Numerade

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Calculate the present value of $5 million to be received in 40 years assuming an annual interest rate of 10%.

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Construct the indicated confidence interval for the population mean µ using the t-distribution. Assume the population is normally distributed.\ c = 0.98, \bar{x} = 12.6, s = 0.55, n = 12\ (\boxed{\text{ }}, \boxed{\text{}})\ (Round to one decimal place as needed.)

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If any, in which context is a monopoly justified? And why? · Provide examples of Merger and Cartel cases. Are there countries where Mergers and Monopolies are legal?

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The collection of proteins and polys sides are found outside of the animal cell is referred to as what

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5. Give the state diagrams of DFAs recognizing the following languages over $\Sigma = \{0, 1\}$: $\{w : w \text{ contains exactly two 1's}\}$ $\{w : |w| \ge 5\}$

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Texts: A ball is thrown straight down (vertically) with a speed of 10.0 m/s from the top of a high-rise building. It takes 8.5 s for the ball to fall to the ground. A) How high is the building? B) How long does it take for the ball to reach a speed of 49 m/s? C) What is the speed of the ball just before it reaches the ground?

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Sally who is 39 years of age and is an Australian resident for tax purposes has provided the following receipts for year ending 30 June 2018 to her tax agent: \begin{itemize} \item Income working as an accountant for Optus-$97,000 \item Income working as a barista part-time at Candy Coffee-$8,777 \item Maintenance payments from husband-$32,000 \item Tatts Lottery winnings-$145,000 \item Sold family home. Purchased in 30 September 1997 for $600,000. Sold 30 September 2017-$1,250,000 \item Bank interest-$212 \item Bank charges-$120 \item Carer payment for looking after sick uncle who is aged 57-$8,009 \end{itemize} Your task: Calculate Sally's assessable income.

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SHOW SOLUTION STEPS AND CALCULATIONS. Do NOT give multiple contradictory answers to a problem. Scratch off any incorrect attempts. 6) (45pts) a) Find the Thevenin model between A and B for the circuit below: 4k$\Omega$ 2k$\Omega$ 6V 3k$\Omega$ A 1k$\Omega$ 3mA +5V B b) What is the value of the voltage between A and B if you connect a load RL=5k$\Omega$ between A and B? c) Which load RL would consume the maximum power from the circuit? $\rightarrow$7) (45pts) The power company supplies 100kW to an industrial load. The load draws $|I_{RMS}| = 240Arms$ from the transmission line. The load power factor is 0.7 lagging. The transmission line consumes 5kW. Compute the value of $|V_{RMS}|$ accross the load.

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6. Find the expression for $V_o$ in terms of $V_1$, $V_2$, $V_3$, R, and $R_F$

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PROBLEM 1: Frequency analysis of noisy data (30pts) Include all plots for parts a) -d) in your PDF report a) (10pts) Determine and plot the amplitude spectrum of N=512 data equispaced points sampled of a T=2.56 s long window (starting at t=0) from the time-discretized function y(t)=0.2*cos(2*pi*f1*t)+0.35*sin(2*pi*f2*t)+0.3*sin(2*pi*f3*t). Assume the values f1=20;f2=50;f3=70; NAME YOUR CODE Sinel.m b) (5pts) What happens if you increase the number of points to N=2048 using the same sampling time (i.e. for a longer total duration T)? Why? Include plots supporting your answer in your report. c) (5pts) What happens if you reduce the number of points to N=128 and keep the duration the same T=2.56s. Include plots supporting your answer in your report. d) (15pts) Add simulated white noise (i.e. zero-mean random noise function) n(t) to the data y(t) using the following matlab command n(t)=A*0.5*randn(size(y)). Y_noisy(t)=y(t)+n(t); Determine and plot the amplitude spectrum of Y_noisy(t) for a value of A=1. e) What happened to the amplitude spectrum when A is increasing (e.g. use A=3) or decreasing (use A=1/3)? Include plots supporting your answer in your report. NAME YOUR CODE SineNoise.m

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miguel w.