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Home Question Bank Math Archive 2024 November 12

Math Questions from Nov 12,2024

Browse the Math Q&A Archive for Nov 12,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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0) \( \left(2 x^{2}+4 x-1\right)\left(3 x^{2}-5\right) \) a) \( 168 \div 12= \) 10) \( \lim _{x \rightarrow \infty} \frac{3 x^{3}-2 x^{2}+1}{7 x^{3}+x-2}= \) Sea \( h(x)=\ln (x) \cos (x) \) It is known that \( 65 \% \) of Facebook users are playing the free games (at least one) advertised by Facebook. A) In a random sample of 327 Facebook users, what's the probability that less than 210 of them are playing the free games? (Round \( \hat{p}, \sigma_{\hat{p}} \) and your answer to 4 decimal places.) B) In a random sample of 981 Facebook users, what's the probability that less than 630 of them are playing the free games? (Round \( \widehat{p}, \sigma_{\hat{p}} \) and your answer to 4 decimal places.) **Notes: Round all z-scores to 2 decimal places. 4) \( k(x)=x^{2}+3 x+8 \), find \( k(-1), k(0) \), and \( k(5) \). \( k(-1)=\quad k(0)=\quad k(5)= \) For the quadratic function \( f(x)=2(x-3)^{2}+5 \), what is the focal length \( c^{\prime} \) ? What is the focal point? What is the equation of the directrix? (4) Find the midpoint \( M \) of the interval joining \( A(1,-3) \) and \( B(-5,7) \). Para cada uno de los siguientes ejercicios, halle todos los puntos \( (a, f(a)) \) de la gráfica de la función \( f \) dada, donde la recta tangente a la gráfica en el punto \( (a, f(a)) \) sea paralela a la recta dada: \( \begin{array}{ll}\text { a. } f(x)=x^{2}-2 x+4 & \text { b. } f(x)=2 x \ln (x) \\ \text { Recta: } y-2 x=1 & \text { Recta: } 2 x-y-2=0\end{array} \) Write \( \frac{19}{20} \) as a decimal number.
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