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# Recent problems solved by 'nerdybill'

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 Money_Word_Problems/313164: How long will it take an investment to double if it is invested at a 5% annual interest rate and compounded continuously? So, I'm really drawing a complete blank on this, i know P=e^rt, so P=e^0.05t, but that's far as I got. Thanks!1 solutions Answer 223907 by nerdybill(6948)   on 2010-06-10 15:38:49 (Show Source): You can put this solution on YOUR website!How long will it take an investment to double if it is invested at a 5% annual interest rate and compounded continuously? . You forgot the "initial principal" in your formula... . Continuously compounded interest: P=(Po)e^rt Where P is the amount after time t Po is the initial investment r is the rate t is the time . So, the "trick" is to assign a variable to the intial investment: Let x=initial investment (Po) So, when we double it we should have: 2x = final amount (P) . Plug in what we know into: P=(Po)e^rt 2x = xe^(.05t) Now, we solve for t: We begin by dividing both sides by x: 2 = e^(.05t) (notice our variable is gone!) ln(2) = .05t ln(2)/.05 = t 13.86 years = t
 test/313159: Alan types a paper in 3hrs. Bill can type the same paper in 2hr. How long would it take them,working together,to type the paper?1 solutions Answer 223904 by nerdybill(6948)   on 2010-06-10 15:20:24 (Show Source): You can put this solution on YOUR website!Alan types a paper in 3hrs. Bill can type the same paper in 2hr. How long would it take them,working together,to type the paper? . Let x = time it takes for them working together then x(1/3 + 1/2) = 1 Multiplying both sides by 6 we get: x(2 + 3) = 6 x(5) = 6 x = 6/5 or x = 1 and 1/5 hours or x = 1 hour and 12 minutes
 Radicals/313141: simplify (3√3)^41 solutions Answer 223903 by nerdybill(6948)   on 2010-06-10 15:18:26 (Show Source):
 logarithm/313125: How do I express this as a single logarithm? 2loga-3logb+4loga1 solutions Answer 223899 by nerdybill(6948)   on 2010-06-10 15:09:02 (Show Source): You can put this solution on YOUR website!Applying rules of log:
 Square-cubic-other-roots/313149: How do you simplify ?1 solutions Answer 223898 by nerdybill(6948)   on 2010-06-10 15:05:54 (Show Source): You can put this solution on YOUR website!How do you simplify ? . You can think of it as: (this is really just the cube root of 64 (look for 3-of-a-kind to remove fron under the radical)
 logarithm/313130: condense 3 log(base 3)5+3 log(base 3)y-log(base 3)251 solutions Answer 223896 by nerdybill(6948)   on 2010-06-10 15:02:02 (Show Source): You can put this solution on YOUR website!3 log(base 3)5+3 log(base 3)y-log(base 3)25 .
 Inequalities/313152: 3(x-2)+7=5+4x i know the answer is 4 i just dont know how to do the step by step work 1 solutions Answer 223894 by nerdybill(6948)   on 2010-06-10 14:56:10 (Show Source): You can put this solution on YOUR website!3(x-2)+7=5+4x Begin by distributing the 3 to each term inside the parenthesis: (3x-6)+7=5+4x 3x -6 +7=5+4x 3x+1=5+4x Subtracting 3x from both sides: 1=5+x Subtracing 5 from both sides: -4 = x . So x is equal to NEGATIVE four
 Miscellaneous_Word_Problems/312943: 8. Answer the question. You will need to use the formula 4.9t2 + v0t = s, where t is the time in seconds, v0 is the initial velocity, and s is the distance in meters. Approximately how far will an object fall in 4 seconds, if it is thrown downward at an initial velocity of 20 meters per second (v0) from a helicopter?1 solutions Answer 223747 by nerdybill(6948)   on 2010-06-09 18:28:40 (Show Source): You can put this solution on YOUR website!8. Answer the question. You will need to use the formula 4.9t2 + v0t = s, where t is the time in seconds, v0 is the initial velocity, and s is the distance in meters. Approximately how far will an object fall in 4 seconds, if it is thrown downward at an initial velocity of 20 meters per second (v0) from a helicopter? . Given equation is: Notice there is a negative sign associated with the 4.9. . Plug in given info: (meters)
 Trigonometry-basics/312927: What is the expanded logarithm of log3 a^61 solutions Answer 223736 by nerdybill(6948)   on 2010-06-09 17:42:58 (Show Source): You can put this solution on YOUR website!What is the expanded logarithm of log3 a^6 . I'm assuming you meant log base 3... . We can pull out the exponent and write it as: Next, we can apply "change of base" to get:
 Probability-and-statistics/312930: if my midterm test was worth 30% of our grade and i got a 62 out of 70 which is ~88% how much of the total 30% percent did i receive???1 solutions Answer 223734 by nerdybill(6948)   on 2010-06-09 17:38:53 (Show Source): You can put this solution on YOUR website!if my midterm test was worth 30% of our grade and i got a 62 out of 70 which is ~88% how much of the total 30% percent did i receive??? . You will receive: 62/70 * 30 = 1860/70 = 26.57%
 Equations/312932: Find 2 consecutive integral numbers whose sum 51??? I tried but i don't know what are consecutive integral numbers.1 solutions Answer 223732 by nerdybill(6948)   on 2010-06-09 17:36:41 (Show Source): You can put this solution on YOUR website!Find 2 consecutive integral numbers whose sum 51??? I tried but i don't know what are consecutive integral numbers. . "Integral numbers" are "whole numbers" that is -- integers. . Let x = smaller consecutive number then x+1 = larger consecutive number . from: "2 consecutive integral numbers whose sum 51" we get our equation: x + x+1 = 51 2x+1 =51 2x = 50 x = 25 (smaller number) . Lareger number: x+1 = 25+1 = 26 . the two numbers are then 25 and 26
 Rate-of-work-word-problems/312902: Jack and Jill are hired to empty a tank. If they work together it takes them 12 minutes. Working alone, Jack would take 10 minutes longer than Jill to empty the tank. How long does it take for Jack to empty the tank himself? How long does it take jill?1 solutions Answer 223716 by nerdybill(6948)   on 2010-06-09 16:32:12 (Show Source): You can put this solution on YOUR website!Jack and Jill are hired to empty a tank. If they work together it takes them 12 minutes. Working alone, Jack would take 10 minutes longer than Jill to empty the tank. How long does it take for Jack to empty the tank himself? How long does it take jill? . Let x = minutes it takes Jill to do it alone then x+10 = minutes it takes Jack to do it alone . 12(1/x + 1/(x+10)) = 1 multiplying both sides by x(x+10) 12((x+10) + x) = x(x+10) 12(2x+10) = x(x+10) 24x+120 = x^2+10x 120 = x^2-14x 0 = x^2-14x-120 0 = (x+6)(x-20) x = {-6, 20} Toss out the negative solution (doesn't make sense) leaving x = 20 minutes (time it takes Jill) . Jack: x+10 = 20+10 = 30 minutes
 Mixture_Word_Problems/312855: How many pounds of 7% fat hamburger must be mixed with 30 pounds of 15% fat hamburger to obtain a 10% fat mixture? 1 solutions Answer 223700 by nerdybill(6948)   on 2010-06-09 14:02:28 (Show Source): You can put this solution on YOUR website!How many pounds of 7% fat hamburger must be mixed with 30 pounds of 15% fat hamburger to obtain a 10% fat mixture? . Let x = pounds of 7% fat hamburger added then .07x + .15(30) = .10(x+30) .07x + 4.5 = .10x+3 4.5 = .03x+3 1.5 = .03x 50 pounds = x
 Finance/312828: \$775 invested for 12 years at 12 percent compounded annually 1 solutions Answer 223676 by nerdybill(6948)   on 2010-06-09 13:16:50 (Show Source): You can put this solution on YOUR website!\$775 invested for 12 years at 12 percent compounded annually . where A is amount after t time P is initial amount r is rate n is number of times compounded in a year . Since it's compounded annually n is 1 Plug in the given numbers: (dollars)
 Geometry_Word_Problems/312777: a flower bed length is 3m. more than twice the width. the flower bed has an area of 20 meters squared find the dementions.1 solutions Answer 223651 by nerdybill(6948)   on 2010-06-09 10:23:21 (Show Source): You can put this solution on YOUR website!a flower bed length is 3m. more than twice the width. the flower bed has an area of 20 meters squared find the dementions. . Let w = width then 2w+3 = length . w(2w+3) = 20 2w^2+3w = 20 2w^2+3w-20 = 0 2w^2+8w-5w-20 = 0 (2w^2+8w)-(5w+20) = 0 2w(w+4)-5(w+4) = 0 (w+4)(2w-5) = 0 w = 5/2 = 2.5 meters (width) . length 2w+3 = 2(5/2)+3 = 5+3 = 8 meters (length) . Dimensions are 2.5 meters by 8 meters
 Expressions-with-variables/312767: I bought a furniture set for 1600 in the month of april and just recently saw an add for the same set on sale for 20%off. Had I waited a couple of months to purchase it how much would I have saved? 1 solutions Answer 223647 by nerdybill(6948)   on 2010-06-09 10:18:28 (Show Source): You can put this solution on YOUR website! I bought a furniture set for 1600 in the month of april and just recently saw an add for the same set on sale for 20%off. Had I waited a couple of months to purchase it how much would I have saved? . 1600 - .20(1600) = 1600-320 = \$1280 You would have saved \$320 (you would save more if you consider the taxes)
 Expressions-with-variables/312768: I bought my two children each a winter coat just a few months ago for next year while they were on clearance. My sons jacket was originally priced at \$74.99 with 25% off and my daughters jacket was originally priced at \$69.99 with 20% off. What was the total for each jacket after the discount. 1 solutions Answer 223640 by nerdybill(6948)   on 2010-06-09 09:57:20 (Show Source): You can put this solution on YOUR website! I bought my two children each a winter coat just a few months ago for next year while they were on clearance. My sons jacket was originally priced at \$74.99 with 25% off and my daughters jacket was originally priced at \$69.99 with 20% off. What was the total for each jacket after the discount. . Son's jacket: (1-.25)74.99 = .75(74.99) = \$56.24 , Daughter's jacket: (1-.20)69.99 = .80(69.99) = \$55.99
 Miscellaneous_Word_Problems/312582: An airplane covered 24 miles of its route while decreasing its altitude by 13,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth [hint: 1 mile = 5280 feet). I am pretty sure that it's going to be rise over run and that I would make the 13,000 feet 2.5 miles but so it should be 2.5/24 but I'm not 100% that's what the teacher is looking for. Any help would be appreciated1 solutions Answer 223479 by nerdybill(6948)   on 2010-06-08 18:23:06 (Show Source): You can put this solution on YOUR website!An airplane covered 24 miles of its route while decreasing its altitude by 13,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth [hint: 1 mile = 5280 feet). I am pretty sure that it's going to be rise over run and that I would make the 13,000 feet 2.5 miles but so it should be 2.5/24 but I'm not 100% that's what the teacher is looking for. Any help would be appreciated . You're close... The altitude is "decreasing" -- this means the "rise" is negative: rise/run = -13000ft/24miles = -13000ft/(24miles * 5280ft/1mile) = -13000ft/(24 * 5280ft) = -13000ft/126720ft = -0.10
 Human-and-algebraic-language/312571: If 8.5 pounds of pecans costs \$29.75, what is the price per pound?1 solutions Answer 223464 by nerdybill(6948)   on 2010-06-08 17:38:40 (Show Source): You can put this solution on YOUR website!If 8.5 pounds of pecans costs \$29.75, what is the price per pound? . Just divide 29.75 by 8.5: 29.75/8.5 = \$3.50 per pound
Quadratic_Equations/312525: Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?
1 solutions

Answer 223451 by nerdybill(6948)   on 2010-06-08 16:40:21 (Show Source):
You can put this solution on YOUR website!
Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?
.
Let x = days it taks Ron to frame it alone
then
x-4 = days it takes Lee to frame it alone
.
4(1/x + 1/(x-4)) = 1
multiplying both sides by x(x-4):
4((x-4) + x) = x(x-4)
4(2x-4) = x(x-4)
8x-8 = x^2-4x
-8 = x^2-12x
0 = x^2-12x+8
x = {11.292, 0.708}
Tossing out the 0.708 (because it won't make sense) leaves us with:
x = 11.292 days (Time it takes Ron)
.
Lee:
x-4 = 11.292-4 = 7.292 days
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=112 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 11.2915026221292, 0.708497377870819. Here's your graph:

 Polynomials-and-rational-expressions/312508: Simplify the following radical expression: 8^1/3 a)2 b)8 c)0 d) 41 solutions Answer 223422 by nerdybill(6948)   on 2010-06-08 14:53:24 (Show Source): You can put this solution on YOUR website!Simplify the following radical expression: 8^1/3 Can be thought of as the cube root of 8 And, because 2*2*2=8 your answer is simply 2
 Geometry_Word_Problems/312504: the equation to convert from degrees celsius to degress fahrenheit is f=1.8*C+32. you tell your canadaian friend that it is 62 degrees fahrenheit in san francisco. since your friend hasnt take math yet, she doesnt know how to convert from fahrenheit to clesius. using the above equation do the conversion for her.1 solutions Answer 223414 by nerdybill(6948)   on 2010-06-08 14:29:09 (Show Source): You can put this solution on YOUR website!f=1.8*C+32 where f is degrees farenheit and C is degrees celcius . Plug in the given temp to find C: f=1.8*C+32 62=1.8*C+32 30 = 1.8C 30/1.8 = C 16.67 celcius = C
 Quadratic_Equations/312503: what quadratic function can represent the solutions of the roots -4 and 5/3?1 solutions Answer 223408 by nerdybill(6948)   on 2010-06-08 14:14:19 (Show Source): You can put this solution on YOUR website!what quadratic function can represent the solutions of the roots -4 and 5/3? . If the roots are -4 and 5/3 then the quadratic function MUST have the following factors: (x + 4) and (x - 5/3) . FOIL the two factors: (x + 4)(x - 5/3) x^2 - 5x/3 + 4x -20/3 x^2 - 5x/3 + 12x/3 -20/3 x^2 + 7x/3 -20/3 (this is your quadratic function)
 Quadratic_Equations/312499: You will need to use the formula 4.9t2 + v0t = s, where t is the time in seconds, v0 is the initial velocity, and s is the distance in meters. Approximately how far will an object fall in 13 seconds (t) when thrown downward at an initial velocity of 10 meters per second (v0) from a plane?1 solutions Answer 223405 by nerdybill(6948)   on 2010-06-08 14:09:30 (Show Source): You can put this solution on YOUR website!You will need to use the formula 4.9t2 + v0t = s, where t is the time in seconds, v0 is the initial velocity, and s is the distance in meters. Approximately how far will an object fall in 13 seconds (t) when thrown downward at an initial velocity of 10 meters per second (v0) from a plane? . Starting with the provided equation: (I think you forgot the negative sign in front of the 4.9) Notice, it said "thrown downward" so Vo will be -10 meters per second. Plug in the given info: (meters) . That is, it will fall 958.1 meters
 Miscellaneous_Word_Problems/312378: Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony’s age. How old is each?1 solutions Answer 223363 by nerdybill(6948)   on 2010-06-08 12:02:26 (Show Source): You can put this solution on YOUR website!Tony and Belinda have a combined age of 56. Belinda is 8 more than twice Tony’s age. How old is each? . Let x = Tony's age then from "Belinda is 8 more than twice Tony’s age." 2x+8 = Belinda's age . From:"Tony and Belinda have a combined age of 56" we get our equation: x + 2x+8 = 56 3x+8 = 56 3x = 48 x = 16 years old (Tony) . Belinda: 2x+8 = 2(16)+8 = 16+8 = 24 years old
 Miscellaneous_Word_Problems/312446: Can you help me with this word problem? Thanks! A population of rabbits is growing exponentially at a rate of 11.2% every 2 months. How many months will be required for the rabbit population to double?1 solutions Answer 223353 by nerdybill(6948)   on 2010-06-08 11:09:32 (Show Source): You can put this solution on YOUR website!A population of rabbits is growing exponentially at a rate of 11.2% every 2 months. How many months will be required for the rabbit population to double? . Exponential growth/decay formula: N(t) = No*e(r*t) . N(t) = Future Population No = Starting population r = growth rate t= number of months . From:"rabbits is growing exponentially at a rate of 11.2% every 2 months" we can determine r (growth rate): Let x = initial population . N(t) = No*e(r*t) 1.112(x) = x*e(r*(2)) 1.112 = e(r*(2)) ln(1.112) = r*(2) ln(1.112) = 2r ln(1.112)/2 = r . Now, we can answer: "How many months will be required for the rabbit population to double?" N(t) = No*e(r*t) N(t) = No*e((ln(1.112)/2)*t) 2x = x*e((ln(1.112)/2)*t) 2 = e((ln(1.112)/2)*t) ln(2) = (ln(1.112)/2)*t ln(2)/(ln(1.112)/2) = t 13.06 = t Or, 13 months = t
 Miscellaneous_Word_Problems/312382: The number of books N to be sold at a bookfare is given by the function N(p) = 25000 / (3p + k) where p is the price per book and k is a constant. If 1000 books are sold at \$7 per book, how many books will be sold at the price of \$10 per book? 1 solutions Answer 223346 by nerdybill(6948)   on 2010-06-08 10:52:05 (Show Source): You can put this solution on YOUR website!The number of books N to be sold at a bookfare is given by the function N(p) = 25000 / (3p + k) where p is the price per book and k is a constant. If 1000 books are sold at \$7 per book, how many books will be sold at the price of \$10 per book? . First, use: "1000 books are sold at \$7 per book" to find k: N(p) = 25000 / (3p + k) 1000 = 25000 / (3(7) + k) 1000 = 25000 / (21 + k) 1000(21 + k) = 25000 21000 + 1000k = 25000 1000k = 4000 k = 4 . Our formula is now: N(p) = 25000 / (3p + 4) Now we can answer: "how many books will be sold at the price of \$10 per book?" N(p) = 25000 / (3(10) + 4) N(p) = 25000 / (30 + 4) N(p) = 25000/34 N(p) = 735.29 But, since we can't sell a partial book: N(p) = 735
 Surface-area/312442: Five hundred feet of fencing is available to enclose a rectangular pasture alongside a river, which serves as one side of the rectangle. Express the area of the rectangular pasture as a function of x. (only 3 sides require fencing)1 solutions Answer 223344 by nerdybill(6948)   on 2010-06-08 10:44:49 (Show Source): You can put this solution on YOUR website!Five hundred feet of fencing is available to enclose a rectangular pasture alongside a river, which serves as one side of the rectangle. Express the area of the rectangular pasture as a function of x. (only 3 sides require fencing) . Draw a diagram of the problem -- it'll help you see the solution. . Let x = width of rectangular pasture then 500-2x = lenght of rectangular pasture . Area = x(500-2x) Area = 500x-2x^2 Area = -2x^2+500x
 logarithm/312413: solve log5 7 + 1/2log5 4= log5X 1 solutions Answer 223342 by nerdybill(6948)   on 2010-06-08 10:41:43 (Show Source): You can put this solution on YOUR website!I'm assuming you mean log base 5:
 Miscellaneous_Word_Problems/312428: Ben is making wooden toys for the next arts and crafts sale. Each toy costs Ben \$1.80 to make. If he sells the toys for \$3.00 each, how many will he have to sell to make a profit of exactly \$36.00 ? And how do I do this problem I couldnt figure out how to solve it.1 solutions Answer 223339 by nerdybill(6948)   on 2010-06-08 10:32:51 (Show Source): You can put this solution on YOUR website!Ben is making wooden toys for the next arts and crafts sale. Each toy costs Ben \$1.80 to make. If he sells the toys for \$3.00 each, how many will he have to sell to make a profit of exactly \$36.00 ? . Profit, as a function of the number of toys sold is: P(n) = n(3.00 - 1.80) Where P(n) is the profit n is the number of toys sold . So, if we want to see a profit of \$36.00, set P(n) to 36 and solve for n: P(n) = n(3.00 - 1.80) 36 = n(3.00 - 1.80) 36 = n(1.20) 36/1.20 = n 30 = n
 Money_Word_Problems/312241: how many years will it take for an amount of money to double when it is compounded annually by a 4.3% interest rate?1 solutions Answer 223238 by nerdybill(6948)   on 2010-06-07 18:50:56 (Show Source): You can put this solution on YOUR website!A = P(1 + r)^t P = principal amount (the initial amount you borrow or deposit) r = annual rate of interest (as a decimal) t = number of years the amount is deposited or borrowed for. A = amount of money accumulated after n years, including interest. . Let x = initial investment then A = 2x Plug in what was given and solve for t: Dividing both sides by x: (years)