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Recent problems solved by 'stanbon'

stanbon answered: 57222 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 , 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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>Next

Numeric_Fractions/210765: x 1 - - - = 2 8 4 On the equation above what is my first step? 1 solutions Answer 159229 by stanbon(57290)   on 2009-09-03 15:19:47 (Show Source): You can put this solution on YOUR website! x 1 - - - = 2 8 4 ---------------------- In general, when you have an equation with fractions, multiply both sides by the least common multiple of the denominators. ---------------------- Your Problem: lcm = 8 Multiply thru by 8 --- x - 2 = 16 x = 18 =============== Cheers, Stan H.

logarithm/210767: This question is from textbook Single Variable Calculus I need help with the problem The question says to solve for the missing variable. SO what i did was made both sides in terms of e and then set the exponents equal to each other and i get 8/11 which i am told is not correct. help please? 1 solutions Answer 159228 by stanbon(57290)   on 2009-09-03 15:16:35 (Show Source): You can put this solution on YOUR website! e^(2x+1)=9e^(1-x) ------------------------ Take the natural log of both sides: --- 2x+1 = ln(9) + (1-x) 3x = ln(9) x = [ln(9)]/3 x = 0.7324.. Cheers, Stan H.

Mixture_Word_Problems/210742: Solve the problem. In 1998, the population of a given country was 37 million, and the exponential growth rate was 5% per year. Find the exponential growth function. A)P(t) = 370.05t , where P(t) is in millions and t is the number of years after 1998. B)P(t) = 37e0.05t, where P(t) is in millions and t is the number of years after 1998. C)P(t) = 37e5t, where P(t) is in millions and t is the number of years after 1998. D)P(t) = 37e0.05, where P(t) is in millions and t is the number of years after 1998 1 solutions Answer 159226 by stanbon(57290)   on 2009-09-03 15:12:24 (Show Source): You can put this solution on YOUR website! In 1998, the population of a given country was 37 million, and the exponential growth rate was 5% per year. Find the exponential growth function. P(t) = 37e^(0.05t) ==================== Cheers, Stan H. ================ A)P(t) = 370.05t , where P(t) is in millions and t is the number of years after 1998. B)P(t) = 37e0.05t, where P(t) is in millions and t is the number of years after 1998. C)P(t) = 37e5t, where P(t) is in millions and t is the number of years after 1998. D)P(t) = 37e0.05, where P(t) is in millions and t is the number of years after 1998

Polynomials-and-rational-expressions/210751: This question is from textbook intermediate algebra Divide Using synthetic division. 16. (3x^4 + 8x - 10)/ (x+2) 1 solutions Answer 159225 by stanbon(57290)   on 2009-09-03 15:06:22 (Show Source): You can put this solution on YOUR website! Divide Using synthetic division. 16. (3x^4 + 8x - 10)/ (x+2) ------------------------- -2)....3....0....8....-10 ........3....-6...20..|..-70 ================================== Quotient: 3x^2-6x+20 Remainder: -70 ============================== Cheers, Stan H.

Linear-systems/210758: find the domain of the function g(x)=2/7-3x 1 solutions Answer 159223 by stanbon(57290)   on 2009-09-03 15:03:33 (Show Source): You can put this solution on YOUR website! find the domain of the function g(x)=2/7-3x --- 7-3x cannot zero. ------------------- If 7-3x=0 3x = 7 x = 7/3 --------------- So domain is All Real Numbers except x = 7/3 ================================================ Cheers, Stan H.

Quadratic_Equations/210762: (6x-5)^2/3 = x^1/3 I have no idea what to do. 1 solutions Answer 159221 by stanbon(57290)   on 2009-09-03 15:01:02 (Show Source): You can put this solution on YOUR website! (6x-5)^2/3 = x^1/3 --- Raise both sides to the 3rd power to get: (6x-5)^2 = x Expand: 36x^2 - 60x + 25 = x 36x^2 - 61x + 25 = 0 -------------------------- Solve using the quadratic formula. Then check your answers and eliminate extraneous zeroes. ----------------------------------- Cheers, Stan H.

Exponents/210763: 1=.5^n 1 solutions Answer 159219 by stanbon(57290)   on 2009-09-03 14:56:30 (Show Source): You can put this solution on YOUR website! 1=.5^n ------------- "n" must be zero; let's see why. ------------- Take the log of both sides: nlog(0.5) = log1 n = log(1)/log(0.5) n = 0/log(0.5) n = 0 ================= Cheers, Stan H.

Rate-of-work-word-problems/210711: Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 days. In how many days will john complete the work? 1 solutions Answer 159203 by stanbon(57290)   on 2009-09-03 13:01:08 (Show Source): You can put this solution on YOUR website! Sam takes 6 days less than the number of days taken by John to complete a piece of work. If both Sam and John together can complete the same work in 4 days. In how many days will john complete the work? ---------------------------------- John DATA: time = x day/job ; rate = 1/x job/day ------------ Sam DATA: time = x-6 days/job ; rate = 1/(x-6) job/day ---------------- Together DATA: time = 4 days/job ; rate = 1/4 job/day ========================================= Equation: rate + rate = together rate 1/x + 1/(x-6) = 1/4 4(x-6) + 4x = x(x-6) 4x - 24 + 4x = x^2 - 6x x^2 - 14x +24 = 0 x^2 - 12x - 2x + 24 = 0 x(x-12)-2(x-12) = 0 (x-12)(x-2) = 0 To get a positive solution for Sam and John: x = 12 days (John time) x-6 = 6 days (Sam time) ======================= Cheers, Stan H.

Graphs/210738: Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph.. State the equation of the line asymptotic to the graph (if any). y = 3(x - 4) 1 solutions Answer 159201 by stanbon(57290)   on 2009-09-03 12:52:49 (Show Source): You can put this solution on YOUR website! Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph.. State the equation of the line asymptotic to the graph (if any). y = 3^(x - 4) ------------------ ----------------------------------------- Asymptote: y = 0 ======================== Cheers, Stan H.

Travel_Word_Problems/210731: As Kayla leaves the gym for a 12 mile run. She starts her run on level terrain where she can run at 8 miles per hour. Then her path becomes hilly and she can only run at 4 miles per hour. Find the amount of time she runs at each speeds if her total running time is 2 hours and 20 minutes. 1 solutions Answer 159199 by stanbon(57290)   on 2009-09-03 12:48:23 (Show Source): You can put this solution on YOUR website! As Kayla leaves the gym for a 12 mile run. She starts her run on level terrain where she can run at 8 miles per hour. Then her path becomes hilly and she can only run at 4 miles per hour. Find the amount of time she runs at each speeds if her total running time is 2 hours and 20 minutes. --------------- Level DATA: rate = 8 mph ; distance = x miles ; time = d/r = x/8 hrs. ---------------------- Hilly DATA: rate = 4 mph ; distance = (12-x) miles ; time = (12-x)/4 hrs ----------------------- Equation: time + time = 2 1/3 hrs x/8 + (12-x)/4 = 7/3 ---- 3x + 6(12-x) = 8*7 3x + 72 - 6x = 56 -3x = -16 x = 16/3 miles (distance run on the level) --- Time on level ground: (16/3)/8 = 2/3 hr. Time on hilly ground: (7/3)-(2/3) = 4/3 hr. =========================================== Cheers, Stan H.

Equations/210733: Describe a situation when solving a system of two equations in two variables using the Graphical Method may not be appropriate for finding the precise numerical solution. 1 solutions Answer 159197 by stanbon(57290)   on 2009-09-03 12:41:11 (Show Source): You can put this solution on YOUR website! Describe a situation when solving a system of two equations in two variables using the Graphical Method may not be appropriate for finding the precise numerical solution. ------------------------------------------ 0.0000331x - 0.0000000042 = 0.1 -23x + 57 y = 0.0000000000001 --------------------------------- This would be a bit difficult to work with the graphical method. =================================== Cheers, Stan H.

Equations/210734: Describe a situation when solving a system of two equations in two variables using the Substitution Method would be preferred over the Graphical or Addition Methods? Specifically, how would the system of equation be presented before solving it? 1 solutions Answer 159195 by stanbon(57290)   on 2009-09-03 12:38:21 (Show Source): You can put this solution on YOUR website! One of the two equations would already be solved for one of the variables. Example: 2x + 3y = 6 x = -y+1 ================= Cheers, Stan H.

Equations/210735: After solving a system of equations in two variables you surmise a solution, (x,y). How can you determine if the solution is correct? 1 solutions Answer 159193 by stanbon(57290)   on 2009-09-03 12:36:07 (Show Source): You can put this solution on YOUR website! Substitute those x/y values into each of the two equations to see if you get two true statements. If you do, the (x,y) solution is correct. Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/210715: What is the smallest root of the polynomial: x^3-10x^2+27x-18 1 solutions Answer 159190 by stanbon(57290)   on 2009-09-03 12:18:05 (Show Source): You can put this solution on YOUR website! What is the smallest root of the polynomial: x^3-10x^2+27x-18 ---------------- Since the coefficients add up to zero, x=1 is a root. It happens to be the smallest root and you will see if you use synthetic division to find the two other roots =================== Cheers, Stan H.

Linear_Equations_And_Systems_Word_Problems/210726: A catering company is setting up tables for a big event that will host 764 people. When they set up the tables they need 2 forks for each child and 5 forks for each adult. If the company ordered a total of 2992 forks, how many adults and how many children will be attending the event? 1 solutions Answer 159189 by stanbon(57290)   on 2009-09-03 12:13:34 (Show Source): You can put this solution on YOUR website! A catering company is setting up tables for a big event that will host 764 people. When they set up the tables they need 2 forks for each child and 5 forks for each adult. If the company ordered a total of 2992 forks, how many adults and how many children will be attending the event? -------------------- People Equation: c + a = 764 Fork Equation:::2c + 5a = 2992 --------------------------------- Multiply thru the people equation by 2 to get: 2c + 2a = 1528 --- Subtract that from the Fork Equation to get: 3a = 1464 a = 488 (# of adults) ---- Substitute to solve for "c": c + 488 = 764 c = 276 (# of children) =============================== Cheers, Stan H.

Money_Word_Problems/210729: a man invested $20,000 at annual interest rate of 7% and $12,000.00 at an annual interest rate of 7.5%. what was his annual income on the two investments? 1 solutions Answer 159187 by stanbon(57290)   on 2009-09-03 12:08:34 (Show Source): You can put this solution on YOUR website! a man invested $20,000 at annual interest rate of 7% and $12,000.00 at an annual interest rate of 7.5%. what was his annual income on the two investments? ----------------------------------- Equation: interest + interest = interest 0.07(20,000)+ 0.075(12,000) = $2300 ==================================== Cheers, Stan H.

Rectangles/210727: This question is from textbook The perimeter of a rectangle is 44 inches and its area is 112 square inches. Find the length and width of the retangel. 1 solutions Answer 159186 by stanbon(57290)   on 2009-09-03 12:02:29 (Show Source): You can put this solution on YOUR website! The perimeter of a rectangle is 44 inches and its area is 112 square inches. Find the length and width of the rectangel. ----- Area = LW = 112 L = 112/W ------------------ Perimeter = 2(L+W) 44 = 2((112/W) + W) 22 = (112/W) + W W^2 - 22W + 112 = 0 (W-14)(W-8) = 0 If W = 14, L= 8. If W = 8, L = 14 ======================= Cheers, Stan H.

Quadratic_Equations/210728: This question is from textbook 1/2X+2=-1/2X 1 solutions Answer 159185 by stanbon(57290)   on 2009-09-03 11:56:57 (Show Source): You can put this solution on YOUR website! 1/2X+2=-1/2X Add (1/2)x to both sides to get x+ 2 = 0 x = -2 ============= Cheers, Stan H.

Miscellaneous_Word_Problems/210714: Suppose a fuel mixture is 7% ethanol and 93% gasoline. How much ethanol (in gallons) must you add to one gallon of fuel so that the new fuel mixture is 10% ethanol? 1 solutions Answer 159184 by stanbon(57290)   on 2009-09-03 11:45:10 (Show Source): You can put this solution on YOUR website! Suppose a fuel mixture is 7% ethanol and 93% gasoline. How much ethanol (in gallons) must you add to one gallon of fuel so that the new fuel mixture is 10% ethanol? ------------------------- Equation: 7%ethanol + 100%ethanol = 10%ethanol 0.07(1 gal) + 100%(x gal) = 0.10(1+x)gal 7 + 100x = 10(1+x) 7 + 100x = 10+10x 90x = 3 x = 0.0333.. gallons (amount of 100% ethanol that must be added) Cheers, Stan H.

Miscellaneous_Word_Problems/210689: The acceleration of a car is proportional tot he hoirsepower of the engine and inversely proportional tot he weight of the passengers A)Show this relationship as an equation B)What ahppens to the acceleration of the car if the horsepower of the engine is tripled? C)What happens tot he acceleration fo the car fi the weight inside is tripled? 1 solutions Answer 159180 by stanbon(57290)   on 2009-09-03 09:57:36 (Show Source): You can put this solution on YOUR website! The acceleration of a car is proportional tot he hoirsepower of the engine and inversely proportional tot he weight of the passengers A)Show this relationship as an equation a = kh/w ----------------- B)What ahppens to the acceleration of the car if the horsepower of the engine is tripled? 3a = k(3h)/w ---------------------- C)What happens to the acceleration of the car if the weight inside is tripled? a/3 = kh/(3w) ---------------------- Cheers, Stan H.

Inequalities/210680: -1/2≤4-3x/5≤1/4 1 solutions Answer 159179 by stanbon(57290)   on 2009-09-03 09:53:57 (Show Source): You can put this solution on YOUR website! -1/2≤4-3x/5≤1/4 --- Multiply thru by 5 to get: (-5/2) <= 4-3x <= (5/4) Subtract 4 along the line to get: (-13/2) <= -3x <= (-11/4) Divide thru by -3 to get: (11/12)<= x <= (13/6) ============================== Cheers, Stan H.

Exponents/210686: how would i factor this equation: 2a^2+7a^1-4 1 solutions Answer 159178 by stanbon(57290)   on 2009-09-03 09:49:34 (Show Source): You can put this solution on YOUR website! factor this equation: 2a^2+7a^1-4 ----------------- Use the AC Method. a = 2 ; b = 7 ; c = -4 -------------------------- Think of two numbers whose product is AC = 2*-4 = -8 and whose sum or difference is b = 7 ======================== The numbers are +8 and -1: -- Replace the "b" term by 8a - a. 2a^2 +8a - a - 4 --- Factor the 1st two and the last two terms separately: 2a(a+4)-(a+4) Factor again to get the final answer: (a+4)(2a-1) ====================== Cheers, Stan H.

Linear-equations/210118: which product represents the solution to the system: -y+7x=14 -x+4y=1 a) [1/27 4/27] . [1] [7/27 1/27] [14] b) [-7/3 4/3] . [1] [-1/3 1/3] [14] c) [7/3 -4/3] . [1] [1/3 -1/3] [14] d) [-1/27 -4/27] . [1] [-4/27 -1/27] [14] 1 solutions Answer 159131 by stanbon(57290)   on 2009-09-02 21:56:01 (Show Source): You can put this solution on YOUR website! which product represents the solution to the system: -y+7x=14 -x+4y=1 --------------------- The problem is needlessly confusing. The solution is "a". ================================================= Cheers, Stan H.

Linear-equations/210120: find the inverse of f(x)=2 sqrt(x+3) a) f^-1(x)=(x-3/2)^2 b)f^-1(x)= (x+3/2)^2 c)f^-1(x)= 1/2 sqrt(x-3) d)f^-1(x)= 1/2 sqrt(x+3) 1 solutions Answer 159126 by stanbon(57290)   on 2009-09-02 21:29:33 (Show Source): You can put this solution on YOUR website! find the inverse of f(x)=2 sqrt(x+3) --- Interchange x and y then solve for "y": x = 2sqrt(y+3) sqrt(y+3) = x/2 y+3 = (x^2/4) y = (x^2/4)-3 --- That is the inverse but it is not listed as one of your options. ================================================================= Cheers, Stan H. a) f^-1(x)=(x-3/2)^2 b)f^-1(x)= (x+3/2)^2 c)f^-1(x)= 1/2 sqrt(x-3) d)f^-1(x)= 1/2 sqrt(x+3)

Graphs/210588: This question is from textbook algebra 1 please help me solve this problem. y is equal to 3 more than the absolute value of x; x= -2,-1,o,1 and 2 1 solutions Answer 159120 by stanbon(57290)   on 2009-09-02 21:15:20 (Show Source): You can put this solution on YOUR website! please help me solve this problem. y is equal to 3 more than the absolute value of x; x= -2,-1,o,1 and 2 ------------------------- y = |x| + 3 --- If x = -2 y = 2+3 = 5 If x = -1 y = 1+3 = 4 If x = 0 y = 0+3 = 3 If x = 1 y = 1+3 = 4 If x = 2 y = 2+3 = 5 -------------------------- Cheers, Stan H.

Linear-equations/210158: solve 3y^2+4y-2<= 0 1 solutions Answer 159119 by stanbon(57290)   on 2009-09-02 21:07:46 (Show Source): You can put this solution on YOUR website! solve 3y^2+4y-2<= 0 ------------------------- Solve the EQUALITY: y = [-4 +- sqrt(16 - 4*3*-2)]/6 y = [-4 +- sqrt(40)]/6 y = [-4 +- 2sqrt(10)]/6 y = (-2/3)+(1/3)sqrt(10) or y = (-2/3)-(1/3)sqrt(10) Approximate solutions: y = 0.3874 or y = -1.721 ===================================================== Solve the INEQUALITY: Draw a number line. Plot the two equality solutions. Check a value in each of the three intervals formed by those solutions to see where the solution for the inequality lie. -------------------- 3y^2+4y-2<= 0 Check y = -10 ; 3(-10)^2+4(-10)-2 < 0 ; false Check y = 0 ; -2 < 0 ; true so solutions in (-1.721,0.3874) check y = 10 ; 3(10)^2-4(10)-2 < 0 ; false ------------------------------------------------- Final solution; (-2/3)-(1/3)sqrt(10) <= y <= (-2/3)+(1/3)sqrt(10) ============================================================================ Cheers, Stan H.

Equations/210571: Angle C and Angle D are supplementary. Angle D is four times the measure of Angle C. Find the measure of Angle D and C. thank you 1 solutions Answer 159116 by stanbon(57290)   on 2009-09-02 20:49:03 (Show Source): You can put this solution on YOUR website! Angle C and Angle D are supplementary. Angle D is four times the measure of Angle C. Find the measure of Angle D and C. -------------------------------------------------- C + D = 180 D = 4C ----------------- Substitute for D to solve for C. ----- C + 4C = 180 5C = 180 C = 36 degrees D = 180-36 = 144 degrees ==================================== Cheers, Stan H.

Inequalities/210570: Write each specification as an absolute value inequality... 6.3 <= h <= 10.3 1 solutions Answer 159105 by stanbon(57290)   on 2009-09-02 20:42:01 (Show Source): You can put this solution on YOUR website! Write each specification as an absolute value inequality... 6.3 <= h <= 10.3 ---------------------------- Process: (10.3+6.3)/2 = 16.6/2 = 8.3 ------------------------------------------ 10.3-8.3 = 2 ------------------------------ Absolute: |h-8.3| <= 2 ====================== Cheers, Stan H.

Linear-equations/210564: Write a system of linear equations in two variables having {(-2, 7)} as a solution set. (More than one system is possible.) Make sure that your system has two equations with two variables! 1 solutions Answer 159086 by stanbon(57290)   on 2009-09-02 20:29:48 (Show Source): You can put this solution on YOUR website! Write a system of linear equations in two variables having {(-2, 7)} as a solution set. (More than one system is possible.) Make sure that your system has two equations with two variables! ------------------------------------------------- Since: 2*-2 + 3*7 = 17 and -2 - 2*7 = -16 ------------------------ the system: 2x + 3y = 17 x - 2y = -16 --- will have solution (-2,7) ======================================== Cheers, Stan H.

Complex_Numbers/210455: how do you write the expression 2i(5+i)(-2+7i) as a complex number in standard form? 1 solutions Answer 159082 by stanbon(57290)   on 2009-09-02 19:36:22 (Show Source): You can put this solution on YOUR website! write the expression 2i(5+i)(-2+7i) as a complex number in standard form? --------------------------------------------------------------- = 2i[-10-7-2i+35i] --- = 2i[-17+33i] --- = -66 - 34i ============================== Cheers, Stan H.

Expressions-with-variables/210540: This question is from textbook texas pre-algebra 21+15 _____ 3+6 1 solutions Answer 159077 by stanbon(57290)   on 2009-09-02 19:02:43 (Show Source): You can put this solution on YOUR website! 21+15 _____ 3+6 -------------------- = 36/9 = 4 ============= Cheers, Stan H.