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Math Questions from Jan 20,2025

Browse the Math Q&A Archive for Jan 20,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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1) \( \{3+[4-(5+2)-9]-2(6)\}= \) The graph of \( f(x)=(x-3)^{2}+5 \) has a shift of 5 units in which direction? Question Let \( f \) be the function defined by \( f(x)=2 \ln (x) \). If four subintervals of equal length are used, what is the value of the trapezoidal sum approximation for \( \int_{1}^{3} 2 \ln (x) \) dx? Round to the neares thousandth if necessary. Answer Attemes Part 1 of 2 Mental Math There are two angles which are supplementary. The measure of the first angle is \( 40^{\circ} \). The second angle is two times the value of \( x \). What is the value of \( x \) ? What is the measure of the second angle? Use pencil and paper. Is it possible for the measures of supplementary angles to be equal? Explain. The value of \( x \) is \( \square \) \( \left[\begin{array}{l}{[x, 7} \\ \text {. Solve using substitution. }\end{array}\right. \) \[ \begin{array}{l} -4 x+y=16 \\ -2 x+y=6 \end{array} \] \( \square \) , \( \square \) ) Submit When a particular type of thumbtack is dropped, it will land point up \( (\perp) \) or point down ( \( < \) ). This experiment was repeated 100 times with the following results: point up: 50 times; point down: 50 times. a. What is the experimental probability that a particular type of thumbtack will land point up? b. What is the experimental probability that a particular type of thumbtack will land point down? c. If the experiment was tried another 100 times would the same results occur? Why? d. Is it expected that nearly the same results occur on a second trial? Why? \[ (-1,3) ;(5,-5) \] What is the slope of the line containing the points \( (-1,3) \) and \( (5,-5) \) ? Seleot the correct choice below and fill in any answer boxes within your choice. A. The slope is \( \square \), Graph the line. B. The slope is undefined. B. The line containing the given points. 7.5 If the total cholesterol values for a certain population are approximately normally distributed with a mean of \( 200 \mathrm{mg} / 100 \mathrm{ml} \) and a standard deviation of \( 20 \mathrm{mg} / 100 \mathrm{ml} \), find the probability that an individual picked at random from this population will have a cholesterol value: \( \begin{array}{ll}\text { (a) Between } 180 \mathrm{and} 200 \mathrm{mg} / 100 \mathrm{ml} & \text { (b) Greater than } 225 \mathrm{mg} / 100 \mathrm{ml} \\ \text { (c) Less than } 150 \mathrm{mg} / 100 \mathrm{ml} & \text { (d) Between } 190 \text { and } 210 \mathrm{mg} / 100 \mathrm{ml}\end{array} \) Graph each of the following functions. \( \begin{array}{ll}\text { a. } n(x)=-4(0.5)^{x}-3 & \text { b. } m(x)=2 \log _{3}(x-2)+1\end{array} \) \[ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}, \quad x_{1} \neq x_{2} \] Let the first point be \( P=(-1,1) \) and the second point be \( Q=(4,-1) \). Substitute values for the numerator. \( m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{\square-(\square)}{x_{2}-x_{1}} \)
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