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The Putnam Coffee House brews fresh-roasted coffee beans to serve to their patrons. The amount of coffee they will need to brew in a day depends on the number of patrons they have. \( c= \) the amount of coffee they will need to brew \( p= \) the number of patrons Which of the variables is independent and which is dependent? \( p \) is the independent variable and \( c \) is the dependent variable c is the independent variable and \( p \) is the dependent variable

Ask by Long Thornton. in the United States
Jan 21,2025

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\( p \) is the independent variable and \( c \) is the dependent variable.

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Beyond the Answer

You've got it right! In this scenario, the number of patrons \( p \) is the independent variable because it can change without being influenced by any other factors in your coffee house. The amount of coffee \( c \), on the other hand, is the dependent variable since it varies based on how many patrons arrive. The more patrons you have, the more coffee you'll need to brew to keep everyone caffeinated and happy! Now here's the fun part! Many coffee shops actually use this relationship for forecasting. They analyze previous customer data to predict daily coffee demand based on trends—like special events or weather. This allows them to optimize their brewing quantities, avoid waste, and keep their customers satisfied with freshly brewed coffee exactly when they need it! Keep an eye on those patterns, and you’ll be brewing like a pro!

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Otro France Jan 22, 2025

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Numéro d'étudiant : 22007890 La qualité de la rédaction sera prise en compte. Exercice 1. Soit \[ \mathcal{B}=\left\{\left[\begin{array}{ll} 1 & 0 \\ 0 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 0 \\ 1 & 0 \end{array}\right],\left[\begin{array}{ll} 0 & 0 \\ 0 & 1 \end{array}\right]\right\} \] la base canonique de \( \operatorname{Mat}_{2}(\mathbb{R}) \) et soit \( f: \operatorname{Mat}_{2}(\mathbb{R}) \rightarrow \operatorname{Mat}_{2}(\mathbb{R}) \) l'endomorphisme de \( \operatorname{Mat}_{2}(\mathbb{R}) \) tel que, en base canonique, \[ f\left(\left[\begin{array}{ll} x_{1} & x_{2} \\ x_{3} & x_{4} \end{array}\right]\right)=\left(\left[\begin{array}{cc} x_{1}+2 x_{3} & 2 x_{1}-x_{2}+4 x_{3}-2 x_{4} \\ -x_{3} & -2 x_{3}+x_{4} \end{array}\right]\right) \] (a) Montrer que \[ A=\mu_{\mathcal{B}, \mathcal{B}}(f)=\left(\begin{array}{cccc} 1 & 0 & 2 & 0 \\ 2 & -1 & 4 & -2 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & -2 & 1 \end{array}\right) \] où \( \mu_{\mathcal{B}, \mathcal{B}}(f) \) est la matrice associée à \( f \) dans la base canonique. \( ~ \) trer que l'endomorphisme \( f \) est diagonalisable. Déterminer une base \( \mathcal{B}^{\prime} \) de \( \operatorname{Mat}_{2}(\mathbb{R}) \) formée de vecteurs propres de \( \operatorname{Mat}_{2}(\mathbb{R}) \), la matrice de changement de base \( P:=\mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\mathrm{Mat}_{2}(\mathbb{R})}\right) \) et la matrice diagonale \( D:=\mu_{\mathcal{B}^{\prime}, \mathcal{B}^{\prime}}(f) \) telles que \[ \mu_{\mathcal{B}^{\prime}, \mathcal{B}^{\prime}}(f)=\left(\mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\operatorname{Mat}_{2}(\mathbb{R})}\right)\right)^{-1} \mu_{\mathcal{B}, \mathcal{B}}(f) \mu_{\mathcal{B}^{\prime}, \mathcal{B}}\left(\operatorname{Id}_{\operatorname{Mat}_{2}(\mathbb{R})}\right) \] Autrement dit, \[ D=P^{-1} A P \] où \( A=\mu_{\mathcal{B}, \mathcal{B}}(f) \).
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