WPP#10: Unit L Concept 9-14 - Basic probability(one event), probability of independent "AND" events(multiple events with and without replacement), probability of "OR" events(mutually and non-mutually exclusive), and probability of events that require Combinations to determine sample space

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Step 4 and Step 5 are switched.

WPP#9: Unit L Concept 4-8 - Calculating possibilities with FCP, combinations(one event and multiple events), permutations, and distinguishable permutations

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SP#6: Unit K Concept 10 - Find Sums of Infinite Geometric Series

Make sure you pay close attention to what numbers to plug into each part of the formula. I tried my best to color code it, so it is easier to follow along. Also, don't forget about that whole number! Adding it to the last part of your problem is what gives you your final answer.

Fibonacci Beauty Ratio (Extra Credit)

Stephanie V. 
Foot to Navel: 99 cm   Navel to top of Head: 63 cm   Ratio: 99/63=1.571 cm 
Navel to chin: 45 cm                      chin to top of head: 23 cm       Ratio:45/23=1.957 cm 
Knee to navel: 53 cm                      Foot to knee: 52 cm                Ratio: 53/52=1.019 cm 

Average: 1.516 cm

Helena C. 
Foot to Navel: 102 cm   Navel to top of Head: 66 cm   Ratio: 102/66=1.545 cm 
Navel to chin: 45 cm                      chin to top of head: 22 cm       Ratio:45/22=2.045 cm 
Knee to navel: 56 cm                      Foot to knee: 45 cm                Ratio: 56/45=1.244 cm 

Average: 1.611 cm

Joshua N. 
Foot to Navel: 102 cm   Navel to top of Head: 67 cm   Ratio: 102/67.=1.522 cm 
Navel to chin: 45 cm                      chin to top of head: 23 cm       Ratio: 45/23= 1.957 cm 
Knee to navel: 61 cm                      Foot to knee: 47 cm                Ratio: 61/47=1.300 cm 

Average: 1.629 cm

Rodolfo R. 
Foot to Navel: 100 cm   Navel to top of Head: 64 cm   Ratio: 100/64 =1.563 cm 
Navel to chin: 46 cm                      chin to top of head: 25 cm       Ratio:46/25=  1.840 cm 
Knee to navel: 54 cm                      Foot to knee: 46 cm                Ratio: 54/46=1.174 cm 

Average: 1.526 cm

Christine N. 
Foot to Navel: 96 cm   Navel to top of Head: 60 cm   Ratio: 96/60= 1.6 cm 
Navel to chin: 42 cm                      chin to top of head: 22 cm       Ratio: 42/22= 1.909 cm 
Knee to navel: 51 cm                      Foot to knee: 45 cm                Ratio: 51/45= 1.133 cm 

Average: 1.547 cm

According to Fibonacci's Beauty Ratio test, Helena C was the most beautiful person I measured. Her measurements were but 0.007 away from the Golden Ratio. Her ratios included: 1.545, 2.045, and 1.244 cm which averaged to 1.611.  I believe the Beauty Ratio is a huge disclaimer because the friends I measured besides Helena were beauty to me as well. Yes, Josh and Rodolfo, too!  However, it did show how proportional parts of our body can be, and that is what makes it stand out to others.  True beauty comes from within; some show their beauty more than others. But as I've said before in my haiku, we are all ugly.

Fibonacci Haiku: We Are All Ugly

Fibonacci

1.618

Golden ratio

Add current previous

Snails are prettier than me

Thanks to Mr. Fib we are all ugly

http://www.the-edison-lightbulb.com/wp-content/uploads/2011/03/snails.jpg

SP#5: Unit J Concept 6 - Partial Fraction Decomposition with Repeated Factors

When decomposing these problems, make sure you count up the powers. If there is an (x-2)^2, make sure you give one factor and (x-2) denominator then the one next to it should have an (x-2)^2 denominator. Also, When you check your answer on a calculator, it should be in Row-Echelon Form. The numerators of the decomposed answer comes directly from what the calculator reads.

SP#4: Unit J Concept 5 - Partial Fraction Decomposition with Distinct Factors

Be sure to combine your like terms correctly. Don't forget the A, B, or C in front of each variable. Also, make sure you distribute the common denominator to the top as well. Without it, your like terms will be completely wrong.

SV#5 Unit J Concept 3-4 - Solving for Matrices

Click HERE to watch my video.

Solving for matrices can be super tricky! Just make sure not to confuse your z's with a 2. That tends to throw many people off. Also, make sure your elementary row operations are correct. This is the easiest part of solving for matrices, but one little mistake will ruin your entire answer.

WPP #6: Unit I Concept 3-5 - Compound Interest & Investment Application Problems

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Missing last step

SV#4: Unit I Concept 2 - Graphing Logarithmic Functions and Identifying Key Parts

To watch my video, click HERE.

In this video, you should be aware of the order that I solved my key parts in.  I skipped key points because I felt like it would be more relevant once I start graphing the equation.  Also, make sure that you plug in the zeros into the correct number for finding x and y intercepts.  Remember that finding x-intercepts require you to plug in zero to the variable "y." For y-intercepts, you plug the zero into the variable "x."

P.S. I apologize for sounding like a dying cat. I had to pause the video a few times to clear my throat.  Sorry if the abrupt changes in volumes and tones scared you.

SP#3: Unit I Concept 1 - Graphing Exponential Functions and Identifying Key Parts

Be sure to carefully plug the graph into the calculator to find your key points. Also, be sure that you write your range correctly. Negative infinity always goes before your asymptote.

SV#3: Unit H Concept 7 - Finding Logs Given Approximations

To watch my video, click HERE.

In order to fully understand this concept, you need to look out for exponents in a log.  If the number after your base has an exponent attached, you need to bring it to the front of the "log."  Also, you need to know how to expand your log accurately. The numbers from your numerator will be positive, and the numbers from your denominator will be negative. 

SV#2: Unit G Concepts 1-7 - Finding Key Parts and Graphing Rational Functions

To watch my video, click HERE.

This video goes over Unit G Concepts 1-7, which is finding all parts of a rational function. My function is f(x)= (x^3-x^2-20x)/(x^2-3x-10). This is a slant asymptote.  You will also need to find the vertical asymptote, holes, domain (with interval notation), and y-intercept. After doing so, graph it!

You may want to look out for what you plug your zeroes into (Yes, I messed up on the x-intercepts, but I fixed it!) It may be confusing knowing whether you plug into the x or y. Just remember Mrs. Kirch's chants! Also, make sure you trace on your calculator correctly. It's an approximation, but you still want your graph to look correct.

WPP#3: Unit E Concept 2 - Path of Pom Pom

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SP#1: Unit E Concept 1 - Identifying All Parts of Quadratics and Graphing Them

This is a quadratic function that we will change into a parent function then graph. After finding the parent function (shown in the 2nd picture), it will help us find our vertex, x-intercept, axis, and x-intercept(s). The problem is color coded to show you were the numbers came from in the problem.

The viewer needs to remember to use (b/2)^2 when completing the square in order to find the x-intercepts. It is a crucial part of the problem that needs to be added to both sides of the equal sign.  When doing the problem, the viewer needs to plug the point into their graphing calculator in order to find their approximated points. They need to trace their left and right bound before the calculator guesses.

SV#1: Unit F Concept 10 - Finding the Zeroes for a given 4th or 5th Degree Polynomial

This concept is about finding the zeroes and factoring for a 4th or 5th degree polynomial.  My problem is f(x)=-35x^4+93x^3-42x^2-15x-1.  Because it is a fourth degree polynomial, we know it will have four zeroes.  This video explains each step needed to find all the zeroes.

Something you should remember when doing this video is to follow all the steps.  Make sure you correctly use the Descartes Rule of Signs to help check your answers to see if you have found the right number of positive and negative zeroes.  If needed, make sure you do use the quadratic formula.  Radicals can be tricky, so make sure all your signs are correct.

WPP#4: Unit E Concept 3 - Maximizing Area

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SP#2: Unit E Concept 7 - Graphing Polynomials

The problem is a polynomial in standard form. With the polynomial you can find it's end behavior, x-intercepts, multiplicities, and y-intercept. You can determine the shape of the graph after finding these and their zeroes.

The viewer must know how to factor the polynomial or their zeroes will not be correct. Also, know which way the arrows go when they approach positive and negative infinity. Make sure to approach each point correctly based off of its multiplicity (1M= through, 2M=bounce, 3M=curve).

WPP#2: Unit A Concept 7 - Profit, Revenue, Cost

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WPP#1: Unit A Concept 6 - Writing and Solving Linear Models

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