For percentage problems such as this, you want to divide the part by the whole and multiply by 100% to get the percentage.
In your example, you need to divide the number of "successes" (156) by the total number of "tries" (300) to get the proportion of successes...
Solving this problem requires the use of exponent rules and how to work with fractions.
First, let's take a look at the denominator: n^(3-n)
We can apply our knowledge of exponent division to get: (n^3)/(n^n)
So we have 6/[(n^3)/(n^n)]...
I see that you are posting a lot of similar problems. Here is one general formula that will help you with these sorts of economics/algebra-based problems. It's the compound interest formula.
A = P(1+r/n)^(nt)
The amount (A) is equal to...
Here is a generic way to set up this type of algebra problem.
d = total amount of dirt at the site (tons)
r = rate or removal (tons/hr)
t = time it takes to remove all of the dirt (hr)
d = rt
The total amount of dirt equals the removal rate times hours spent...
You had a good hunch with the 30-60-90 triangle. Actually, you have a 30-60-90 triangle that is part of the unit circle! N is a point at the standard starting position of the unit circle. Remember, the unit circle has a radius of 1, and at 0 degrees you
would be at (1,0).
You could start by calculating a z-score for 145
z = (145 - 132) / 9
z = 1.444
You could use a table or your graphing calculator to calculate the percentage above that z-score.
Then multiply the percentage by 862 (the number of values)...
You have a numerator of 84 x-to-the-fifths and a denominator of -7 x-to-the-fifths.
The x^5 cancel, leaving 84/(-7).
84 divided by -7 is -12.
Probability always seems a little trickier when they make up these odd scenarios. Let's start by translating the problem into probability terms:
3 independent events (each wheel is considered an event, the wheels don't interact
10 possible outcomes...
One approach to this type of word problem is to list the information you are given:
$19.95 = basic monthly charge
$0.05 = per minute charge$23.74 = total monthly billx = the number of minutes used
Next, put these things into an algebraic...
Here are two ways to do this problem. Let's use 6 people (Ms. Beckman plus 5 friends, if you use 5 your answer would end up being 10 handshakes).
Let's model this by assigning each person a letter:
a b c d e f <-- our 6 people
The handshakes would...
Here's another option for you:
y = (-3/7)x - 9
Add 9 to both sides
y + 9 = (-3/7)x
Multiply both sides by (-7/3)
(-7/3)y - 9(7/3) = x
x = (-7/3)y - 63/3
x = (-7/3)y - 21
For this algebra equation, you'll want to use substitution. Take the value of y (874.90) and plug it into your equation.
874.90 = (x * 0.4175) + x
Now let's combine the terms on the right side of the equation.
874.90 = 1...
This is an algebra word problem that can be solved by setting up a system of equations. Stay with me! It only sounds complicated, but we will make it easy.
We have two consecutive integers, let's call them x and y.
Let's say y comes after x, so that means y = x+1 ...
You are correct, the lines fit neither condition.
The equations are already in slope-intercept form, so you can see the slope of the first line is 4 and the slope of the second line is 1/4.
1.) To be parallel, the slopes would need to be equal.
2.) To be perpendicular,...
The minimum value is at the vertex, so all you need to do is find the y-coordinate of the vertex. Here are the steps to find the vertex from your standard form equation:
The equation you have is in standard form (y = ax^2 + bx + c), so we can use the formula -b/(2a) to find...
The equation you have is in standard form (y = ax^2 + bx + c), so we can use the formula -b/(2a) to find the x-coordinate of the vertex.
x = -(-10)/(2*1)
x = 5
Now plug 5 into your equation to solve for the y-coordinate of the vertex.
y = 5^2 - 10(5)...
Scientific notation makes it easier for us to estimate quantities because we don't get lost in all those zeros.
15,000 becomes 1.5 x 1,000
which is the same as 1.5 x 10^4
1.5 x 10^4 blinks per day
Kelly thinks that translates to 300,000,000...
You could also use point-slope form to solve for your equation.
m = (y1-y2)/(x1-x2)
m = (3-5)/(2-4) = (-2)/(-2) = 1
y - y1 = m(x - x1)
y - 3 = 1(x - 2)
y - 3 = x - 2
Add 3 to both sides to isolate y - leaving...
Let x stand for the "mystery number" you are trying to find.
75% of x plus 75 = x
0.75x + 75 = x
Bring the variable terms to the left side of the equation by subtracting x from both sides.
-0.25x + 75 = 0
At first glance, you might be unsure of what you're solving for in this equation, since there are 2 variables. Do you notice any similarities between the left and right sides?
Both sides have a v, which means this variable will cancel out and disappear from...