WPP#10: Unit L Concept 9-14 - Basic Probability, And/Or Events, and Possibility of Union/Events

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WPP#9 Unit L Concept 4-8 - Fundamental Counting Principle, Combination, Permutation

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SP#6: Unit K Concept 10 - Write Repeating Decimal as Rational Number Using Geometric Series

Remember to pay close attention when I'm substituting the numbers into the equation. Don't forget to add five at the end when you're done solving because there was a five in the beginning of the problem.

In the above picture, I found that "a" sub one is 0.25. However, you must convert it to a fraction which would be 25/100. "r' is 1/100 because I took the preceding term and divided it by the first.

This picture is self explanatory, after I found 25/99, I still had to add five. I multiplied five by 99 to find the common denominator and then added to find my final answer.

Fibonacci Beauty Ratio

Measurements:
Chelsea A.:
Foot to Navel: 99 cm
Navel to top of Head: 58 cm
Ratio: 99/58=1.707 cm
Navel to chin: 39 cm
Chin to top of Head: 21 cm
Ratio: 39/21= 1.857 cm
Knee to Navel: 53 cm
Foot to Knee: 46 cm
Ratio: 53/46=1.152
Average: 1.572 cm

Christine N.:
Foot to Navel: 96 cm
Navel to top of Head: 59 cm
Ratio: 96/59=1.627 cm
Navel to Chin: 40 cm
Chin to top of Head: 22 cm
Ratio: 40/22=1.818 cm
Knee to Navel: 51cm
Foot to Knee: 48 cm
Ratio: 51/46=1.109 cm
Average: 1.518 cm

Katie W.:

Foot to Navel: 103 cm

Navel to top of Head: 63 cm

Ratio: 103/63=1.635

Navel to Chin: 44 cm

Chin to top of Head: 22 cm

Ratio: 44/22=2

Knee to Navel: 57 cm

Foot to Knee: 48 cm

Ratio: 57/48=1.188

Average: 1.608 cm

Stephanie V.:

Foot to Navel: 99 cm

Navel to top of Head: 60 cm

Ratio: 99/60=1.65 cm

Navel to Chin: 44 cm

Chin to top of Head: 22 cm

Ratio: 44/22=2 cm

Knee to Navel: 53 cm

Foot to Knee: 44 cm

Ratio: 53/44=1.205 cm

Average: 1.618 cm

Leslie N.:

Foot to Navel: 96 cm

Navel to top of Head: 63 cm

Ratio: 96/63=1.524 cm

Navel to Chin: 45 cm

Chin to top of Head: 20 cm

Ratio:45/20=2.25 cm

Knee to Navel: 53 cm

Foot to Knee: 44 cm

Ratio: 53/44=1.178 cm

Average: 1.651 cm

Based on the Beauty Ratio, Stephanie is the most beautiful because her ratio was 1.618. This also happens to be the exact number of the "Golden Ratio". I believe that a number can't decide how how beautiful someone is. Everyone is beautiful differently, whether it's their personality or intellect. In my opinion, the Beauty Ratio is valid in proving how proportionate a person is but it's not valid in proving how beautiful a person is.

Fibonacci Haiku: I Believe

Christmas

Santa

Doesn't exist

Ruined my childhood

No more presents from Santa

At least the tooth fairy is still real

http://www.celebuzz.com/photos/top-10-cutest-christmas-animals/sour-puss-2/

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

Remember to pay close attention when adding all the like terms and remember to show all your work because it is very easy to make mistakes, especially when you have four variables.

Step 1: You first find a common denominator and multiply it to the four varaibles. Once you've done that you add up all the like terms and separate them into the common terms. Then, you can start canceling out the like terms and the results will be the system.

Step 2: Next, you take the first and second equations and add them together. Then, you can use the elimination method in the third and fourth equation, in the picture above, I eliminated D. Once you have the two equations, you use elimination on them as well and I eliminated C.

Step 3: This picture shows what I did to solve for the four variables. The picture is pretty much self-explanatory. I just solved for A first and then used the substitution method to find the other equations.

This will be your final answer in the end.

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

Be sure to pay close attention in distributing the numerator and be very careful when plugging in the numbers into the calculator. Also, remember to use the rref feature and check if the answers are correct.

Part 1: First, you would have to find the common denominator. In this case it's (x+4)(x-2)(x+1). Then, you distribute them to the numerator but remember to foil it out first. Once you have completed this step, you add up all the like terms.

Part 2: Now you have to replace the numerator with letter values. Then, you multiply by the common denominator again. This time, instead of distributing a number, you'll be distributing a letter. Next, you set the distributed product equal to the original and add up any like terms (like terms highlighted in above picture). After, you've found the like terms, you can start canceling out and the end product will be the system (as shown above).

Part 3 : The last step is to plug in the system into the calculator. Then you use the rref feature to find your answer. Once you have found what A,B, and C equals, plug them back into the original 3 fractions.