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 Equations/356987: Allyson is a nurse in the intensive care unit of a hospital. She works with units daily in administering drugs through intravenous (i.v.) tubes. A common dosage for the drug dopamine is 2 to 5 micrograms per kilogram of body weight per minute. She will put 400 milligrams of dopamine into 250 cc (cubic centimeters) of fluid and administer it into a patient through an i.v. tube. At what rate, in cc/hr, should she set the flow to achieve a dosage of 3 micrograms per kilogram per minute into a patient with a mass of 75kg? 1 solutions Answer 254927 by mananth(12270)   on 2010-10-16 01:29:12 (Show Source): You can put this solution on YOUR website!body weight of patient = 75 kg dosage = of body weight .. For 75 Kgs. 75*3= Total dosage = ... she put 400 mg in 250 cc 1mg = 1000 400000 in 250 cc 1 cc will contain 400000/250 = 1600 ... But dosage is 225 = ? cc ... 0.14 cc/hour should be given. ... m.ananth@hotmail.ca
 Geometry_Word_Problems/356969: Roopa Patel won a prize for her sculpture. She invested part of the money in a certificate of deposit at 4% and \$3000 more than that amount in a bond paying 6%. Her annual interest income was \$780. How much did Roopa invest at each rate?1 solutions Answer 254922 by mananth(12270)   on 2010-10-16 00:38:38 (Show Source): You can put this solution on YOUR website!Roopa Patel won a prize for her sculpture. She invested part of the money in a certificate of deposit at 4% and \$3000 more than that amount in a bond paying 6%. Her annual interest income was \$780. How much did Roopa invest at each rate? ... \$ x in CD @ 4% \$(x+3000) in bond @ 6 % total interest income in 1 year was \$780 ... Interest equation 0.04x+0.06x(x+3000)= 780 0.04x+0.06x+180 = 780 0.1x = 780-180 0.1x=600 x=600/0.1 x= \$6000 @ 4% \$3000 more @6% 6000+3000=\$9000 @6% ... m.ananth@hotmail.ca
 Rectangles/356992: how do you find the total length of a rectangle?1 solutions Answer 254920 by mananth(12270)   on 2010-10-16 00:26:04 (Show Source): You can put this solution on YOUR website!A rectangle has 4 sides The sum of all four sides is called the perimeter the opposite sides are equal The lengths are equal and the widths are equal. .. Let us say the length is L cm there are 2 lengths in a rectangle so the total of lengths = L+L = 2L ... Let width be W cm two widths so total of widths = 2W ... Add the lengths & the widths (2L +2W)cms OR 2(L+W) cms. ... example find the perimeter of rectangle whose length is 10 meters & width is 6 meters Perimeter = 2*(L+W) plug the value of L & W Perimeter = 2*(10+6) Perimeter = 2*16 Perimeter = 32 meters ... m.ananth@hotmail.ca
 Linear_Equations_And_Systems_Word_Problems/356970: thank you in advance here is the problem......... a theatre group made appearences in two cities.The hotel charges before tax in the second city were \$1500 higher than in the first.The tax on the hotel bill was 9.5% in the first city and 6% in the second.After the trip,the total tax paid on accomodation expenses was \$826.25.How much was the hotel bill in the first city before tax?1 solutions Answer 254918 by mananth(12270)   on 2010-10-15 23:53:26 (Show Source): You can put this solution on YOUR website!a theatre group made appearences in two cities.The hotel charges before tax in the second city were \$1500 higher than in the first.The tax on the hotel bill was 9.5% in the first city and 6% in the second.After the trip,the total tax paid on accomodation expenses was \$826.25.How much was the hotel bill in the first city before tax? ... let the pre tax bill in first city be x the pretax bill in second city = x+1500 ... Tax in firts city = 9.5% Tax in the second city = 6% .. bill first city + bill second city = Total bill x*(1.095)+(x+150)*1.06 = 826.25 1.095x+1.06x+159 =826.25 2.155x = 826.25-159 2.155x =667.25 x= 667.25/2.155 x=\$309.62 pretax bill in first city \$459.62 pretax bill in second city .... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/356988: I need to factor 8x^3-8x^2-x+1 how do factor this problem1 solutions Answer 254912 by mananth(12270)   on 2010-10-15 23:26:15 (Show Source): You can put this solution on YOUR website!8x^3-8x^2-x+1 8x^2(x-1)-1(x-1) (x-1)(8x^2-1)
 Linear-equations/356976: You and your sister decide to combine your weekly overtime earnings to buy a birthday gift for your mother. Your overtime rate is \$18 per hour and your sister's overtime rate is \$24 per hour. The total amount earned for the gift was \$288. If you worked two more hours of overtime than your sister, how many overtime hours did each of your work?1 solutions Answer 254911 by mananth(12270)   on 2010-10-15 23:24:51 (Show Source): You can put this solution on YOUR website!You and your sister decide to combine your weekly overtime earnings to buy a birthday gift for your mother. Your overtime rate is \$18 per hour and your sister's overtime rate is \$24 per hour. The total amount earned for the gift was \$288. If you worked two more hours of overtime than your sister, how many overtime hours did each of your work? ... let sister work x overtime hours I work x+2 overtime hours .. sister's rate /h= 24 my overtime rate = 18 .. 24x+18(x+2)=288 24x+18x+36=288 42x=288-36 42x=252 /42 x= 6 hours overtime by sister 8 hours overtime by me. ... 6*24+18*8=288 ... m.ananth@hotmail.ca
 Problems-with-consecutive-odd-even-integers/356980: Find three consecutive odd integers such that the sum of the first integer twice the second integer and three times the third is 70? 1 solutions Answer 254908 by mananth(12270)   on 2010-10-15 23:13:00 (Show Source): You can put this solution on YOUR website!Find three consecutive odd integers such that the sum of the first integer twice the second integer and three times the third is 70? ... let the integers be x,x+2,x+4 x+2(x+2)+3(x+4)=70 x+2x+4+3x+12=70 6x+16=70 add -16 6x+16-16=70-16 6x=54 /6 x= 9 ... the integers are 9,11,13
 Travel_Word_Problems/356983: A small plane flies from Big Lake to Pine city everyday, with a 30min layover in Summerville. The distance between BL and Summerville is 575mi, the distance between Summerville and Pine city is 325mi. If the plane flies at an average speed of 200mph, how long does the whole trip (including any stops) from BL to Pine city take? 1 solutions Answer 254907 by mananth(12270)   on 2010-10-15 23:08:46 (Show Source): You can put this solution on YOUR website!time = distance/speed first leg 575/200 = 2.875 hours .. second leg 325/200 = 1.625 hours .. stopover time = 0.5 hours ... total time = 2.875+1.625+0.5= 5 hours ... total distance = 575+325=900 miles total time = 5 hours ... speed = distance /time 900/5= 180 mph is the average speed between Big lake to pine city ... m.ananth@hotmail.ca
 Inverses/356981: Solve the equation using inverse operations to isolate the variable. 7a+9=301 solutions Answer 254906 by mananth(12270)   on 2010-10-15 22:58:53 (Show Source): You can put this solution on YOUR website!7a+9=30 7a+9-9=30-9 7a=21 multiply by 1/7 7a*1/7 = 21*1/7 a= 3 ...
 Quadratic_Equations/356898: The body mass index,I, can be used to determine an individuals risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the formula, or model, I=(700w/H^2), where W=weight, in pounds, and H=height, in inches. Francis wieghs 216 pounds and stands 74 inches tall. What is his approcimate body mass index? Find an ineqyality describing all weights W that Francis can have and be in the low-risk category.1 solutions Answer 254904 by mananth(12270)   on 2010-10-15 21:29:03 (Show Source): You can put this solution on YOUR website!The body mass index,I, can be used to determine an individuals risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the formula, or model, I=(700w/H^2), where W=weight, in pounds, and H=height, in inches. Francis wieghs 216 pounds and stands 74 inches tall. What is his approcimate body mass index? Find an ineqyality describing all weights W that Francis can have and be in the low-risk category. w=216 h=74 I= (700*216)/(74)^2 I = 27.61 ... 25= (700*w)/(74)^2 25*(74)^2=700w (25*974)^2/700 = w 196 pounds {xeR|x<196} ... m.ananth@hotmail.ca
 Expressions-with-variables/356917: A chemist has two large containers of salt solution. The concentration of the salt is different in the two containers. She blends 80mL of the first solution with 320 mL of the second solution to obtain a solution with concentration 56g/mL. She blends 300 mL of the first solution with 200 mL of the second solution to obtain a solution with concentration 48g/mL. What are the concentrations of the original solutions. 1 solutions Answer 254901 by mananth(12270)   on 2010-10-15 21:07:42 (Show Source): You can put this solution on YOUR website!A chemist has two large containers of salt solution. The concentration of the salt is different in the two containers. She blends 80mL of the first solution with 320 mL of the second solution to obtain a solution with concentration 56g/mL. She blends 300 mL of the first solution with 200 mL of the second solution to obtain a solution with concentration 48g/mL. What are the concentrations of the original solutions. Solution A concentration be x% solution B concentration be y% .. 0.8x+3.2y=400*0.56 0.8x+3.2y= 224 multiply by 10 8x+32y=2240....................1 3x+2y= 240......................2 multiply by -16 and add to first equation -48x-32y=-3840 add -40x=-1600 x= 40% solution A plug value of x in equation 2 120+2y=240 2y=120 y=60% solution B ... m.ananth@hotmail.ca
 Geometry_Word_Problems/356953: A rectangle is twice as long as it is wide. If the width is increased by 25% and the length is decreased by 25%, the resulting rectangle will have 200 fewer square units of area than the original rectangle. What is the original width of the rectangle?1 solutions Answer 254895 by mananth(12270)   on 2010-10-15 20:49:16 (Show Source): You can put this solution on YOUR website!A rectangle is twice as long as it is wide. If the width is increased by 25% and the length is decreased by 25%, the resulting rectangle will have 200 fewer square units of area than the original rectangle. What is the original width of the rectangle? ... width be x length be 2x Area = x*2x=2x^2 .. width increase by 25% which means the width becomes 1.25x length is decreased by 25% which means it becomes 0.75*2x=1.5x Area = 1.25x*1.5x= 1.875x^2 ... 2.0x^2 - 1.875x^2= 200 0.125x^2=200 x^2= 200/0.125 x^2=1600 x= 40 the width length = 3x = 120 units ... m.ananth@hotmail.ca
 Travel_Word_Problems/356918: A boat can travel 45 mph in still water. If it travels 200 miles with the current in the same length of time it travels 160 against the current,what is the speed of the current?1 solutions Answer 254894 by mananth(12270)   on 2010-10-15 20:40:15 (Show Source): You can put this solution on YOUR website!A boat can travel 45 mph in still water. If it travels 200 miles with the current in the same length of time it travels 160 against the current,what is the speed of the current? ... let current speed be x mph speed in still water = 45 mph .. Upstream speed = 45-x mph downstream speed = 45+x mph .. time = Distance /speed 160/45-x = 200/45+x 160(45+x)=200(45-x) 7200+160x=9000-200x 200x+160x=9000-7200 360x=1800 x= 1800/360 x=5 mph the speed of current ... m.ananth@hotmail.ca
 Money_Word_Problems/356709: Lani has a certain number of dollar bills in her purse. She has no other money. Lani spends half the money on a blouse and gives a dollar to a beggar outside the store. She spends half the remaining dollars for lunch and tips the waiter \$2. She spends half the remaining dollars for a book, then goes to an ice cream parlor and spends \$3 on a banana split. Lani now has one dollar bill left. Assuming that she never changed a dollar bill, how many bills did Lani start with?1 solutions Answer 254739 by mananth(12270)   on 2010-10-15 11:06:56 (Show Source): You can put this solution on YOUR website!Lani has a certain number of dollar bills in her purse. She has no other money. Lani spends half the money on a blouse and gives a dollar to a beggar outside the store. She spends half the remaining dollars for lunch and tips the waiter \$2. She spends half the remaining dollars for a book, then goes to an ice cream parlor and spends \$3 on a banana split. Lani now has one dollar bill left. Assuming that she never changed a dollar bill, how many bills did Lani start ... let her have \$ x x/2 for blouse balance x/2 -1 beggar x/2 -1 =(x-2)/2 .. 1/2 * (x-2)/2 for lunch =(x-2)/4 for lunch. -2 waiter (x-2)/4 -2 =(x-2-8)/4 =(x-10)/4 1/2 (x-10)/4 for book (x-10)/8 -3 x-10-24 /8 x-34/8 =1 x-34=8 x=42 dollars ... 42 /2 = (blouse)21 -(beggar)1=20 1/2 *20= (lunch)10 -(tip)2=8 1/2 *8=(book)4 -(split)3= 1 .. m.ananth@hotmail.ca
 Human-and-algebraic-language/356743: Chris is four times as old as Peter. Sara is 6 years younger than Chris. the total age of Chris, Sara and Peter is 66 years. How old is Sara.1 solutions Answer 254694 by mananth(12270)   on 2010-10-15 09:36:14 (Show Source): You can put this solution on YOUR website!let peter's age be x now chris will be 4x sara will be4x-6 ... their sum = 66 x+4x+4x-6 =66 9x-6=66 add 6 9x=66+6 9x=72 x= 8 .. sara = 4x-6 = 32-6 = 26 years ... m.ananth@hotmail.ca
 Quadratic_Equations/356782: 3x^2+4x+1=01 solutions Answer 254693 by mananth(12270)   on 2010-10-15 09:30:16 (Show Source): You can put this solution on YOUR website!3x^2+4x+1 3x^2+3x+x+1 3x(x+1)+1(x+1) (3x+1)(x+1) ... m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/356780: As long as I understand how to add and subtract polynomials, I can select the format, horizontal or vertical, that works best for me. yes or no and give an example please 1 solutions Answer 254692 by mananth(12270)   on 2010-10-15 09:28:57 (Show Source): You can put this solution on YOUR website!yes you can add them vertically or horizontally. the answer will be the same. But vertical adding will become tedious later on in higher classes involving many terms. it is better to practise grouping the like terms and adding or subtracting them horizontally. .. m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/356778: can I add like monomials by adding both their coefficients and the exponents that appear on their common variable factor. explain please and givbe me example 1 solutions Answer 254687 by mananth(12270)   on 2010-10-15 09:24:52 (Show Source): You can put this solution on YOUR website!2x+3x= 5x 3y+5y=8y 10x+13x=23x ... a^2+2a^2= 3a^2 6y^2+10y^2=16y^2 ... If the terms are same then you add the co-efficients. m.ananth@hotmail.ca
 Polynomials-and-rational-expressions/356777: can I use the product rule for exponents to multiply x7 and y9 and why or why not? 1 solutions Answer 254686 by mananth(12270)   on 2010-10-15 09:21:31 (Show Source): You can put this solution on YOUR website!you cannot use the product rule because the base is not the same. x^7 & y^9 the product rule is a^m*a^n= a^(m+n) ... m.ananth@hotmail.ca
 Complex_Numbers/356770: Solve by using the quadratic formula (Put in standard form first) 2x2+3x=-7 the first part is 2x to the power of 2 1 solutions Answer 254685 by mananth(12270)   on 2010-10-15 09:19:05 (Show Source): You can put this solution on YOUR website!2x2+3x=-7 2x^2+3x+7=0 compare with ax^2+bx+c a=2,b=3,c=7 .. b^2-4ac=9-56=-47 x1= -3+sqrt(-47)/4 x1=-3/4 +sqrt(-47)/4 x1=-0.75+sqrt(-47)/4 x2=-0.75-sqrt(-47)/4
 Inequalities/356771: 57-4t is greater or equal to 131 solutions Answer 254677 by mananth(12270)   on 2010-10-15 09:07:38 (Show Source): You can put this solution on YOUR website!57-4t>=13 add -57 57-57-4t>=13-57 -4t>=-44 divide by -4 t<=11
 Linear_Equations_And_Systems_Word_Problems/356750: The length of a rectangle is 1cm more than four times the width. If the perimeter of the rectangle is 22cm, what are its dimesions?1 solutions Answer 254674 by mananth(12270)   on 2010-10-15 09:01:23 (Show Source): You can put this solution on YOUR website!let width be x cm length = 4x+1 ... Perimeter = 2(L+W) 22=2(4x+1+x) 22=2(5x+1) 22=10x+2 10x=20 x= 2 cm width length = 4x+1 = 8+1=9 cm ... 9*2+2*2=22 ... m.ananth@hotmail.ca
 Word_Problems_With_Coins/356764: A collection of 52 dimes and nickels is worth \$4.50. How many nickels are there?1 solutions Answer 254667 by mananth(12270)   on 2010-10-15 08:13:48 (Show Source): You can put this solution on YOUR website!let nickels be x dimes will be 52-x .. 5x+10(52-x)=450 5x+520-10x=450 -5x=-70 x=14 nickels dimes = 52-14 = 38 ... 38*10+5*14= 450 ... m.ananth@hotmail.ca
 Travel_Word_Problems/356739: If i am traveling at 80kmh how long will it take me to travel 126km?1 solutions Answer 254663 by mananth(12270)   on 2010-10-15 05:43:42 (Show Source): You can put this solution on YOUR website!time = distance / speed distance =126 km speed =80kmph 126/80 =1.57 hours
 Linear-systems/356740: 8x^3-271 solutions Answer 254662 by mananth(12270)   on 2010-10-15 05:41:56 (Show Source): You can put this solution on YOUR website!8x^3-27 (2x)^3-(3)^3 (2x-3)(4x^2+6x+9)
 Travel_Word_Problems/356742: An airline travels for 6 hours at an average speed of 650 km/h. What was the distance covered in that period?1 solutions Answer 254661 by mananth(12270)   on 2010-10-15 05:38:41 (Show Source): You can put this solution on YOUR website!time = 6 hours speed = 650km/h distance = speed * time D=6*650 =3900 km ...
 Linear-equations/356676: tell whether youmultiply or divide by 10, 100, 1000. 68m=---cm1 solutions Answer 254656 by mananth(12270)   on 2010-10-15 03:20:52 (Show Source): You can put this solution on YOUR website!multiply by 100 68*100 = 6,800 cm
 Quadratic_Equations/356679: 6x^2+11x-10=0 x^2=7x (x-5)(x+2)=181 solutions Answer 254654 by mananth(12270)   on 2010-10-15 03:19:04 (Show Source): You can put this solution on YOUR website!6x^2+11x-10 6x^2-15x+4x-10=0 3x(2x-5)+2(2x-5)=0 (2x-5)(3x+2)=0 x= 2/5 OR x=-2/3 ... x^2=7x divide by x x=7 ... (x-5)(x+2)=18 x^2-3x-10=18 x^2-3x-28=0 x^2-7x+4x-28=0 x(x-7)+4(x-7)=0 (x+4)(x-7)=0 x=-4, x=7 ... m.ananth@hotmail.ca
 Linear-systems/356725: graph the line with the given slope that contains the given point. slope=-1/2;(3,1) 1 solutions Answer 254653 by mananth(12270)   on 2010-10-15 03:11:07 (Show Source): You can put this solution on YOUR website!slope =-1/2 (3,1) find b 1=-1/2*3+b 1+3/2=b 5/2=b y=-x/2 +5/2 ... ... m.ananth@hotmail.ca
 Inequalities/356720: 1:the product of -2 and a number is less than or equal to -52 2:the difference of a number and 4 is at least 18 my answer-x+4>181 solutions Answer 254644 by mananth(12270)   on 2010-10-15 02:16:40 (Show Source): You can put this solution on YOUR website!-2x<=-52 ... x-4 >=18
 Inequalities/356721: 4: EIGHT LESS THAN 5 TIMES A NUMBER IS AT MOST -23 5: THE PRODUCT OF A NUMBER AND -6 IS GREATER THAN OR EQUAL TO 721 solutions Answer 254643 by mananth(12270)   on 2010-10-15 02:13:23 (Show Source): You can put this solution on YOUR website!5x-8<=-23 ... -6x>=72 ... m.ananth@hotmail.ca