Updated Chapter 3 Vocabulary Flashcards

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Verified questions

statistics

The geometric mean (GM) is defined as the $n$ th root of the product of $n$ values. The formula is

GM =\sqrt[n]{\left(X_1\right)\left(X_2\right)\left(X_3\right) \cdots\left(X_n\right)}

The geometric mean of 4 and 16 is

GM =\sqrt{(4)(16)}=\sqrt{64}=8

The geometric mean of 1,3 , and 9 is

GM =\sqrt[3]{(1)(3)(9)}=\sqrt[3]{27}=3

The geometric mean is useful in finding the average of percentages, ratios, indexes, or growth rates. For example, if a person receives a $20 \%$ raise after I year of service and a $10 \%$ raise after the second year of service, the average percentage raise per year is not 15 but $14.89 \%$ , as shown.

GM =\sqrt{(1.2)(1.1)} \approx 1.1489

or

GM =\sqrt{(120)(110)} \approx 114.89 \%

His salary is $120 \%$ at the end of the first year and $110 \%$ at the end of the second year. This is equivalent to an average of $14.89 \%$ , since $114.89 \%-100 \%=$ $14.89 \%$ .

This answer can also be shown by assuming that the person makes $\$ 10,000$ to start and receives two raises of $20 \%$ and $10 \%$ . Raise $1=10,000 \cdot 20 \%=\$ 2000$ Raise $2=12,000 \cdot 10 \%=\$ 1200$ His total salary raise is $\$ 3200$ . This total is equivalent to

\begin{aligned} &\$ 10,000 \cdot 14.89 \%=\frac{\$ 1489.00}{\$ 11,489 \cdot 14.89 \%}=\frac{\$ 1710.71}{\$ 3199.71} \approx \$ 3200 \end{aligned}

Determine the geometric mean of each of these.

a. The growth rates of the Living Life Insurance Corporation for the past 3 years were 35,24, and $18 \%$ .

b. A person received these percentage raises in salary over a 4year period: $8,6,4$ , and $5 \%$ .

c. A stock increased each year for 5 years at these percentages: $10,8,12,9$ , and $3 \%$ .

d. The price increases, in percentages, for the cost of food in a specific geographic region for the past 3 years were 1,3, and $5.5 \%$ .

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discrete math

make a truth table for the statement.

(p \vee q) \vee \sim q

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geometry

Draw any

\angle A B C.

Then construct line m through A so hat

m \| \underset{BC}\leftrightarrow

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precalculus

Determine whether the formula determines y as a function of x. If not, explain why not.

x+2y^2

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