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# Recent problems solved by 'stanbon'

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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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

 Polynomials-and-rational-expressions/303528: Simplify the third root of -1/64 I came up with I came up with -1/4, but that is incorrect. Please Help!1 solutions Answer 217528 by stanbon(57307)   on 2010-05-11 22:03:06 (Show Source): You can put this solution on YOUR website!It IS correct. Cheers, Stan H.
 Probability-and-statistics/303471: how many license plates can there be if it consists of 4 letters and 3 digits? I tried the combination formula with the letters and then the digits and I multiplied the two. I got 14950 x 120=1794000. But i don'tknow if its right. thank you, i would really appreciate your help1 solutions Answer 217524 by stanbon(57307)   on 2010-05-11 21:55:22 (Show Source): You can put this solution on YOUR website!how many license plates can there be if it consists of 4 letters and 3 digits? ------------------------------------ If repetition is allowed, the answer is 26^4*10^3 = 456,976,000 ---- If repetition is not allowed, the answer is 26*25*24*23*10*9*8 = 258,336,000 ======================= Cheers, Stan H.
 Percentage-and-ratio-word-problems/303510: initially, a tank contains 20 gallons of 30% antifreeze solution. how many gallans of 80% antifreeze solution should be added to the tank in order to have the concentration of the antifreeze in the tank increase to 50%?1 solutions Answer 217512 by stanbon(57307)   on 2010-05-11 21:12:44 (Show Source): You can put this solution on YOUR website!initially, a tank contains 20 gallons of 30% antifreeze solution. how many gallans of 80% antifreeze solution should be added to the tank in order to have the concentration of the antifreeze in the tank increase to 50%? ------------------------------------------- Equation: alcohol + alcohol = alcohol 0.30*20 + 0.80*x = 0.50(20+x) --- Multiply thru by 100 and solve for "x": 30*20 + 80x = 50*20 + 50x 30x = 20*20 x = (2/3)*20 x = 13 1/3 gallons (amt of 80% antifreeze needed in the mixture) ======================= Cheers, Stan H.
 Polynomials-and-rational-expressions/303509: Please help! I am supposed to use rational exponents to write x^1/2 * y^1/6 * z^1/8 as a single radical expression. I came up with the 24th root of x^12y^4z^3, but for some reason this doesn't look right to me. Thank you for your time!1 solutions Answer 217504 by stanbon(57307)   on 2010-05-11 20:59:41 (Show Source): You can put this solution on YOUR website!Correct ============== Cheers, Stan H.
 Travel_Word_Problems/303501: at 2:00 p.m. a runner heads north on a highway jogging at 10mph. at 2:30 p.m. a driver heads north on the same highway to pick up the runner. if the car travels at 55 mph, how long will it take the driver to catch the runner?1 solutions Answer 217500 by stanbon(57307)   on 2010-05-11 20:57:55 (Show Source): You can put this solution on YOUR website!at 2:00 p.m. a runner heads north on a highway jogging at 10mph. at 2:30 p.m. a driver heads north on the same highway to pick up the runner. if the car travels at 55 mph, how long will it take the driver to catch the runner? ------------ Runner DATA: rate = 10 mph ; time = x hrs ; distance = rt = 10x miles ----------------------------- Driver DATA: 55 mph ; time = x-(1/2) hrs ; distance = rt = 55(x-(1/2)) ---- Equation: distance = distance 10x = 55(x-(1/2)) 10x = 55x - 27.5 45x = 27.5 x = 0.6111 hrs x = 0.6111(60)= 36 2/3 minutes =============================== Cheers, Stan H. ===============================
 Square-cubic-other-roots/303484: WHAT IS 4 THE SQUARE ROOT OF 5 DIVIDED BY 4 THE SQUARE ROOT OF 31 solutions Answer 217487 by stanbon(57307)   on 2010-05-11 20:45:03 (Show Source): You can put this solution on YOUR website!WHAT IS 4 THE SQUARE ROOT OF 5 DIVIDED BY 4 THE SQUARE ROOT OF 3 ----- [4th rt of 5]/[4th rt of 3] --- Multiply numerator and denominator by 4th root of 3^3 to get: --- [(5)^(1/4)*(3)^(3/4)]/[(3^(1/4))*(3^(3/4)] --- = [4th rt of (5*27)] / 3 --- = [4th rt of (135)] / 3 ========================== Cheers, Stan H.
 Mixture_Word_Problems/303480: a chemist needs a 30% iron alloy. how many grams of a 70% iron alloy must be mixed with 16 grams of a 20% iron alloy to obtain the required 30% alloy1 solutions Answer 217482 by stanbon(57307)   on 2010-05-11 20:35:50 (Show Source): You can put this solution on YOUR website!a chemist needs a 30% iron alloy. how many grams of a 70% iron alloy must be mixed with 16 grams of a 20% iron alloy to obtain the required 30% alloy ------------------------ Equations: alloy + alloy = alloy --- 0.70x + 0.20*16 = 0.30(x+16) --- Multiply thru by 100 and solve for "x": 70x + 20*16 = 30x + 30*16 40x = 10*16 x = 4 grams (amt. of 70% alloy needed for the mixture) ================================= Cheers, Stan H. ==============
 Probability-and-statistics/303478: Expand the binomial, (x^2+1)^41 solutions Answer 217477 by stanbon(57307)   on 2010-05-11 20:28:34 (Show Source): You can put this solution on YOUR website!Expand the binomial, (x^2+1)^4 --------------------------------- 4C4*(x^2)^4 + 4C3*(x^2)^3 + 4C2*(x^2)^2 + 4C1*(x^2) + 4C0(x^2)^0 ---------------------- = x^8 + 4x^6 + 6x^4 + 4x^2 + 1 ---------------------- Cheers, Stan H.
 Polynomials-and-rational-expressions/303475: Please help! Multiply (-3n)^2(4n^9)^2 I worked through this and came up with 144n^20, but that number seems really high. Can anyone tell me if I am on the right track? Thank you!1 solutions Answer 217471 by stanbon(57307)   on 2010-05-11 20:23:46 (Show Source): You can put this solution on YOUR website!You are correct. Cheers, Stan H.
 Coordinate-system/303137: How will I beable graph the cubic function on a graph?1 solutions Answer 217257 by stanbon(57307)   on 2010-05-11 09:22:02 (Show Source): You can put this solution on YOUR website!How will I be able graph the cubic function on a graph? ---- If y = x^3, plot some points and connect them with a smooth curve. -------------- If x = -3, y = -27 If x = -2, y = -8 If x = -1, y = -1 If x = 0, y = 0 If x = 1, y = 1 If x = 2, y = 8 If x = 3, y = 27 ------------------------- Plot those points and connect them with a curve to get: ======================================= Cheers, Stan H.
 logarithm/303147: Supply and Demand. The supply and demand for the sale of stereos by Sound Ideas are given by S(x)=e^x and D(x)=162,755e^-x, where S(x) is the price at which the company is willing to supply x stereos and D(x) is the demand price for a quantity of x stereos. Find the equilibrium point. 1 solutions Answer 217256 by stanbon(57307)   on 2010-05-11 09:17:19 (Show Source): You can put this solution on YOUR website!Supply and Demand. The supply and demand for the sale of stereos by Sound Ideas are given by S(x)=e^x and D(x)=162,755e^-x, where S(x) is the price at which the company is willing to supply x stereos and D(x) is the demand price for a quantity of x stereos. Find the equilibrium point. ------------ Equilibrium occurs when Revenue = Cost. ---- Solve : e^x = 162,755e^-x --- Multiply both sides by e^x to get: e^(2x) = 162755 Take the natural log and solve for "x": 2x = ln(162755) ------- x = 6 --- Find the equilibrium point. e^x = e^6 = 403.43 ------------------------- Cheers, Stan H.
 Divisibility_and_Prime_Numbers/303152: Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24 hour period. Julio sample about 140 bottles an hour and rejects the line if he finds more than of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?1 solutions Answer 217251 by stanbon(57307)   on 2010-05-11 09:04:38 (Show Source): You can put this solution on YOUR website!An essential number is missing from your post. Cheers, Stan H.
 Quadratic_Equations/303150: what is the axis of symetry if the equation is two x squared plus twelve x plus nine?1 solutions Answer 217250 by stanbon(57307)   on 2010-05-11 09:03:04 (Show Source): You can put this solution on YOUR website!what is the axis of symmetry if the equation is two x squared plus twelve x plus nine? ------------------------- y = 2x^2+12x+9 a = 2 ; b = 12 ; c = 9 --- The axis of symmetry occurs where x = -b/2a --- x = -12/(2*2) = -3 ---- Cheers, Stan H.
 Quadratic_Equations/303114: Factor Don't understand what to do 5x^2+2x=01 solutions Answer 217239 by stanbon(57307)   on 2010-05-11 07:19:11 (Show Source): You can put this solution on YOUR website!Factor Don't understand what to do 5x^2+2x=0 --- Common factor: x -- x(5x+2) = 0 --- Since the product is zero, one of the factors must be zero. x = 0 or 5x+2 = 0 x = 0 or 5x=-2 x = 0 or x = -2/5 ====================== cheers, Stan H.
 logarithm/303096: Find exact value of each expression. Log (Base 1/2) 16 & Log (Base sq root of 3) 9 1 solutions Answer 217238 by stanbon(57307)   on 2010-05-11 07:16:54 (Show Source): You can put this solution on YOUR website!Find exact value of each expression. Log (Base 1/2) 16 & Log (Base sq root of 3) 9 ------------------------------------- log(base 1/2)16 = x (1/2)^x = 16 2^(-x) = 2^4 -x = 4 x = -4 --------------------- log(base sqrt(3))9 = x (sqrt(3))^x = 9 3^(x/2) = 3^2 x/2 = 2 x = 4 ===================== Cheers, Stan H.
 Angles/303115: Hello Can someone show me an example of how to figure out the central angle, I work most of the problem but I don't know how to figure the central angle of a pie chart here is what I did on the problem. The total problem is: Below are the home states of 20 college students. Texas Arizona Mississippi Mississippi Pennsylvania California Pennsylvania Texas Georgia Texas Arizona Texas Pennsylvania Pennsylvania Alabama Mississippi Arizona California Georgia Georgia Make a frequency table using these 7 states: Alabama Arizona California Georgia Mississippi Pennsylvania Texas This is what I did so far. Thank you so much Home State............Freq........% of total.....Measure Cenral Angle degrees Alabama...............1..........0.05.................? Arizona...............3..........0.15.................? California............2..........0.1..................? Georgia...............3..........0.15.................? Mississippi...........3..........0.15.................? Pennsylvania..........4..........0.2..................? Texas.................4..........0.2..................? I could not post my table but that what it look like the first column is State, Second is the frequency, third is the % and fourth should be the central angle in degrees. Yes it the Central Angle in a pie chart if that helps. 1 solutions Answer 217237 by stanbon(57307)   on 2010-05-11 07:10:56 (Show Source): You can put this solution on YOUR website!This is what I did so far. Thank you so much Home State............Freq........% of total.....Measure Cenral Angle degrees Alabama...............1..........0.05.................? Arizona...............3..........0.15.................? California............2..........0.10.................? Georgia...............3..........0.15.................? Mississippi...........3..........0.15.................? Pennsylvania..........4..........0.20.................? Texas.................4..........0.20.................? I could not post my table but that what it look like the first column is State, Second is the frequency, third is the % and fourth should be the central angle in degrees. Yes it the Central Angle in a pie chart if that helps. -------------------------------- Answer: Each central angle is a % of 360 degrees. For example: Alabama.....1.....0.05......0.05(360) = 18 degrees Arizona.....3.....0.15......0.15*360 = 54 degrees ........ Cheers, Stan H.
 Equations/303124: what was the initial weight ,in pounds, of a person who now weights x pounds and who lost y pounds and the gained 5 pounds ? a) x + y - 5 b) y – x + 5 c) x + y + 5 d) y – x – 5 e) x – y + 5 1 solutions Answer 217236 by stanbon(57307)   on 2010-05-11 07:03:23 (Show Source): You can put this solution on YOUR website!what was the initial weight ,in pounds, of a person who now weights x pounds and who lost y pounds and the gained 5 pounds ? ------------------------- Let initial weight be "w". Equation: x = w-y+5 --- w = x+y-5 ================== Cheers, Stan H. a) x + y - 5 b) y – x + 5 c) x + y + 5 d) y – x – 5 e) x – y + 5
 Probability-and-statistics/303116: I see that the Alpha is different and is at a = 0.05,How do I do this one The players on last year’s football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team’s average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team’s progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows: 346 412 332 285 396 461 321 275 246 315 298 347 430 419 406 311 a. State the appropriate null and alternative hypotheses. b. Calculate the test statistic. c. At a = 0.05, should Coach Juarez reject the null hypothesis? d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw 1 solutions Answer 217235 by stanbon(57307)   on 2010-05-11 06:57:17 (Show Source): You can put this solution on YOUR website!I see that the Alpha is different and is at a = 0.05,How do I do this one The players on last year’s football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team’s average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team’s progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows: 346 412 332 285 396 461 321 275 246 315 298 347 430 419 406 311 -------------------------------------- The mean of the sample is 350 The std of the sample is 63.18 n = 16 ; df = 15 ---------------------------------- a. State the appropriate null and alternative hypotheses. Ho: u = 312 Ha: u > 312 -------------------- b. Calculate the test statistic. t(350) = (350-312)/[63.18/sqrt(16)] = 2.4058 -------------------- c. At a = 0.05, should Coach Juarez reject the null hypothesis? p-value = P(t > 2.4058 when df = 15) = 0.0147 --- Since the p-value is less than 5%, reject Ho. ------------------------------------------------------ d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw. The training program was beneficial. ======================================== Cheers, Stan H.
 Linear_Equations_And_Systems_Word_Problems/303074: I have two questions. 1. Model A takes 2hrs to build at a cost of \$25 2. Model B takes 3 hrs to build at a cost of \$ 35 As a buisness owner I only have 34 hours and \$350 for these two modles how many of each models can be made in a day? 1 solutions Answer 217222 by stanbon(57307)   on 2010-05-10 23:10:09 (Show Source): You can put this solution on YOUR website!I have two questions. 1. Model A takes 2hrs to build at a cost of \$25 2. Model B takes 3 hrs to build at a cost of \$ 35 As a business owner I only have 34 hours and \$350 for these two models how many of each model can be made in a day? ------- Equations: Hours Equation: 2A + 3B = 34 hours Cost Equation: 25A +35B = 350 dollars ---------------------------------------------- Multiply the 1st equation by 25 Multiply the 2nd equation by 2 --------------------------------------------- 50A + 75B = 850 50A + 70B = 700 ------ Substract the 2nd from the 1st equation and solve for "B": 5B = 850-700 5B = 150 B = 30 (# of B houses to build) ---- Comment: Something is wrong with your data. 30 of the B houses would cost 30*35 = #1050 and you only have 350 dollars available. =============================================== Check your Data ================== Cheers, Stan H. ----- Substitute into 2A + 3B = 34 to solve for "A: 2A + 3*30 = 34
 Rate-of-work-word-problems/302994: One inlet pipe can fill an empty pool in 4 hours, and a drain can empty the pool in 10 hours. How long will it take the pipe to fill the pool if the drain is left open? thanks :)1 solutions Answer 217183 by stanbon(57307)   on 2010-05-10 20:56:22 (Show Source): You can put this solution on YOUR website!One inlet pipe can fill an empty pool in 4 hours, and a drain can empty the pool in 10 hours. How long will it take the pipe to fill the pool if the drain is left open? -------------------- Filling rate: 1/4 pool/hr Emptying rate: 1/10 pool/hr --- Together rate: 1/x pool/hr ============================== Equation: rate - rate = together rate 1/4 - 1/10 = 1/x (10-4)/40 = 1/x 6/40 = 1/x x = 40/6 = 20/2 = 6 2/3 hrs (time to fill the pool ============================== cheers, Stan H.
 Trigonometry-basics/302970: State the amplitude, period, phase shift, and vertical shift for the following function, then graph the function. y = 2 sin (0 + pi/2) - 31 solutions Answer 217179 by stanbon(57307)   on 2010-05-10 20:52:38 (Show Source): You can put this solution on YOUR website!State the amplitude, period, phase shift, and vertical shift for the following function, then graph the function. y = 2 sin (theta + pi/2) - 3 ----------------------------- y = a*sin(bx + c) + d --- amp = |a| = 2 period = 2(pi)/b = 2Pi phase shift = -c/b = -(pi/2)/1 = -pi/2 vert shift = d = -3 ============================================= ==================================================== Cheers, Stan H.
 Radicals/302985: 5-3x x+1 _____ - _____ x^2-2x+1 x^2-2x+1 simplify if possible1 solutions Answer 217176 by stanbon(57307)   on 2010-05-10 20:44:18 (Show Source): You can put this solution on YOUR website!5-3x x+1 _____ - _____ x^2-2x+1 x^2-2x+1 =============================== The denominators are the same so combine the numerators to get: [5-3x-(x+1)]/(x^2-2x+1) --- Simplify: [-4x+6]/[(x-1)^2] --- Factor: [-2(2x-3)]/(x-1)^2 ======================= Cheers, Stan H. =======================
 Probability-and-statistics/302981: i need help because im only in sixth grade and i dont know anything ahhh zc-16 zc-19 HELP!!!!!!!!!!!!!!!!! (algebra book 1)1 solutions Answer 217175 by stanbon(57307)   on 2010-05-10 20:40:55 (Show Source): You can put this solution on YOUR website!This might be what you are asked to do with the expression: zc-16zc-19 ------- = (1-16)zc -19 --- = -15zc-19 ==================== Cheers, Stan H. ====================
 Volume/302980: the Valium of cylindrical can is 50.2 in3 if the diameter is 4 inch find the hight use pie=3.14.1 solutions Answer 217174 by stanbon(57307)   on 2010-05-10 20:35:43 (Show Source): You can put this solution on YOUR website!the Volume of a cylindrical can is 50.2 in^3. if the diameter is 4 inches, find the height. use pie=3.14. =================== V = Bh -- B = (pi)r^2 B = 3.14*2^2 = 12.56 sq in ----- 50.2 = 12.56*h h = 3.9968 inches ========================= Cheers, Stan H.
 Rational-functions/302978: square root of 2 over square root of 131 solutions Answer 217173 by stanbon(57307)   on 2010-05-10 20:31:45 (Show Source): You can put this solution on YOUR website!square root of 2 over square root of 13 --- sqrt[2/13] Multiply numerator and denominator by 13 to get: = sqrt[(2*13)/13^2] Take the sqrt of the numerator and the square root of the denominator: = sqrt(26)/13 Rewrite as follows: = (1/13)sqrt(26) ===================== Cheers, Stan H.
 Probability-and-statistics/302971: Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. - You bought 4 tires. What is the probability that the average mileage of the 4 tires exceeds 66,000 miles? a.) 0.0013 b.) 0.9987 c.) 0.4987 d.) 0.9544 - What is the probability that 1 tire will last 72,000 miles or more? a.) 0.0013 b.) 0.9987 c.) 0.4987 d.) 0.9544 Thank you for your help!1 solutions Answer 217172 by stanbon(57307)   on 2010-05-10 20:28:16 (Show Source): You can put this solution on YOUR website! Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. - You bought 4 tires. What is the probability that the average mileage of the 4 tires exceeds 66,000 miles? --- z(66,000) = (66000-60000)/[4000/sqrt(4)] = 6000/2000 = 3 P(x > 66000) = P(z> 3) = 0.0013 a.) 0.0013 b.) 0.9987 c.) 0.4987 d.) 0.9544 ---------------------------------- - What is the probability that 1 tire will last 72,000 miles or more? z(72000) = (72000-60000)/4000 = 12000/4000 = 3 P(z> 72000)= P(z > 3) = 0.0013 --- a.) 0.0013 b.) 0.9987 c.) 0.4987 d.) 0.9544 Thank you for your help! ================================== Cheers, Stan H.
 Geometry_Word_Problems/302890: If the area of the yard is 256 ft.2 and the walkway is 4 ft. wide, what is the area of the walkway? 1 solutions Answer 217149 by stanbon(57307)   on 2010-05-10 18:26:09 (Show Source): You can put this solution on YOUR website!If the area of the yard is 256 ft.2 and the walkway is 4 ft. wide, what is the area of the walkway? ---------------------- Draw the picture. You have a rectangle inside a larger rectangle. --- Equations: The smaller rectangle has area xy = 256 sq ft. The larger rectangle has area (x+8)(y+8) = xy +8x + 8y + 64 ---- Area of the walkway = larger area - smaller area --- = xy+8x+8y+64-256 --- Substitute for xy: = 256 + 8(x+y) - 256 --- = 8(x+y) sq. ft. ========================== Cheers, Stan H. ==========================
 Miscellaneous_Word_Problems/302886: suppose that 4000 is invested at an interest rate of 5.5% per year, compounded continuouly. what is the balance after 8 years?1 solutions Answer 217145 by stanbon(57307)   on 2010-05-10 18:15:30 (Show Source): You can put this solution on YOUR website!suppose that 4000 is invested at an interest rate of 5.5% per year, compounded continuouly. what is the balance after 8 years? ---------------- A(t) = P*e^(rt) A(8) = 4000*e^(0.055*8) = \$6210.83 ======================================= Cheers, Stan H. ==============
 Quadratic-relations-and-conic-sections/302873: Determine whether each function has a maximum or minimum value. Then find the maximum or minimum value of each equation. 3/4x^2-5x-2 So, three-fourths a number squared minus five times the same number minus two. :) I know that it opens up and has a minimum value, since A is positive. :) But the finding the actual value part messes me up. It is an odd problem, so the answer is in the back of the book. The back of the book says it is -10 1/3. Please help on how to solve it? D: I don't need a graph at all (:1 solutions Answer 217140 by stanbon(57307)   on 2010-05-10 17:57:56 (Show Source): You can put this solution on YOUR website!find the maximum or minimum value of each equation. f(x) = (3/4)x^2-5x-2 ----- The vertex occurs where x = -b/(2a) = 5/(2(3/4)) = 5/(3/2) = 10/3 -------------------- f(10/3) = (3/4)(10/3)^2 - 5(10/3) -2 = (3/4)(100/9) - (50/3) - 2 --- = (25/3) - (50/3) - (6/3) --- = -31/3 --- = -10 1/3 =============== Solution: ((10/3) , -10 1/3) =============== Cheers, Stan H. ===============
 Finance/302876: I need help: I have to find the LCD for the given rational expressions, and then convert each retional expression into an equivalent rational expression with the LCD as the common denominator. 4/x-y and 5x/2y-2x thanks in advance.1 solutions Answer 217133 by stanbon(57307)   on 2010-05-10 17:37:04 (Show Source): You can put this solution on YOUR website!find the LCD for the given rational expressions, and then convert each retional expression into an equivalent rational expression with the LCD as the common denominator. 4/(x-y) and 5x/(2y-2x) ----------------------- Factor: 4/(x-y) and 5x/[-2(x-y)] --- LCD: -2(x-y) --- Rewrite each fraction with LCD as its denominator: (-2*4)/LCD and (5x)/LCD ---- -8/(-2(x-y)) and 5x/(-2(x-y)) ============================== Cheers, Stan H. ==============================
 Circles/302874: What coordinate pair rule represents the shift from (13,12)to(3,4)?1 solutions Answer 217129 by stanbon(57307)   on 2010-05-10 17:30:35 (Show Source): You can put this solution on YOUR website!What coordinate pair rule represents the shift from (13,12)to(3,4)? --- 13 went to 3, so x goes to x-10 ---- 12 went to 4, so y goes to y-8 ---- Cheers, Stan H.