Drag measurements were taken for a 5 cm diameter sphere in water at 20 °C to predict the drag force of a 1 m diameter balloon rising in air with standard temperature and pressure. Given kinematic viscosity of water (v) = 1.0 X 10^-6 m²/s and kinematic viscosity of air (v) = 1.46 X 10^-5 m²/s.

1. Perform the Buckingham Pi theorem to generate a relationship for F_D as a function of the independent variables. Assume the drag F_D is a function of diameter (d), velocity (V), fluid density (ρ) and kinematic viscosity (v)

Suppose that a decision-maker’s preferences over the set A={a, b, c} are represented by the payoff function u for which u(a) = 0, u(b) = 1, and u(c) = 4.

(a) Are they also represented by the function v for which v(a) =−1, v(b) = 0, and v(c) = 2?

(b) How about the function w for which w(a) =w(b) = 0 and w(c) = 8?

(c) Give another example of a function f:A→R that represents the decision-maker’s preferences.

(d) Is there a function that represents the decision-maker’s preferences and assigns negative numbers to all elements of A?

2. The Dean of Students at the University of Waterloo wanted to estimate the proportion of students who are willing to report cheating by fellow students. So, her staff surveyed the 172 students currently enrolled in the introduction to biology class. The students were asked, “Imagine that you witness two students cheating on a quiz. Would you tell the professor?” 19 of the surveyed students responded “yes.” (11 points total)
a. Using these data, calculate the 90% confidence interval for the proportion of all students at the University of Waterloo that would report cheating. (4 points)
b. Interpret the confidence interval from part “a” in a sentence. Interpret in terms of percentages, rather than proportions. (4 points)
c. Is it appropriate to use these data to estimate the proportion of all students at the university that would report cheating? Why or why not? (3 points)

There are 10 CS students, 12 CPRE students and 8 SE students, to form a committee.

(a) How many different committees of size 3 can you pick if you need one representative from each program?

(b) How many different committees of size 2 can you pick if you cannot pick both representatives from the same program?

(c) In how many ways can you pick a president, a secretary, and a treasurer from the group of students if they cannot all be CS students?

2.1)

What is the speed of an electron that accelerates from rest starting close to the negative plate of a capacitor just before it hits the positive plate? The electric field between the plates is 300 V/m and the distance between the plates is 0.050 m.

2.2)

A charge of +2.00 nC is on the Y axis at the point (0, 2.00) m. A charge of -3.00 nC is on the X axis at the point (3.00, 0) m. Find the direction of the electric field at the Origin.

2.3)

The electric field at a point A has the components E_x = 3.00 V/m   and E_y = +2.50 V/m. Find the direction of the force acting on a charge -14.0 nC placed at the point A. Express your answer as an angle measured counterclockwise from the positive X axis.

2.4)

A charge of 3.00 nC is on the Y axis at the point (0, 2.00) m. A charge of -2.00 nC is on the X axis at the point (-3.00, 0) m. Find the magnitude of the electric field at the Origin.

In University of Kansas, the ratio of international students:out-state native students:instate students is 2:3:6 Department of mathematics has 234 freshmen in total with 42 international students, 52 out-state students and 140 in-state students. Is the ratio of students in department mathematics is same as that of the university at 0.05 level?

the voltage for the electrochemical cell shown below was .450 V.

Pt(s)|Cd(NO₃)₂ (aq)(.0100M) || Cl^- (aq) | AgCl (s)| Ag(s)

The standard reduction potentials are

Cd²⁺+2e^---> Cd (s) E^o= -.402 V

AgCl+e^---> Ag(s) + Cl^-  E^o=.222V

Calcuate the concentration of Cl^- if the cell potential was determined to be 0.605 V

An electrochemical cell is composed of pure copper and pure lead electrodes immersed in solutions of their respective divalent ions. For a 0.7 M concentration of Cu²⁺, the lead electrode is oxidized yielding a cell potential of 0.520 V. Calculate the concentration of Pb²⁺ ions if the temperature is 25˚C. The standard potentials for Cu and Pb are +0.340 V and -0.126 V.

Please show your work!

A new machine is purchased by a business for $200,000. For tax reasons, we assume the machine will lose $40,000 in value each year. If t is the number of years since the machine was purchased, and if V (t) represents the value of the machine after t years, write an equation in the form V (t)=mt+b for the value of the machine. Determine the domain and range for the function V (t).