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# Recent problems solved by 'nerdybill'

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 Finance/301265: Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?1 solutions Answer 216003 by nerdybill(7008)   on 2010-05-06 09:01:28 (Show Source): You can put this solution on YOUR website! Ten liters of a 4% acid solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? . Let x = liters of 10% solution needed then .04(10) + .10x = .06(10+x) .4 + .10x = .6+.06x .4 + .04x = .6 .04x = .2 x = 5 liters
 Reduction-of-unit-multipliers/301249: how do I find how many hours it took to make 3510 products when it took only 36 minutes to make 1. whats the conversion please many thanks Kay1 solutions Answer 216002 by nerdybill(7008)   on 2010-05-06 08:58:41 (Show Source): You can put this solution on YOUR website!how do I find how many hours it took to make 3510 products when it took only 36 minutes to make 1. . Since it takes 36 minutes for each: 36*3510 = 126360 minutes . Converting to hours: 126360/60 = 2106 hours . Converting to days: 2106/24 = 87.75 days or 87 days and 18 hours
Miscellaneous_Word_Problems/301267: A picture 19 inches by 24 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 188 square inches?
1 solutions

Answer 215999 by nerdybill(7008)   on 2010-05-06 08:42:23 (Show Source):
You can put this solution on YOUR website!
A picture 19 inches by 24 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 188 square inches?
.
Let w = width of border
then
"area of border" = "area of mat" - "area of picture"
188 = (19+2w)(24+2w) - 19(24)
188 = 456+38w+48w+4w^2 - 456
188 = 38w+48w+4w^2
188 = 4w^2+86w
0 = 4w^2+86w-188
0 = 2w^2+43w-94
Solve using the quadratic formula. Doing so yields:
w = {2, -23.5}
Of course, we can toss out the negative solution leaving:
w = 2 inches
.
 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=2601 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2, -23.5. Here's your graph:

If the cost ,C(x) for manufactoring x units of a certain product is given by
C(x)=x^2-125x+50, find thye units manufactored at a cost of \$9500
1 solutions

Answer 215865 by nerdybill(7008)   on 2010-05-05 18:35:20 (Show Source):
You can put this solution on YOUR website!
If the cost ,C(x) for manufactoring x units of a certain product is given by
C(x)=x^2-125x+50, find thye units manufactored at a cost of \$9500
.
C(x)=x^2-125x+50
where
C(x) is the cost
x is the number of units
.
Simply plug in the given cost and solve for x:
C(x)=x^2-125x+50
9500 = x^2-125x+50
0 = x^2-125x-9450
Apply the quadratic formula when then yields:
x = {178.07, -53.07}
.
Throw out the negative solution leaving:
x = 178 units
.
 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=53425 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 178.069243313262, -53.0692433132622. Here's your graph:

 Pythagorean-theorem/300752: Two planes take off from an airport at the same time. They fly at right angles to each other and one hour later they are 390km apart. If one plane travels 210km/hr faster than the other, what is the speed of the two planes? I tried to apply Pythagoras Theorem, making the hypotenuse 390, and the sides x and x+210. I squared 390 = the sum of the squares of x and x+210, but my answers always come out wrong. 1 solutions Answer 215727 by nerdybill(7008)   on 2010-05-05 06:10:41 (Show Source): You can put this solution on YOUR website!Two planes take off from an airport at the same time. They fly at right angles to each other and one hour later they are 390km apart. If one plane travels 210km/hr faster than the other, what is the speed of the two planes? . Let x = speed of slower plane then x+210 = speed of faster plane . x^2 + (x+210)^2 = 390^2 x^2 + (x+210)(x+210) = 390^2 x^2 + x^2+420x+44100 = 152100 2x^2+420x+44100 = 152100 x^2+210x+22050 = 76050 x^2+210x-54000 = 0 (x+360)(x-150) = 0 x={150, -360} Throw out the negative: x = 150 km/hr (slower plane) . faster plane: x+210 = 150+210 = 360 km/hr
 Miscellaneous_Word_Problems/300724: bill has a collection of 65 nickels and dimes. their total worth is \$5.50. find how many nickels and dimes bill has1 solutions Answer 215720 by nerdybill(7008)   on 2010-05-05 01:24:14 (Show Source): You can put this solution on YOUR website! bill has a collection of 65 nickels and dimes. their total worth is \$5.50. find how many nickels and dimes bill has . Let n = number of nickels then 65-n = number of dimes . .05n + .10(65-n) = 5.50 .05n + 6.5 - .10n = 5.50 6.5 - .05n = 5.50 -.05n = -1 n = 20 (number of nickels) . number of dimes: 65-n = 65-20 = 45
 Rectangles/300727: The area of a square is 5 more times than its perimeter. Find the length of a side.1 solutions Answer 215719 by nerdybill(7008)   on 2010-05-05 01:20:55 (Show Source): You can put this solution on YOUR website! The area of a square is 5 times than its perimeter. Find the length of a side. . Let x = length of one side of square then "area of square" = "5 more times than its perimeter" x^2 = 5(4x) x^2 = 20x x^2 - 20x = 0 x(x - 20) = 0 x = {0, 20} . length of side must be 20
 Polynomials-and-rational-expressions/300713: Solve by factoring and using the principle of zero products. 9t^2=251 solutions Answer 215718 by nerdybill(7008)   on 2010-05-05 00:07:56 (Show Source): You can put this solution on YOUR website!9t^2=25 9t^2-25 = 0 (3t)^2 - 5^2 = 0 The above is a "difference of squares": (3t-5)(3t+5) = 0 t = {-5/3, 5/3}
 logarithm/300705: How long will it take for the population of a certain country to double if its annual growth rate is 3.5%? (Round to the nearest year) Use the exponential growth modle P(t) = poe kt1 solutions Answer 215717 by nerdybill(7008)   on 2010-05-04 23:26:49 (Show Source): You can put this solution on YOUR website!How long will it take for the population of a certain country to double if its annual growth rate is 3.5%? (Round to the nearest year) Use the exponential growth modle P(t) = poe kt . P(t) = poe^kt . Let x = initial population then 2x = xe^(.035t) dividing both sides by x: 2 = e^(.035t) ln(2) = .035t ln(2)/.035 = t 19.80 = t round to nearest year: 20 years = t
 Mixture_Word_Problems/300675: To reduce 16 ounces of a 18% saline solution to a 10% solution, how much distilled water (to the nearest tenth oz.) should a nurse add? The nurse should add ________ oz. of distilled water. 1 solutions Answer 215693 by nerdybill(7008)   on 2010-05-04 22:00:04 (Show Source): You can put this solution on YOUR website!To reduce 16 ounces of a 18% saline solution to a 10% solution, how much distilled water (to the nearest tenth oz.) should a nurse add? . Let x = ounces of distilled water to add then .18(16) = .10(16+x) 2.88 = 1.6+.10x 1.28 = .10x 12.8 = x . The nurse should add 12.8 oz. of distilled water.
 Quadratic_Equations/300563: Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet. --They want me to use the quadratic formula, but I don't know how to set the equation up. That's all I'm having trouble with. I know how to use the quadratic formula fairly well. Can you please help me? ~Thanks!1 solutions Answer 215647 by nerdybill(7008)   on 2010-05-04 19:01:12 (Show Source): You can put this solution on YOUR website!Find the dimensions of a rectangular lawn whose perimeter is 100 feet and whose area is 600 square feet. . Let x = length and y = width . 2(x+y) = 100 (equation 1) xy = 600 (equation 2) . Solve equation 2 for y: xy = 600 y = 600/x . Substitute the above into equation 1 and solve for x: 2(x+y) = 100 2(x+600/x) = 100 x+600/x = 50 x^2+600 = 50x x^2-50x+600 = 0 (x-20)(x-30) = 0 . x = {20,30} . Dimensions are 20 feet by 30 feet
 Quadratic_Equations/300547: Suppose you are going to construct a circular fish pond in your garden. You want the pond to cover an area of 300ft^2. What is the radius of the pond?1 solutions Answer 215645 by nerdybill(7008)   on 2010-05-04 18:51:19 (Show Source): You can put this solution on YOUR website! Suppose you are going to construct a circular fish pond in your garden. You want the pond to cover an area of 300ft^2. What is the radius of the pond? . Since area of a circle is (1/2)(pi)r^2 . 300 = (1/2)(pi)r^2 300 = (1/2)(3.14)r^2 600 = (3.14)r^2 600/3.14 = r^2 191.0828 = r^2 3.72 feet = r
 Polynomials-and-rational-expressions/300548: Can someone please solve the below and explain. Thank you so much. Factor Completly. Remember to look first for a common factor. Check by multiplying. If a polynomoal is prime state this. 3y^2-9y-84. Thanks again1 solutions Answer 215643 by nerdybill(7008)   on 2010-05-04 18:47:32 (Show Source): You can put this solution on YOUR website!3y^2-9y-84 3(y^2-3y-28) 3(y-7)(y+4)
 Polynomials-and-rational-expressions/300489: Reduce the rational expression (please show steps) 1 solutions Answer 215640 by nerdybill(7008)   on 2010-05-04 17:27:59 (Show Source): You can put this solution on YOUR website!Starting with: . Factor numerator and denominator: . Cancel like-terms:
 logarithm/300393: How long will it take for the population of a certain country to double if its annual growth rate is 5.1%? I have been dividing ln2 by 5.1%? A)14 yr B)6 yr C) 39 yr D) 1 yr1 solutions Answer 215573 by nerdybill(7008)   on 2010-05-04 15:03:45 (Show Source): You can put this solution on YOUR website!. Apply: A = Pe^(rt) . Let x = current population then 2x = xe^(.051t) 2 = e^(.051t) ln 2 = .051t ln 2/.051 = t 13.6 years =t . Closest answer would be B
 Radicals/300409: what is 2(squareroot)2=(squareroot)u and how do you do it1 solutions Answer 215568 by nerdybill(7008)   on 2010-05-04 14:55:45 (Show Source): You can put this solution on YOUR website!2(squareroot)2=(squareroot)u . Square both sides:
 percentage/300381: I am terrible at math, can you please help me? Thank you again. A saleswoman is working on a 6% commission basis. If she wants to make \$2,400 in one month, how much must she sell?1 solutions Answer 215564 by nerdybill(7008)   on 2010-05-04 14:33:53 (Show Source): You can put this solution on YOUR website!A saleswoman is working on a 6% commission basis. If she wants to make \$2,400 in one month, how much must she sell? . Let x = amount she sells then .06x = 2400 x = 2400/.06 x = \$40,000 She must sell \$40,000 worth of merchandise
 logarithm/300357: How do I solve the following equation: The correct answer is 0.4, but I am not understanding how to get that. 7.1= 6.8 + Log .8/X 71.-6.8 = .3, so .3= Log .8/x I am not sure where to go from there. I appreciate the help.1 solutions Answer 215548 by nerdybill(7008)   on 2010-05-04 12:50:40 (Show Source): You can put this solution on YOUR website!7.1= 6.8 + Log .8/X Subtracting 6.8 from both sides: .3 = Log .8/x 10^(.3) = 10^(Log .8/x) 10^.3 = .8/x x = .8/10^.3 x = .401
 Percentage-and-ratio-word-problems/300304: sixty percent of the 30 students in the class are girls. write sixty percent as a reduced fraction. then find the number of girls in the class1 solutions Answer 215539 by nerdybill(7008)   on 2010-05-04 11:13:42 (Show Source): You can put this solution on YOUR website! sixty percent of the 30 students in the class are girls. write sixty percent as a reduced fraction. then find the number of girls in the class . % is interpreted as "per one hundred" therefore sixty percent = 60% = 60/100 . Reducing: 60/100 = 6/10 = 2/5 . 2/5 of 30 students then is: 2/5 *30 = 2*6 = 12 girls
 Mixture_Word_Problems/300324: In a chemistry class, 12 L of a 12% alcohol solution must be mixed with a 20% solution to get a 14% solution. How many liters of the 20% solution are needed?1 solutions Answer 215538 by nerdybill(7008)   on 2010-05-04 11:11:23 (Show Source): You can put this solution on YOUR website! In a chemistry class, 12 L of a 12% alcohol solution must be mixed with a 20% solution to get a 14% solution. How many liters of the 20% solution are needed? . Let x = liters 20% solution to be added then .12(12) + .20x = .14(12+x) .12(12) + .20x = .14(12+x) 1.44 + .20x = 1.68 + .14x .20x = .24 + .14x .06x = .24 x = 4 liters
 Mixture_Word_Problems/300319: In a chemistry class, 5 liters of 4% silver solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?1 solutions Answer 215531 by nerdybill(7008)   on 2010-05-04 10:53:12 (Show Source): You can put this solution on YOUR website! In a chemistry class, 5 liters of 4% silver solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? . Let x = liters of 10% solution added then .04(5) + .10x = .06(5+x) .04(5) + .10x = .06(5+x) .2 + .10x = .3 + .06x .04x = .1 x = 2.5 liters
 Rectangles/300301: Rectangle A is 4.5 times as long as it is wide. Rectangle B is 8 inches wider and 20 inches shorter. The rectangles have the same area. What is the width of Rectangle B?1 solutions Answer 215530 by nerdybill(7008)   on 2010-05-04 10:51:05 (Show Source): You can put this solution on YOUR website! Rectangle A is 4.5 times as long as it is wide. Rectangle B is 8 inches wider and 20 inches shorter. The rectangles have the same area. What is the width of Rectangle B? . Rect A: Let x = width then 4.5x = length . Rect B: x+8 = width 4.5x-20 = length . Since area is the same: x(4.5x) = (x+8)(4.5x-20) 4.5x^2 = 4.5x^2-20x+36x-160 4.5x^2 = 4.5x^2+16x-160 0 = 16x-160 160 = 16x 10 inches = x . Width of rectangle B: x+8 = 10+8 = 18 inches
 Triangles/300313: If AB = 21 centimeters, and BC = 28 centimeters, which does AC equal?1 solutions Answer 215528 by nerdybill(7008)   on 2010-05-04 10:45:51 (Show Source): You can put this solution on YOUR website! If AB = 21 centimeters, and BC = 28 centimeters, which does AC equal? . AC = AB + BC AC = 21 + 28 AC = 49 centimeters
 Polynomials-and-rational-expressions/300302: Factor -7m3n -28mn3 1 solutions Answer 215527 by nerdybill(7008)   on 2010-05-04 10:44:27 (Show Source): You can put this solution on YOUR website!-7m^3n -28mn^3 -7mn(m^2 - 4n^2) -7mn(m^2 - (2n)^2) Notice, we now have a "difference of squares": (-7mn)(m-2n)(m+2n)
 logarithm/300315: Write Ln 3x + 4 Ln x - Ln 3xy as a single logarithm1 solutions Answer 215524 by nerdybill(7008)   on 2010-05-04 10:41:53 (Show Source):
 Miscellaneous_Word_Problems/300184: A chef is using a mixture of two brands of Italian dressing. The first brand contains 10% vinegar, and the second brand contains 15% vinegar. The chef wants to make 260 milliliters of a dressing that is 13% vinegar. How much of each brand should she use? 1 solutions Answer 215466 by nerdybill(7008)   on 2010-05-04 01:41:43 (Show Source): You can put this solution on YOUR website!A chef is using a mixture of two brands of Italian dressing. The first brand contains 10% vinegar, and the second brand contains 15% vinegar. The chef wants to make 260 milliliters of a dressing that is 13% vinegar. How much of each brand should she use? . Let x = milliliters of 10% vinegar then 260-x = milliliters of 30% vinegar . .10x + .30(260-x) = .13(260) .10x + 78 - .30x = 33.8 78 - .20x = 33.8 -.20x = -44.2 x = 221 milliliters of 10% vinegar . 30% vinegar: 260-x = 260-221 = 39 milliliters
 expressions/300222: The sum of two numbers is 50 . The larger number is 10 more than the smaller number. What are the numbers? Larger# and smaller #1 solutions Answer 215465 by nerdybill(7008)   on 2010-05-04 01:35:50 (Show Source): You can put this solution on YOUR website!The sum of two numbers is 50 . The larger number is 10 more than the smaller number. What are the numbers? . Let x = smaller number then x+10 = larger number . x + x+10 = 50 2x+10 = 50 2x = 40 x = 20 (smaller number) . Larger number: x+10 = 20+10 = 10
 logarithm/300223: if \$5500 is invested in a long-term trust fund with an interest rate of 10% compounded continuously, what is the amount of money in the account after 30 years?1 solutions Answer 215464 by nerdybill(7008)   on 2010-05-04 01:33:34 (Show Source): You can put this solution on YOUR website!if \$5500 is invested in a long-term trust fund with an interest rate of 10% compounded continuously, what is the amount of money in the account after 30 years? . Continuously compound interest formula: A = Pe^(rt) A = 5500e^(.10*30) A = 5500e^3 A = \$110,470.45
 Rate-of-work-word-problems/300150: It takes Jack 9 hours longer to paint the fence than Mike. Together, they can paint the fence in 20 hours. How long will it take each person to paint the fence? I tried solving this as an inverse work-rate problem using 1/A + 1/B = 20 but I can't get it to work. 1 solutions Answer 215440 by nerdybill(7008)   on 2010-05-03 21:50:32 (Show Source): You can put this solution on YOUR website!It takes Jack 9 hours longer to paint the fence than Mike. Together, they can paint the fence in 20 hours. How long will it take each person to paint the fence? . Let m = hours it takes Mike to paint fence then m+9 = hours it takes Jack to paint fence . 20(1/m + 1/(m+9)) = 1 Multiplying both sides by m(m+9): 20((m+9) + m) = m(m+9) 20(2m+9) = m(m+9) 40m+180 = m^2+9m 0 = m^2-31m-180 0 =(x-36)(x+5) x = {36, -5} Throw away the negative solution leaving: x = 36 hours (Mike) . Jack: x+9 = 45 hours
 Mixture_Word_Problems/300140: How much water should be added to 800 cc of a 70% solution of boric acid to make it a 40% solution of boric acid1 solutions Answer 215424 by nerdybill(7008)   on 2010-05-03 20:30:10 (Show Source): You can put this solution on YOUR website! How much water should be added to 800 cc of a 70% solution of boric acid to make it a 40% solution of boric acid . Let x = amount (cc) of water to be added then .70(800) = .40(800+x) 560 = 320+.40x 240 = .40x 600 cc = x (amount of water to add)
 Quadratic_Equations/300035: Hello! this is an s.o.s. fI need to figure out this problem for class and keep getting stuck. I am supose to translate this problem into two a pair of linear equations in two variables. solve the equation using the elimination or substitute method. Roberto invested some money at 7%, and then invested \$2000 more than twice this amount at 9%. His total annual income from the two investments was \$2930. How much was invested at 9% ? I started out like this, but keep getting stumped!!! x(0.07) + x*2+2000=2930 or 2930 - s(0.07)=n 2930- 2s+2000(0.09)=n See wwhat I mean? 1 solutions Answer 215413 by nerdybill(7008)   on 2010-05-03 18:37:37 (Show Source): You can put this solution on YOUR website!Roberto invested some money at 7%, and then invested \$2000 more than twice this amount at 9%. His total annual income from the two investments was \$2930. How much was invested at 9% ? Let x = amount invested at 7% then 2x+2000 = amount invested at 9% . x(0.07) + (2x+2000)(0.09) = 2930 .07x + 0.18x+180 = 2930 0.25x+180 = 2930 0.25x = 2750 x = \$11000 (amount invested at 7%) . Amount invested at 9% then: 2x+2000 = 2(11000)+2000 = 22000+2000 = \$24,000 (amount invested at 9%)