Question 4

An interesting topic in fluid mechanics is Bernoulli's equation, which relates pressures and velocities of a fluid with the density of rho at different heights, eq. 13.12. It has applications in the airspace. It can be used to measure flow speed in a pipe with a device named the Venturi meter (see figure 13.34). If the cross sections are 21 cm2 and 13 cm2, and the height difference resulted from the pressure difference is 0.2 m, calculate the speed of the flow in the pipe, v1 . Give your answer to one decimal point. Your Answer:Question 4 options:

Answer units

A company makes TV advertisements to promote its products. Based on the survey results it is known: The chance of someone buying the product is 0.2, the chance someone sees the ad is 0.4, and the chance of someone buying the product and seeing the ad is 0.12.
a. what is the chance someone does not buy the product and see the ad b. what is the chances of someone buying a product if it is known he saw an ad
c. what is the chance for someone to buy the product if it is known he did not see the ad
d. Is the occurrence of a product purchase independent of the incident seeing the ad

Answer using R Studio

1. Here we consider the amount of data needed to perform hypothesis testing.
   1. Suppose we are testing a coin using observations of tosses. We wish to test H₀: p = 0.5 against an alternative of H_A : p = 0.6 (in this question use one-sided tests only). How many tosses are needed to guarantee a size Æ∑ 0.05 and Ø∑ 0.2?
   2. Now generalize to consider H_A : p = 0.5+delta. Choose sensible values for delta and quantify the number of observations needed as a function of delta

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 11.7 fluid ounces and a standard deviation of 0.2 fluid ounce. A drink is randomly selected.

(a) Find the probability that the drink is less than 11.6 fluid ounces.

(b) Find the probability that the drink is between 11.5 and 11.6 fluid ounces.

(c) Find the probability that the drink is more than 12 fluid ounces. Can this be considered an unusual event? Explain your reasoning.

Is a drink containing more than 12 fluid ounces an unusual event?

A stock's returns have the following distribution: Demand for the Company's Products Probability of This Demand Occurring Rate of Return If This Demand Occurs Weak 0.2 (22%) Below average 0.1 (7) Average 0.5 15 Above average 0.1 40 Strong 0.1 68 Assume the risk-free rate is 3%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places. Stock's expected return: Standard deviation: Coefficient of variation: Sharpe ratio:

1. You are shown the following data. If the correlation coefficient between the combined portfolio of A+B and C is 0.2, what would happen to the overall volatility of the new portfolio if we invested 50% in A+B and the remaining 50% in C? You could potentially avoid computations.

1. Volatility will lie somewhere between 32% and 40%.
2. Volatility will lie somewhere between 27% and 32%.
3. Volatility will be below 27%.
4. Volatility will be above 40%.
5. Volatility will become zero.

Using Gaussian dispersion equations, the stability class, and dispersion coefficient data for a source emitting SO2 at a rate of 50 g/sec on a very sunny summer day with a wind speed at anemometer height of 2.9 m/sec, and effective stack height of 30 m at temperature = 293K, determine the stability class and dispersion coefficients for receptor distances of 200, 500, 800 m and 1000 m. Calculate and draw the ground level concentrations in ppbv as a function of distance (T=20 Celsius and P =1atm). The wind exponential coefficient = 0.2. ANSWER: Class B

(C++) Follow the template given to calculate and print the monthly salary of an employee. We assume the employee works for 50 weeks during the year with an hourly rate of $25. Your program should ask the user the workHoursPerWeek. If it's over 40, then the excess hours (i.e., workHoursPerWeek over 40) are paid with 20% overtime rate. Note: just print out the monthly salary.

Example: If I work for 45 hours with a rate of $30/hr, then my weekly pay is 40x30+(45-40)x(1+0.2)x30=1200+180=1380.

Suppose that the production function is given by Y=K^(1/2)L^(1/2)

a. Derive the steady state levels of capital per worker and output per worker in terms of the saving rate, s, and the depreciation rate, δ.

b. Suppose δ = 0.05 and s = 0.2. Find out the steady state output per worker.

c. Suppose δ = 0.05 but s increases to 0.5. Find out the steady state output per worker and compare your result with your answer in part b. Explain the intuition behind your results.