Subjects algebra

Exponents And Absence Table

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Exponents And Absence Table


1. Evaluate $2^{-4}$. Recall that $a^{-n} = \frac{1}{a^n}$. So, $2^{-4} = \frac{1}{2^4}$. Calculate $2^4 = 2 \times 2 \times 2 \times 2 = 16$. Thus, $2^{-4} = \frac{1}{16}$. 2. Create a two-way table for absences of Classes A and B for three terms: Autumn, Spring, Summer. Given for Class A: - Autumn term absences = 90 - Spring term absences = 120 - Summer term absences = 40 Class B absences are calculated as follows: - Autumn: 3/10 fewer than Class A means Class B has $90 \times (1 - \frac{3}{10}) = 90 \times 0.7 = 63$ absences. - Spring: 5% more than Class A means Class B has $120 \times (1 + 0.05) = 120 \times 1.05 = 126$ absences. - Summer: 7 more absences than Class A means Class B has $40 + 7 = 47$ absences. 3. Complete the two-way table: | Term | Class A Absences | Class B Absences | |--------|------------------|------------------| | Autumn | 90 | 63 | | Spring | 120 | 126 | | Summer | 40 | 47 |