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# Recent problems solved by 'checkley71'

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 Linear-systems/115151: This question is from textbook Julio Mendez is a carpenter. He is building a staircase between the first and second floors of a house, a height of 9 feet. The tread, or depth of each step, must be 10 inches. The slope of the staircase cannot exceed 3/4. What is the measure of the riser, or height of each step?1 solutions Answer 83949 by checkley71(8403)   on 2007-12-07 21:39:32 (Show Source): You can put this solution on YOUR website!WHAT YOU HAVE IS A RIGHT TRIANGLE WITH A SIDE=9 FEET AND A SLOPE OF 3/4. THUS YOU HAVE 3/4=9/X OR 3X=36 OR X=36/3 OR X=12 FOR THE SECONF SIDE OF THE RIGHT TRIANGLE. 12 FEET=144 INCHES. WITH A TREAD LENGTH OF 10 INCHES THERE IS ONLY ROOM FOR 144/10=14.4 STEPS. SO TO KEEP WITHIN THE 3/4 SLOPE RESTRICTION YOU CAN ONLY HAVE 14 STEPS. THE 9 FEET HEIGHT=108 INCHES. 108/14~7.7 INCH RISERS FOR THE 14 STEPS.
 Probability-and-statistics/115152: There are 30 qualified applicants for 5 openings in the sales department. In how many different ways can the group of 5 be selected?1 solutions Answer 83947 by checkley71(8403)   on 2007-12-07 21:28:46 (Show Source): You can put this solution on YOUR website!THE FIRST APPLICANT PICKED CAN BE 1 OF 30, THE SECOND CAN BE 1 OF 29 ETC. THEREFORE THE TOTAL NUMBER OF WAYS TO PICK 5 APPLICANTS IS: 30*29*28*27*26=17,100,720
 percentage/115174: This question is from textbook algebra 1 state whether each percentof change is a percent of increase or a percent of decrease. Then find the percentof increas or decrease. Round to the nearest whole percent. original: 97 cases new: 115 cases1 solutions Answer 83946 by checkley71(8403)   on 2007-12-07 21:24:47 (Show Source): You can put this solution on YOUR website!115/97=1.185567 OR THIS IS AN INCREASE OF 19 %.
 Proportions/115177: This question is from textbook Algebra 1 a forest contains about 500 trees. You randomly pick 67 trees and find that 27 of them are oaks. What is the experimental probability that a tree in the forest is an oak?1 solutions Answer 83945 by checkley71(8403)   on 2007-12-07 21:22:34 (Show Source): You can put this solution on YOUR website!27/67=.40 OR 40% OF THE SAMPLE ARE OAKS. THEREFORE 40% OF THE 500 ARE PROBABLY OAKS. .4*500=200 IN THIS FOREST 200 ARE PROBABLY OAKS.
 Equations/115202: A long-distance phone calls \$0.96 for the first minute and \$0.72 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding \$6.1 solutions Answer 83944 by checkley71(8403)   on 2007-12-07 21:19:12 (Show Source): You can put this solution on YOUR website!.96+.72M=6 .72M=6-.96 .72M=5.04 M=5.04/.72 M=7 MINUTES IS THE MAXIMUM AMOUNT OF TIME THAT CAN BE USED WITHOUT EXCEEDING \$6 PROOF LETM>7.1 .96+.72*7.1>6 .96+5.112>6 6.072>6
 Systems-of-equations/115306: This question is from textbook Beginning Algebra Multiply. (x- (1/3) (x+ (1/3)) X minus one-third multiplied by X plus one-third. I am not sure what to do.1 solutions Answer 83943 by checkley71(8403)   on 2007-12-07 21:10:25 (Show Source): You can put this solution on YOUR website!THE EASIEST WAY TO SOLVE THESE TYPE OF PROBLEMS IS TO USE VERTICLE MULTIPLICATION: X-1/3 X+1/3 ----------------------- X^2-X/3+X/3-1/9 X^2-1/9 ANSWER.
 Equations/115323: Can someone please help me with this I have to write this fraction in simplest form -15x^3 y^3/-20xy^41 solutions Answer 83942 by checkley71(8403)   on 2007-12-07 21:06:57 (Show Source): You can put this solution on YOUR website!-15X^3Y^3/-20XY^4 FACTORING THE INTEGERS WE GET BY DIVIDING BOTH BY -5 (-15/-20=3/4) factoring the x terms x^3/x we get x^2 x^[3-1]=x^2 factoring the y terms y^3/y^4 we get 1/y y^[3-4)=y^-1 or 1/y 3X^2/4Y ANSWER.
 Equations/115325: Given f(x) = x2 + 2x + 1, find f(0).1 solutions Answer 83941 by checkley71(8403)   on 2007-12-07 21:00:35 (Show Source): You can put this solution on YOUR website!F(X)=X^2+2X+1 F(0)=0^2+2*0+1 F(0)=1
 Equations/115328: Solve the system by substitution. 3x – y = –7 x + y = –9 1 solutions Answer 83940 by checkley71(8403)   on 2007-12-07 20:58:22 (Show Source): You can put this solution on YOUR website!X+Y=9 OR X=-Y-9 SUBSTITUTE (-Y-9) FOR X IN THE OTHER EQUATION & SOLVE FOR Y. 3(-Y-9)-Y=-7 -3Y-27-Y=-7 -4Y=-7+27 -4Y=20 Y=20/-4 Y=-5 ANSWER. X-5=-9 X=-9+5 X=-4 ANSWER. PROOF 3*-4-(-5)=-7 -12+5=-7 -7=-7
 Equations/115329: Solve the system by graphing. 3x + y = –1 9x + 3y = –3 1 solutions Answer 83939 by checkley71(8403)   on 2007-12-07 20:51:52 (Show Source): You can put this solution on YOUR website!3x+y=-1 or y=-3x-1 (red line) 9x+3y=-3 or 3y=-9x-3 or y=-9x/3-3/3 or y=-3x-1 (green line) NOTICE THAT THESE 2 EQUATIONS ARE THE SAME THUS THE LINES ARE SUPERIMPOSED GREEN ON RED. (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, of TWO functions y = -3x -1 and y = -3x -1).
 Equations/115332: Graph f(x) = –x – 2.1 solutions Answer 83937 by checkley71(8403)   on 2007-12-07 20:46:42 (Show Source): You can put this solution on YOUR website!f(x)=-x-2 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -x -2).
 Rational-functions/115234: This question is from textbook Algebra and trigonometry structure and method how much pure antifreeze must be added to 12L of a 40% solution of antifreeze to obtain a 60& solution?1 solutions Answer 83854 by checkley71(8403)   on 2007-12-07 11:21:21 (Show Source): You can put this solution on YOUR website!.4*12+1X=.6(12+X) 4.8+X=7.2+.6X X-.6X=7.2-4.8 .4X=2.4 X=2.4/.4 X=6 LITERS OF PURE ANTIFREEZE MUST BE ADDED. PROOF .4*12+6=.6(12+6) 4.8+6=.6*18 10.8=10.8
 Geometry_Word_Problems/115254: a ladder is resting against a wall. the top of the ladder touches the wall at the height of 18 ft. find the length of the ladder if the length is 6 ft more than its distance from the wall 1 solutions Answer 83853 by checkley71(8403)   on 2007-12-07 11:15:41 (Show Source): You can put this solution on YOUR website!HERE YOU HAVE A RIGHT TRIANGLE WITH SIDE=18 FEET & THE HYPOTENUSE=BASE+6. A^2+B^2=C^2 18^2+B^2=(B+6)^2 324+B^2=B^2+12B+36 12B=324-36 12B=288 B=288/12 B=24 IS THE LENGTH FROM THE FOOT OF THE LADDER TO THE BUILDING. 24+6=30 FEET IS THE LENGTH OF THE LADDER. PROOF 18^2+24^2=30^2 324+576=900 900=900
 Miscellaneous_Word_Problems/115261: The sum of two numbers is 39 and their difference is 7. What are the numbers?1 solutions Answer 83849 by checkley71(8403)   on 2007-12-07 11:03:51 (Show Source): You can put this solution on YOUR website!X+Y=39 OR X=39-Y X-Y=7 NOW REPLACE X BY (39-Y) IN THE SECOND EQUATION & SOLVE FOR Y. 39-Y-Y=7 -2Y=7-39 -2Y=-32 Y=-32/-2 Y=16 ANSWER. X+16=39 X=39-16 X=23 ANSWER. PROOF 23-16=7 7=7
 Length-and-distance/115188: A fence builder wishes to determine the cost of fencing a rectangular yard with a perimeter of 68 feet. Suppose that the length of the yard is 4 feet less than its width. Find the length and width of the room.1 solutions Answer 83800 by checkley71(8403)   on 2007-12-06 21:06:02 (Show Source): You can put this solution on YOUR website!L=W-4 PERIMETER=2W+2L 2W+2(W-4)=68 2W+2W-8=68 4W=68+8 4W=76 W=76/4 W=19 FEET IS THE WIDTH L=19-4=15 FEET FOR THE LENGTH. PROOF 2*19+2*15=68 38+30=68 68=68
 Equations/115179: A service station wishes to mix 40 L of a 78% antifreeze solution. How many litres of a 75% solution and a 90% solution should be used in forming the mixture? ( using two unknowns, write two equations and solve.)1 solutions Answer 83798 by checkley71(8403)   on 2007-12-06 20:44:58 (Show Source): You can put this solution on YOUR website!.9X+.75(40-X)=40*.78 .9X+30-.75X=31.2 .15X=31.2-30 .15X=1.2 X=1.2/.15 X=8L OF 90% IS NEEDED. 40-8=32L OF 75% IS NEEDED. PROOF .9*8+.75*32=40*.78 7.2+24=31.2 31.2=31.2
 Equations/115178: Is this correct? An 800 g solution of acid and water contains 128 g of acid. What percent of the solution is acid? 16%1 solutions Answer 83796 by checkley71(8403)   on 2007-12-06 20:35:18 (Show Source): You can put this solution on YOUR website!YOU ARE CORRECT!!!!! 128/800=.16 OR 16%
 Equations/115176: Ching leaves San Francisco and travels toward Los Angeles at 50 miles a hour. An hour later Phil leaves Los Angeles and travels toward San Francisco at 60 miles a hour. If the two cities are 380 miles apart, how many hours will it take for Ching to meet Phil? Please explain! 1 solutions Answer 83795 by checkley71(8403)   on 2007-12-06 20:33:43 (Show Source): You can put this solution on YOUR website!50T+60(T-1)=380 50T+60T-60=380 110T=380+60 T=440/110 T=4 HOURS AFTER CHING LEAVES THEY WILL MEET. PROOF: 50*4+60*3=380 200+180=380 380=380
 Equations/115173: Translate into an algebraic equation. 6 times a number is 14 more than that number 1 solutions Answer 83792 by checkley71(8403)   on 2007-12-06 20:30:17 (Show Source): You can put this solution on YOUR website!6X=X+14 6X-X=14 5X=14 X=14/5 ANSWER. PROOF 6*14/5=14/5+14 84/5=(14+5*14)/5 84/5=(14+70)/5 84/5=84/5
 Equations/115171: 6(2-x)=4x1 solutions Answer 83790 by checkley71(8403)   on 2007-12-06 20:25:46 (Show Source): You can put this solution on YOUR website!6(2-X)=4X 12-6X=4X -6X-4X=-12 -10X=-12 X=-12/-10 X=1.2 ANSWER. 6(2-1.2)=4*1.2 6*.8=4.8 4.8=4.8
 Expressions-with-variables/115165: After a downturn in the economy, a company downsized by 35%. If there are still 78 employees, how many employees were there prior to the layoffs?1 solutions Answer 83788 by checkley71(8403)   on 2007-12-06 20:22:52 (Show Source): You can put this solution on YOUR website!1-.35=.65 WHICH IS THE AMOUNT OF EMPLOYEES LEFT AFTER THE DOWNSIZING. .65X=78 X=78/.65 X=120 IS THE NUMBER OF EMPLOYEES PRIOR TO THE LAYOFFS.
 Equations/115167: -3(x+1)=2(x-8)+31 solutions Answer 83787 by checkley71(8403)   on 2007-12-06 20:18:52 (Show Source): You can put this solution on YOUR website!-3(X+1)=2(X-8)+3 -3X-3=2X-16+3 -3X-2X=-16+3+3 -5X=-10 -5X=-10 X=-10/-5 X=2 ANSWER. PROOF: -3(2+1)=2(2-8)+3 -3*3=2*-6+3 -9=-12+3 -9=-9
 Expressions-with-variables/115164: In a recent election in Texas for a seat on the United States House of Representatives, Max Sandlin received 25,557 more votes than opponent Dennis Boerner. If the total number of votes was 135,821, find the number of votes for each candidate. I need to turn it into an equation and solve. thanks1 solutions Answer 83786 by checkley71(8403)   on 2007-12-06 20:14:59 (Show Source): You can put this solution on YOUR website!X+(X+25,557)=135,821 2X+25,557=135,821 2X=135,821-25,557 2X=110,264 X=110,264/2 X=55,132 NUMBER OF VOTES FOR THE LOOSER. 55,132+25,557=80,689 55,132+80,689=135,821 135,821=135,821
 Expressions-with-variables/115163: Over the past few years the satellite Voyager II has passed by the planets Saturn, Uranus, and Neptune, continually updating information about these planets, including the number of moons for each. Uranus is now believed to have 13 more moons than Neptune. Also, Saturn is now believed to have 2 more than twice the number of moons of Neptune. If the total number of moons for these planets is 47, find the number of moons for each planet. I'm not sure how to turn that into an equation to solve. thanks1 solutions Answer 83783 by checkley71(8403)   on 2007-12-06 19:59:42 (Show Source): You can put this solution on YOUR website!U=N+13 S=2N+2 U+S+N=47 (N+13)+(2N+2)+N=47 4N+15=47 4N=47-15 4N=32 N=32/4 N=8 MOONS FOR NEPTUNE. U=8+13=21 MOONS FOR URANUS. S=2*8+2=16+2=18 MOONS FOR SATURN. PROOF: 8+21+18=47 47=47
 Expressions-with-variables/115161: -(4a-7)-5a=10+a I have to solve for a. I've done TONS of problems like this before, but this one I just can't seem to figure out for some reason.1 solutions Answer 83782 by checkley71(8403)   on 2007-12-06 19:53:31 (Show Source): You can put this solution on YOUR website!-(4A-7)-5A=10+A -4A+7-5A=10+A -4A-5A-A=10-7 -10A=3 A=3/-10 A=-.3 ANSWER. PROOF -(4*-.3-7))-5*-.3=10-.3 -(-1.2-7)+1.5=9.7 -(-8.2)+1.5)=9.7 8.2+1.5=9.7 9.7=9.7
 Linear-systems/115097: This question is from textbook Introductory Algebra Graph an Equation of the form Ax + By = C 3x + y = 31 solutions Answer 83781 by checkley71(8403)   on 2007-12-06 19:46:52 (Show Source): You can put this solution on YOUR website!3X+Y=3 Y=-3X+3 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -3x +3).
 Polynomials-and-rational-expressions/115100: IF Y VARIES DIRECTLY WITH X, AND IF Y=30 WHEN X=6, FIND Y WHEN X IS 111 solutions Answer 83780 by checkley71(8403)   on 2007-12-06 19:44:04 (Show Source): You can put this solution on YOUR website!30/6=Y/11 NOW CROSS MULTIPLY 6Y=30*11 6Y=330 Y=330/6 Y=55 IS THE ANSWER FOR Y WHEN X=11. PROOF: 30/6=55/11 5=5
 Miscellaneous_Word_Problems/115139: If chocolate is 8.49 per pound and caramel is 3.65 per pound, how many pounds of each would you need to end up with 2.5 lbs of cany at an average cost of \$5.50 per pound?1 solutions Answer 83778 by checkley71(8403)   on 2007-12-06 19:38:27 (Show Source): You can put this solution on YOUR website!8.49X+3.65(2.5-X)=2.5*5.50 8.49X+9.125-3.65X=13.75 4.84X=13.75-9.125 4.84X=4.625 X=4.625/4.84 X=.9556 POUNDS OF CHOCOLATE IS NEEDED. 2.5-.9556=1.5444 POUNDS OF CARAMEL IS NEEDED. PROOF 8.49*.9556+3.65*1.5444=13.75 8.113+5.637=13.75 13.75=13.75
 Probability-and-statistics/115155: If a customer purchases a new stereo system during the spring sale, he may choose any 6 cd's from 20 classical and 30 jazz collections. In how many ways can the customer choose 3 of each?1 solutions Answer 83777 by checkley71(8403)   on 2007-12-06 19:29:42 (Show Source): You can put this solution on YOUR website!20*19*18+30*29*28=6840+24360=31,200 CHOICES FOR 6 cd's OF 3 CLASSICAL + 3 JAZZ.
 Equations/115156: My son needs help solving this equation: 1/2(5m+2)=1/3(7m+12). I am helping him with his homework, and I am unable to explain that equation.. Thanks1 solutions Answer 83775 by checkley71(8403)   on 2007-12-06 19:25:54 (Show Source): You can put this solution on YOUR website!1/2(5m+2)=1/3(7m+12) (5m+2)/2=(7m+12)/3 now cross multiply: 3(5m+2)=2(7m+12) 15m+6=14m+24 15m-14m=24-6 m=18 answer. proof: 1/2(5*18+2)=1/3(7*18+12 1/2(90+2)=1/3(126+12) 1/2*92=1/3*138 46=46
 Probability-and-statistics/115154: A professor grades homeowrk by randomly checking 7 of the 20 problems assigned. in how many different ways can this be done?1 solutions Answer 83774 by checkley71(8403)   on 2007-12-06 19:20:42 (Show Source): You can put this solution on YOUR website!20*19*18*17*16*15*14=390,700,800 ways to select 7 out of 20 problems.