Write the Word or Phrase That Best Completes Each Statement $72 ^ { \circ }$

question 95

Essay

Write the word or phrase that best completes each statement or answers the question.
-Penrose tiles are formed from a rhombus WXYZ with sides of length 1 and interior angles $72 ^ { \circ }$ and $108 ^ { \circ }$ . (Refer to the illustration.) $A$ point $O$ is chosen on the diagonal 1 unit from $Y$ . Line segments $O X$ and $O Z$ are drawn to the o vertices. The two resulting tiles are called a kite (figure $\mathrm { OXYZ }$ ) and a dart (figure $\mathrm { OXWZ }$ ). Find the area of the kit and the dart tile, correct to the nearest $0.01$ .

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Definitions:

Standard Deviation

An indicator of the degree to which values in a dataset spread out or deviate from the average value of the collection.

Mean

The average of a set of numbers, obtained by dividing the sum of the numbers in the set by their quantity.

Cumulative Binomial Probabilities

Cumulative binomial probabilities represent the probability of obtaining a certain number of successes or fewer in a fixed number of independent Bernoulli trials.

Approximate Binomial Distribution

Using a normal distribution to estimate the outcomes of a binomial distribution when the sample size is large and the probability of success is neither very small nor very large.