Considering the set up in the figure below, use deductive reasoning to find the measure of x.  Start with “Draw l2…”.

INSTRUCTIONS As discussed in class, you may use any material that I put on Canvas and you may use any material you have on your laptop.  You may not go to any site (e.g., Gemini, Claude, or any Python related site) for help on the exam.  You may not use Python techniques or functions that we have not covered in class. You may go to OneDrive for materials you have stored there, though I suggest you download any materials you might need to your laptop. For each problem below, copy your code and output to a Word file. A screen shot is acceptable if I can read it – if I have trouble reading it, you will get no credit for that problem – and be forewarned that many screen shots students have submitted are not readable. Do not submit a Python file.  Only submit a single Word file. Put your name at the top of the Word file.   You get 1 point for simply putting your name at the top of the Word file. There are 3 problems, each worth 3 points. My rubric is 0 points if you did not attempt the problem 1 point in your code makes minimal progress towards a solution 2 point if you made good progress on the problem 3 points if you solved, or almost solved, the problem  Task 0. (1 point) put your name (first & last) at the top of the Word file. Task 1. (3 points)  This task is to be done in Excel using the file 3000 words.txt (TXT file) Create a professional-looking bar chart which shows the total number of occurrences of the vowel “a” in all words of length 5, and on the same chart, shows the total number of occurrences of the vowel “a’ in all words of length 6.  Do NOT submit your XLS file. Instead, copy the bar chart from Excel and paste it into a Word document.  You may also insert any text that you want me to read. Task 2.  This task is to be done in Python. Write a function calculate_total_cost( ) that takes three values:  (a) price, (b) quantity, and (c) tax_rate,  and returns the total cost of an order including tax, using the formula: total = price * quantity * (1 + tax_rate) Call your function with price=25, quantity=4, and tax_rate=0.08, and print the result.  Paste your code and the output into the same Word document you used for Task 1.  You may also insert any text that you want me to read. Task 3. (3 points) This task is to be done in Python. Write a function called average_score(scores) that takes a list of numbers and returns their average, using sum() and len(). Your function must include a docstring describing what it does, and at least one comment (using a single hashtag #) explaining a calculation step. Call the function on the list [82, 91, 76, 88] and print the result.   Paste your code and the output into the same Word document you used for Tasks 1 and 2.  You may also insert any text that you want me to read. Submit only a Word document.  Do not submit an Excel or Python file.

Find the measure of x in the following diagram using a deductive argument (in the style shown above) and the properties we developed in class.  Remember to back up any algebraic equations formed based on geometric properties by naming that property afterwards in parentheses.  This goes for all the deductive arguments on the test.

Problem 5 (10 points, CCOs 2 & 5) A spacecraft engineering team is evaluating a new thermal protection panel for atmospheric entry. The panel contains several conductive layers, and its surface temperature depends on aerodynamic heating and temperature-dependent radiation. The thermal protection panel is modeled using three temperature nodes. Applying an energy balance at each node gives

Equation Sheet – Module 4: Curve fitting and interpolation Linear least squares regression: linear function that best fits n given data points :

Problem 2 (4 points, CCOs 1, 2) A model calculates the pressure in a pipe as a function of the pipe diameter. You are tasked to find the pipe diameter for a given target pipe pressure within a given tolerance of the diameter. Part (A) From the given list of options below, which is the appropriate accuracy measure to solve this problem? true tolerance tolerance in solution absolute error true relative error tolerance in function truncation error round-off error Part (B) From the given list of options below, which method covered in this class should be used to find the diameter?  Secant method Newton’s method Bisection method Gauss-Jordan with partial pivoting cubic spline interpolation linear least squares regression

Problem 3 (10 points, CCO 2) An experiment produces 4 measurements for the pair . The experiment is repeated 4 times resulting in the below 4 different data sets A, B, C, and D. Data Set A2 measurements yielding the same values of 2 3 3 4 4 5 5 7 Data Set Bsame value of in all entries 0 1 2 3 5 5 5 5   Data Set Csame value of  in all entries 2 2 2 2 -1 0 7 5   Data Set D4 unique data pairs with unsorted -2 -1 2 1 -1 5 0 1   For the methods as covered in class, answer the following questions with either Y for Yes, or N for No. Can linear least squares regression be used for data set A? Can linear least squares regression be used for data set B? Can linear least squares regression be used for data set C? For data set A, does polynomial regression for a quadratic polynomial result in a function that passes through all data points? For data set A, can interpolation with Lagrange polynomials be done? For data set B, can interpolation with Lagrange polynomials be done? Does the method covered in class to generate a cubic spline result in a valid interpolation method for data set D?

All of the following are reasons hysterosalpingography are performed, except:Choose one or multiple correct answers.

Choose the structures that are included as components of the alimentary canal. Choose one or multiple correct answers.

A large learning rate can speed up learning but risks overshooting the optimal weights.