1. Roll a pair of dice (one is red and the other is green). Let A be the event that the red die is 4 or 5. Let B be the event that the green die is 1 Let C be the event that the dice sum is 7 or 8.

1. Calculate P(A), P(B), P(C)
2. Calculate P(A|C), P(A|B)
3. Are the events A and C independent?

2. Suppose box 1 has four black marbles and two white marbles, and box 2 has two black marbles and five marbles. If you picked one marble from one of the two boxes at random, what it the probability that you picked from box 1 given that the marble you picked is black?

3. A raffle has 5000 tickets with the following prizes: 1 ticket has $2000 prize, 10 tickets have $200 prize, and 20 tickets have $50 prize and 500 tickets have a $20 prize. If to buy a ticket costs $15, and X is the random variable that measures net profit:

1. Calculate the pdf table of X
2. Calculate E(X), Var(X)

4. If a fair coin is flipped 120 times, what is the probability that:

1. The number of heads is more than 70
2. The number of heads between 50 and 70?

5. According to a study, 21.1% of 507 female college students were on a diet at the time of the study.

a) Construct a 99% confidence interval for the true proportion of all female students who were on a diet at the time of this study.

b) Explain what this interval means.

c) Is it reasonable to think that only 17% of college women are on a diet?

6. A used car dealer says that the mean price of a 2008 Honda CR-V is at least $20,500. You suspect this claim is incorrect and find that a random sample of 14 similar vehicles has a mean price of $19,850 and a standard deviation of $1084. Is there enough evidence to reject the dealer’s claim at α = 0.05?

1 Ideal Gas Law The ideal gas law is familiar to anyone who has taken a college chemistry course: P V = νRT. This problem will show you why the ideal gas law has this form. We can arrive at this expression just by using classical mechanics! Consider a box of volume V containing N particles, each having mass m, that are moving horizontally with average speed v. The particles bounce back and forth between the end walls of the container, which have area A. They are spread out uniformly in the box, so that there are n = N/V particles per cubic meter.

Single Collision — Consider a single particle bouncing off a wall of the container. In an elastic collision, how much momentum is transferred to the wall of the container? (The wall has a much greater mass than a particle.)

Multiple Collisions — If there are N collisions like the one you analyzed in the preceding question, how much momentum will be transferred to the wall? Time Interval — How many collisions will occur in time ∆t? Express your result N in terms of the average speed v, the particle density n, the area of the wall A, and the time interval ∆t. (Remember: At any given time, only half the particles will be moving toward the wall; the other half will be moving away.)

Average Force — What is the average force on the wall due to the N collisions of the previous question? (Recall Newton’s Second Law: F = ∆p/∆t.)

Average Pressure — What is the average pressure on the wall?

Kinetic Energy — Rewrite your result in terms of the average kinetic energy of the particles: E = 1/ 2mv^2 .

Ideal Gas Law? — Rearrange your result to resemble the ideal gas law. That is, derive an expression that relates P, V , N, and E.

Average Energy — What value of the average energy E would give the physicists’ version of the ideal gas law, P V = N kBT?

In matlab I have created the following function that calculates the distance a projectile travels when shot from
a cannon given initial velocity and theta.

function [distance, xplot, yplot] = Cannon_lab8(V, theta)

g = -9.81; % gravity m/s^2
k = 0.35; % drag coefficient
Vx = V*cos(theta); %velovity in x-direction
Vy = V*sin(theta); %velovity in y-direction
dt = 0.01; % seconds, time step
x = 0;
y = 0;
xplot(1) = 0;
yplot(1) = 0;
i = 2;

while y >= 0
ax = -k*Vx;
ay = -k*Vy + g;
Vix = Vx;
Viy = Vy;
Vx = Vx + ax*dt;
Vy = Vy + ay*dt;
Vx_avg = (Vix +Vx)/2;
Vy_avg = (Viy +Vy)/2;
dy = Vy_avg * dt;
dx = Vx_avg * dt;
y = y + dy;
x = x +dx;
xplot(i) = x;
yplot(i) = y;
i = i + 1;
end

distance = x; % meters

scatter(xplot,yplot)
axis equal

I am now trying to determine the theta value needed to hit a target. The general aproach to solving for theta is by creating a new function that takes the guess value of theta, the initial velocity, and target distance, and solves for theta needed to hit the target. In this function the distance that the cannon misses the taret by can be calculated and this can be repeaditly calculated until the miss is within 2. so far I have:  

function [theta_target] = aim_lab9(theta_guess, target, V)
miss = Cannon_lab8(V, theta) - target;
dtheta = 0.1;
while abs(miss) > 2
miss = Cannon_lab8(V, theta_guess) - target;   
theta_new = theta_guess + dtheta;
miss2 = Cannon_lab8(V,theta_new) - target;
end

I need help determining the theta_target. I would also like for the code to check and see if the target is within range.

thank you!

Read these instructions carefully, and then read the text “The Highs and Lows of Vocational
Education” on the next page. Then write an essay of 350-400 words* in response to this essay title:

You must support your ideas with:
- Evidence taken from the ‘The Highs and Lows of Vocational Education” reading text (at
least one item, which must be referenced with an in-text citation)
AND
- Other evidence regarding either Hong Kong OR China (which you may have read and can
reference correctly, or which you have made up and should be referenced with your family
name and the current year, e.g. (Fan, 2019). You are not required to write a reference list.

Describe the advantages and disadvantages of studying vocational education, in either Hong

Kong or China, and in another country.

The Highs and Lows of Vocational Education [adapted]

by Matt Barnum (2017)
What’s one education topic that right wing, left wing, and all politicians support? It is vocational
training - something they’ve all said America needs in order to create a balance of practical as well
as academic school leavers. While President Trump praised Germany’s approach to vocational
education recently, he actually plans to reduce funding for it, but, at least in theory, there’s wide
support for helping more students learn career-specific skills.
Yet new international research points to a significant downside of such programs: Students may
benefit early in their careers, but are harmed later in life as the economy changes and they lack the
less specific skills necessary to adapt. The study raises concerns about the positive and negative
effects of expanding vocational training in the United States. “Individuals with general education
initially face worse employment outcomes, but with improved experience as they become older,
they have increased employment opportunities, relative to individuals with vocational education,”
write four researchers in the study.
Many European and developing countries provide extensive vocational training, including
apprenticeships with involvement from industry, the authors note. That stands in contrast with the
U.S., which has reduced or eliminated separate vocational tracks in most high schools. Looking at
11 European countries, the researchers compared students within the same country who went on the
vocational track to similar students who went through a general-education program. The result is
that although vocational students make higher salaries and are more likely to be employed as young
adults, this advantage fades over time; by their late forties, those who went through a general
education program have higher employment rates. Those findings were confirmed with more
detailed data from Germany. “The advantages of vocational training in smoothing entry into the
labor market have to be set against disadvantages later in life,” the study concludes.
At age 10, Germany requires students to choose a vocational high school, academic high school, or
what one article described as “something in between.” Students have frequent opportunities to move
between these choices as they progress with their studies. However, in the U.S., vocation-focused
courses are often just a small part of a student’s course load. As of 2009, the average American
student took 3.6 vocational classes in high school.
The authors of the latest research say the findings don’t imply that vocational education is
necessarily a bad idea, just that it is important to understand the advantages and disadvantages of
each choice. The results also suggest that policymakers looking only at the short-term impacts of
such programs may not be getting an accurate understanding of their effects. One recent study of
Arkansas’s high-school vocational program, which requires students to take six career-focused
classes in high school in order to graduate and allows them to concentrate in specific areas, found
that participants had higher earnings and employment rates as young adults. Longer-run impacts
were not examined, however.

In the circuit of Figure P32.48, the battery emf is 80 V, the resistance R is 240 , and the capacitance C is 0.500 µF. The switch S is closed for a long time, and no voltage is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance L?

The following groups are stakeholders of a public company:I) shareholders; II) the government; III) suppliers; IV) employees; V) bondholders; VI) management Select one:

a. I, II, III, IV, V, and VI

b. I and II only c. I, II, III, and IV only

d. I, II, and III only

Use the Gram-Schmidt process to construct an orthogonal basis of the subspace of V = C ∞[0, 1] spanned by f(x) = 1, g(x) = x, and h(x) = e x where V has the inner product defined by < f, g >= R 1 0 f(x)g(x)dx.

A particle with mass m and energy E is moving in one-dimension from right to legt. It is incident on the step potential V(x)=0 for x<0 nd V(x)=V0 for x>0 where E>V0>0. Find the reflection coefficient R in terms of m,E and V0, and h-bar.

Use the postulates of the kinetic moleclar theory (KMT) to explain why boyle's law, charles's law, avogadro's law, and dalton's law of partial pressures hold true for ideal gases. Use the KMT to explain the P versus n (at constant V and T) relationship and the P versus T (at constant V and n) relationship.

1. Explain how an automatic pipette (like the one pictured) below works. Briefly explain how to use it
2. How can you accurately aliquot a highly viscous solution using an automatic pipette?
3. What does the term “specific gravity” mean? What is the specific gravity of a 50% (v/v) ethanol (in water) solution?