Numerade

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Question 2. (8 points) Determine whether the statement is true or false. (1) $ f(2 x+1) $ is obtained from $ f $ by compressing horizontally by a factor of 2 , then shifting to the left by 1 unit. (True, false) (2) Let $ f(x)=e^{3-x} $ then $ f^{-1}(x)=3-\ln (x) $. (Irue. False) (3) $ f(2 x)=\cot ^{-1}\left(\frac{1}{1+x}\right) $, then $ f^{\prime}(0)=-\frac{1}{4} $. (True, False) (4) Let $ g(x)=\left\{\begin{array}{ll}c+x^{2}+e^{x} & \text { if } x \geq 0 \\ \frac{\sin 2 x}{x} & \text { if } x<0\end{array}\right. $. If $ g(x) $ is continuous at $ x=0 $, then $ c=1 $. (Irue False)

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E. Suppose that the number of slits is doubled and the distance between adjacent slits is halved. (See below.) The new slits are labeled 1a-10a. (The diagram uses the same scale as the preceding one.) Would the first minimum in this case be located at the same angle $\theta$ as in part B? Explain. $sin\theta \lambda = \frac{\lambda}{d}$ F. If we continued to add slits in this way (i.e., doubling the number of slits, but halving the distance between adjacent slits), would the angle to the first minimum change? Explain. When the number of slits becomes very large as shown below, how can the slits be paired to determine the angle to the first minimum?

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Number in order the structures that protect the brain from supetficial to deep

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Advocates of multicultural education argue that A) It emphasizes academic success for the best students. B) It is fundamental to the democratic ideas of the United States. C) It is easy to correct inaccuracies and omissions in the curriculum. D) Mono-cultural schools can be effective in a multicultural society.

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The activities that make up a project, their duration and priorities of the activities are given below. Activity X A B C D TO F G H Z Priority - X B B A, B C ALSO D, F G, H Duration (days) 2 3 5 4 8 6 7 10 11 3 According to the above; "Project network should be drawn using artificial activity. "The earliest completion time of the project day. "A maximum of one day delay can be made in activity D in order not to affect the earliest completion time of the project. "In order not to affect the earliest completion time of the project, the maximum A daily delay may be made. "Write the number of critical activities that make up the critical path.

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The following data represent the cost of a 75" Sunny very smart TV 2695 3714 2503 2987 3458 3215 4196 4490 4236 3750 3385 What class width would you use to construct the frequency distribution for the TV cost? Note: use the rules and convention discussed in lectures (from textbook) to construct the frequency distribution. 100 500 250 200

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Which of the following ions would prefer to undergo nucleophilic substitution rather than elimination? t-butoxide ion methoxide ion chloride ion None of these ions prefer substitution over elimination

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(a) The position of a particle at time $t$ is $\vec{r}(t) = (2\ln(t+1))\vec{i} + t^2\vec{j} + (t^2/2)\vec{j}$. Find the particle's velocity and acceleration at time $t = 1$. (b) Find the length of the curve $\vec{r}(t) = \cos^3(t)\vec{i} + \sin^3(t)\vec{j}$, where $0 \le t \le \pi/2$. (c) Find $\lim_{(x,y)\to(2,-2)} \frac{x+y}{x^2 - y^2}$ if it exists. Otherwise explain.

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2) [30 points] Considering typical characteristics and unit cost of sand casting, die casting and investment casting, which process do you prefer to produce the following components? Type your answers in the Table and explain why you selected that process briefly. A. 125 magnesium components with very high precise dimension B. 150,000 aluminum thin-wall section components C. 100,000 aluminum components with very complex shape D. 100 titanium rocket components E. 5000 cast iron components with very good surface finish Component Which Process? Why? A B C D E

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Exercise 6-11 a-c Suppose this information is available for PepsiCo, Inc. for 2020, 2021, and 2022. 2021 2022 $2,100 $2,400 $2,500 (in millions) 2020 Beginning inventory Ending inventory 2,400 2,500 2,700 Cost of goods sold 19,350 20,825 20,280 Sales revenue 41,000 42,500 42,430 Calculate the inventory turnover for 2020, 2021, and 2022. (Round inventory turnover to 1 decimal place, e.g. 5.1.) Inventory turnover 2020 times 2021 times 2022 times Calculate the days in inventory for 2020, 2021, and 2022. (Round days in inventory to 1 decimal place, e.g. 5.1.) Days in inventory 2020 days 2021 days 2022 days Calculate the gross profit rate for 2020, 2021, and 2022. (Round gross profit rate to 1 decimal place, e.g. 5.1%). 2020 Gross profit rate % 2021 2022 % % Click if you would like to Show Work for this question: Open Show Work

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anthony k.