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A highway has the following pavement design daily traffic: 300 single axles at 10,000 lb each, 120 single axles at 18,000 lb each, 100 single axles at 23,000 lb each, 100 tandem axles at 32,000 lb each, 30 single axles at 32,000 lb each, and 100 triple axles at 40,000 lb each. A flexible pavement is designed to have 4 inches of sand-mix asphalt wearing surface, 6 inches of soil-cement base, and 7 inches of crushed stone subbase. The pavement has a 10-year design life, a reliability of 85%, an overall standard deviation of 0.30, drainage coefficients of 1.0, an initial PSI of 4.7, and a TSI of 2.5. What is the minimum acceptable soil resilient modulus? (Ans: MR = 9009.8 lb/in2)
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Mapping Parameters to Moments I 2 points possible (graded) Let $ ft( {R}, ft\{N ft( , ^{2} ) \}_{ {R}, >0} )$ be the statistical model of a normal random variable $X$. Let \[ m_{k}( , )= {E} ft[X^{k} ] \] denote the $k$-th moment of $X$. Let $ : {R} (0, ) arrow {R}^{2}$ be defined by $ ( , )= ft(m_{1}( , ), m_{2}( , ) )$. (Since we have two parameters of interest, $ $ and $ $, it makes sense to work with the first two moments. The hope is that the two moments will uniquely determine the paramters of interest $ $ and $ $.) Express $m_{1}( , )$ and $m_{2}( , )$ in terms of $ $ and $ $. \[ {l} m_{1}( , )= \\ m_{2}( , )= \] ? STANDARD NOTATION Submit You have used 0 of 3 attempts Save
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Robust Statistics and the Median 4 points possible (graded) In this problem, you will see how some estimators are more resilient to corruptions or mistakes in the data than others. Such estimators are referred to as robust . Researchers in a lab observe the following data set \[ \{0.5,1.8,-2.3,0.86,0.32\} {. } \] In reality, these numbers are generated from the standard normal distribution $ {N}(0,1)$, but as in most statistical problems, this distribution is unknown to the researchers. Their goal is to estimate the mean of this unknown distribution, and they will try two different statistics for doing so: the sample mean and the median. What is the sample mean $ {X}_{5}$ of the data set? 0.236 What is the median $M_{5}$ of the data set? (For a discrete data set, we define the median to be the middle number when the data set is sorted from smallest to largest.) Suppose now that one of the lab assistants makes a typo, and instead records the data set \[ \{0.5,1.8,-23,0.86,0.32\} {. } \] (Note that the number -2.3 from the sample has been erroneously changed to -23 .)
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drawCirclefunction at position (300, 400) with a radius of 40 and color blue, which is the correct function call? As a reminder, here's the function header fordrawCircle: function drawCircle(radius, color, x, y)" style="display: block; overflow-wrap: break-word; overflow: auto hidden; text-align: start; --d2l-document-direction: ltr;">If we want to draw a circle using our helpful drawCircle function at position (300, 400) with a radius of 40 and color blue, which is the correct function call? As a reminder, here's the function header for drawCircle: function drawCircle(radius, color, x, y)Question 5 options:drawCircle(300, 400, 40, Color.blue); drawCircle(300, 400, Color.blue, 40); drawCircle(40, Color.blue, 300, 400); drawCircle(radius, color, x, y);
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$ {E}_{4.17} ft( {LO}_{3}, 5 )$ (Various Reporting Formats) The following information was taken from the records of Vega SA for the year 2022: income tax applicable to income from continuing operations $ {R} \$ 119,000$, income tax savings applicable to loss on discontinued operations R\$25,500, and unrealized holding gain on non-trading equity securities $ {R} \$ 15,000$, net of $ {tax}$. {|l|r|r|r|} Gain on sale of plant assets & R\$ 95,000 Cash dividends declared & R\$ & 150,000 \\ {l} Loss on discontinued \\ operations & Retained earnings, January 1, & \\ Administrative expenses & 240,000 2022 & 600,000 \\ Rent revenue & 40,000 Selling expenses & 850,000 \\ Loss on impairment of land & 60,000 Sales revenue & 300,000 \\ Ordinary shares outstanding during 2022 were $100,000$. Instructions a. Prepare a comprehensive income statement for 2022 using the one statement approach. b. Prepare a retained earnings statement for 2022 .
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Title ZXY is a family firm, and Jim is currently CEO. The company is quite large, and engages in real... Description ZXY is a family firm, and Jim is currently CEO. The company is quite large, and engages in real estate transactions at many levels. Jim and prior family members in management have always maintained an all equity capital structure; they have been unusually concerned about bankruptcy risk, despite the fact that ZXY has an excellent financial track record. The company currently has $16 {~m}$ shares of outstanding common stock, w/current price of $\$ 46.75$. At this stock price, the current cost of equity is $10.5 \%$. ZXY is currently evaluating a project to develop an extremely large area of land, valued at $\$ 95 {~m}$, with a plan to lease the land to tenant farmers. This model has been highly successful for them in the past, and this land is unusually good for farming. The projection is that the project will provide $\$ 21.2 {~m}$. in annual case flows -in perpetuity -- for the firm. The firm must raise capital to finance the project. You have been assisting in valuing this project, and want to make a case to Jim that the firm should consider using debt. After much analysis, and discussion w/your investment bankers, you can support the following: (1) the firm is a good candidate to go to the debt markets, as it would have the highest bond rating, (b) a target D/E structure in your industry of $30 \%$ debt and $70 \%$ equity makes sense for your firm, as this would allow you to keep the top bond rating, and (3) were you to issue debt you would need to offer a $7 \%$ annual coupon rate on the debt. The firm has a $21 \%$ tax rate. Ignore ST Assets 8 Liabilities. Fill in the values for a simple market value balance sheet, with NO DEBT and before the project is initiated. HINT: The asset value of the firm must equal the equity value {cr|} lticolumn{2}{|c|}{ Pre-Project Market Value Balance Sheet: } \\ & Debt \\ Orginal Assets & Equity \\ & Total Shareholder \\ Total ASSETS & \& Debtholder \\ & Value \\ Find the value of the new project to the firm, i.e., find the NPV. Show your calculation in the cell below. HINT: This is a very simple calculation. NPV: Continue to ignore ST Assets \& Liabilities, other htan new Cash added from equity financing (assume no financing costs, so the firm keeps the entire $\$ 95 {~m}$ ). . Fill in the values for a simple No DEBT balance sheet for the firm, including the value added from the project.
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You are playing Dota2 and are currently in the middle lane, which has $n$ heroes. Each hero has the following attributes: - Position: Given as a 0-indexed integer array. All integers are unique. The index in the array refers to a particular hero, and the value at that index indicates the position. - Health: Given as a 0-indexed integer array. The index in the array refers to a particular hero, and the value at that index indicates the health. - Team: Given a string ( $ {R}$ for radiant, $ {D}$ for Dire). All heroes move simultaneously at the same speed on the lane, each going in its given direction. Radiant moves up, and Dire moves down the middle lane. If two heroes ever meet in the same position, they have a battle. When this happens, the hero with less health is removed from the lane, and the health of the other hero drops by one. If both heroes have the same health, they both get removed. Return an array containing the health of the remaining heroes (in the order they were given in the input), after no further battle can occur. Constraint : - $1 q$ positions.length, healths.length $ q 10^{5}$ - $1 q$ healths $[i]$, positions $[i] q 10^{9}$ Input: positions $=[5,4,3,2,1]$, healths $=[2,17,9,15,10]$, Team $=$ "RRRRR" Output: $[2,17,9,15,10]$ Explanation: No fight occurs in this example since all heroes move in the same direction. So, all the heroes' health is returned in initial order $[2,17,9,15,10]$.
