# Posts by qwerty

Total # Posts: 351

Science

Science
How could the development of a smart grid help protect the environment? a. a smart grid uses only renewable energy sources b. a smart grid burns fossil fuels without producing pollution c. a smart grid connects nonrenewable energy sources, making them renewable d. a smart grid...

math algebra
x=(15+(x/12)) 11x=180 x=16.36 Time=3:16:21.81

Math
A rectangular garden bed is 3 2/3 ft by 4 1/2 ft. Bricks that are 1/2 ft wide are being laid inside the perimeter of the garden. What is the perimeter of the garden bed outside the brick edging? What is the area of the garden bed inside the brick edging?

math
A hollow cylinder with outer radius r0 and inner radius ri is loaded by a uniformly distributed load q across its length L. The beam is supported by a roller at its left end and a pin L5 from its right end. What is the maximum bending moment in the beam? Express your answer in...

math, mechanics
Calculate the ratio of the moments of inertia I1/I2 of two beams of rectangular cross section of the same width, one with a height h and the other, made up of three thinner beams of height h/3.

material science, math
Calculate the ratio of the moments of inertia I1/I2 of two beams of rectangular cross section of the same width, one with a height h and the other, made up of three thinner beams of height h/3. I1/I2 = ?

Probability
Consider a Markov chain X0,X1,X2,… described by the transition probability graph shown below. The chain starts at state 1; that is, X0=1. Find the probability that X2=3. P(X2=3)= - unanswered Find the probability that the process is in state 3 immediately after the ...

Probability
A dedicated professor has been holding infinitely long office hours. Undergraduate students arrive according to a Poisson process at a rate of λu=3 per hour, while graduate students arrive according to a second, independent Poisson process at a rate of λg=5 per hour...

Probability
Let θ be an unknown constant. Let W1,…,Wn be independent exponential random variables each with parameter 1. Let Xi=θ+Wi. What is the maximum likelihood estimate of θ based on a single observation X1=x1? Enter your answer in terms of x1 (enter as x_1) ...

Probability
Uncle Henry has been having trouble keeping his weight constant. In fact, during each week, his weight changes from the beginning of the week to the end of the week by a random amount, uniformly distributed between -0.5 and 0.5 pounds. Assuming that his weight change during ...

Probability
Suppose that you move to a new house and you are 10% sure that your new house's phone number is 561290. To verify this, you use the house's phone to dial 561290, obtain a busy signal, and conclude that this is indeed your phone number. (Suppose that you were incorrect...

Probability
Let X and Y be independent random variables, each uniformly distributed on the interval [0,2]. Find the mean and variance of XY. E[XY]= - unanswered   var[XY]= - unanswered Find the probability that XY≥1. Enter a numerical answer. P(XY≥1)= - unanswered

Probability
b) min Xi

Probability
A fair coin is tossed repeatedly and independently. We want to determine the expected number of tosses until we first observe Tails immediately preceded by Heads. To do so, we define a Markov chain with four states, {S,H,T,HT}, where S is a starting state, H indicates Heads ...

Probability
Let Θ be an unknown random variable that we wish to estimate. It has a prior distribution with mean 1 and variance 2. Let W be a noise term, another unknown random variable with mean 3 and variance 5. Assume that Θ and W are independent. We have two different ...

Probability
Consider a fire alarm that senses the environment constantly to figure out if there is smoke in the air and hence to conclude whether there is a fire or not. Consider a simple model for this phenomenon. Let Θ be the unknown true state of the environment: Θ=1 means ...

Probability
Manhole explosions (usually caused by gas leaks and sparks) are on the rise in your city. On any given day, the manhole cover near your house explodes with some unknown probability, which is the same across all days. We model this unknown probability of explosion as a random ...

Probability
Let N,X1,Y1,X2,Y2,… be independent random variables. The random variable N takes positive integer values and has mean a and variance r. The random variables Xi are independent and identically distributed with mean b and variance s, and the random variables Yi are ...

Probability
Let X be a random variable that takes non-zero values in [1,∞), with a PDF of the form fX(x)=⎧⎩⎨cx3,0,if x≥1,otherwise. Let U be a uniform random variable on [0,2]. Assume that X and U are independent. What is the value of the constant c? c= - ...

Probability
Let U, V, and W be independent standard normal random variables (that is, independent normal random variables, each with mean 0 and variance 1), and let X=3U+4V and Y=U+W. Give a numerical answer for each part below. You may want to refer to the standard normal table . What ...

Probability
Consider three random variables X, Y, and Z, associated with the same experiment. The random variable X is geometric with parameter p∈(0,1). If X is even, then Y and Z are equal to zero. If X is odd, (Y,Z) is uniformly distributed on the set S={(0,0),(0,2),(2,0),(2,2)}. ...

Probability
We are told that events A and B are conditionally independent, given a third event C, and that P(B∣C)>0. For each one of the following statements, decide whether the statement is “Always true", or “Not always true." A and B are conditionally ...

Probability
Consider three random variables X, Y, and Z, associated with the same experiment. The random variable X is geometric with parameter p∈(0,1). If X is even, then Y and Z are equal to zero. If X is odd, (Y,Z) is uniformly distributed on the set S={(0,0),(0,2),(2,0),(2,2)}. ...

Probability
Let A,B,C be three events and let X=IA, Y=IB, Z=IC be the associated indicator random variables. We already know that X⋅Y is the indicator random variable of the event A∩B. In the same spirit, give an algebraic expression, involving X, Y, Z for the indicator random...

Probability
A fair, 6-sided die is rolled 6 times independently. Assume that the results of the different rolls are independent. Let (a1,…,a6) denote a typical outcome, where each ai belongs to {1,…,6}. Find the probability that the results of the 6 rolls are all different. (...

Probability
A binary communication system is used to send one of two messages: (i) message A is sent with probability 2/3, and consists of an infinite sequence of zeroes, (ii) message B is sent with probability 1/3, and consists of an infinite sequence of ones. The ith received bit is &#...

Probability
Consider a sequence of independent tosses of a biased coin at times k=0,1,2,…,n. On each toss, the probability of Heads is p, and the probability of Tails is 1−p. A reward of one unit is given at time k, for k∈{1,2,…,n}, if the toss at time k resulted in...

Probability
Each one of n persons, indexed by 1,2,…,n, has a clean hat and throws it into a box. The persons then pick hats from the box, at random. Every assignment of the hats to the persons is equally likely. In an equivalent model, each person picks a hat, one at a time, in the ...

Probability
The newest invention of the 6.041x staff is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2 with probability 1/4, and 3 with probability 1/4. Consider a sequence of six independent rolls of this die. 1. Find the probability that exactly two...

Probability
Consider the communication network shown in the figure below and suppose that each link can fail with probability p. Assume that failures of different links are independent. Assume that p=1/3. Find the probability that there exists a path from A to B along which no link has ...

Probability
Before leaving for work, Victor checks the weather report in order to decide whether to carry an umbrella. On any given day, with probability 0.2 the forecast is “rain" and with probability 0.8 the forecast is “no rain". If the forecast is “rain"...

Probability
Oscar has lost his dog in either forest A (with probability 0.4) or in forest B (with probability 0.6). If the dog is in forest A and Oscar spends a day searching for it in forest A, the conditional probability that he will find the dog that day is 0.25. Similarly, if the dog...

Probability
You roll two five-sided dice. The sides of each die are numbered from 1 to 5. The dice are “fair" (all sides are equally likely), and the two die rolls are independent. Part (a): Event A is “the total is 10" (i.e., the sum of the results of the two die ...

Economy
Consider a competitive firm with a total cost function given by TC(q)=q^2/1000. Suppose that, in order to incentivize higher production, the government decides to refund firms for their cost of producing the FIRST q units produced, up to 1000 of them. What is the LARGEST ...

Economy
Consider a competitive firm that can sell its products at a price of p=10 \$/unit. It's variable cost function is given by VC(q)=q^2/1000, and it has SFC=FC=\$1000. What is the amount supplied by the firm?

Economy
What is the cost of producing 100 units of output for a firm with a production function given by F(k,l)=10(min(2k,l))^0.5? Assume that r=20 \$/unit and w=10 \$/unit

language arts
Wolfart is right, 100%

Neuroscience
You continue to record the spikes of a ganglion cell. Even in total darkness, there is some nonzero rate of spiking (sometimes called “spontaneous” spiking). When you shine light at a particular point (let’s call it Q) in the retina, the rate of spiking goes ...

Neuroscience
The video compared a retinal neuron to a spy looking through a keyhole at the world. The keyhole is analogous to the 1. lens of the eye 2. pupil of the eye 3. receptive field

Neuroscience
Consider two ganglion cells with cell bodies that are adjacent to each other in the retina. Their receptive fields are 1. overlapping 2. border each other 3. nearby but do not touch

Neuroscience
If you move your eyes to the right, the receptive fields of your neurons will shift in the visual world to the 1.left 2.right 3.up

Neuroscience
The DNA of a neuron is located in its 1. dendrite 2. axon 3. cell body 4. Golgi apparatus

Neuroscience
The longest neurite of a neuron is typically a: 1. cell body 2. dendrite 3. axon 4. none of the above

Neuroscience
A neuron has: 1. a single cell body or soma 2. one or two cell bodies or somata 3. its nucleus in the axon 4. none of the above

Mechanical Behavior of Materials
Consider a sample of well-annealed copper. Find the Burger's vector given that the energy per unit line length is 1.4×10−9J/m, E=177GPa and ν=0.36. Assume α=0.5. b (in nm):

Mechanical Behavior of Materials
What is the exact strain energy per unit length of an edge dislocation for a material that has a Young's modulus E of 50GPa, a Burger's vector b of 0.25nm, a dislocation density ρ of 108cm−2, and a Poisson's ratio ν of 0.3? Uedge (in J/m): What is ...

Mechanical Behavior of Materials
A material has a Young's modulus E of 50GPa, a Burger's vector b of 0.25nm, and a Poisson's ratio ν of 0.3. What is the approximate line tension for a dislocation in this material?

Logic
Use Propositional Resolution to show that the clauses {p, q}, {¬p, r}, {¬p, ¬r}, {p, ¬q} are not simultaneously satisfiable. Proof takes 8 steps including the premises and the goal.

Logic
Given the premises (p ⇒ q) and (r ⇒ s), use Propositional Resolution to prove the conclusion (p ∨ r ⇒ q ∨ s). Proof takes 8 steps including the premises and the goal.

Statics
Calculate the elastic buckling collapse stress (the compressive strength), σ∗el, for an open-cell polystyrene foam with a relative density of 0.1. (Es for polystyrene = 3.5GPa). Recall that C2=0.05. Give the results in MPa. σ∗el (in MPa): The energy ...

Statics
Compare the Young's modulus E∗ of two open-cell foams. Which Young's modulus is higher? Recall that C1=1. 1. polystyrene: (Es∼3.5GPa), ρ∗/ρs=0.3 2. Al 7075-T651: (Es∼72GPa), ρ∗/ρs=0.1 E∗PS (in GPa): E∗Al (in...

Statics
You have a stainless steel hollow rod (E=193GPa,ν=0.29) that has an inner radius r of 1.2cm, a wall thickness t of 0.7mm, and a length L of 5cm. Calculate the critical loads, in kN, for local buckling and Euler bucking (Pcr,local and Pcr,Euler, respectively). Which would ...

Statics
You have 1kg of aluminum (E=69GPa) to make a cylindrical tube with a high Euler buckling load. The tube must have a length L of 0.5m. You can either make a solid tube, or a thin walled tube with a wall thickness, t=0.5cm. The density of aluminum is 2700kg/m3. The tubes are pin...

Statics
Four identical pin-pin ended solid concrete cylindrical columns that are L=10m tall need to be able to withstand 6.8×108N of force before Euler buckling. What should be the diameter, d, in meters, of each column if the force is uniformly distributed? The Young’s ...

Statics
Calculate the deflection v at the free end, B, for the beams shown below. Both beams have the same rectangular cross section. Give your solution in terms of P,L,E and I.

Statics
A rectangular beam, with cross-sectional width b, height h, Young's modulus Erect, has the same flexural rigidity as a circular beam with the same cross-sectional area. What is the Young's modulus, Ecirc, of the circular beam in terms of Erect,b, and h? What aspect ...

Statics
A cantilever beam, made of a material with a Young's modulus, E with a rectangular cross section with a moment of inertia I, is under a uniformly distributed load, q, across the length L of the cantilever at a point load P at the free end of the cantilever. What is the ...

Materials Science
A hollow cylinder with outer radius r0 and inner radius ri is loaded by a uniformly distributed load q across its length L. The beam is supported by a roller at its left end and a pin L5 from its right end. What is the maximum bending moment in the beam? Express your answer in...

Materials Science
A 4-point bending test is performed on the same beam, with symmetric loads of 5kN separated by 2m. Draw the bending moment and shear force diagrams for the beam. Then answer the following questions about the shear force V and bending moment M. What is the shear force in the ...

Materials Science
A 3-point bending test is performed on a simply supported beam of length L=4m and of rectangular cross-section, with width b and height h. For a central load of 10kN, draw the bending moment and shear force diagrams for the beam. Then answer the following questions about the ...

Materials Science
Calculate the ratio of the moments of inertia I1I2 of two beams of rectangular cross section of the same width, one with a height h and the other, made up of three thinner beams of height h/3. I1/I2 = ?

Materials Science
A 3m long balance beam is simply supported with an overhang at each end of a=0.5m. A gymnast weighing 50kg is standing a distance c to the right of support A and a distance b to the left of support B. How does the maximum bending moment in the beam depend on the distance c? ...

Materials Science
A thin-wall cylindrical tank has radius R, wall thickness t≪R and is subjected to an internal pressure p. The cylindrical wall of the tank is constructed by welding steel plates along 45∘ seams, Consider a small element of the cylindrical wall, and define local ...

Materials Science
At a point in a plate subjected to plane stress loading along its surface, the cartesian stress components acting on the x-face of an element oriented along the (x,y) frame are σx=40MPa and τxy=70MPa, The maximum allowable shear stress, to prevent yielding of the ...

Materials Science
In this problem, you will construct the 2D Mohr's circle for two plane stress states defined in terms of the Cartesian components of the stress tensor in the x,y reference frame: [ σx,σy,τxy]. For each of these stress states, you must construct and use the ...

Materials Science
A compression bar, having a square cross section of side length b, must support a compressive load of magnitude W, uniformly distributed over the bar cross section. The bar is made of two segments connected by a glued joint along plane pq, which is at an angle α to the ...

Algorithms
Arrange the following functions in increasing order of growth rate (with g(n) following f(n) in your list if and only if f(n)=O(g(n))). a)2^2^n b)2^n^2 c)n^2 * log(n) d)n e)n^2^n

Networks
Consider the "Hybrid Model" described in lecture 3.4, with m=10. Let us compare the cases of a=0.8 and a=0.2. At date t=10,000, consider a node born at date i=20 and a node born at date i=9999. Recall that the approximation of the expected degree at time t of a node ...

Networks
Consider the "Preferential Attachment Model" described in lecture 3.3, with m=10. At date t=40, what are: (1) the expected degree for node 15 (born at time i=15), and (2) the expected degree for node 30 (born at time i=30)? [Hint: Use the approximation for the ...

Networks
Consider the model of "Growing Random Networks" described in lecture 3.1 (so the first model where links are added to existing nodes uniformly at random), with m=10. At date t=40, what are: (1) the expected degree for node 15 born at i=15, and (2) the expected degree...

Physics
Which of the following processes is used in order to fabricate monocrystalline silicon? Note that more than one correct answer is possible. The Czochralski process Silicon ribbon process The float-zone process The silicon casting process

Physics
The width of the space charge region at a p-n junction is reduced by applying a voltage bias over the p-n junction. What is the correct statement on both the bias voltage and the p-n junction? The voltage is a forward bias and the diffusion of the majority charge carriers ...

Logic
Consider a propositional language with three propositional constants - mushroom, purple, and poisonous - each indicating the property suggested by its spelling. Using these propositional constants, encode the following English sentences as Propositional Logic sentences. Use ~ ...

Big Data
Suppose ABC is a frequent itemset and BCDE is NOT a frequent itemset. Given this information, we can be sure that certain other itemsets are frequent and sure that certain itemsets are NOT frequent. Other itemsets may be either frequent or not. Which of the following is a ...

Big Data
Imagine there are 100 baskets, numbered 1,2,...,100, and 100 items, similarly numbered. Item i is in basket j if and only if i divides j evenly. For example, basket 24 is the set of items {1,2,3,4,6,8,12,24}. Describe all the association rules that have 100% confidence. Which ...

Big Data
Suppose we want to assign points to whichever of the points (0,0) or (100,40) is nearer. Depending on whether we use the L1 or L2 norm, a point (x,y) could be clustered with a different one of these two points. For this problem, you should work out the conditions under which a...

Big Data
The edit distance is the minimum number of character insertions and character deletions required to turn one string into another. Compute the edit distance between each pair of the strings he, she, his, and hers. Then, identify which of the following is a true statement about ...

Big Data
Suppose our input data to a map-reduce operation consists of integer values (the keys are not important). The map function takes an integer i and produces the list of pairs (p,i) such that p is a prime divisor of i. For example, map(12) = [(2,12), (3,12)]. The reduce function ...

Physics
Let's assume that solar light reaches a silicon solar cell with an angle of incidence of θi=0o. For simplicity, let's consider the refractive index of silicon to be nSi=3.5. The refractive index of air is nair=1. What percentage of light would be lost due to ...

Physics
A solar cell with dimensions 12cm x 12cm is illuminated at standard test conditions. The cell presents the following external parameters: Voc=0.8V,Isc=3A,Vmp=0.75V,Imp=2.5A Calculate the fill factor in percentage [%]: Calculate the efficiency (in %):

Physics
The current density of an ideal p-n junction under illumination can be described by: J(V)=Jph−J0(e^qV/kT−1) where Jph is the photocurrent density, J0 the saturation current density, q the elementary charge, V the voltage, k the Boltzmann's constant, and T the ...

Physics
The width of the space charge region at a p-n junction is reduced by applying a voltage bias over the p-n junction. What is the correct statement on both the bias voltage and the p-n junction? The voltage is a forward bias and the diffusion of the majority charge carriers ...

Materials Science
εx= εy= εz= γyz= γxz= γxy

Materials Science
A cube of the isotropic, linear elastic epoxy resin E=2GPa, ν=0.3, α=50×10−6K−1 at 20∘C is unloaded. It is then heated to 60∘C. What is the corresponding strain matrix? The temperature is held constant at 60∘C. What stress is ...

Materials Science
An isotropic epoxy resin (E=2GPa, ν=0.3) is reinforced by unidirectional glass fibers (Eglass=70GPa), aligned in the 2 direction, such that the fiber composite is transversely isotropic, with the 1-3 plane being the plane of isotropy. The elastic constants of the fiber ...

Materials Science
εx= εy= εz= γyz= γxz= γxy

Materials Science
A linear elastic, isotropic epoxy resin with elastic modulus, E=2GPa, and Poisson’s ratio, ν=0.3, is loaded by the following stress state: σ=⎡⎣10 5 0 5 −20 0 0 0 0⎤⎦MPa Give numerical values for all strain components in the ...

Materials Science
Rubber particles, roughly 1mm in diameter, have been added to an epoxy resin to increase its resistance to crack growth. Estimate the Young's modulus of the composite, given that the Young's moduli of the epoxy and the rubber are, respectively, 2GPa and 10MPa, and that...

Materials Science
Shear modulus G (in GPa):???

Materials Science
Aluminum is a cubic crystal, with S11=1.59×10−11 m2/N S12=−0.58×10−11 m2/N S44=3.52×10−11 m2/N What are the Young's modulus, Poisson's ratio and shear modulus, corresponding to these values? Young's modulus E (in GPa): ...

Materials Science
-8.4 *10^-5 wrong!

Materials Science
A cylindrical pressure vessel, with a diameter of 40cm and a wall thickness of 10mm is made of steel (isotropic, with Young’s modulus = 200GPa; Poisson’s ratio = 0.28) and is pressurized to 20MPa. The longitudinal and hoop stresses in the wall, σl and σh, ...

Material Sciences
The molar crosslink density of a rubber is measured to be 468mol/m3 for a temperature T=300K. What is the Young's modulus of the rubber in MPa? What happens to the modulus of the rubber when the temperature is increased? Young's modulus decreases Young's modulus ...

Material Sciences
Imagine a container is removed from a hot oven and plunged into cold water. Use your answer from Question 3 to justify which material would be more likely to have better thermal shock resistance. Glass: α=9∗10−6C−1 Pyrex: α=4∗10−6C−...

Material Sciences
A steel bar of length L and cross-sectional area A is fitted between rigid supports. Write an expression for the stress in the bar when the temperature is raised by an amount ΔT. Write your answer in terms of α,E and ΔT. Is the stress compressive or tensile? ...

Material Sciences
Given an aluminum shell perfectly bonded to a steel core, what is the thermal stress in the aluminum shell when the system is heated from the unstressed state (20∘C) to 180∘C? Consider only deformations in the axial directions. Give your answer in MPa αAl=23.6...

Material Sciences
The energy-separation curve for two atoms, a distance, r, apart is: U(r)=−A/r^m+B/r^n Derive and expression for the stiffness of the bond at the equilibrium spacing, in terms of A, B, m, n, and r0. S=dF/dr at r=r0:

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