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Answers by Katherine P.

6/(n raise to 3 - n) (answer)

Hi Michael,   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)]...

Financing Word Problem - HELP! (answer)

Hi Natalie,   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...

Rotating a segment 30 degrees around the origin (answer)

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).   When...

Word problem for algebra 2 (answer)

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)...

84x^5/-7x^5 (answer)

Hi Pat,   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 (answer)

Hi Maddie, Probability always seems a little trickier when they make up these odd scenarios. Let's start by translating the problem into probability terms:   We have: 3 independent events (each wheel is considered an event, the wheels don't interact 10 possible outcomes...

ms. beckman invites 5 of her friends to her birthday party (answer)

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).   Method 1: Let's model this by assigning each person a letter: a b c d e f <-- our 6 people   The handshakes would...

solving for variables (answer)

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   Simplify x = (-7/3)y - 63/3 x = (-7/3)y - 21    

Need to Find X (answer)

Hi Jessica,   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...

HELP ME OUT PLEASE SOLVE IT.............. (answer)

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,...

What's the minimum y-value on the graph of y= f(x) (answer)

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...

I need help finding the vertex of this parabola (answer)

Hi Harry, 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)...

scientifc notation 2 (answer)

Scientific notation makes it easier for us to estimate quantities because we don't get lost in all those zeros.   Step 1: 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   Step 2: Kelly thinks that translates to 300,000,000...

(2,3) and (4,5) (answer)

You could also use point-slope form to solve for your equation.   Slope: m = (y1-y2)/(x1-x2) m = (3-5)/(2-4) = (-2)/(-2) = 1   Point-slope form: y - y1 = m(x - x1) y - 3 = 1(x - 2) y - 3 = x - 2   Add 3 to both sides to isolate y - leaving...

2v(5)=3v(x) (answer)

2v(5)=3vx   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...