1. If you apply the potential difference V to a parallel plate capacitor, it is charged to the charge value Q. Now you double the separation between the plates keeping the same V. As a result, charge on the plates will be equal to:

A. 2Q;

B. 4Q;

C. Q;

D. Q/2;

E. Q/4;

2. You have several capacitors of different capacitances. Which statement is correct?

A. If the capacitors connected to a battery in series, charges on all capacitors are the same, but potential differences are different;

B. If the capacitors connected to a battery in series, charges on all capacitors are different, but potential differences are the same;

C. If the capacitors connected to a battery in parallel, charges on all capacitors are different, but potential differences are the same;

D. If the capacitors connected to a battery in parallel, charges on all capacitors are the same, but potential differences are different;

E. A and C;

F. B and D.

3. If you apply voltage V to a long aluminum wire, the power P is dissipated in the wire. If you apply the same voltage V to another aluminum wire which has the same diameter, but is 2 times longer, the dissipated power will be equal to:

A. 4P;

B. 2P;

C. P;

D. P/2;

E. P/4.

1) Determine the angle between vectors:

U = <2, -3, 4> and V= <-1, 3, -2>

2) determine the distance between line and point

P: -2x+3y-4z =2

L: 3x – 5y+z =1

3) Determine the distance between the line L and the point A given by

L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1)

4) Find an equation of the line given by the points A, B and C.

A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)

5) Determine whether the lines are parallel, perpendicular or neither.

(x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 = (z-2)/6

6) A) Find the line intersection of vector planes given by the equations

-2x+3y-z+4=0 and 3x-2y+z=-2

B) Given U = <2, -3, 4> and V= <-1, 3, -2>

Find

a. U . V

b. U x V

7) Find the angle between the planes:

3x -5y+7z -4=0 and 3x -2y+5z +3 =0

Numeric responses must be either an integer (if exact) or a real number with three decimal places, with the least significant number rounded. Do not use commas. If there are units, the integer part must be between 1 and 999. Use the following units: Ohm, kOhm, mOhm resistors, etc. Conductances: S, mS, MS, etc. Voltage: V, kV, mV, MV, etc. Current: A, mA, kA, uA, nA, etc. Power: W, mW, kW, uA, pW, etc. Time: s, hrs, ks, ms, etc.

1. Voltage amplifiers are available with Avoc = 8 V / V, Rin = 1.8 kΩ, Ro = 850 Ω. With a 12 V DC power source, each amplifier consumes 1.5 mA average current.

a. How many amplifiers do you need to cascade to get at least a 1000 voltage gain with a load resistance of 1.0 kΩ?

b.What is the voltage gain Av obtained? (Respond with a rounded whole number)

c. For the cascade connection, find the open circuit voltage gain. (Respond with a rounded whole number)

d. If you have a 1.5 mV input, how efficient is the equivalent amplifier?

e. Find the transconductance of the entire circuit.

Assume that the following relationship holds:

Maintenance Costs = (v * Machine Hours) + f

REQUIRED

Estimate the values of v and f and the cost equation, using,

1. The Linear Regression method.

Note, to use the linear regression method, you MUST use the Microsoft Excel program.

Make sure to report

1. The values of v and f;

2. A scatter plot of the data points, and

3. The adjusted R-square; explain what the adjusted R-square means.

4. The cost equation in the form of Y = vx + f, substituting the values for v and f from the regression output.

YOUR SUBMISSION MUST BE IN EXCEL.

Three resistors with resistances R₁, R₂, R₃ are connected in parallel across a battery with voltage V. By Ohm’s law, the current (amps) is

I = V* [ (1/R₁) + (1/R₂) + (1/R₃) ]

Assume that R₁, R₂, R_3, and V are independent random variables

where R₁ ~ Normal (m = 10 ohms, s = 1.5 ohm)

            R₂ ~ Normal (m = 15 ohms, s = 1.5 ohm)

            R₃ ~ Normal (m =20 ohms, s = 1.0 ohms)

            V ~ Normal (m = 120 volts, s = 2.0 volts

(a) Use Monte Carlo Simulation (10,000 random draws from each input random variable) to estimate the mean and standard deviation of the output variable current. (b) Assess whether the output variable current is normally distributed. (c) Assess whether the inverse of current squared (1/ I2 ) is normally distributed. (d) Estimate the probability that the current is less than 25 amps assuming that the inverse of current squared is normally distributed. (e) Compare your answer to (d) with your simulation results – how many of the 10,000 random results for current are below 25 amps via the Stat > Tables > Tally command?

In each case state whether you expect the two variables x and y indicated to have positive, negative, or zero correlation.

A. the number x of pages in a book and the age y of the author

B. the number x of pages in a book and the age y of the intended reader

C. the weight x of an automobile and the fuel economy y in miles per gallon

D. the weight x of an automobile and the reading y on its odometer

E. the amount x of a sedative a person took an hour ago and the time y it takes him to respond to a stimulus

****YOU MUST SHOW ALL OF YOUR WORK, OR PROVIDE SUBSTANTIAL EXPLANATION TO YOUR ANSWER IN ORDER TO RECEIVE CREDIT****

Chapter 11: Using the attached dataset “Chapter 11 Data Set 1” to test the research
hypothesis that males raise their hands in class more often than females. (Please note that
these data are not exactly the data provided by the author).
a. Is this a directional or non-directional hypothesis?
b. Should you use a one-tailed or two-tailed test?
c. What is the corresponding null hypothesis?
d. Conduct the between groups t-test using Excel (either method). Use the .05
confidence level. What is your conclusion about the null hypothesis?

Chapter 11 Data Set 1

group 1: 7,3,3,2,3,8,8,5,8,5,5,4,6,10,10,5

group 2: 5,4,4,5,5,7,8,8,9,8,3,2,5,4,4,6

Subjects in the weapon condition were only slightly, but not significantly, less accurate than controls on the 20-item questionnaire. Weapon present subjects were correct on 45.8% of the items, while control (weapon absent) subjects were correct on 50.3% of the items, t(34) = 1.37, p > .05, one tailed.

What kind of study design is this (experimental or correlational)?

If experimental, what is the independent variable?

If experimental, what is the dependent variable?

What kind of statistical test did the author run, and how do you know the used this test?

What do you think the null and alternative hypotheses are in this study? You might have to guess, but make it an educated guesses

The past few years have seen an erosion of trust between the police and the general public. This is not the first time this has occurred in US history, but is a "current issue" that continues to make news. This is a good time to look at how we "measure police effectiveness".

After reading the article "The Good Cop: Knowing The Difference Between Lawful and Effective Policing and Rightful Policing- And Why It Matters"

a. Compare and contrast "Lawful/Effective Policing" and what the author calls "Rightful Policing".

b. Which do yo think is the best way to measure our law enforcement system in the US? Explain in detail.

Answer each part of the Discussion Question thoroughly and substantively