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# Recent problems solved by 'oberobic'

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 Permutations/248855: how many ways can a committee of 3 men and 3 women be formed from a group of 9 men and women1 solutions Answer 181330 by oberobic(2304)   on 2009-12-11 22:31:29 (Show Source): You can put this solution on YOUR website!It depends on how men and women there are in the group of 9.
 Money_Word_Problems/248843: A salesperson has two job offers. Company A offers a weekly salary of \$200 plus commission of 10% of sales. Company B offers a weekly salary of \$400 plus commission of 5% of sales. What is the amount of sales at which Company A's offer is the same as Company B's? 1 solutions Answer 181329 by oberobic(2304)   on 2009-12-11 22:30:21 (Show Source): You can put this solution on YOUR website!Salary = Base + Commission . Company A: Base = \$200 Commission = 10% of sales = .1*S A = .1S + 200 . Company B: Base = 400 Commission = .05*S B = .05S + 400 . We're looking for the point where they're equal. . 200 + .1S = 400 + .05S . multiply by 100 to get rid of decimals . 20000 + 10S = 40000 + 5S Subtract 20000 from both sides 10S = 20000 + 5S Subtract 5S from both sides 5S = 20000 Divide both sides by 5 S = 4000 . So, at \$4000 sales, the two jobs pay the same. . You have to always check your work. This can be done by plugging the values into the basic equations and determining if they check. Or we can graph the two lines and see where they cross. . Company A: 200 + .1(4000) = 200 + 400 = 600 Company B: 400 + .05(4000) = 400 + 200 = 600 . Graphs
 Problems-with-consecutive-odd-even-integers/248575: a rectangle is 24 cm long and 16 cm wide. when each dimension is increased by the same amount, the area is doubled. what are the new dimensions?1 solutions Answer 181154 by oberobic(2304)   on 2009-12-10 23:20:44 (Show Source): You can put this solution on YOUR website!In solving word problems, always use as few unknowns as possible. Typically, this means you strive to define each unknown in terms of another. . We also consider what we know about the figure. We are told it is a rectangle. So we know: Perimeter = 2L + 2W Area = L * W . We also are told the dimensions of the base rectangle: L = 24 W = 16 A = 24 * 16 = 384 . We also are told that if you add the same amount, say 'c', to both dimensions, then the area is doubled. The problem does not ask us to find 'c' so perhaps that doesn't matter. We could just use ratios. . 24 * 16 = 384 which can be described as ratios 24/16 = 1.5 ,so 1.5x*x = 384 . Doubling the area = 2*384 = 768 . 1.5x^2 = 768 x^2 = 768/1.5 = 512 x = sqrt(512) = 22.6274 = W . L= 1.5x = 33.9411 . Checking the area: 33.9411*22.6274 = 767.9988 . So this estimate is off by only 12 in ten thousand. Very close indeed...
 Functions/248574: find the outputs (y) for the function rule y=3/2x . what is the output when the input (x) is 6 ?1 solutions Answer 181150 by oberobic(2304)   on 2009-12-10 22:53:50 (Show Source): You can put this solution on YOUR website!Substitute x=6 in the function So This defines the point (6,9). . Substituting x=0 in the function, we get y=0, which defines the point (0,0). . You can plot these two points and draw the graph. . The graph is:
 Graphs/248566: y=-2x+5 and y=1/2x indicate if each pair of lines is parallel, perpendicular, or neither.1 solutions Answer 181148 by oberobic(2304)   on 2009-12-10 22:48:31 (Show Source): You can put this solution on YOUR website!The two equations are: . For lines to parallel thus must have the same slope. Perpendicular lines have slopes that are the negative inverse of each other. . The negative inverse of -2 is 1/2, so it appears these lines are perpendicular. . We can graph them as:
 Rectangles/248553: the length of a rectangle is 20 meters and the width is 15 meters. find the ratio of the width to the length1 solutions Answer 181147 by oberobic(2304)   on 2009-12-10 22:18:58 (Show Source): You can put this solution on YOUR website!Ratio can be express as, for example, 2 to 1 or 2:1 or 2/1. In this case, it asks for a ratio of L to W, which can be shown as L/W. 20/15 is the ratio. or 1.33 to 1 or 1 & 1/3 to 1 . Is 20 really one-third more than 15? Or is is 1/4? . To check a change, the formula is .
 Word_Problems_With_Coins/248513: A bank contains 30 coins, consisting of nickles, quarters, and dimes.there are twice as many nickles as quarters and the remaining are dimes.if the total value of the coins is \$3.35, what is the number of each type of coin in the bank?1 solutions Answer 181146 by oberobic(2304)   on 2009-12-10 22:14:15 (Show Source): You can put this solution on YOUR website!When you work with coins, you have to keep in mind that there will be counts of the coins and values of the coins to balance. n = number of nickels 5n = the value of the nickels in cents d = number of dimes 10d = value of the dimes in cents q = quarters 25q = value of the quarters in cents . We are told the total value: 5n + 10d + 25q = 335 cents . Note that everything needs to be in terms of cents. . We are told: n + d + q = 30. . We also are told: n = 2q , which means the number of nickels is twice the number of quarters. . So we have defined 3 equations and we have 3 unknowns...hmmm... . 5n + 10d + 25q = 335 n + d + q = 30 n = 2q . Substituting 2q for n, we have . 5(2q) + 10d + 25q = 335 2q + d + q = 30 . Simplifying, we have 10q + 10d + 25q = 335 10d + 35q = 335 . 2q + d + q = 30 3q + d = 30 . d = 30 - 3q , which seems obvious if you think about it. . 10(30-3q) + 35q = 335 300 - 30q + 35q = 335 5q = 35 q = 7 , so we think we have 7 quarters . n = 2q n = 14 nickels . Since there are 30 coins, then there must be 9 dimes. . We can check the values to see if they total 335. 5n + 10d + 25q = 335 cents 5n = 5(14) = 70 cents 7q = 7(25) = 175 cents 9d = 9(10) = 90 cents 70 + 175 + 90 = 335 cents So it checks. Done.
 Polynomials-and-rational-expressions/248548: A child weighing 70 lbs sits 5 ft. from the fulcrum on a teeter totter, How far should the other child who weighs 85 lbs sit from the fulcrum in order to keep the teeter board balanced? Which concept would you use, from the ones you learned this week, to solve this problem? Discuss different approaches to solve it.1 solutions Answer 181144 by oberobic(2304)   on 2009-12-10 21:57:45 (Show Source): You can put this solution on YOUR website!You multiply the weight by the distance from the fulcrum. 70 lb * 5 ft = 350 ft-lb . On the other end, the person is 85 lb. . We want them to balance, so... . 85 lb * x ft = 350 ft-lb . 85x = 350 . Divide both sides by 85 . x = 4.1176471 ft
 Age_Word_Problems/248531: Zelma is 18 years older than her son. She was 3 times as old as he was 1 year ago. How old are they now?1 solutions Answer 181141 by oberobic(2304)   on 2009-12-10 21:52:30 (Show Source): You can put this solution on YOUR website!Zelda is 18 years older than her son. Z = S + 18 . A year ago, she was 3 times her son's age. We have to say Z-1 and S-1 to represent their ages 1 year ago. Z-1 = 3*(S-1) Z-1 = 3S -3 Z = 3S -2 . We now have Z defined by two equations. . S+18 = 3S-2 . Subtract S from both S 18 = 2S-2 . Add 2 to both sides 20 = 2S 2S = 20 . Divide both sides by 2 S = 10, so the son is 10 years old. . Looking back at the setup equations. Z = S + 18 Z = 10 + 18 = 28, so Zelda is 28. . How old were they last year? S = 10-1 = 9 Z = 28-1 = 27 . To check, was Zelda 3 times as old as her son a year ago? 3*9 = 27 Yes, she was. . Done.
 Functions/248541: Rewrite the Equation So y is a function of x 2/3x+4=2x1 solutions Answer 181140 by oberobic(2304)   on 2009-12-10 21:43:11 (Show Source): You can put this solution on YOUR website! multiply everything by 3 2x + 12 = 6x subtract 2x from both sides 12 = 6x 6x = 12 divide by 6 x = 2 . But there is no y
 Miscellaneous_Word_Problems/248529: an icecream cone costs 1.10 and a sunday costs 2.35. if 170 cones & sunday receipt were sold for a total of 294.4.how many cones were sold?1 solutions Answer 181139 by oberobic(2304)   on 2009-12-10 21:38:29 (Show Source): You can put this solution on YOUR website!c = number of cones 110c = revenue generated by the sale of cones in cents s = number of sundaes 235s = revenue generated by the sale of sundaes in cents . 110c + 235s = 29440 (given) . And we have another fact: c + s = 170 . Two equations and two unknowns is solvable. . We can easily determine c. c = 170 - s . Now substitute into the other equation. 110c + 235s = 29440 110(170-s) + 235s = 29440 18700 - 110s + 235s = 29440 125s = 10740 s = 85.92 sundaes sold 2.35s = 201.912 . c = 170 - s = 170 - 85.92 c = 84.08 1.10c = 92.488 . Total = 201.912 + 92.488 Total = 294.4 . These are hard numbers to work with, but the answer checks.
 Linear-equations/248518: dertermine if whether each equation is a linear if so write it in standard form 3x=5y1 solutions Answer 181129 by oberobic(2304)   on 2009-12-10 21:13:25 (Show Source): You can put this solution on YOUR website!If there are no exponents, then it is linear. Standard form is Ax + By = C . 3x - 5y = 0
 Human-and-algebraic-language/248519: Please help me help my son with this word problem ... A boat travels 60 km upstream (against the current) in 5 hours. The boat travels the same distance downstream in 3 hours. What is the rate of the boat in still water? What is the rate of the current?1 solutions Answer 181125 by oberobic(2304)   on 2009-12-10 21:10:28 (Show Source): You can put this solution on YOUR website!We start with what we know about distance problems. d = r * t, where d=distance, r=rate, and t=time . Upstream info: 60=r*5 r = 12 mph . Downstream 60 = r*3 r = 20 . We need to assume the boat runs as fast as possible in both directions, otherwise we cannot solve the problem. . Let's call the upstream rate: U Let's call the downstream rate: D Let's call the unknown maximum rate: X And finally, the current is flowing at C mph. . Upstream: U = X-C In English, the upstream rate = max speed of the boat MINUS the current flowing against it.; X - C = 12, as shown above. . Downstream: D = X + C In English, the downstream rate = max speed of the boat PLUS the current pushing it along. X+C=20 . So we have two equations and two unknowns. Piece of cake. Right? X - C = 12 X + C = 20 . Let's add them. 2X = 32 X = 16 . So the unknown maximum speed X is 16. . Now we check our work, as we always do... . Looking back at what we know, X-C = 12 16-C=12 C=4 OK . And we know X+C = 20 16 + C = 20 C=4 . Checking the upstream rate... 60/(16-4)= 60/12 = 5, which is how long we were told it took. Checking the downstream rate... 60/(16+4) = 60/20 = 3, which is how long we were told it took. Done.
 Equations/248489: The sum of the measures of any triangle is 180 degrees. Find the angle measures of a triangl if the second angle measures 10 degerees less than twice the first, and the third angle measures 25 degrees more than the second.1 solutions Answer 181108 by oberobic(2304)   on 2009-12-10 20:45:18 (Show Source): You can put this solution on YOUR website!You have 3 angles: a, b & c. a + b + c = 180 . To define the equations, you can just start with a. a = ? . b = 2a - 10 (twice a minus 10) . c = b + 25 (25 more than b) . Substitute for b c = (2a-10) + 25 . Now substitute back into a+b+c=180 a + (2a-10) + (2a-10+25) = 180 . Eliminate the parentheses a + 2a - 10 + 2a - 10 + 25 = 180 . Combine like terms 5a + 5 = 180 . Subtract 5 from both sides 5a = 175 . Divide both sides by 5 a = 35 . Substitute into the equation for b. b = 2a -10 = 2*35 - 10 = 70 - 10 = 60 . Add 25 to b to get c. c = 60 + 25 = 85 . Check by adding them up. 35 + 60 + 85 = 180 Done.
 Radicals/248068: How can I simplify the square root of 81 m to the power of 101 solutions Answer 180813 by oberobic(2304)   on 2009-12-09 21:42:37 (Show Source): You can put this solution on YOUR website!Assuming you trying to simplify . You can see that = + 9 or - 9. . The square root of is . So the
 Quadratic_Equations/248067: using the quadratic formula, what is the length and width of a rectangle if the length is 3 inches longer than twice the width and the area of the rectangle is 5 in^2?1 solutions Answer 180811 by oberobic(2304)   on 2009-12-09 21:36:50 (Show Source): You can put this solution on YOUR website!L = 2W + 3 (length = twice the width + 3) A = L * W = 5 square inches . Substituting what we know. A = (2W +3) * W = 5 2W^2 + 3W = 5 . Subtract 5 from both sides . 2W^2 + 3W - 5 = 0 . We do not need to use the quadratic to solve this because it can be factored. . (2W + 5)(W - 1) = 0 . So we have two candidate values for W: W = 1 and W = -5/2. . Since it is not possible to have a negative value for the width, W =1 is the candidate answer. . L = 2W + 3 L = 2(1) + 3 L = 5 . Our candidate answer is: L = 5 W = 1 . Checking the work. Is L*W = 5? yes. So, we accept that answer.
 Numbers_Word_Problems/248047: the difference of two positive numbers is 3 and the sum of their square is 45. Find the numbers.1 solutions Answer 180802 by oberobic(2304)   on 2009-12-09 21:03:09 (Show Source): You can put this solution on YOUR website!The difference of two positive numbers is 3. x - y = 3 . x^2 + y^2 = 45 . We can use the first equation to solve the second. x - y = 3 . Add y to both sides x = y + 3 . Substitute in the second equation and solve. x^2 + y^2 = 45 (y+3)^2 + y^2 = 45 (y^ + 6y + 9) + y^2 = 45 . Collect terms 2y^2 + 6y + 9 = 45 . Subtract 45 from both sides. 2y^2 + 6y - 36 = 0 . Divide by 2 . y^2 + 3y - 18 = 0 . Can we factor 18 into two terms that are 3 apart? Yes, 3 & 6. . (y + 6)(y - 3) = 0 . So we have two candidate answers: y = -6 and y = 3. . The problem says the numbers are positive, so we assume y = 3 is one answer. . Given x^2 + y^2 = 45, we know y^9 = 9. x^2 + 9 = 45 . Subtract 9 from both sides x^2 = 36 . Take the square root. x = 6. . So our second candidate answer is x = 6. . Checking our work. . What does x^2 + y^2 equal 45? 3^2 + 6^2 = 9 + 36 = 45 . Does x - y = 3? 6-3 = 3 . OK
 Linear-equations/248027: how do use the slope and y intercept to graph the following equations, y=2x-3 and y=2/3x-4.1 solutions Answer 180794 by oberobic(2304)   on 2009-12-09 20:48:52 (Show Source): You can put this solution on YOUR website!The slope-intercept formula is: y = mx+b. The slope = m = change in y divided by change x. . We have an equation y = 2x -3. m = 2 = slope It means that for every change in y = 2, there is a change in x = 1. This extends indefinitely in both directions. change in y = 4, means change in x = 2. Etc. . The y-intercept = -3, so the related point is (0, -3) . Adding 4 to y means we add 2 to x, which produces the point (2, 1). . Plot these two points and draw the line connecting them. . . The same logic applies to the second equation. y = 2/3x - 4. . When x =0, y = -4, so we have the point (0, -4) . The slope = 2/3, which means for every change of 2 in y, there is a change of 3 in x. So we can use this information to calculate a second point. Add 2 to y and add 3 to x: (3, -2) Plot these point and draw a line. . . You can plot both on the same graph to check if they intercept one another. .
 Expressions-with-variables/248015: 5r-4s= -6 and 4r+5s=691 solutions Answer 180785 by oberobic(2304)   on 2009-12-09 20:26:42 (Show Source): You can put this solution on YOUR website!5r - 4s = -6 4r + 5s = 69 . Subtract the second equation from the first . r - 9s = -75 . Add 9s to both sides. r = 9s - 75 . Substitute . 4r + 5s = 69 4(9s - 75) + 5s = 69 36s - 300 + 5s = 69 . Add 300 to both sides 36s + 5s = 300 + 69 . Collect terms. 41s = 369 . Divide both sides by 41. s = 369/41 = 9 . Substitute into the other equation. 4r + 5(9) = 69 4r + 45 = 69 . Subtract 45 from both sides. 4r = 24 . Divide both sides by 4. r = 6 . So, we have the candidate answer is: s = 9 r = 6 . Check by substituting the values into the original equations. . 5r - 4s = -6 5r = 30 4s = 36 5r - 4s = -6 OK . 4r + 5s = 69 4r = 24 5s = 45 4r + 5s = 69 OK
 Proportions/248005: two rectangles are similar. the first is 4 in wide and 15 in long. the second is 9 in wide. find the length of the second rectangle.1 solutions Answer 180783 by oberobic(2304)   on 2009-12-09 20:12:54 (Show Source): You can put this solution on YOUR website!Since they are similar, you can use ratios to find the missing value. . 4/15 = 9/x . Cross multiply. 4x = 135 . Divide both sides by 4. x=33.75 . You can check by computing the ratios. 4/15 = .266667 . 9/33.75 = .266667 . OK
 Evaluation_Word_Problems/247671: The perimeter of a rectangle is 106 mm. The length is one more than three times the width. What is the area? 1 solutions Answer 180601 by oberobic(2304)   on 2009-12-09 00:47:01 (Show Source): You can put this solution on YOUR website!P = 2L + 2W L = 3W + 1 (length is 1 more than 3*width) . substituting P = 2(3W+1) + 2W . P = 106 (given) . substituting for P 2(3W+1) + 2W = 106 . multiply thru 6W + 2 + 2W = 106 . collect terms and subtract 2 from both sides 8W = 104 . divide both sides by 8 W = 13 . substitute back into the formula to solve for L L = 3W+1 = 3(13)+1 = 40 . Checking to see if P = 2L + 2W 2L = 80 2W = 26 P = 106 OK . Check to see if L = 3W + 1 3W = 39 + 1 = 40 OK
 Probability-and-statistics/247651: I need your help with my homework. A group of 10 peopleincludes one married couple. If 4 people are sellected ar random, what is the probability that the married couple is selected? Thank very much.1 solutions Answer 180600 by oberobic(2304)   on 2009-12-09 00:41:48 (Show Source): You can put this solution on YOUR website!There are 10 people, so there are 10 ways you could pick the first person. Those are the possibilities. Two of them are married, so the chance that you pick either one of the married couple is 2/10 = 1/5 or 20%. . Now that you have picked one member of the married couple, there are 9 ways you can pick the next person. But only 1 of those is the spouse. So the probability is 1/9. . So the chance you pick the couple = 1/5 * 1/9 = 1/45 . As a check, you can determine the number of combinations of 2 people from a set of 10. That defines the number of possibilities. . . The 8! terms cancel. So we have . There is only 1 way you pick the couple. 1/45. .
 Quadratic_Equations/247659: How do you solve ? 1 solutions Answer 180599 by oberobic(2304)   on 2009-12-09 00:29:31 (Show Source): You can put this solution on YOUR website! . Multiply both sides by . Subtract 4 from both sides or . Factor . So, or
 Linear-equations/247668: graph the equation y = 3x + 2.1 solutions Answer 180598 by oberobic(2304)   on 2009-12-09 00:22:45 (Show Source):
Quadratic_Equations/247661: How do I use this formula x=(-bą√(b^2-4ac))/2a and find out what a, b, and c are, then plug those numbers in and get x-intercepts? The equation to solve is
y=x^2+4x-1
1 solutions

Answer 180597 by oberobic(2304)   on 2009-12-09 00:16:49 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=20 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.23606797749979, -4.23606797749979. Here's your graph:

 Linear-equations/247667: graph the equations y = 3x and y = -3x1 solutions Answer 180596 by oberobic(2304)   on 2009-12-09 00:15:23 (Show Source):
Quadratic-relations-and-conic-sections/247662: How do i determine whether the given quadratic function has a maximum value or a minimum value and then find that value?
x^2+2x-6
1 solutions

Answer 180595 by oberobic(2304)   on 2009-12-09 00:14:09 (Show Source):
You can put this solution on YOUR website!

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=28 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.64575131106459, -3.64575131106459. Here's your graph:

 Graphs/247666: can you please show me how to write an equation that is parallel to the line y=4x + 1. I would really like to know how to solve this myself. I just need the steps. I don't get it! Thank you for your assistance. judi 1 solutions Answer 180593 by oberobic(2304)   on 2009-12-09 00:09:49 (Show Source): You can put this solution on YOUR website!The given equation is y = 4x + 1. It is slope-intercept form: y = mx + b. So any line that has slope 4 will be parallel to the first line. For example, y = 4x + 3
 Polynomials-and-rational-expressions/247663: x-7y=6 5x+5y=110 What is the y coordinate of that?1 solutions Answer 180592 by oberobic(2304)   on 2009-12-09 00:06:29 (Show Source): You can put this solution on YOUR website!Put the equations in slope-intercept form. . Solve: x-7y=6 subtract x from both sides... -7y = -x +6 divide both sides by -7... y = 1/7*x + 6/7 . Solve: 5x+5y=110 divide both sides by 5... x + y = 22 Subtract x from both sides... y = -x + 22 . Graph the two lines... .