answer:In the United States, keys bearing the "DO NOT DUPLICATE" stamp are generally not legally protected from being copied. The Associated Locksmiths of America (ALA) suggests that these keys can be duplicated unless they are part of a patented/restricted key control system, a master-key system, or if the technician suspects wrongful intent. Many locksmiths confirm that the "DO NOT DUPLICATE" message is not legally binding and that such keys are often duplicated on the honor system. However, there are some exceptions in specific jurisdictions. For example, in North Dakota, it is illegal to duplicate a key with the "DO NOT DUPLICATE" marking (ND Code 12.1-23-08.4). In Nebraska, while the "DO NOT DUPLICATE" label is mentioned, it is only an offense if the key is a master key, and it is not unlawful to reproduce other types of keys marked with the same words (Nebraska Revised Statute 28-1316). Therefore, while the "DO NOT DUPLICATE" stamp is not a universal legal restriction, there may be local laws that dictate otherwise. It is important to be aware of these variations in different states or countries.

answer:** f(-8) = sin left(frac{9}{2}-2(-8)right) = sin left(frac{9}{2}+16right) = sin left(frac{41}{2}right) approx 0.997. **Explanation:** To evaluate the function f(x)=sin left(frac{9}{2}-2xright) at the point x=-8, we simply need to substitute x=-8 into the function and evaluate the result. f(-8) = sin left(frac{9}{2}-2(-8)right) First, we simplify the expression inside the parentheses: f(-8) = sin left(frac{9}{2}+16right) Next, we add the fractions in the parentheses: f(-8) = sin left(frac{41}{2}right) Finally, we use a calculator to evaluate the sine of frac{41}{2}: f(-8) = sin left(frac{41}{2}right) approx 0.997 Therefore, the value of the function f(x) at the point x=-8 is approximately 0.997.

answer:To understand the fluctuation in profit, let's analyze the profit for each year (2014, 2015, and 2016) using both absorption costing and variable costing methods: **Absorption Costing:** In absorption costing, both fixed and variable costs are allocated to the units produced. | Year | Units sold | Cost of Goods Sold (COGS) | Gross Profit | Operating Income | | --- | --- | --- | --- | --- | | 2014 | 5,000 | 425,000 | 700,000 | 695,000 | | 2015 | 5,000 | 416,667 | 708,333 | 703,333 | | 2016 | 5,000 | 433,333 | 691,667 | 686,667 | The profit fluctuates due to changes in inventory levels, which impact the COGS. When production exceeds sales (2015), the excess inventory absorbs some fixed costs, reducing COGS and increasing profit. Conversely, when production is lower than sales (2016), the inventory available to absorb fixed costs is less, increasing COGS and reducing profit. **Variable Costing:** In variable costing, only variable costs are included in COGS, while fixed costs are treated as operating expenses. | Year | Units sold | Cost of Goods Sold (COGS) | Contribution Margin | Operating Income | | --- | --- | --- | --- | --- | | 2014 | 5,000 | 375,000 | 750,000 | 695,000 | | 2015 | 5,000 | 375,000 | 750,000 | 695,000 | | 2016 | 5,000 | 375,000 | 750,000 | 695,000 | Under variable costing, profit remains consistent since fixed production costs are treated as period costs, not tied to inventory fluctuations. This highlights that the profit fluctuations in absorption costing are due to the timing of recognizing fixed production costs, not changes in operations or sales. In summary, the profit fluctuates in absorption costing because a portion of fixed production costs is deferred or recognized based on changes in inventory levels, while in variable costing, profit remains steady as fixed costs are treated as an expense in the period they incur.

answer:The matrix product (AB) is computed as follows: AB = left( begin{array}{cccc} 0 & -2 & 2 & 0 3 & 0 & -2 & 0 0 & -1 & -1 & -2 0 & 0 & -1 & 2 end{array} right) left( begin{array}{cc} 1 & 1 -2 & 1 -2 & 0 2 & -2 end{array} right) = left( begin{array}{cc} 0(-2) + 2(-2) + 0(2) + 0(2) & 0(1) - 2(1) + 2(0) + 0(-2) 3(1) + 0(-2) + (-2)(-2) + 0(2) & 3(1) + 0(1) + (-2)(0) + 0(-2) 0(1) - 1(-2) + (-1)(-2) + (-2)(2) & 0(1) - 1(1) + (-1)(0) + (-2)(-2) 0(1) + 0(-2) + (-1)(-2) + 2(2) & 0(1) + 0(1) + (-1)(0) + 2(-2) end{array} right) = left( begin{array}{cc} 0 - 4 + 0 + 0 & 0 - 2 + 0 + 0 3 + 4 + 4 + 0 & 3 + 0 + 0 + 0 0 + 2 + 2 - 4 & 0 - 1 + 0 + 4 0 + 0 + 2 + 4 & 0 + 0 + 0 - 4 end{array} right) = left( begin{array}{cc} -4 & -2 11 & 3 0 & 3 2 & -4 end{array} right)