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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

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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

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Applying rules of log:

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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)

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3 log(base 3)5+3 log(base 3)y-log(base 3)25
.

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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

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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)

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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:

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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%

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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

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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

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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

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$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)

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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

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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)

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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

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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

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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

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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:

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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

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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

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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)

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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

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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

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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

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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

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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

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I'm assuming you mean log base 5:

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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

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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)