (2) (2) (2) OK
 Evaluation_Word_Problems/550968: Together, Lake Superior and Lake Michigan cover 54 thousand square miles. Lake Superior is approximately 10 thousand square miles larger than Lake Michigan. Find the size of each lake. Divide 54 into 2= 27, then subtract 5 from one side and then add it to the other side x=32 y=22 22+32=54, I understand but how do I put this in a formula? I know the answer but I'm not too sure how I would present it on paper?1 solutions Answer 359263 by josmiceli(9668)   on 2011-12-29 21:35:12 (Show Source): You can put this solution on YOUR website!Let = area of L.S. Let = area of L.M. given: (1) sq. mi. (2) sq. mi. ------------------------ (2) Add the equations and, since The area of Superior is 32,000 sq mi The area of Michigan is 22,000 sq mi
 Age_Word_Problems/550914: The woman is three times as old as her son. If she is half as old as her father, her father is commonly how many times older than her son?1 solutions Answer 359225 by josmiceli(9668)   on 2011-12-29 17:11:21 (Show Source): You can put this solution on YOUR website!let = Woman's age Let = Father's age Let = Son's age given: By substitution: Her father is 6 times older than her Son
 Radicals/550915: simplify cube root 54 x^10 please show steps and help me to understand why the steps work1 solutions Answer 359221 by josmiceli(9668)   on 2011-12-29 17:01:54 (Show Source): You can put this solution on YOUR website! answer Note that so,
 Rate-of-work-word-problems/550912: Ares had h hours of homework to do, but he just worked w hours. What fractional part of his homework remains?1 solutions Answer 359219 by josmiceli(9668)   on 2011-12-29 16:53:55 (Show Source): You can put this solution on YOUR website!He has hours of homework left to do fractional part of his homework remains
 Geometric_formulas/550886: what is the equation of the line that passes through (0, -2) and (4, 6)?1 solutions Answer 359218 by josmiceli(9668)   on 2011-12-29 16:49:21 (Show Source): You can put this solution on YOUR website!Use the point-slope formula Here's the plot:
 Rate-of-work-word-problems/550903: the amount of time it takes to paint a house varies inversly with the number of painters. if it takes 4 painters 40 hours how long would it take 10 painters? A.100 HOURS B.26 HOURS C.20 HOURS D.16 HOURS ...... how did you get the answer?1 solutions Answer 359212 by josmiceli(9668)   on 2011-12-29 16:39:49 (Show Source): You can put this solution on YOUR website!They want you to show the inverse relation which is where = number of painters = hours it takes them to paint a house = constant of proportionality ------------------------------ You have to find given: Now you can say: (D) 16 hours is the answer
 Linear-equations/550904: simplify (a3b)(ab)41 solutions Answer 359207 by josmiceli(9668)   on 2011-12-29 16:32:46 (Show Source): You can put this solution on YOUR website! answer
 Numbers_Word_Problems/550867: The tens digit of a certain two digit number is 1 more than 3 times the units digit. The original number is 9 less than 3 times the number formed by interchanging the digits. Find the original number. Please help me answer this!1 solutions Answer 359200 by josmiceli(9668)   on 2011-12-29 16:21:45 (Show Source): You can put this solution on YOUR website!Let = tens digit Let = units digit given: (1) (2) --------------------------- (2) (2) Substitute (1) into (2) (2) (2) (2) (2) Either I made a mistake, or this is impossible to solve. Did you copy it right?
 Expressions-with-variables/550830: The reader has two teenaged children and wants to choose the best plan. The first plan has a flat charge of \$.40 each day plus \$.08 per minute of phone calls. Write an expression for the daily cost of one phone, letting x represent the number of minutes of phone calls used in one day. Complete the expression 9( ) The second plan charges \$.25 per minute of phone calls with no additional daily charges. Write and expression for the daily cost of two phone calls letting x represent the number of minutes of phone calls used in one day. B. Write an exression you would use to find the number of minutes of phone calls it takes for the costs to be the same.1 solutions Answer 359127 by josmiceli(9668)   on 2011-12-29 10:06:11 (Show Source): You can put this solution on YOUR website!(1) The first plan has daily cost = (2) The 2nd plan has daily cost = (3) The costs will be the same when: The costs are the same when 2 minutes and 21 seconds of phone calls are used in one day
 Triangles/550783: Determine whether the given coordinates are vertices of a triangle. R(1,3),S(4,0),T(10,-6)1 solutions Answer 359082 by josmiceli(9668)   on 2011-12-28 23:26:25 (Show Source): You can put this solution on YOUR website!If the slope from R to S is different from the slope from S to T, then The points cannot lie on the same line, and they must form a triangle ---------- Slope R to S: Slope S to T: --------- The slopes are the same, so 2 line segments joined together with the same slope form a straight line, so The 3 points do not make a triangle
 Human-and-algebraic-language/550769: An acid solution was made by mixing 10 gal. of a 20% acid solution and 5 gal. of a 80% acid solution. What is the concentration of the mixture?1 solutions Answer 359070 by josmiceli(9668)   on 2011-12-28 21:43:17 (Show Source): You can put this solution on YOUR website! gal of acid in 20% solution gal of acid in 80% solution concentration = = The concentration is 40%
 Equations/550665: I need to expand this quadratic equation: (3r+8)^2 I answered 3r^2-+2(8*3)+64 ,but it was counted wrong. Could anyone help me?1 solutions Answer 358977 by josmiceli(9668)   on 2011-12-28 13:50:09 (Show Source): You can put this solution on YOUR website! answer ---------------------- There's a very simple way to check this Pick a small prime number like 13 and say and OK
 Miscellaneous_Word_Problems/550658: each spring, the conservation authority stocks the local lake with 10 000 bass and perch. if there were three times as many bass and twice as many perch, the total number of fish would be 22 000. How many of each type of fish make up 10 000?1 solutions Answer 358973 by josmiceli(9668)   on 2011-12-28 13:40:12 (Show Source): You can put this solution on YOUR website!Let = number of bass Let = number of perch given: (1) (2) ----------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, from (1) (1) (1) There are 2,000 bass and 8,000 perch
 Trigonometry-basics/550663: what is the solution set of the equation x^2-7x =-61 solutions Answer 358971 by josmiceli(9668)   on 2011-12-28 13:32:20 (Show Source): You can put this solution on YOUR website! Complete the square take the square root of both sides and, taking the negative square root, The solution set is (6,0) and (1,0) check: OK
 Age_Word_Problems/550659: Sally is 12 years old. She is four years older than twice the age of Jan.1 solutions Answer 358968 by josmiceli(9668)   on 2011-12-28 13:21:50 (Show Source): You can put this solution on YOUR website!Let = Jan's age Jan is 4
 Travel_Word_Problems/550660: a new airplane can travel at speeds up to 4,680 miles per hour. how many miles can the airplane travel in 10 seconds?1 solutions Answer 358965 by josmiceli(9668)   on 2011-12-28 13:17:22 (Show Source): You can put this solution on YOUR website!With just units and no numbers: ( miles / hour ) x ( hours / minute ) x ( minutes / second ) x ( seconds ) = miles ----------- and with numbers: The airplane can travel 13 miles in 10 seconds
 absolute-value/550594: In order to entice people to work for them, a local used car lot advertises that it will pay a commission to its employees in the amount of 12% of the employees total sales for each month. 1. How much in total sales would an employee have to sell in one month to earn \$2700 in commission. 2. How much would an employee earn in commission if they sold \$76,000 worth of used cars in one month?1 solutions Answer 358959 by josmiceli(9668)   on 2011-12-28 13:01:53 (Show Source): You can put this solution on YOUR website!(1) Let = total sales for 1 month The employee would have to make \$22,500 in sales for the month (2) The commission is \$9,120
 Equations/550522: Please help me find the equation of the line perpendicular to -4x-8y=-5 that contains the point (-2,5). A.y=1/2x+6 B.y=2x+1 C.y=-2x+1 D.y=2x+91 solutions Answer 358866 by josmiceli(9668)   on 2011-12-28 01:45:02 (Show Source): You can put this solution on YOUR website! First, multiply both sides by This is in the form where Any line which is perpendicular to this line will have slope = ------------------ So far I have I need to find Plug in the point (-2,5) The equation is D:
 Mixture_Word_Problems/550577: How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?1 solutions Answer 358863 by josmiceli(9668)   on 2011-12-28 01:35:32 (Show Source): You can put this solution on YOUR website!Let = liters of 20% solution needed given: liters of alcohol in 50% solution liters of alcohol in 20% solution ------------- 80 liters of 20% solution are needed check: OK
 percentage/550509: Peter bought a computer that normally costs \$1,500. The computer is on sale for 15% off. Peter paid 7% sales tax on the sale price of the computer. How much did peter pay for the computer?1 solutions Answer 358841 by josmiceli(9668)   on 2011-12-27 21:43:11 (Show Source): You can put this solution on YOUR website!The sale price is and Peter paid \$1.364.25
 Rectangles/550531: The perimeter of a rectangle is 50 m. The length is 1 m more than twice the width. Find the dimensions. I am having trouble figuring out how to find the width so I can find the length.1 solutions Answer 358836 by josmiceli(9668)   on 2011-12-27 20:57:49 (Show Source): You can put this solution on YOUR website!Let = length Let = width given: Perimeter = m (1) m ---------------- The formula for perimeter is (2) Substitute (1) into (2) (2) (2) (2) (2) m and, since (1) (1) (1) m The dimensions are 8 x 17 m2 check: m
 Money_Word_Problems/550448: if a 30000 machine deprecated 1% of its original value each year, find a function f that expresses the machine's value V after t years have elapsed1 solutions Answer 358769 by josmiceli(9668)   on 2011-12-27 15:12:13 (Show Source): You can put this solution on YOUR website!Let , the initial value Let = value after years given: ----------------------- I can say
 Geometric_formulas/550463: Find the value of k so that the given points are 26 units apart. (–8, k ), (–7, 0)1 solutions Answer 358763 by josmiceli(9668)   on 2011-12-27 14:50:10 (Show Source): You can put this solution on YOUR website!Applying the distance formula: also If is assumed to be negative Hope I got it
 test/550407: Express f(x) = |x + 4| − 6 in piecewise form without using absolute values.1 solutions Answer 358724 by josmiceli(9668)   on 2011-12-27 11:20:32 (Show Source): You can put this solution on YOUR website!If , then This is simply ------------- If , then ------------- Here's the plot: The solution is above where the lines meet
 Quadratic_Equations/550389: an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express train in km/hr.1 solutions Answer 358704 by josmiceli(9668)   on 2011-12-27 09:42:26 (Show Source): You can put this solution on YOUR website!Let = speed of express train = speed of slower train Let = time for express train to cover km ------------ Express train: (1) Slower train: (2) ------------------------- (2) Substitute (1) into (2) (2) (2) (2) Substitute this into (1) (1) (1) (1) (1) Complete the square (1) (1) (1) (1) (1) (1) The speed of the express train is 60 km/hr check answer: (1) (1) (1) hrs and (2) (2) (2) (2) (2) hrs OK