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# Recent problems solved by 'ilana'

Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329, >>Next

 Miscellaneous_Word_Problems/633076: m varies directly as n and inversely as p. If m = 2 when n = 16 and p = 16, find p when m = 16 and n = 251 solutions Answer 398654 by ilana(307)   on 2012-07-30 04:09:41 (Show Source): You can put this solution on YOUR website!If m varies directly as n, then m=k*n, where k is some number. If m also varies inversely as p, then m=k*n/p. So plug in the values to solve for k and get a general formula. m=k*n/p (Note that (k*n)/p is the same as k*(n/p).) 2=k*16/16 2=k*1 2=k So the formula is m=2*n/p. Now plug in the other values. m=2*n/p 16=2*25/p 16=50/p 16*p=50 (I cross-multiplied.) p=50/16 p=3.125
 Volume/633075: a coal bin is 4 meters wide and 5 meters long. To what depth must it be filled to contain 60 cubic meters of coal? My formula is My solution is 4^2*5 =16*5 =80 I hope i got the answer right :)1 solutions Answer 398653 by ilana(307)   on 2012-07-30 04:03:25 (Show Source): You can put this solution on YOUR website!You are correct in using a volume formula and plugging in given values. The problem is you used the wrong volume formula and therefore had to plug in your values for the wrong variables. The formula you used, V=s^2*h, is for a rectangular prism with a square base. This coal bin has a rectangular base- it has 3 different dimensions instead of having 2 that are equal. So you need the formula Volume=length*width*height, or in this case, Volume=length*width*depth. Now let's plug in our values. V=l*w*d 60=5*4*d 60=20*d 60/20=d 3=d The bin must be filled to a depth of 3 meters.
 Angles/474938: the difference between the measures of two supplementary angles is 20 degrees. Find the measure of each angle.1 solutions Answer 325686 by ilana(307)   on 2011-07-27 06:49:53 (Show Source): You can put this solution on YOUR website!If the measures are x and y degrees, and they are supplementary, then their sum is 180 degrees. So you can write and solve a system of equations. x + y = 180 x - y = 20 Now you can use any method to solve. Let's use the elimination method by adding the equations together. x + x + y - y = 180 + 20 2x = 200 x = 100 Now solve for y. 100 + y = 180 y = 80 So the angles measure 100 and 80 degrees.
 test/466683: If rain is falling at the rate of 2 inches per hour, how many inches of rain will fall in x minutes? (A). 30/x. (B). x/30. (C). 60/x. (D). 2x1 solutions Answer 319970 by ilana(307)   on 2011-07-02 23:51:21 (Show Source): You can put this solution on YOUR website!You can just plug in 60 for x and see which answer gives you 2, since you know it should be 2 inches in 60 minutes. The answer is B since 60/30 = 2.
 Linear-systems/460260: i fogot the steps to eliminations. 0.3x - 0.2y = 4 0.5x + 0.3y = - 7/17 can someone help me 1 solutions Answer 315727 by ilana(307)   on 2011-06-12 18:09:44 (Show Source): You can put this solution on YOUR website!To use the elimination method, make either the x terms or the y terms cancel out when you add or subtract the equations. You can start by multiplying both equations by 10 to get rid of the decimals. 3x - 2y = 40 5x + 3y = -70/17 Multiply the first equation by 3 and the second equation by 2 so you can add -6y and 6y to get 0. 9x - 6y = 120 10x + 6y = -140/17 [I got -140/17 by multiplying -70/17 by 2. Anything you do to one side of the equation you have to do to the other in order for the equation to still work. So we multiplied each term on each side by 2.] Now add the equations. 19x = 120 - 140/17 19x = (2040 - 140)/17 19x = 1900/17 x = 1900/(17*19) x = 1900/323 Now plug this x into either equation to solve for y. 3x - 2y = 40 3(1900/323) - 2y = 40 5700/323 - 2y = 40 2y = 5700/323 - 40 2y = (5700 - 12920)/323 2y = -7220/323 y = -7220/646 The approximate solution is (5.88, -11.18).
 Radicals/455637: determine the domain of sqrt 6-3x write answer in interval notation1 solutions Answer 312828 by ilana(307)   on 2011-05-30 20:50:59 (Show Source): You can put this solution on YOUR website!6-3x must be greater than or equal to 0. -3x must be greater than or equal to -6. x must be less than or equal to 2. In interval notation: x is in (-infinity, 2]
 test/455315: An isosceles triangle has a perimeter of 370 millimeters. The base of the triangle is 40 millimeters. Longer than the two equal sides. What is the lenght of each side? Thank u : )1 solutions Answer 312625 by ilana(307)   on 2011-05-29 19:45:56 (Show Source): You can put this solution on YOUR website!Since the triangle is isosceles, the sides are the same length, x. The base is then x + 40. So x + x + x + 40 = 370 3x + 40 = 370 3x = 330 x = 110 The lengths of the sides are 110 mm, 110 mm, and 150 mm.
 Parallelograms/455343: The base of a parallelogram is 28.4 centimeters. The height is one fourth of the base. Find the area of the parallelogram1 solutions Answer 312624 by ilana(307)   on 2011-05-29 19:43:33 (Show Source): You can put this solution on YOUR website!The area of a parallelogram is base times height. The height is one-fourth times the base, or 28.4/4 = 7.1 cm. So the area is (28.4)(7.1) = 201.64 cm^2.
 Mixture_Word_Problems/455325: Solve the system using the substitution method. If the system has no solution or an infinite number of solutions, state this. 5x+y=13 2x=-3y1 solutions Answer 312622 by ilana(307)   on 2011-05-29 19:41:36 (Show Source): You can put this solution on YOUR website!Substitution method means make one of the equations "x=_" or "y=_", and then substitute that into the other equation. Since the first equation has a y with no coefficient, solve for y in that equation. 5x + y = 13 --> y = 13 - 5x Now substitute "13 - 5x" for y in the second equation. 2x = -3y --> 2x = -3(13 - 5x) Solve for x. 2x = -39 + 15x 39 = 15x - 2x 39 = 13x x = 3 Now solve for y using the equation y = 13 - 5x y = 13 - 5x y = 13 - 5(3) y = 13 - 15 y = -2 The solution is x=3, y=-2.
 Geometry_Word_Problems/455327: The vectors (3,6) and (-2,k) are parallel. Find the value of k?1 solutions Answer 312612 by ilana(307)   on 2011-05-29 19:21:13 (Show Source): You can put this solution on YOUR website!If these vectors are parallel, the slope of the line through (0,0) and (3,6) must be equal to the slope of the line through (0,0) and (-2,k). The slope of the line through (0,0) and (3,6) is (6-0)/(3-0), or 2. So the slope through (0,0) and (-2,k) must be 2. (k-0)/(-2-0)=2 k/-2=2 k=-4
 Triangles/455332: Graph a rectangular solid that contains the point R (-1, 3, 2) and the origin as vertices. Label the points of each vertex.1 solutions Answer 312608 by ilana(307)   on 2011-05-29 19:16:34 (Show Source): You can put this solution on YOUR website!There are 8 vertices- 4 are part of the rectangle that is at height 0 like the origin. This is the bottom face of the rectangular solid. The other 4 are part of the rectangle that is at height 2 like the given point R. This is the top face of the rectangular solid. The bottom rectangle has vertices (0, 0, 0), (0, 3, 0), (-1, 3, 0), and (-1, 0, 0). The top rectangle has vertices (-1, 3, 2), (-1, 0, 2), (0, 0, 2), and (0, 3, 2).
 Radicals/453615: I need to simplify sqrt(15)(2sqrt(3)-4sqrt(5))1 solutions Answer 311678 by ilana(307)   on 2011-05-24 19:16:40 (Show Source): You can put this solution on YOUR website!Distribute sqrt(15) to both terms. sqrt(15)(2sqrt(3) - 4sqrt(5)) = 2sqrt(15)sqrt(3) - 4sqrt(15)sqrt(5) = 2sqrt(5)sqrt(3)sqrt(3) - 4sqrt(5)sqrt(3)sqrt(5) = 2sqrt(5)*3 - 4sqrt(3)*5 = 6sqrt(5) - 20sqrt(3)
 Probability-and-statistics/453680: A bag contains yellow and red blocks, there are 4 more red blocks than yellow. When pulling two blocks out, one at a time, you can not replace the first block. What is an expression that represents the probability of pulling out a red block first, then a yellow block? Thank you.1 solutions Answer 311677 by ilana(307)   on 2011-05-24 19:10:27 (Show Source): You can put this solution on YOUR website!Use x for the number of yellow blocks. Then there are x + 4 red blocks. So there are x + x + 4, or 2x + 4 blocks in all. P(red) = (x + 4)/(2x + 4) P(yellow after red) = x/(2x + 3) So the probability is the product, x(x + 4)/(2x + 4)(2x + 3).
 Geometry_Word_Problems/453667: a square has an area of 36 square centemeters a rectangle has the same area as the square if the rectangle long sides mesure 9 centemters what is the rectangles perimeter 1 solutions Answer 311676 by ilana(307)   on 2011-05-24 19:04:15 (Show Source): You can put this solution on YOUR website!If the rectangle's area is 36 square centimeters, and its length is 9 cm, then its width must be 36/9 = 4 cm. perimeter = 2l + 2w = 2*9 + 2*4 = 18 + 8 = 26 cm
 Word_Problems_With_Coins/453640: In a coin collection there are 9 pennies, 8 nickels, 12 dimes, 16 quarters, 11 half-dollars and 4 dollar pieces. A coin is randomly selected from the collection by a blind folded boy who gets to keep the coin picked. What is the expected value?1 solutions Answer 311674 by ilana(307)   on 2011-05-24 18:52:53 (Show Source): You can put this solution on YOUR website!The expected value is the sum of each probability times its value. P(penny) = 9/60 P(nickel) = 8/60 P(dime) = 12/60 P(quarter) = 16/60 P(half-dollar) = 11/60 P(dollar) = 4/60 Expected value = 1*9/60 + 5*8/60 + 10*12/60 + 25*16/60 + 50*11/60 + 100*4/60 = (9 + 40 + 120 + 400 + 550 + 400)/60 = 1519/60 = approx. \$25.32
 Geometry_Word_Problems/453659: Given U = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, A = {12, 14, 16, 18, 20}, and B = {11, 13, 14, 15, 18, 19, 20}. Find A′ ∩ B′. Show your work, finding A’, then B’ then find their intersection.1 solutions Answer 311673 by ilana(307)   on 2011-05-24 18:43:54 (Show Source): You can put this solution on YOUR website!A' contains the elements that are in U but not A. A' = {10, 11, 13, 15, 17, 19} B' contains the elements that are in U but not B. B' = {10, 12, 16, 17} Their intersection contains the elements in both. A′ ∩ B′ = {10, 17}
 Radicals/452762: what is the midpoint of the line segment from -3,4 and -1,-6 ?1 solutions Answer 311164 by ilana(307)   on 2011-05-22 18:49:55 (Show Source): You can put this solution on YOUR website!Find the average of the x values and the average of the y values. x: (-3 + -1)/2 = -4/2 = -2 y: (4 + -6)/2 = -2/2 = -1 The midpoint is (-2, -1).
 Graphs/452728: As a mother, I am having problems remembering the - and + on the algebra. 9<-3X If I am correct then it would be -31 solutions Answer 311162 by ilana(307)   on 2011-05-22 18:46:43 (Show Source): You can put this solution on YOUR website!No, it would be -3 > x. When you divide by a negative number (-3 here), you need to flip the sign. You can also test the direction of the inequality symbol by testing a value for x. In the original inequality, 9<-3x, the value -10 works for x. (9<30 is true.) But if the solution were -3
 Evaluation_Word_Problems/452748: what value of x will make the rational expression x-3/x+7 undefined?1 solutions Answer 311158 by ilana(307)   on 2011-05-22 18:41:29 (Show Source): You can put this solution on YOUR website!A rational expression is undefined when the denominator is 0. So in this case, solve the equation x + 7 = 0. It will be undefined when x = -7.
 Probability-and-statistics/452753: A bag contains 25 gummy bears: five each of green, red, black, orange, and yellow. If you pick 2 gummy bears from the bag, what is the probability that the gummy bears will be the same color? 1 solutions Answer 311157 by ilana(307)   on 2011-05-22 18:39:40 (Show Source): You can put this solution on YOUR website!The first gummy bear you pick can be any color, so it can be any one of the 25. The probability of that is 25/25, or 1. The second then has to be one of the 4 others of that color. The probability of that is 4/24, or 1/6. So the probability is 1 * 1/6, or 1/6.
 Travel_Word_Problems/452758: What is the 5017th number in the sequence? 3, 2, 8, 9, 3, 2, 8, 9, ..., _____ Thanks for helping1 solutions Answer 311155 by ilana(307)   on 2011-05-22 18:35:30 (Show Source): You can put this solution on YOUR website!There are 4 terms that keep repeating. So any number divisible by 4 (4, 8, 12, 16, 20,...) will be 9. Which number near 5017 will that be? #5016. That means the 5017th number is the one right after, which will be 3.
 Rational-functions/452756: Please help me solve this problem? ^3sqrt5x+8 +6=1 what is x?1 solutions Answer 311154 by ilana(307)   on 2011-05-22 18:32:35 (Show Source): You can put this solution on YOUR website!^3sqrt5x+8 +6=1 Subtract 6 from each side. ^3sqrt5x+8 = 1 - 6 ^3sqrt5x+8 = -5 Cube each side. 5x + 8 = (-5)^3 5x + 8 = -125 Subtract 8 from each side. 5x = -133 x = -133/5, or -26.6
 Linear_Equations_And_Systems_Word_Problems/452750: Susan wants to mix 10 pounds of Virginia peanuts that cost \$3.50 a pound with Spanish peanuts that cost \$3.00 a pound to obtain a mixture that costs \$3.40 a pound. How many pounds of Spanish peanuts should she use? I have given this problem some thought but I do not know how you would solve. Thanks 1 solutions Answer 311153 by ilana(307)   on 2011-05-22 18:29:05 (Show Source): You can put this solution on YOUR website!There will be 10 pounds of Virginia peanuts and x pounds of Spanish peanuts. The total cost will be 3.5(10) + 3(x). The total amount of pounds will be 10 + x. You want the cost per pound to be \$3.40, so the (total cost)/(total pounds) should be 3.4, so solve the equation: (35 + 3x)/(10 + x) = 3.4 35 + 3x = 3.4(10 + x) 35 + 3x = 34 + 3.4x 1 = 0.4x x = 1/(4/10) x = 10/4 x = 2.5 She should use 2.5 pounds of Spanish peanuts. Then the total cost will be 35 + 7.5, or \$42.50. The total weight will be 10 + 2.5, or 12.5 pounds. The total cost per pound will be 42.5/12.5 = \$3.40/pound.
 Rectangles/452744: An airplane ticket has an area of 70 square centimeters. Its perimeter is 34 centimeters. What are the dimensions of the ticket?1 solutions Answer 311152 by ilana(307)   on 2011-05-22 18:22:19 (Show Source): You can put this solution on YOUR website!If it's length and width are x and y, then its area is xy and its perimeter is 2x + 2y. So you can write 2 equations and solve the system. xy = 70 2x + 2y = 34 Substitute 70/y for x (from the first equation) into the second equation. 2(70/y) + 2y = 34 140/y + 2y = 34 Multiply everything by y. 140 + 2y^2 = 34y 2y^2 - 34y + 140 = 0 Divide everything by 2. y^2 - 17y + 70 = 0 (y - 10)(y - 7) = 0 y = 7 or 10 So the dimensions are 7 cm by 10 cm.
 Miscellaneous_Word_Problems/452737: A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg?1 solutions Answer 311149 by ilana(307)   on 2011-05-22 17:48:19 (Show Source): You can put this solution on YOUR website!Say the length of the longer leg is x. Then the hypotenuse measures x + 60. So, using the Pythagorean Theorem, x^2 + 180^2 = (x + 60)^2. x^2 + 32400 = x^2 + 120x + 3600 32400 = 120x + 3600 120x = 28800 x = 240 The longer leg measures 240 m.
 Volume/452715: What is the equation of the parabola that moves the parent graph y=x^2 to the left 9 units?1 solutions Answer 311147 by ilana(307)   on 2011-05-22 17:27:56 (Show Source): You can put this solution on YOUR website!Shifting the parabola to the left 9 units means that to get a certain y-value, you now need to add 9 to the x-value to compensate for the shift. So you plug in "x + 9" for x. So the equation is y=(x+9)^2.