Consider an n-channel MOSFET with tox = 4.5 nm, n = 445 cm2 /V·s, Vt = 0.55 V, and W/L = 15. What is the value of k’n ? (6 points) Identify the region of operation and find the drain current in the following four cases. (5 points each) Use r = 3.9 for Silicon.
a. vGS = 2.0 V and vDS = 2.5 V b. vGS = 2.5 V and vDS = 1.5 V c. vGS = 2.0 V and vDS = 1 V d. vGS = vDS = 2.0 V

1) What is the current through and voltage across a capacitor after it is fully charged in a DC circuit?

a) I=0, V=0

b) I=0, V=max

c) I=max, V=0

d) I=max, V=max

2) What is the current through and voltage across a capacitor after it is fully discharged?

a) I=0, V=0

b) I=0, V=max

c) I=max, V=0

d) I=max, V=max

1. (1) Suppose that V is a vector space and that S = {u,v} is a set of two vectors in V. Let w=u+v, let x=u+2v, and letT ={w,x} (so thatT is another set of two vectors in V ). (a) Show that if S is linearly independent in V then T is also independent. (Hint: suppose that there is a linear combination of elements of T that is equal to 0. Then ....). (b) Show that if S generates V then T also generates V . (Hint: try solving for u and v in terms of w and x.). (c) Summarize the results of parts (a) and (b), correctly employing the word “basis”.

Write a program to sort the student’s names (ascending order), calculate students’ average test scores and letter grades (Use the 10 point grading scale). In addition, count the number of students receiving a particular letter grade. You may assume the following input file data :

Johnson 85 83 77 91 76

Aniston 80 90 95 93 48

Cooper 78 81 11 90 48

Gupta 92 83 30 69 87

Muhammed 23 45 96 38 59

Clark 60 85 45 39 67

Patel 77 31 52 74 83

Abara 93 94 89 77 97

Abebe 79 85 28 93 82

Abioye 85 72 49 75 63

1. (40%) Use four arrays: a one-dimensional array to store the students’ names, a (parallel) two dimensional array to store the test scores, a one-dimensional array to store the student’s average test scores and a one-dimensional array to store the student’s letter grades.

2. (60%) Your program must contain at least the following functions :

   1. A function to read and store data into two arrays,

   2. A function to calculate the average test score and letter grade,

   3. A function to sort all the arrays by student name, and

   4. A function to output all the results (i.e. sorted list of students and their corresponding grades)  

   5. Have your program also output the count of the number of students receiving a particular letter grade.  

NOTE : No non-constant global variables are to be used. You can name the arrays and functions anything you like. You can use the operator >= to sort the strings.

In C++

Prove the follwing statements

Suppose that S is a linearly independent set of vectors in the vector space V and let w be a vector of V that is not in S. Then the set obtained from S by adding w to S is linearly independent in V.

If U is a subspace of a vector space V and dim(U)=dim(V), then U=V.

Women athletes at the University of Colorado – Boulder have a long-term graduation rate of 62% (Source: The Chronicle of Higher Education). Over the past several years, a simple random sample of 42 women athletes at the school showed that 22 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the University of Colorado – Boulder is now less than 62%? Use a 5% significance level and the Traditional method.

check the requirements

Establish H0 and H1.

Is this a 2-tailed test, left-tailed, or right-tailed?

Calculate the value of the test statistic. Round to three figures after the decimal point. Use correct sign.

Determine the critical value. Use correct sign.

Is there sufficient evidence to reject the claim that the population proportion of women athletes who graduate from UC equals to 0.62?

Group of answer choices

Stet by step in R and attach R file and R codes too - Thanks

Use one of the real-world example data sets from R (not previously used in the R practice assignment) or a dataset you have found, and at least two of the tests and R functions covered in the practice assignment to conduct a hypothesis test then report your findings and give proper conclusion(s).

Use the following supporting materials for R syntax, data sets and tools, along with other resources found in this module or that you find on your own.

• Using T-Tests in R from the Department of Statistics at UC Berkley

• Test of equal or given proportions from R Documentation

• F-Test: Compare Two Variances in R from STHDA (Statistical tools for high-throughput data analysis)

Please answer step by step with R files attached and R codes

1.Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = sin(x) + 5 0 < x < 2π increasing decreasing

2. Identify the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.) f(x) = x + 2 cos(x), 0 < x < 2π increasing decreasing

3. Consider the following function. f(x) = x + 1 x2 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing decreasing (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = relative minimum (x, y) =

4. s(t) = t3 − 5t2 + 3t − 290 (a) Find the velocity function v(t) of the particle at any time t ≥ 0. v(t) = (b) Identify the time interval(s) on which the particle is moving in a positive direction. (Enter your answer using interval notation.) (c) Identify the time interval(s) on which the particle is moving in a negative direction. (Enter your answer using interval notation.) (d) Identify the time(s) at which the particle changes direction. (Enter your answers as a comma-separated list.) t =

5. An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 75 miles from the point and has a speed of 450 miles per hour. The other is 100 miles from the point and has a speed of 600 miles per hour. (a) At what rate is the distance between the planes changing?-------- mph (b) How much time does the controller have to get one of the airplanes on a different flight path? -------h

6. An airplane flies at an altitude of y = 5 miles toward a point directly over an observer (see figure). The speed of the plane is 600 miles per hour. Find the rates (in radians per hour) at which the angle of elevation θ is changing when the angle is θ = 30°, θ = 60°,and θ = 80°. (a) θ = 30° rad/hr (b) θ = 60° rad/hr (c) θ = 80° (Round your answer to two decimal places.) rad/hr

7. The formula for the volume of a cone is given below. Find the rate of change of the volume for each of the radii given below if dr/dt is 8 inches per minute and h = 18r. V = (1/3)πr2h (a) r = 9 in V' = π in3/min (b) r = 30 in V' = π in3/min

1. C++ program that will ask the user for how many test scores will be entered.
2. Setup a while loop with this loop iteration parameter. The data will include the student’s first name and midterm score
3. Print out the completed test scores to a file (midTermScores.txt) .
4. Print out list of students names and grades
5. in the print out, a letter grade should replace numeric score using standard grading (a = 90 – 100, b=80-90, c=70-80, d=60-70, f=below 60)