Numerade

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5. (06.05 MC) $ \int_{-2}^{3} [2f(x) + 2]dx = 18 $ and $ \int_{1}^{2} f(x)dx = -8 $, then $ \int_{1}^{3} f(x)dx $ is equal to which of the following? (10 points)

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3) Assume the artic nation of Jasonia is currently engaged in free trade for bananas with the rest of the world, buying or selling bananas at the world price of $2 per kilogram, while the autarky price in Jasonia would be $5 per kilogram. In order to protect workers in the Jasonian banana industry from the unfair competition of countries that can grow bananas outside (cheaters), a tariff of $2 per kilogram is levied on international trade in bananas. a. Who will gain from the banana tariff? b. Show in a graph how much this group will gain from the tariff. c. Who will lose from the banana tariff? d. Show these loses in a graph. e. Show the revenue that the Jasonian government will collect from the banana tariff in a graph. f. How much will this policy hurt the citizens of Jasonia? Show it in a graph.

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A naval radar system operates at a wavelength of 1.4 cm, transmitted from a circular antenna of diameter d = 2.4 m. At a distance of 6.1 km, what is the smallest distance between two small boats such that the radar system can resolve them as two separate objects? Be careful with units: recall that 1 cm = $10^{-2}$ m and 1 km = $10^3$ m. Distance of separation = m If the separation between two small boats is only 16 m, what is the maximum distance from the antenna that they can be such that the antenna can resolve them as two separate objects? Distance from antenna = km

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Consider the following. P?(3, 9), P?(4, 7), P?(5, 5), P?(7, 4), P?(9, 3) (a) Find an equation of the least-squares line for the data. (Round your numerical values to two decimal places. Assume y is a function of x.) y = (b) Draw a scatter diagram for the data and graph the least-squares line.

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A double-threaded worm with a lead angle of 20 degrees and axial pitch of 12.7 mm/tooth drives a worm gear with a velocity reduction of 16 to 1. a) Determine the following for the worm gear: i) The pitch radius. ii) The number of teeth. iii) The helix angle. b) Determine the pitch radius of the worm and compute the center distance.

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1- What is the value of the integral $\int \frac{x}{\sqrt{x} + 1} dx$. a) $-\frac{1}{2}ln(\sqrt{x} + x) + C$ b) $2ln(\sqrt{x} + 1) + C$ c) $-2ln(x^2 + \sqrt{x} + 1) + C$ d) $2(\frac{(x+1)^{\frac{3}{2}}}{3} - \sqrt{x+1}) + C$ e) $ln(\sqrt{x}+1)] + C$

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Q13. To inform their promotional activities, a clothes retailer would like to know if there is any difference between the average amount a customer spends on a Friday and on a Saturday. The retailer randomly selects five Fridays and five Saturdays over a three month period and records the average spend on each occasion. Average spend on a Average spend on a Friday (£) Saturday (£) 52.11 44.90 81.96 53.53 93.46 68.16 69.44 96.72 52.96 87.21 Perform a suitable statistical test to answer the clothes retailer's question to 5% sig- nificance, stating your assumptions. Comment on any potential issues in how the experiment has been set up that might affect the validity of the statistical test. (5 marks) Q13. To inform their promotional activitics,a clothes retailer would like to know if there is any difference between the average amount a customer spends on a Friday and on a Saturday The retailer randomly selects five Fridays and five Saturdays over a three month period and records the average spend on each occasion. Average spend on a Average spend on a Friday Saturday() 52.11 68.16 44.90 69.44 81.96 96.72 53.53 52.96 93.46 87.21 Perform a suitable statistical test to answer the clothes retailer's question to 5% sig nificance, stating your assumptions. Comment on any potential issues in how the experiment has been set up that might affect the validity of the statistical test. 5marks)

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Name: 9. Work one of the following problems. You may work the second problem for extra credit if you have time. Problem 1: (a) Convert the decimal number 201 to an octal number. (b) Convert the hexadecimal numeral C1E$_{16}$ to a binary numeral. (b) Trace this algorithm when n = 19. (Trace = "complete a table that identifies each value of each variable as the algorithm is executed, make sure you record the output of the algorithm) procedure base 2 expansion (n: positive integer) q = n k = 0 while q \neq 0 a$_k$ = q mod 2 q = q div 2 k = k + 1 return ($a_k$, ..., $a_1$, $a_0$) Problem 2: Use induction to prove that if n is an integer \geq 2 and G is a tree with n vertices then G has n-1 edges.

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Fixed Business Investment. In this problem, we will derive the function for fixed business investment and analyze its implications. a.) To build the investment function, we consider two different types of firms: production firms and rental firms. How do the two firms differ? b.) The cost of capital for a rental firm can be written in equation form as: Cost of Capital = iP + P. What do each of the three terms (iP, P, and P) represent, and how do each of them affect the cost of capital? In other words, how does a change in iP affect a rental firm's ability to invest in capital? c.) Recall that the nominal interest rate is equal to the real interest rate plus inflation (i = r + Ï€). Use substitution to simplify the equation such that the cost of capital is written in terms of its price, the real interest rate, and the depreciation rate. d.) Firm investment is a function of the profit rate of investing capital, which is equal to real rental revenue minus the real cost of capital. What is the real rental rate of capital equal to? Use this and your answer to part c.) to write the profit rate equation. e.) Total fixed business investment is equal to the sum of this function of the profit rate and what other factor? Why?

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SQL> Select PERCENT_RANK() OVER (ORDER BY Price) as PerentageRank, ArtID, price as p from Arts; PERENTAGERANK ARTID P ----- ? A0111 174.69 .090909091 A0104 174.99 .181818182 A0103 179.99 .272727273 A0112 189.39 .363636364 A0102 189.59 .454545455 A0106 219.99 .545454545 A0108 274.89 .636363636 A0113 289.49 .727272727 A0109 289.99 .727272727 A0107 289.99 .909090909 A0105 314.99 PERENTAGERANK ARTID 1 A0110 12 rows selected. P 316.99

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cindy c.