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Home Question Bank Math Archive 2024 December 12

Math Questions from Dec 12,2024

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

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Tom wants to clean his second story windows and plans to buy a ladder that will reach at least 20 feet high. If he leans the ladder against the house so that the base of the ladder makes a 59 degree angle with the ground, how long of a ladder should he buy? Round to a whole number as necessary. The ladder length is \( \square \) feet. (Round to a whole number as needed.) Or Fandon Amdadi Mochanlcal Englneering (Total 15 Mark) Tests on high voltage insulators manufactured by a company indicated that their breakdown voltages were normally distributed with a mean of 192 kV . A sample of size 48 insulators is taken at random and their breakdown voltage was found to be 189 kV with the standard deviation of 48 kV . Test at \( 10 \% \) if the breakdown voltage is still 192 kV . Complete the steps below for this hypothesis test. step 1-Determine the null and altenrnative Hypotheses. Which expression is equivalent to \( \sqrt{10^{3}} \) ? \( 10^{\frac{2}{3}}-10^{\frac{3}{2}} \) \( 10^{\frac{1}{3}}-10^{6} \) Which expression is equivalent to \( \sqrt[3]{8 x^{2}} ? \) \( \left.8 x^{\frac{2}{3}}+2\right)^{\frac{2}{3}} \) \( (8 x)^{\frac{2}{3}}-\frac{2}{3} \) The population of a southern city follows the exponential law. Use this information to answer parts a and b . (a) If N is the population of the city and t is the time in years, express N as a function of t . \( \mathrm{N}(\mathrm{t})= \) (Type an expression using t as the variable and in terms of \( e \).) (b) If the population doubled in size over 19 months and the current population is 50,000 , what will the population be 3 years from now? The population will be approximately \( \square \) people. (Do not round until the final answer. Then round to the nearest whole number as needed.) Which expression is equivalent to \( \sqrt{9 z^{3}} \) ? \( 3 z^{\frac{2}{3}} \frac{3 z^{3}}{2} \) \( 3 z^{3}-\frac{3}{2} \) The one-to-one functions \( g \) and \( h \) are defined as follows. \[ \begin{array}{l}g=\{(-6,9),(0,-4),(1,-8),(9,1)\} \\ h(x)=\frac{x-9}{7} \\ \text { Find the following. } \\ g^{-1}(9)=\square \\ h^{-1}(x)=\square \\ \left(h \circ h^{-1}\right)(-1)=\square\end{array} \] The marginal cost of a product can be thought of as the cost of producing one additional unit of output. For example, if the marginal cost of producing the 50 th product is \( \$ 6.20 \), it cost \( \$ 6.20 \) to increase production from 49 to 50 units of output. Suppose the marginal cost \( C \) (in dollars) to produce \( x \) thousand mp3 players is given by the function \( C(x)=x^{2}-140 x+8800 \). A. How many players should be produced to minimize the marginal cost? B. What is the minimum marginal cost? A. To minimize the marginal cost, \( \square \) thousand mp3 players should be produced. B. The minimum marginal cost is \( \$ \square \). Which expression is equivalent to \( t^{\frac{7}{8}} \) ? \( \sqrt[7]{t^{8}} \frac{\sqrt[7]{t}}{8} \) \( \sqrt[8]{t^{7}} \frac{\sqrt[7]{t}}{\sqrt[8]{t}} \) Question 14 Find all \( x \) - and \( y \)-intercepts. Answers in nondecimal, Change of Base, and round 3 decimals. \( \begin{array}{l}y=7 \sqrt{x-5}-7 \\ \text { Use the editor to format your answer }\end{array} \) Und
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