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(20 points) Parts (a) and (b) are distinct from each other. (a) Use Stokes’ Theorem to evaluate \(\displaystyle \iint_S \text{curl} \vec{G} \cdot d\vec{S}\), where \(\vec{G}(x,y,z)= \langle yz, xy, xz \rangle\) and \(S\) is the part of the sphere \(x^2+y^2+z^2=4\) with \(x \geq 0\) oriented in the direction of the positive x-axis that lies inside the cylinder \(y^2+z^2=1\). (b) Consider the solid region E bounded below by the cone \(z=\sqrt{x^2+y^2}\) and above by the paraboloid \(z=2-(x^2+y^2)\). Use the Divergence Theorem and cylindrical coordinates to evaluate \(\displaystyle \iint_S \vec{F} \cdot d\vec{S}\), where \(\vec{F} (x,y,z)= (5x\sin^2(z)+\arctan(y))\vec{i}+(5y\cos^2(z)-\ln(1+x^2))\vec{j}+(7z-e^{x-y})\vec{k}\), and S is the boundary of the region E.   PLEASE READ THE INSTRUCTIONS BELOW CAREFULLY: When you have completed your entire exam do not hit “Submit” to submit the exam on Canvas yet, get your phone and scan your written work for questions 6, 7 and 8 (only) to upload to Gradescope www.gradescope.com or use the gradescope app. Make sure that all pages have been uploaded to Gradescope. Once you’re done scanning and uploading to Gradescope, then submit the exam on Canvas. If you experience any difficulties uploading your solutions to Gradescope, only then submit a single .pdf file in the space provided below. Do not close the current Honorlock session until you have submitted your solutions to Gradescope and then submitted the exam on Canvas. Submitting any solutions to Gradescope or Canvas after the Honorlock proctoring session has ended constitutes a violation of the UMass Academic Honesty policy and will be dealt with accordingly.

Book Chapter: What is the primary goal of using antenarratives in historiography?

Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Construct a 98% confidence interval for the population mean, μ of the repair bill. Assume the population has a normal distribution. A study of 14 car owners showed that their average repair bill was $192 with a standard deviation of $8. Show work for the all the steps below. (2pts) Point estimate  (3pts) Critical value (round to 3 decimal places): (3pts) Margin of Error (round to 3 decimal places) : (3pts) CI (round to a whole number): (1pt) Interpretation:  

 Plants that are of similar ages and that grew in the same soil could produce different radiocarbon ages due to:

Dating techniques tell us _____________ about cultural activities.

Trees have alternating dark and light rings.  The dark rings are:

When faced with a choice of wood to use in tree-ring dating, which of the following would yield the best results?

Dendrochronology provides a(n) _________ measure of time, while the Law of Superposition allows for a(n) ________ measure of time.

Electron spin resonance is a trapped charge dating method primarily used to date:

Soil development occurs: