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Recent problems solved by 'stanbon'

stanbon answered: 57911 problems
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 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509 , 3510..3539 , 3540..3569 , 3570..3599 , 3600..3629 , 3630..3659 , 3660..3689 , 3690..3719 , 3720..3749 , 3750..3779 , 3780..3809 , 3810..3839 , 3840..3869 , 3870..3899 , 3900..3929 , 3930..3959 , 3960..3989 , 3990..4019 , 4020..4049 , 4050..4079 , 4080..4109 , 4110..4139 , 4140..4169 , 4170..4199 , 4200..4229 , 4230..4259 , 4260..4289 , 4290..4319 , 4320..4349 , 4350..4379 , 4380..4409 , 4410..4439 , 4440..4469 , 4470..4499 , 4500..4529 , 4530..4559 , 4560..4589 , 4590..4619 , 4620..4649 , 4650..4679 , 4680..4709 , 4710..4739 , 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Exponents/112150: This question deals with the half-life formula. Use the approximate half-life formula in this exercise. Be sure to discuss whether the formula is valid for the case described. 32. A clean-up project is reducing the concenration of a pollutant in the water supply with an 8% decrease per week. What is the half-life of the concentration of the pollutant? What fraction of the original amount of the pollutant will remain when the project ends after 1 year (52 weeks)? This is the approximate half-life formula: For a quantity decaying exponentially at a rate of P% per time period, the half-life is approximately Thalf = approximately 70/P. This approximation works best for small decay rates and breaks down for decay rates about 15%. 1 solutions Answer 81823 by stanbon(57984)   on 2007-11-25 10:15:29 (Show Source): You can put this solution on YOUR website! A clean-up project is reducing the concenration of a pollutant in the water supply with an 8% decrease per week. What is the half-life of the concentration of the pollutant? What fraction of the original amount of the pollutant will remain when the project ends after 1 year (52 weeks)? --------------------------- This is the approximate half-life formula: For a quantity decaying exponentially at a rate of P% per time period, the half-life is approximately T(half) = approximately 70/P. This approximation works best for small decay rates and breaks down for decay rates about 15%. --------------------------- T(half) = 70/8 = 8.75 per week T(half) = 8.75*52 = 455 per year ------------------------------ Comment: This all seems rather strange but that's the result using the formula. Cheers, Stan H.

Radicals/112155: Will someone please help me solve this problem. Simplify and express with positive intergers as exponents: radical 3x/2y 1 solutions Answer 81822 by stanbon(57984)   on 2007-11-25 10:03:15 (Show Source): You can put this solution on YOUR website! radical 3x/2y ------------- sqrt(3x/2y) Multiply numerator and denominator by 2y to get: [sqrt(6xy)]/2y ================= Cheers, Stan H.

Equations/112157: Please Help, What is the product of 2Radical 7 + 3 radical 5 and is conjugate? also Solve the following equations: a) 4 + radical x+1 = 5 b) 2/7 = 5/3x-1 c) c-7/c+2 = 1/4 Thank you for your help... 1 solutions Answer 81821 by stanbon(57984)   on 2007-11-25 10:00:21 (Show Source): You can put this solution on YOUR website! What is the product of 2Radical 7 + 3 radical 5 and is conjugate? (2sqrt7 + 3sqrt5)(2sqrt7 - 3sqrt5) = 4*7 -9*5 = 28-45 = -17 ----------------------------- also Solve the following equations: a) 4 + radical x+1 = 5 sqrt(x+1) = 1 Square both sides to get: x+1=1 x=0 --------------- b) 2/7 = 5/3x-1 Cross-multiply to get: 2(3x-1) = 35 6x-2 = 35 6x = 37 x = 37/6 ---------------- c) c-7/c+2 = 1/4 Cross-multiply to get: 4(c-7) = c+2 4c-27 = c+2 3c = 29 c = 29/3 ============== Cheers, Stan H.

Expressions-with-variables/112159: find the x-intercepts. Y= x^2+ x - 6 1 solutions Answer 81820 by stanbon(57984)   on 2007-11-25 09:53:38 (Show Source): You can put this solution on YOUR website! find the x-intercepts. Y= x^2+ x - 6 ---------------- Let y = 0 and solve for "x": x^2+x-6=0 Factor to get: (x+3)(x-2)=0 x = -3 or x=2 ============= Cheers, Stan H.

Exponents/112151: This question deals with an exact formula. In the following exercise use the approximate and exact formulas to find the doubling time. Also answer the given question. 38. A family of 100 termites invades your house and grows at a rate of 20% per week. How many termites will be in your house after 1 year? The approximate doubling time formula (rule of 70): for a quantity growing exponentially at a rate of P% per time period, the doubling time is approximately Tdouble = 70/P. This approximation works best for small growth rates and breaks down for growth rates over about 15%. This is the exact doubling time formula: For an exponentially growing quantity with a fractional growth rate r, the doubling time is Tdouble = log10 2/log10(1 + r). For an exponentially decaying quantity, we use a negative value for r (for example, if the decay rate is 5% per year, we set r = -0.05 per year); the half-life is Thalf= - log10 2/log10(1 + r). Note that the units of time used for T and r must be the same. For example, if the fractional growth rate is 0.05 per month, then the doubling time will also be measured in months. 1 solutions Answer 81819 by stanbon(57984)   on 2007-11-25 09:51:25 (Show Source): You can put this solution on YOUR website! 38. A family of 100 termites invades your house and grows at a rate of 20% per week. How many termites will be in your house after 1 year? -------------- The approximate doubling time formula (rule of 70): for a quantity growing exponentially at a rate of P% per time period, the doubling time is approximately Tdouble = 70/P. This approximation works best for small growth rates and breaks down for growth rates over about 15%. T(double) = 70/20= 3.5 per week T(double) = 3.5*52 = 182 per year ----------------------------- This is the exact doubling time formula: For an exponentially growing quantity with a fractional growth rate r, the doubling time is Tdouble = log10 2/log10(1 + r). For an exponentially decaying quantity, we use a negative value for r (for example, if the decay rate is 5% per year, we set r = -0.05 per year); the half-life is Thalf= - log10 2/log10(1 + r). Note that the units of time used for T and r must be the same. For example, if the fractional growth rate is 0.05 per month, then the doubling time will also be measured in months. T(double)= log(base 10)2/log(base 10)(1+e) T(double) = 0.3010299957/log(1+0.20) = 3.801078... per week T(double) = 3.801078...*52 = 197.6927.. per year =============== Cheers, Stan H.

Expressions-with-variables/112090: Use the quadratic formula to solve the following quadratic equation. __ 4x^2+ 5x = 6 1 solutions Answer 81786 by stanbon(57984)   on 2007-11-24 21:29:04 (Show Source): You can put this solution on YOUR website! Use the quadratic formula to solve the following quadratic equation. __ 4x^2+ 5x = 6 ------------- x = [-5 +- sqrt(25-4*4*-6)]/8 x = [-5 +- sqrt(121)]/8 x = [-5 +- 11]/8 x = 3/4 or x = -2 ================ Cheers, Stan H.

Miscellaneous_Word_Problems/111998: This question is from textbook Construction: The Santa Teresa municipal building code specidies that public buildings have a handicapped access ramp with an incline of no more than 10 degrees. What length of ramp is needed if the ramp climbes 3 ft. 8 inch? Express the answer in feet an inches to the nearest inch.(Hint: work the problem in inches only, then convert the answer to feet and inches.) 1 solutions Answer 81785 by stanbon(57984)   on 2007-11-24 21:25:25 (Show Source): You can put this solution on YOUR website! public buildings have a handicapped access ramp with an incline of no more than 10 degrees. What length of ramp is needed if the ramp climbes 3 ft. 8 inch? Express the answer in feet an inches to the nearest inch.(Hint: work the problem in inches only, then convert the answer to feet and inches.) ------------------ Draw the picture of a right triangle with height = 44 inches and angle opposite that side equal to 10 degrees -------------- The hypotenuse is the ramp. -------------- sin(10 degrees) = 44/length of ranp ----------- length of ramp = 44/sin(10) = 253.39 inches length of ramp >= 253.39/12 = 21' 1.39 inches ==================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/112003: Sue Flay and Cassa Roll obtain a franchise to operate a hamburger stand for a well-known national hamburger chain. They pay $20,000 for the franchise, and have additional expenses of $250 per thousand hamburgers they sell. They sell the hamburgers for $.75 each, so they take in a revenue of $750 per thousand burgers. Let r(x) be the number of dollars revenue they take in by selling x thousand burgers. Write the particular equation for function r. Let c(x) be the total cost of woning the hamburger stand, including the $20,000 franchise fee. Write the particular eaquation for function c. 1 solutions Answer 81783 by stanbon(57984)   on 2007-11-24 21:16:34 (Show Source): You can put this solution on YOUR website! They pay $20,000 for the franchise, and have additional expenses of $250 per thousand hamburgers they sell. They sell the hamburgers for $.75 each, so they take in a revenue of $750 per thousand burgers. Let r(x) be the number of dollars revenue they take in by selling x thousand burgers. Write the particular equation for function r. r(x) = 0.75x where "x" is the number of hamburgers sold. ---------------------------- Let c(x) be the total cost of woning the hamburger stand, including the $20,000 franchise fee. Write the particular eaquation for function c. c(x) = 20000+ 250(x/1000) where x is the number of hamburgers sold. ==================== Cheers, Stan H.

Polynomials-and-rational-expressions/112057: I have to solve the equation by factoring first and then applying the zero product principle. so, can someone help me solve x^3 +x^2-7x=7. any help would be appreciated. 1 solutions Answer 81782 by stanbon(57984)   on 2007-11-24 21:09:07 (Show Source): You can put this solution on YOUR website! solve x^3 +x^2-7x=7 x^3+x^2-7x-7=0 x(x+1)-7(x+1)=0 (x+1)(x-7)=0 x = -1 or x=7 ================ Cheerd, Stan H.

Polynomials-and-rational-expressions/112083: I need help solving this problem (x+3)(x-2)=14. I need to foil first and then I think I have to solve using the ABC method. 1 solutions Answer 81780 by stanbon(57984)   on 2007-11-24 21:05:58 (Show Source): You can put this solution on YOUR website! (x+3)(x-2)=14 x^2+x-6 = 14 x^2+x-20=0 (x+5)(x-4)=0 x = -5 or x = 4 =============== Cheers, Stan H.

test/112085: State whether the system is consistent and independent,consisten and dependent,or inconsistent: 4x+2y=8 2x+y=1 1 solutions Answer 81779 by stanbon(57984)   on 2007-11-24 21:03:10 (Show Source): You can put this solution on YOUR website! State whether the system is consistent and independent,consisten and dependent,or inconsistent: 4x+2y=8 2x+y =1 ---------------- Multiply thru the 2nd equation be 2 to get: 4x+2y = 2 This is the same as the 1st equation. So, the system is consistent and dependent. =============== Cheers, Stan H.

Expressions-with-variables/112082: Solve the following quadratic equation by completing the square. 2x^2- 8x +5 = 0 1 solutions Answer 81778 by stanbon(57984)   on 2007-11-24 21:00:04 (Show Source): You can put this solution on YOUR website! Solve the following quadratic equation by completing the square. 2x^2- 8x +5 = 0 -------------- 2x^2-8x = -5 2(x^2-4x + ?) = -5 +2*? 2(x^2-4x+4) = -5 +2*4 2(x-2)^2= 3 (x-2)^2 = 3/2 x-2 = sqrt(3/2) or -sqrt(3/2) x = 2 + (1/2)sqrt(6) or x = 2-(1/2)sqrt(6) ================ Cheers, Stan H.

Radicals/112073: Hello out there,I really need some help with some tough problems,the first one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,1)and(3,2).The next one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(4,0)and(6,3).The third one is Find the distance between the two points given.Round to the nearest tenth,if necessary,(5,2)and(5,-2).And the last one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,3)and(1,5).Thanks to whoever can help. 1 solutions Answer 81775 by stanbon(57984)   on 2007-11-24 20:38:55 (Show Source): You can put this solution on YOUR website! Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,1)and(3,2). ----------------------------- Formula: d = sqrt[(1-3)^2 + (1-2)^2)] = sqrt[4 + 1] = sqrt(5) ================================ The next one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(4,0)and(6,3). -------------------------------- d = sqrt[(4-6)^2 + (0-3)^2] = sqrt[4+9] = sqrt(13) =========================== The third one is Find the distance between the two points given.Round to the nearest tenth,if necessary,(5,2)and(5,-2). --------------------------- Follows the same pattern. ======================= And the last one is,Find the distance between the two points given.Round to the nearest tenth,if necessary,(1,3)and(1,5). ------------------ Follows the same pattern. ======================== Cheers, Stan H.

Probability-and-statistics/112078: Use the union rule to answer the question If n(A)=5, n(B)=11, and n(A\cap B)=3,what is n(A\cup B)? 1 solutions Answer 81772 by stanbon(57984)   on 2007-11-24 20:31:34 (Show Source): You can put this solution on YOUR website! If n(A)=5, n(B)=11, and n(A\cap B)=3,what is n(A\cup B)? ---------------------- n(A cup B) = n(A) + n(B) - n(A cap B) n(A cup B) = 5 + 11 - 3 = 13 ===================== Cheers, Stan H.

Graphs/111973: Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coins does she have? 1 solutions Answer 81686 by stanbon(57984)   on 2007-11-24 10:51:56 (Show Source): You can put this solution on YOUR website! Jill has $3.50 in nickels and dimes. If she has 50 coins, how many of each type of coins does she have? --------------- Let number of nickels be "x" ; value of these is 5x cents # of dimes is "50-x" ; value of these is 10(50-x)= 500-10x cents ------------------ EQUATION: value + value = 350 cents 5x + 500-10x = 350 -5x = -150 x = 30 ( # of nickels) 50-x=20( # of dimes) ==================== Cheers, Stan H.

Expressions-with-variables/111983: Hi I am trying to figure out how to solve this equation: 3x = 6y = 0 x = 2/3 I can either solve it by substitution or additon. What I think should be done is to first substitute the x=2/3 into the first problem. So, now I have 3 and 2/3 = 6y= 0 then I can make the 3 and 2/3 into an improper fraction so I now have 11/3 + 6=0 If I subtract the 11/3 from both sides I then have 6y= -11/3 The 11/3 is also a fraction 3.6 and repeating. If I divide by 6 to isolate the y I then have y= -0.6 Is there a better way to approach this problem so I don't get stuck with a negative decimal as I will still have to go back in and replace the y with the -0.6 If I do the problem like I showed then I come up with x = - 1.2 1 solutions Answer 81685 by stanbon(57984)   on 2007-11-24 10:46:10 (Show Source): You can put this solution on YOUR website! You have two equal signs in the 1st equation. Should you? Cheers, Stan H.

Radicals/111969: Will someone please help me solve this problem? It says to simplify and express final results with positive intergers as exponents: (15x^-2y)^2/ 5x^-5y^3 the whole problem should be in () 1 solutions Answer 81684 by stanbon(57984)   on 2007-11-24 10:43:17 (Show Source): You can put this solution on YOUR website! (15x^-2y)^2/(5x^-5y^3) --------- = [(15(x^-2)y]^2/[(5x^-5)(y^3)] =[15/5][x^-2/x^-5][y^2/y^3] = 3[x^3][1/y] =[3x^3]/[y] ====================== Cheers, Stan H.

Graphs/111975: Solve each of the following systems by addition. If a unique solution does not exist, state whether the system is inconsistent or dependent. x+5y=10 -2x-10y=-20 1 solutions Answer 81682 by stanbon(57984)   on 2007-11-24 10:35:52 (Show Source): You can put this solution on YOUR website! 1st: x + 5y=10 2nd: -2x-10y=-20 ---------------- Multiply 1st by -2 to get -2x-10y = -20 ------------------ The two equations are essentially the same. The system is "dependent" ============== Cheers, Stan H.

Graphs/111886: Please help me with understanding how to solve each system by graphing. For example, I have to solve, then graph the below: -y -9 = -x (answer y=-1x+9) -12-6y = x (answer y=6x+2) I understand how to get the answer if the answer is actually correct, however, I need to understand how I then graph it. Please help. 1 solutions Answer 81634 by stanbon(57984)   on 2007-11-23 18:26:31 (Show Source): You can put this solution on YOUR website! -y -9 = -x Add "y" to both sides; Add "x" to both sides to geet y = x-9 --------- You need to find and plot two points: then draw a line thru them. Points: If x = 0, y = 0-9 = -9 If x = 2, y = 2-9 = 7 ------ That gives you points: (0,-9) and (2,-7) (0,-9) is 9 below (0,0) on the y-axis. To plot (2,-7) start at (0,0); move 2 to the right, then move 7 down. Put a point where you end up at *9,-7) ----------------------------------- Plot and draw to get the following: ============================ -12-6y = x Add 6y to both sides; Subtract "x" from both sides to get: 6y = -x-12 Divide all terms by 6 to get y = (-1/6)x-2 ------- Let x=0, then y = -2 Let x=6, then y = -3 Points: That gives you points: (0.-2) and (6,-3) Plot the draw to get the following: For (0,-2), start at (0,0); move two down the y-axis and put a point there. For (6,-3); start at (0,0); move 6to the right along the x-axis; then move three down; put a point there =============== Cheers, Stan H.

Word_Problems_With_Coins/111891: Please help. Number problems. You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer. Thanks JMS 1 solutions Answer 81631 by stanbon(57984)   on 2007-11-23 18:16:19 (Show Source): You can put this solution on YOUR website! You have at least $30 in change in your drawer, consisting of dimes and quarters. Write an inequality that shows the different number of coins in your drawer. ---------------- Let "d" be the number of dimes and "q" be the number of quarters. The value of the dimes is 10d cents; the value of the quarters is 25q cents ------------------ INEQUALITY: 10d + 25q >= 3000 cents ================= Cheers, Stan H.

Finance/111892: This question is from textbook practica business math procedures Hi! I realy need some help with this problem if anyone knows how to do it. The dollar mark-up is $4.70 The percent mark-up on cost is 102.17% I need to know the cost as well as the selling price based on the information above and round to the nearest hundredth place. Thanks in advance for your help! 1 solutions Answer 81630 by stanbon(57984)   on 2007-11-23 18:10:32 (Show Source): You can put this solution on YOUR website! The dollar mark-up is $4.70 The percent mark-up on cost is 102.17% I need to know the cost as well as the selling price based on the information above and round to the nearest hundredth place. ------------------------------ That percent markup implies that that 2.17%x = 4.70 dollars where x is the selling price. ------------------ EQUATION: 0.0217x = 4.70 deollars x = $216.59 is the silling price before the markup =============== Cheers, Stan H.

Equations/111653: In a shipment of 750 parts, 75 were found to be defective. What percent of the parts were faulty? This is my last question, please help, my reading just does not make sense with all this stuff. I am hoping someone can help me by explaining how to do the problem. 1 solutions Answer 81489 by stanbon(57984)   on 2007-11-22 10:31:43 (Show Source): You can put this solution on YOUR website! In a shipment of 750 parts, 75 were found to be defective. What percent of the parts were faulty? ------------------ Percent means "per 100". So set up a proportion with 100 in the denominator: 75/750 = x/100 Then: x = 100*75/750 x = 100*(1/10) x = 10 --------------- Solution : 10% of the parts were faulty. =============== Cheers, Stan H.

Equations/111652: Identify the rate, base, and amount in each statement or question. HELP ME!Please. I am aweful at all of this stuff? 150 is 75% of what number? 1 solutions Answer 81488 by stanbon(57984)   on 2007-11-22 10:27:55 (Show Source): You can put this solution on YOUR website! Identify the rate, base, and amount in each statement or question. HELP ME! 150 is 75% of what number? Let the number be "x". EQUATION: 150 = (75%)*x ----- amount = 150 rate = 75% base = x ================== Cheers, Stan H.

Quadratic_Equations/111604: Will you please help me solve the following quadratic equation? m=(m[0])/sqrt(1-(v^2/c^2)) solving for c This is what I've attempted... multiply both sides by the LCM sqrt1-(v^2/c^2)to get rid of the fraction (m)qrt1-(v^2/c^2)=m[0] then multiply both sides again to get rid of the fraction in the sqrt? (mc^2)sqrtc^2-v^2=m[0] then divide both sides by (m)sqrt(c^2-v^2) c^2=(m[0])/(m)sqrt(c^2-v^2) square both sides with a final answer of c=sqrt(m[0])/(m)sqrt(c^2-v^2) Thank you in advance for your help!! Brenda 1 solutions Answer 81487 by stanbon(57984)   on 2007-11-22 10:24:23 (Show Source): You can put this solution on YOUR website! m=(m[0])/sqrt(1-(v^2/c^2)) solving for c ----------------- Interchange m and [sqrt(1-(v^2/c^2)) to get: sqrt(1-(v^2/c^2)) = m[0]/m ----------------------- Square both sides to get 1-(v^2/c^2) = [m[0]/m]^2 ------------- Then v^2/c^2 = 1-[m(0]/m]^2 -------------- And c^2 == v^2/[1-[m[0]/m]^2] ------------- Take the sqrt to find "c". ================ Cheers, Stan H.

Equations/111654: Solve each of the following problems involving percent. 6.5% of what number is 325? Can someone please help me with this problem? I do not no where to start. I litterally do not no where to start. 1 solutions Answer 81486 by stanbon(57984)   on 2007-11-22 10:15:27 (Show Source): You can put this solution on YOUR website! 6.5% of what number is 325 ----------- Let the number your are looking for be "x". Write an equation based on the wording of the problem: EQUATION: 325 = 0.065*x x = 325/0.065 x = 5000 ===================== Cheers, Stan H.

Matrices-and-determiminant/111687: find the value of "a" and "b" so that the system of the of equation 2x+3y+5z=9 7x+3y-2z=8 2x+3y+az=b has 1)no solution 2)a unique solution 3)an infinite number of solution 1 solutions Answer 81485 by stanbon(57984)   on 2007-11-22 10:10:30 (Show Source): You can put this solution on YOUR website! find the value of "a" and "b" so that the system of the of equation 2x+3y+5z=9 7x+3y-2z=8 2x+3y+az=b has ----------------------- 1)no solution Find the determinant of the "coefficient matrix". Let that determinant be zero. Solve for "a". I get a=5 -------------------- 2)a unique solution There will be a unique solution as long as a is not 5; b may be any value ---------------------------- 3)an infinite number of solution Cause the 3rd equation to be a multiple of the 2nd equation. Multiply thru the 3rd equation by (7/2) to find (7/2)a=-2 and (7/2)b=16/7 Then solve for and b. ================================ Cheers, Stan H.

Proportions/111696: A NEW VIRUS IS RELEASED ON THE INTERNET; THE ADMINISTRATOR OF A DEPARTMENTS LOCAL ARE NETWORK (LAN) IS GIVEN FIVE MINUTES BY A MANAGER TO ESTIMATE THE IMPACT. THE ADMINISTRATOR SAMPLES 12 OF THE PCs CONNECTED TO THE LAN, AND FINDS THAT 7 ARE INFECTED; USE PROPORTION TO ESTIMATE THE NUMBER OF INFECTED PCs IF THERE ARE A TOTAL OF 117 PCs CONNECTED TO THE LAN. 1 solutions Answer 81484 by stanbon(57984)   on 2007-11-22 09:58:11 (Show Source): You can put this solution on YOUR website! A NEW VIRUS IS RELEASED ON THE INTERNET; THE ADMINISTRATOR OF A DEPARTMENTS LOCAL ARE NETWORK (LAN) IS GIVEN FIVE MINUTES BY A MANAGER TO ESTIMATE THE IMPACT. THE ADMINISTRATOR SAMPLES 12 OF THE PCs CONNECTED TO THE LAN, AND FINDS THAT 7 ARE INFECTED; USE PROPORTION TO ESTIMATE THE NUMBER OF INFECTED PCs IF THERE ARE A TOTAL OF 117 PCs CONNECTED TO THE LAN. ---------------- x/117=7/12 x = 117(7/12) x is at least 69 =============== Cheers, Stan H.

Proportions/111697: AN ADMINISTRATOR OF A POPULAR WEB SITE IS TOLD THAT A NEW SERVER CAN HANDLE 11,000 HITS (USERS ACCESSING THE SITE) PER SECOND. THE WEB SITE CURRENTLY EXPERIENCES A PEAK DEMAND OF ABOUT 85,000 HITS PER SECOND; BUT EVERY MONTH THE PEAK DEMAND INCREASES BY 3500 HITS PER SECOND. USE A PROPORTION EQUATION TO DETERMINE HOW MANY NEW SERVERS THE ADMINISTRATOR SHOULD BUY TO ADDRESS EXPECTED TRAFFIC FOR THE NEXT 18 MONTHS. 1 solutions Answer 81483 by stanbon(57984)   on 2007-11-22 09:54:15 (Show Source): You can put this solution on YOUR website! AN ADMINISTRATOR OF A POPULAR WEB SITE IS TOLD THAT A NEW SERVER CAN HANDLE 11,000 HITS (USERS ACCESSING THE SITE) PER SECOND. THE WEB SITE CURRENTLY EXPERIENCES A PEAK DEMAND OF ABOUT 85,000 HITS PER SECOND; BUT EVERY MONTH THE PEAK DEMAND INCREASES BY 3500 HITS PER SECOND. USE A PROPORTION EQUATION TO DETERMINE HOW MANY NEW SERVERS THE ADMINISTRATOR SHOULD BUY TO ADDRESS EXPECTED TRAFFIC FOR THE NEXT 18 MONTHS. ------------------------------ If the current number of servers is handlng 85000 hit at a rate of 11000 hits per server, there must be more than 85000/11000 servers on line at present; or > 8. ----------------- Using 8 as the present # of servers set up the proportion: x/[85000+18*3500] = 8/85000 x/148000 = 8/85000 x = 148000*(8/85000) x = 13.93 --------------- They will need at least 14 servers in 18 months, or 6 additional ones. ================= Cheers, Stan H.

Equations/111558: Car Selling. Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. Ronald still owes $11,025 on the car. Ronald must get enough to at least pay off the loan. What is the range of the selling price? 1 solutions Answer 81389 by stanbon(57984)   on 2007-11-21 08:37:02 (Show Source): You can put this solution on YOUR website! Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. Ronald still owes $11,025 on the car. Ronald must get enough to at least pay off the loan. What is the range of the selling price? ---------- Let "x" be the selling price. INEQUALITY x >= 11,025 + 0.10(11,025) x>= (1+0.10)(11,025) x >= 1.1(11025) x >= $12,127.25 =============== Cheers, Stan H.

Polynomials-and-rational-expressions/111589: Multiply: (5√[2] + 3)(√[2] – 2√[3]) 1 solutions Answer 81388 by stanbon(57984)   on 2007-11-21 08:30:41 (Show Source): You can put this solution on YOUR website! Multiply: (5√[2] + 3)(√[2] – 2√[3]) ------------- Use FOIL: F: 5sqrt(2) * sqrt(2) = 10 O: 5sqrt(2) * -2sqrt(3) = -10sqrt(6) I: 3 * sqrt(2) = 3sqrt(2) L: 3*-2sqrt(3) = -6sqrt(3) ----------------- Combine to get: 10(1-sqrt(6))+3(sqrt2-2sqrt(3) ============== Comment: Are you sure that "3" in the problem you posted is not really "sqrt(3)"?? =========== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/111584: what is the algebra statement for Three times the sum of a number and seven yields the same result as the twice the same number decreased by four. 1 solutions Answer 81387 by stanbon(57984)   on 2007-11-21 08:22:35 (Show Source): You can put this solution on YOUR website! what is the algebra statement for Three times the sum of a number and seven yields the same result as the twice the same number decreased by four. ---------------- 3(x+7)=2(x-4) ========== Cheers, Stan H.