Hi Jamie,
For continuous compounding, use Balance = Pert where r=annual rate as a decimal, you are solving for t. Since you want his money to triple, Balance = 3*4500 = 13,500. To solve for r, you will need to take the natural log of both sides, then divide by r=.073.
Its...

first convert loga10a to loga10+logaa = loga10+1
do the same with loga0.2525=25loga0.25
now you need to just deal with loga10 and loga0.25. Can we do a combination of 25 and 4 (given logs) to get 10 and 0.25??
10 = sqrt(25*4) = (25*4)1/2
0.25 =...

"two score years" is 14 years...
Since you are compounding weekly, your m=52 which divides your interest (periodic interest) and multiplies your years (total periods). P=initial principal, i=annual interest written as a decimal, n=years
When m=1: Balance...

You can determine the original function y=f(x) by taking the anti-derivative of f'(x), substituting x=2/y=3, and solving for C.
However, if you just need to "solve for f'(x)", the slope of the f(x) function at any point x, then all you need to do is substitute 2 for...

Is x a function of t?

You will be forming a right triangle with the information, then using the Pythagorean Theorem (or distance formula) to determine the answer. The buoys are 21 miles apart (E-W = 3 - (-18)). The East sub is 7 miles down and the West sub is 1 mile down. That is a difference of 6 miles.
So...

For continuous interest you will need the relationship A=Pert where A is your future amount ($7000), P is your initial amount (unknown), r is the annual rate of interest (.04) and t is the number of years it is invested (4). e of course is the constant and is the base of the natural log function,...

Let x = gallons of Canola Oil
Let y - gallons of Corn Oil
x + y is the gallons of 11% blended oil that you will have at the end.
You are given that x = 600, now you just have to find y.
The fat content of the Canola Oil is 7% of x = .07x
The...

Hi Sally - use the cos2(x)=1-sin2(x) identity on the left after setting cot(x)=cos(x)/sin(x) then multiplying by cos(x)
So transform the left side to result in the right side. That is how the subtraction shows up.

M - Please do not make the common mistake that the expression you were given is equal to anything. You are merely simplifying it. If your teacher said that the expression was equal to 10, a would not be -8. Don't ASS-U-ME...
Equations have Equal signs and so must...

Question - is 114 the standard deviation or the variance of the distribution? I'll assume the variance given its relative size to the mean 515.
Step 1) You will have to find the z-score such that 20% of the area under the Standard Normal Distribution Curve lies to the right...

A standardize score of +1.23 represents that the raw score is 1.23 standard deviations ABOVE the mean. (NOTE: If the standardized score was -1.23, then the raw score would be 1.23 standard deviations BELOW the mean)
The mean is 100 and the size of the standard deviation...

The product of 2 binomials is also referred to as "FOIL" or double distribution.
Each term in the first factor must be multiplied by each term in the second factor. These terms are added.
So, the 2x needs to be multiplied by (2x-8) and the +8 needs to be also...

Hi Jazlyn,
Did the function need to be graphed on a set of axes? If so, maybe I can walk you through it. The answer from Shaung will give you the inverse function since it solved for x but didn't address the topic of transformation.
First off - it is a transformation...

I think this would be easier to use improper fractions since you are going to have to multiply. Also, since 2-11/63 is NOT a reasonable width, possibly the area of the kitchen is 1.75 the area of the room (not 1 minus 3/4 = 1/4). So here goes:
The area of the room is 99-3/7...

"What is the probability that no consecutive heads occur on three tosses of a coin?" This can be interpreted to include any occurrences of HH as well as HHH on the 3 tosses.
Using Vivian's set of all possibilities, "no consecutive heads" appear on outcomes...

I think this is what you are looking for:
The distributive property is multiplication (or division) over addition (or subtraction).
6*13 = 6*(10+3) = 6*10+6*3 = 60+18 = 78
This rewrites the 13 as 10+3 and clears the parenthesis by multiplying over them. ...

What if you write it like this:
pi * 25 * 12
3
When you multiply by 1/3 it is the same as dividing by 3. Since multiplication and division are on the same level in Order of Operations, you can see that 12/3 = 4. So the...

If its the metric system, I use the following to remember the prefixes:
King Henry Drank My Delicious Chocolate Milk
Kilo, Hecto, Decka, middle, Deci, Centi, Milli
"middle" can be replaced by Meter, Liter, Gram. Those ending in "i" are smaller than the unit...

It seem that there is more to the problem with the "use x as the variable" directions. The absolute value of an expression is a function that "wipes away" the sign. It represents the distance from zero.
The absolute value of a => |a| in symbols
decreased...