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auditor selects a sample from the file of shipping documents to determine whether invoices were prepared. This test is performed to asse- uthorization and accuracy. ompleteness. ntoff. currence.

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The allowance for doubtful accounts is a contra-account paired with: Multiple Choice 1 points accounts receivable. net income. cash. expenses.

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u= 4x+2y+min(x,y) What's the budget constraint? What's the first order conditions? What's the ordinary demand functions? Some change in price, what's the substitution and income effects? Suppose price change, what income is needed to be indifferent?

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4. Sea la siguiente tabla de eventos: Tiempo Número de Eventos Total de población en Riesgo 6 3 21 7 1 17 10 1 15 13 1 12 16 1 11 22 1 7 23 1 6 Además se sabe que: $\hat{S}(13) = 0.690$ con desviación estandar 0.107. (a) (1 punto) Determine el estimador de Kaplan Meier para t = 16. (b) (5 puntos) Estime $\hat{S}(16)$ y su desviación estandar. (c) (5 puntos) Determine el estimador de Nelson-Aalen, $\hat{H}(t)$ y el estimador de la varianza respectivo para t = 8.

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In the following Lotka-Volterra model for competition: $\frac{dN_1}{dt} = r_1N_1(\frac{K_1 - N_1 - \alpha N_2}{K_1})$ The symbol $\alpha$ represents: Othe carrying capacity of species 1's population. Othe carrying capacity of species 2's population. Othe sum of the densities of species 1's population and species 2's population. Othe per capita impact that species 1's population has upon species 2's population carrying capacity. Othe per capita impact that population 2 has upon species 1's population carrying capacity.

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QUESTION 3 IT Guru Limited (trading as Gurus) is an entity formed by two friends who met while doing B Com information system at the University of the Western Cape. Guru, entered into a contract with a customer to transfer a software licence, perform an installation service and provide unspecified software updates and technical support (online and telephone) for a two-year period. The entity sells the licence, installation service and technical support separately. The installation service includes changing the web screen for each type of user (for example, marketing, inventory management and information technology). The installation service is routinely performed by other entities and does not significantly modify the software. The software remains functional without the updates and the technical support. The accountant of Guru Limited concluded that the promises in the contract are both capable of being distinct and distinct in the context of the contract. Based on this assessment, the accountant correctly identified four performance obligations in the contract for the following goods or services: • The software license. • An installation service. • Software updates; and 200 000 • Technical support. The contract price was set at R1 700 000 payable in two years from the contract date. Guru normally sells these products or services separately at the prices indicated below. Product Price Rand Software licence R500 000 Installation R150 000 Software updates R200 000 Technical support R175 000 The appropriate discount rate was correctly calculated as 10% per annum. Assume any significant financing component was significant. Required (a) Calculate and allocate the transaction price for the contract with the customer. 10 marks

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Question 5 Solve the Separable Differential Equation with the given Initial Value. $\frac{dy}{dx} = \frac{x+1}{e^y}$ $y(0) = 2$ ? $e^y = \frac{x^2}{2} + x + C$ ? $y = 2e^{\frac{x^2}{2}}$ ? $y = 2 + e^{\frac{x^2}{2} + x}$ ? $y = 2 + ln|\frac{x^2}{2} + x + 1|$

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Assume m and n are co-prime positive integers, and x and y any pair of integers. If x ≡ y mod mn, then x ≡ y mod m and x ≡ y mod n

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Q. 14 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 1. ?c(?) -8000? 0 8000? Fig 1 (rad/s) According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal $X_s(j\Omega)$ and $X(e^{j\omega})$. Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency $\Omega_s$? What should be the cutoff of the low pass filter H(j?) to avoid aliasing of the resultant signal? Also plot the Fourier Transforms of the sampled signal $X_s(j\Omega)$, $X(e^{j\omega})$. Label the resulting signals appropriately (both in frequency and amplitude axis).

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Question II (30 points) For the following Binary Search Tree, answer the questions below: 19 31 77 15 27 53 83 14 17 24 59 81 a) Show the tree after deleting the root? (10 Points) b) Show the tree after inserting node 82. (10 Points) c) What is the complexity of Searching for key in the Binary search tree? Explain your answer. (5 Points) d) Perform Pre-order traversal on the tree. Show the sequence of nodes that results. (5 Points)

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james h.