Numerade

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Suppose that 𝑋 is a Normal random variable with mean 𝜇 = 3 and variance 𝜎 2 = 1.5625. a. Compute 𝑃(𝑋 > 5.925). At the very least, show the standardized 𝒙 values (𝒛 values). b. Compute 𝑃(1.40 < 𝑋 ≤ 4.225). At the very least, show the standardized 𝒙 values (𝒛 values). c. Compute the 25 th percentile of 𝑋. d. Determine 𝑥 so that 𝑃(𝑥 < 𝑋 ≤ 1.5) = 0.0939. Show supporting work.

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Please select ALL the TRUE statements related to the information below. Please note that there might be one or more correct statements. For the question to be marked as ‘correct’ you must identify all correct statements. Paraguay produces two goods: fertilisers ( and soy (. Fertilisers are produced using labour ( and capital (, while Soy is produced using land ( and labour ( as inputs. Workers can move freely between the two industries but capital and land can only be used in the production of fertilisers and soy respectively. Paraguay trades both goods internationally with no barriers. Suppose that Paraguay’s capital stock increases due to a large inflow of foreign direct investment. Then: Question 5Answer a. The value of the marginal product of labour in the soy industry falls. b. The marginal product of labour in fertilisers increases. c. Labour will relocate away from soy to the production of fertilisers. d. Paraguay will fully specialise in the production of fertilisers. e. Paraguay’s comparative advantage will shift away from soy to fertilisers.

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A standard (fair, well shusfled) deck of 52 playing cards is cut, the cut card recorded and not returned, and then the deck is again cut and the cut card recorded. Let $ E $ be the event that the first card was a number card (so not ace, King queen, or Jack) and let F be the event that the second card was an even number card (so 2, 4, 6, 8, or 10 ). A. Find (E) B. Find (F) C. Find $ (E $ and $ F) $ D. Find $ (F \mid E) $ E. Are events $ E $ and $ F $ independent or dependent? Are they mutually exclusive?

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2. (5 points) Find as many 2 \times 2 matrices which satisfy $A^2 = I$ where $I$ is the identity matrix.

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Please answer the following questions to the best of your ability: a) What measurement method can you use to directly measure the lifetime of photoexcited charges in a semiconductor? b) Can you determine the mobility of electrons in an n-type semiconductor simply by measuring the conductivity? Prove your answer using equations. 3) What measurement method can you use to directly measure the mobility of charges in a semiconductor?

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A company. has a project available with the following cash flows: Year Cash FloW 0 -$35,270 1 12,660 2 14,740 3 19,870 4 11,180 If the required return for the project is 8.2 percent, what is the project's NPV?

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A composite material consists of long fibers aligned in a viscoelastic matrix. The volume fractions of fiber and matrix are V and Vm respectively. By modeling the fiber as an elastic spring of modulus E and the matrix as a Maxwell's element with modulus Em and viscosity n, find an expression for the composite strain as a function of time when a uniform stress Oc is applied to the composite in the fiber direction. [Hint: this problem requires solving a first-order differential equation]

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Using the Maxwell-Boltzmann speed distribution function, verify Equations 16.21, and 16.22, $v_{rms} = \sqrt{\overline{v^2}} = \sqrt{\frac{3k_BT}{m_0}}$, $v_{avg} = \sqrt{\frac{8k_BT}{\pi m_0}}$, for (a) rms speed and (b) the average speed of the molecules of a gas at a temperature T. The average value of $v^n$ is $\overline{v^n} = \frac{1}{N} \int_0^\infty v^n N_v dv.$

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Let $f(x) = 3\sqrt{x}$ If $g(x)$ is the graph of $f(x)$ shifted down 2 units and right 3 units, write a formula for $g(x)$ g(x)= Enter $\sqrt{x}$ as sqrt(x)

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Design a boost converter with the following specifications: Input voltage = 12 V Output voltage = 48 V Output voltage ripple = +/- 2% Maximum output current = 10 A Inductor current ripple = 5% Switching frequency = 100 kHz Duty Cycle = 0.75 a) Estimate the ripple current in the output capacitor and calculate the power losses, assuming a rise time of 100 ns, a fall time of 100 ns, and Rdson = 10 mÎ©, and a diode voltage drop of 0.7 V. b) Find the output current in the boundary of discontinuous conduction mode.

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joanna f.