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 logarithm/249519: Evaluate the logarithmic equation for three values of x that are less than -1, three values of x that are between 0 and -1, and at x = -1. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the equation of the line asymptotic to the graph (if any). y = -log3.5 (-x) The 3.5 is a, or the subscript Thank you for any help you can offer. 1 solutions Answer 181740 by Theo(3464)   on 2009-12-14 03:11:22 (Show Source): You can put this solution on YOUR website!your equation is: y = -log(3.5,(-x)) graph of this equation looks like this: you can use the conversion formula to change the base of the logarithm so you can solve it using your calculator. the conversion formula is: log(a,(x)) = log(b,x) / log(b,a) what this formula says is: log of x to the base of a equals the log of x to the base of b divided by the log of a to the base of b. in your problem, this conversion formula becomes: -log(3.5,(-x)) = - (log(10,(-x)) / log(10,3.5) you can now use your calculator to solve for selected points of that log. you get: y = - (log(10,(-x)) / log(10,3.5) substitute the following values for x: y = - (log(10,-(-4)) / log(10,3.5) = -1.106589511 y = - (log(10,-(-3)) / log(10,3.5) = -.87695144 y = - (log(10,-(-2)) / log(10,3.5) = -.553294756 y = - (log(10,-(-1)) / log(10,3.5) = -0 y = - (log(10,-(-.1)) / log(10,3.5) = 1.838005394 y = - (log(10,-(-.0000001)) / log(10,3.5) = 12.86603776 the graph appears to be asymptotic at x = 0 the closer you get to 0, the bigger y gets. the value of y is undefined at x = 0 all you need to do is plot the points on a piece of graph paper and draw the resulting curve.
 Trigonometry-basics/249561: Hi, this is a trig word problem involving height of buildings and I want it soved by tomorrow (12/14/2009, PST) by the latest. Here it is: The window on the fourth floor of a building is 30 m above the ground. From the window, the angle of depression to the base of a nearby building is 31 degrees and the angle of elevation to the top of the building nearby is 40 degrees. How tall is the nearby building to the nearest metre? I just want to know how to draw out the problem. Your help is most appreciated, thanks! ~S.N.1 solutions Answer 181738 by Theo(3464)   on 2009-12-14 02:20:10 (Show Source): You can put this solution on YOUR website!here's your diagram. http://theo.x10hosting.com/problems/249561.html you draw a line parallel to the ground from the window to the opposite building. that would be line AB you draw a line from the windoiw to the base of the building next door. that would be line AC. you draw a line from the window to the top of the building next door. that would be line AE. your angle of depression is angle BAC. your angle of elevation is angle EAB. line AD is 30 feet. so is line BC because it's on the opposite end of the rectangle that you drew which is rectangle ABCD. you need to find the length of line AB. use tan(31) = BC/AB go get line AB. use tan(40) = EB/AB to get line EB. height of building is line EC which is the sum of lines EB and BC. any further questions, send me an email. i'll be checking in the morning.
 Miscellaneous_Word_Problems/249145: If 100 bushels of corn is distributed among 100 people in such a manner that each man receives 3 bushels, each woman 2, and each child 1/2 of a bushel, which one of the following is a possible value for the number of men ? (A)16 (B) 12 (C) 8 (D) 4 (E) 0 1 solutions Answer 181538 by Theo(3464)   on 2009-12-13 09:12:15 (Show Source): You can put this solution on YOUR website!I would have to say selection (C) which is equal to 8. Here's why: you have 2 equations in 3 unknowns which means the best you can do is find a relationship between 2 of the variables. Let: x = number of men y = number of women z = number of children your equations are: ``` x + y + z = 100 3x + 2y + z/2 = 100 ``` you can eliminate one of the variable by multiplying the second equation by 2 to get: ``` x + y + z = 100 minus: 6x + 4y + z = 200 equals: -5x - 3y = -100 ``` you can solve for y in the resulting equation as follows: your equation to solve is: -5x - 3y = -100 add 5x to both sides to get: -3y = -100 + 5x multiply both sides by -1 to get: 3y = 100 - 5x divide both sides by 3 to get: y = (100-5x)/3 you equation you need to work with is: y = (100-5x)/3 look at all your solutions and solve for the given value of x. when x = 16, y = 6.67 when x = 12, y = 13.33 when x = 8, y = 20 when x = 4, y = 26.67 when x = 0, y = 33.33 in all of these, the only integer value is 20, so the only possible solution would be x = 8 and y = 20 that means that there could be 8 men and 20 women which means that there must be 72 children because x + y + z = 100 if so, then the distribution is among 8 men, 20 women, and 72 children. each man gets 3 bushels so the men get 24 bushels each woman gets 2 bushels so the women get 40 bushels each child gets 1/2 bushel so the children get 36 bushels. 24 + 40 + 36 = 100 bushels so that checks out ok. your answer is selection (C) which is 8 men as a possible solution. there could be other solutions as well since you did not solve for the number of women. you only solved for the number of women in relataion to the number of men. example: if x = 2, then (100-5x)/3 = 90/3 = 30 women. you could have 2 men, 30 women, and 68 children 3*2 = 6 2 * 30 = 60 68 * .5 = 34 60 + 34 + 6 = 100 number of men equals 2 is a possibility as well.
 Triangles/249156: Find the largest possible area of a triangle that has two sides of lengths 30 and 401 solutions Answer 181536 by Theo(3464)   on 2009-12-13 08:43:39 (Show Source): You can put this solution on YOUR website!if it has sides of length 30 and 40 then the area is fixed at 30*40 = 1200. area = L*W = 30*40 = 1200
 Equations/249126: the ratio of lenght to width of a rectangle corral is to be 8 to 5. enough lumber is available for a 78-yard fence the (perimeter). What will be the length and width of the corral if all the lumber is used? write two equations and in two unknowns and solve1 solutions Answer 181534 by Theo(3464)   on 2009-12-13 08:40:51 (Show Source): You can put this solution on YOUR website!ratio of length to width is 3/5 p = 78 2*L + 2*W = 78 L/W = 3/5 cross multiply to get 3W = 5L divide both sides by 3 to get: W = 5L/3 substitute for W in perimeter equation to get: 2*L + 2*(5*L/3) = 78 simplify by removing parentheses to get: 2*L + 10*L/3 = 78 multiply both sides of equation by 3 to get: 3*2*L + 10*L = 78*3 simplify to get: 6*L + 10*L = 234 combine like terms to get: 16*L = 234 divide both sides by 16 to get: L = 234/16 = 14.625 W = 5*L/3 = 5*14.625/3 = 24.375 you have: L = 14.625 W = 24.375 L/W = 3/5 = .6 L/W = 14.625/24.375 = 3/5 after you divide both numerator and denominator by 4.875 ratio is good. perimeter is equal to: 2*L + 2*W which becomes: 2*14.625 + 2*24.375 = 29.25 + 48.75 = 78 perimeter is good. your answer is: length = 14.625 yards width = 24.375 yards
 Triangles/249099: this is my homework assignment from the geometry book. it says sketch a triangle and label its vertices. Name two sides and the included angle between the sides1 solutions Answer 181533 by Theo(3464)   on 2009-12-13 08:27:19 (Show Source): You can put this solution on YOUR website!here's your triangle. ``` A x x x x x x x x x x x x x x x x x x x B xxxxxxxxxxxxxxxxxxxxxx C ``` it is labeled triangle ABC. There is an angle at point A, point B, point C. There are labeled angle A, angle B, angle C They are also labeled angle BAC, angle ABC, angle BCA The vertex of the angle is the point where the two sides of the angle meet. These would be the sides that include the angle. There are 3 sides to the triangle. They are sides AB, BC, and AC. The sides are labeled by their endpoints. The sides are also called line segments. Two of the sides of this triangle are AB and BC. The included angle between these sides would be at the intersection of the 2 sides which would be at the common point of the two sides which would be at point B. Angle B, otherwise labeled as ABC or CBA, is included between the sides of AB and BC.
 Miscellaneous_Word_Problems/249146: If I were to give \$ 7 to each of the beggars at my door, I would have \$24 left. I lack \$32 of being able to give them \$9 apiece. What is the sum of my money and the number of beggars at my door ?1 solutions Answer 181530 by Theo(3464)   on 2009-12-13 08:13:11 (Show Source): You can put this solution on YOUR website!x = number of beggars y = money you have. your formulas are: y - 7x = 24 (equation 1) y - 9x = -32 (equation 2) subtract equation 1 from equation 2 to get: 2x = 56 solve for x to get: x = 28 substitute in first equation to get: y - 7*28 = 24 solve for y to get: y = 7*28 + 24 = 220 you have \$220 dollars and there are 28 beggars at your door. 220 - 7*28 = 24 (true) 220 = 9*28 = -32 (true)
 Mixture_Word_Problems/249149: by weight one fertilizer is 20% potassium, 30% nitrogen and 50% phosphorus. a second fertilizer has percents of 10%, 20% and 70% respectively and a third fertilizer has percentage of 0%, 30% and 70% respectively. how much of each should be mixed to get 200 kg of fertilizers with percents of 12%, 25% and 63% respectively?1 solutions Answer 181524 by Theo(3464)   on 2009-12-13 07:27:17 (Show Source): You can put this solution on YOUR website!x = amount of fertilizer 1 y = amount of fertilizer 2 z = amount of fertilizer 3 it helps to make a table for this. your table would look like this: ```amount of fertilizer in kilograms fertilizer total potassium nitrogen phosphorus 1 x .2x .3x .5x 2 y .1y .2y .7y 3 z --- .3z .7z 4 200 24 50 126 ``` the amounts of potassium, nitrogen, and phosphorous for fertilizer 4 are given to you by weight because you are told the proportions and you know what the total weight is. potassium = .12 * 200 = 24 nitrogen = .25 * 200 = 50 phosphorus = .63 * 200 = 126 you wind up with 3 equations that need to be solved simultaneously. note that these equations are from the vertical columns for potassium, nitrogen, and phosphorus in your original table above. those equations are: ``` .2x + .1y + .0z = 24 (equation 1) .3x + .2y + .3z = 50 (equation 2) .5x + .7y + .7z = 126 (equation 3) ``` once you solve these simultaneously, you will have the amounts of x,y,z that you need which are the amounts of fertilizer 1, fertilizer 2, fertilizer 3 that you need. we will eliminate the decimals first so they won't bother us. multiply all equations by 10 to get: ``` 2x + 1y + 0z = 240 (equation 1) 3x + 2y + 3z = 500 (equation 2) 5x + 7y + 7z = 1260 (equation 3) ``` first we will take equation 1 and 2 and eliminate the y variable. we will do that by multiplying equation 1 by 2 and then subtract equation 2 from equation 1 to get equation 4. ``` 4x + 2y + 0z = 480 (equation 1 multiplied by 2) minus: 3x + 2y + 3z = 500 (equation 2) equals: 1x - 3z = -20 (equation 4) ``` next we will take equation 2 and 3 and eliminate the y variable. we will do that by multiplying equation 2 by 7 and multiplying equation 3 by 2 and then subtracting equation 3 from equation 2. ``` 21x + 14y + 21z = 3500 (equation 2 multiplied by 7) minus: 10x + 14y + 14z = 2520 (equation 3 multiplied by 2) equals: 11x + 7z = 980 (equation 5) ``` next we will take equation 4 and equation 5 and eliminate the x variable. we will do that by multiplying equation 4 by 11 and then subtracting equation 5 from equation 4 ``` 11x - 33z = -220 (equation 4 multiplied by 11) minus: 11x + 7z = 980 (equation 5) equals: - 40z = -1200 ``` we solve for z to get: z = 30 we use this value of z and substitute in equation 5 to get: 11x + 7z = 980 becomes: 11x + 7*(30) = 980 which becomes: 11x + 210 = 980 subtract 210 from both sides to get: 11x = 980-210 = 770 divide both sides by 11 to get: x = 70 next we use the values of z = 30 and x = 70 and go to equation 3 to get: 5x + 7y + 7z = 1260 becomes: 5*(70) + 7y + 7*30) = 1260 which becomes: 350 + 7y + 210 = 1260 which becomes 7y + 560 = 1260 subtract 560 from both sides to get: 7y = 1260 - 560 = 700 divide both sides by 7 to get: y = 100 we have values for x,y,z. they are: x = 70 y = 100 z = 30 we need to test these values to see if they are good. our original equations are: ``` .2x + .1y + .0z = 24 (equation 1) .3x + .2y + .3z = 50 (equation 2) .5x + .7y + .7z = 126 (equation 3) ``` first we check to see if x + y + z = 200. it does. that's good because the total of fertilizer 1, 2, 3 should equal 200 and it does. next we substitute in all 3 equations to get: ``` .2x + .1y + .0z = 24 (equation 1) .3x + .2y + .3z = 50 (equation 2) .5x + .7y + .7z = 126 (equation 3) ``` becomes: ``` .2*70 + .1*100 + .0*30 = 24 (equation 1) .3*70 + .2*100 + .3*30 = 50 (equation 2) .5*70 + .7*100 + .7*30 = 126 (equation 3) ``` we simplify to get: ``` 14 + 10 + 0 = 24 (equation 1) 21 + 20 + 9 = 50 (equation 2) 35 + 70 + 21 = 126 (equation 3) ------------------- total: 70 + 100 + 30 = 200 (sum of equations 1,2,3) ``` Looks like we have the answer. he needs: 70 pounds of fertilizer 1 100 pounds of fertilizer 2 30 pounds of fertilizer 3 he will get: 200 pounds of fertilizer 4 that contains: 24 pounds of potassium 50 pounds of nitrogen 126 pounds of phosphorus
 Proportions/249132: Speed varies inversly with time of travel. It takes 6 seconds to travel between two highway markers at 45 mph. write the equation and show the proportionality constant. How fast are you driving if it takes 5 seconds to travel between the markers?1 solutions Answer 181512 by Theo(3464)   on 2009-12-13 03:16:29 (Show Source): You can put this solution on YOUR website!let t = time let s = speed s = k/t k is the constant of variation. let t = 6 seconds let s = 45 miles per hour. use these values to find k. equation of s = k/t becomes: 6 seconds = k / 45 miles per hour without changing the units used, the constant of variation here would be: k = 6*45 = 270 If it takes 5 seconds, then the equation becomes: 5 = 270 / x and you get x = 270/5 = 54 miles per hour. with changing the units used, the equation of: 6 = k/45mph becomes: 6 = k/.0125 miles per second. now the units are consistent with each other. solve for k to get: k = .0125*6 = .075 with 5 seconds, the equation now becomes: 5 = .075 / x solve for x to get: x = .075/5 = .015 miles per second. convert to miles per hour to get 54 miles per hour. you get the same answer whether you converted the units or not. the constant of proportionality took care of the difference in the units used. if you divide the constant of proportionality by 3600 which is what we did to convert the miles per hour to miles per second, then the constant of proportionality of 270 becomes .075. mathematically the two answers are equivalent to each other. you did not have to convert the units to make them consistent in this case. however, in a lot of other cases, you will need to, so converting to similar units for all variables in the equation is always a good idea.
 Pythagorean-theorem/249133: If the distance between the point at which a kite is held and the point at which it is directly overhead is 60 feet, and 100 feet of string has been let out, how far above the ground is the kite? (pythagorean theorem)1 solutions Answer 181511 by Theo(3464)   on 2009-12-13 02:57:47 (Show Source): You can put this solution on YOUR website!the string is the hypotenuse of the right triangle. the point which it is directly overhead forms the adjacent side of the angle of the triangle that you need. you need to find the angle first and then you can find the height. cosine (angle) = adjacent divided by hypotenuse. let the angle be called A. adjacent side is 60 feet (length on the ground from the point of the holding of the kite to the point just underneath the kite. hypotenuse side is 100 feet (length of the string holding the kite). cosine (A) = 60/100 = .6 look up in the cosine tables to find that arccosine(.6) = 53.13010235 deegrees. arccosine (x) means the angle whose cosine is x. In this case we solved for arcosine (.6) to get our answer. now that we know what the angle is, we can solve for the opposite side of the angle to get the height. we can use either of 2 equations. sine (53.13010235) = opposite / hypotenuse = x/100 tangent (53.13010235) = opposite / adjacent = x/60 both equations will lead to the same answer. solving for x, first equation becomes x = 100 * sine (53.13010235) = 80 feet. x = 60 * tangent (53.13010235) = 80 feet. your triangle looks like this: ``` (C) x x x x x 100 x x x x x x (B) x x x x x x x (A) 60 ``` The triangle is ABC The right angle is CBA The person holding the string is at A. Point B is directly beneath the kite. Point C is the kite. The line AC is the string The line BA is the distance from the person holding the string to the point directly underneath the kite. The angle you need to find is angle A, otherwise known as angle CAB.
 Functions/249140: Find f(g(2)) if f(x)=sqroot of x+2 and g(x)=2x+31 solutions Answer 181510 by Theo(3464)   on 2009-12-13 02:42:58 (Show Source): You can put this solution on YOUR website!f(x) = sqrt(x+2) g(x) = (2x+3) you want: f(g(2)) first find g(2) in the equation of g(x) = (2x+3), you replace x with 2 to get: g(2) = (2*2 + 3) = 4+3 = 7 in the equation of f(x) = sqrt(x+2), you replace x with g(x) to get: f(g(x) = sqrt(g(x)+2) since g(x) = 7, you replace g(x) with 7 to get: f(7) = sqrt(7+2) = sqrt(9) = 3 the equation is the rules by which you relate the independent variable to the dependent variable. the independent variable is the variable that does not depend on any rules to establish a value for it. the dependent variable is the variable that depends on the rules of the equation to establish a value for it. when x is a certain value, y has to be a certain value. x is also called the argument of the function. the argument of the function is the variable that the rules of the equation are working on. y = f(x) = x^2 means the independent variable in the equation is x. y = f(a) = a^2 means the independent variable in the equation is a. the rules are the same. the only difference is the variable that the equation is working with. that is why when you say f(x) = x^2, f(x) becomes the dependent variable and x is the independent variable. when you say f(2) using the same equation, then the rules stay the same but the independent variable becomes 2 instead of x. f(2) = 2^2 = 4. when you say f(g(x)), then the independent variable in the equation becomes g(x). g(x), however, was the dependent variable in another equation, so it's value had to be calculated before you could put it into f(g(x)). that's exactly what we did above. we solved for g(2) to get 7. then we solved for f(g(x)) to get f(7) = 3. you are placing g(x) into the argument of the equation f(x) = sqrt(x+2) which means you are replacing the existing argument of x with the argument of g(x).
 Probability-and-statistics/248957: I need someone to tell me where "m" come from? If \$1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10years? compute the answer to the nearist cent. Compound interest formula: A=P(1+(r/m))^(mt) P=1,000 r=0.1 m=12 t=10 A=1,000(1+(0.10/12)^((12)(10)) A=\$2,707.041 solutions Answer 181387 by Theo(3464)   on 2009-12-12 11:15:15 (Show Source): You can put this solution on YOUR website!m looks like it is months. usually you are given the annual interest rate and you have to divide that by the number of months to get the monthly interest rate. this assumed the compounding of the interest rate is monthly. It could be: semi-annually (2) quarterly (4) monthly (12) yours is monthly. if the compounding is monthly, then the number of time periods have to be in months. if they are specified in years, then you have to multiply them by 12 to get months. your formula is: If \$1,000 is invested in an account paying 10% compounded monthly, how much will be in the account at the end of 10years? compute the answer to the nearist cent. Compound interest formula: A=P(1+(r/m))^(mt) P=1,000 ***** money invested in the account today. r=0.1 ***** annual interest rate of 10% per year. m=12 ***** compounding period is in months and there are 12 months to the year. t=10 ***** number of years A=1,000(1+(0.10/12)^((12)(10)) A=\$2,707.04 you take the annual interest rate and divide it by 12 to get the monthly interest rate per time period equal to .000833333333 you take the number of years and multiply it by the number of months in a year to get the number of time periods equal to 120 your formula becomes: A = 1,000 * (1.00833333^120) Your answer of 2707... is correct. A more general formula would be: F = P * (1+(r/c)^(n*c)) where: F = future value P = present amount r = annual interest rate c = number of compounding periods per year n = number of years this works with all compounding periods, not just months.
 Trigonometry-basics/248865: What is the Cosecant of a 22.5 degree angle?1 solutions Answer 181381 by Theo(3464)   on 2009-12-12 09:02:36 (Show Source): You can put this solution on YOUR website!cosecant is equal to 1 / sine. find the sine and then divide that into 1 and you get your answer. sine (22.5) = .382683432 1/.382683432 = 2.61312593 you can use this online trigonometry calculator to find the answer directly. You can change the number of significant digits by scrolling down further and entering the number of digits accuracy you want. Don't press the enter key. It resets the calculator. Just enter the number of digits accuracy you want and then scroll back up and continue without pressing the enter key. If you entered your angle and it's still in the input box, then press csc. Otherwiee re-enter the angle and press csc. That's the only bug with this calculator. Otherwise it works fine.
 Average/248912: If your average score on your first six mathematics tests was 84 and your average score on your first seven mathematics tests was 85, then your score on the seventh test was (A) 86 (B) 88 (C) 90 (D) 911 solutions Answer 181380 by Theo(3464)   on 2009-12-12 08:50:31 (Show Source): You can put this solution on YOUR website!average score on first 6 mathematics tests is 84. total score on first 6 tests = 6 * 84 = 504 average score on first 7 mathematics tests is 85. total score on first 7 tests = 7 * 85 = 595 score on your 7th test is 595 - 504 = 91 (504 + 91) / 7 = 85 average on 7 tests.
 Rate-of-work-word-problems/248812: A printing press can print 300,000 cards in 12 hours. An older press requires 18 hours to print 300,000 copies of a card. How long would it take for both presses working together to print 300,000 copies? I need the rate of work (R), the time of work (T) , and the work done (W) the equation is RT = W. It would help if I am provided a detailed explanation1 solutions Answer 181379 by Theo(3464)   on 2009-12-12 08:44:32 (Show Source): You can put this solution on YOUR website!Formula is RT = W From this formula, you can derive: T = W/R and R = W/T printing press can print 300,000 cards in 12 hours. T = 12 W = 300,000 R = W/T = 300,000/12 = 25,000 cards per hour. older press requires 18 hours to print 300,000 cards. T = 18 W = 300,000 R = W/T = 16,666.66666667 cards per hour. working together, their rates will combine. you get: T = x W = 300,000 R = 25,000 + 16,666.66666667 = 41,666.66666667 cards per hour. When solving for T, formula becomes: T = W/R This equation becomes: T = 300,000/41,666.66666667 = 7.2 hours. In 7.2 hours, the printing press has completed 25,000 * 7.2 = 180,000 cards. In 7.2 hours, the old press has completed 16,666.66666667 * 7.2 = 120,000 cards. total cards produced is 180,000 + 120,000 = 300,000
 Equations/248874: The volume, V, of a given mass of a gas varies directly as the temperature, T, and inversely as the pressure, if V=231cm^3 when T=42 and P=20kg/cm^2, what is the volume when T=30 and P=15kg/cm?1 solutions Answer 181376 by Theo(3464)   on 2009-12-12 08:23:32 (Show Source): You can put this solution on YOUR website!V = k*T/P where: V = volume T = temperature P = pressure k = constant of variation. When: V = 231 cm^3 T = 42 degrees P = 20kg/cm^2, The formula becomes: 231 = k*42/20 Solve for k to get: k = 110 The constant of variation is equal to 110. When T = 30 and P = 15 and k = 110, the formula becomes: V = 30*110/15 = 220 cm^3 Here's a reference that explains how the variation formulas work.
 Percentage-and-ratio-word-problems/248915: Mr. Goyal receives a 10% raise every year. His salary after four such raises has gone up by what percent ? (A) less than 10% (B) 40% (C) 44% (D) more than 45%1 solutions Answer 181373 by Theo(3464)   on 2009-12-12 08:00:21 (Show Source): You can put this solution on YOUR website!(1.10)^4 = 1.4641 His salary has gone up 46.41% which is more than 45% so your answer is selection (D). Here's what happened. Assume his salary was \$30,000 a year. At the end of the first year it became \$30,000 * 1.10 = \$33,000 At the end of the second year it became \$33,000 * 1.10 = \$36,300 At the end of the third year it became \$36,300 * 1.10 = \$39,930 At the end of the fourth year it became \$39,930 * 1.10 = \$43,923 \$43,923 minus \$30,000 is an increase of \$13,923 \$13,923 / \$30,000 is an increase proportion of .4641 * 100% equals an increase percent of 46.41%. This is the same as \$30,000 * (1.10)^4 = \$30,000 * 1.4641 = \$43,923.
 Money_Word_Problems/248918: How long would it take for an amount of money invested at an annual rate of 6% compounded semiannually, to triple?1 solutions Answer 181371 by Theo(3464)   on 2009-12-12 07:34:49 (Show Source): You can put this solution on YOUR website!future value is 3 present amount is 1 annual interest rate is 6% 6% / 2 = 3% every half a year. interest rate equals interest rate percent divided by 100% = .03 every half a year. the formula you need is: 3 = 1 * (1.03)^x you need to solve for x. formula becomes: 3 = (1.03)^x take the log of both sides of the equation to get: log(3) = log((1.03)^2) by the rules of logarithms, this equation becomes: log(3) = x*log(1.03) divide both sides of this equation by log(1.03) to get: x = log(3)/log(1.03) solve for x to get: x = 37.16700967 this means that it would take 37.16700967 half years to triple your money. divide this by 2 to get: 18.58350483 years. We required half years because our interest rate was every half a year (semi-annually). these would be called semi-annual time periods. there are 37.16700967 semi-annual time periods which equate to 18.58350483 years.
 Miscellaneous_Word_Problems/248917: The number halfway between 1/6 and 1/4 is a) 1/10 b) 1/5 c) 5/24 d) 7/24 1 solutions Answer 181368 by Theo(3464)   on 2009-12-12 07:26:38 (Show Source): You can put this solution on YOUR website!what you would be lookikng for is 1/4 minus 1/6 divided by 2. 1/6 is equivalent to 2/12 1/4 is equivalent to 3/12 3/12 minus 2/12 equals 1/12 1/12 divided by 2 is equal to 1/24 if you add 1/12 to 1/6 then you will find your number. 1/6 is the same as 4/24. 4/24 plus 1/24 is equal to 5/24. your anser is selection (c). since you added 1/24 to get halfway, then you add 1/24 again and you will be all the way. 5/24 + 1/24 = 6/24 which is the same as 1/4. your answer is confirmed to be halfway between 1/6 and 1/4.