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Question: If K is a field and X ⊂ AqK, then X ⊂ V (I(X)) with equality if X is an affine variety ? Let J be an ideal of a polynomial ring S over a field K. Prove that J ⊂ I(V (J)) with equality if J is the ideal of an affine variety.
Solve the following system of equations 1, x+2y=2 -4x+3y=25
To buy a laptop, Susan receives a $2000 loan at a 6.5% annual interest rate on January 10. The loan is due May 15. The year is not a leap year. Round the answers to the nearest cent (nearest hundredths)
Provide one example to show how you can use the Expected Value computation to assess the fairness of a situation (probability experiment). Provide the detailed steps and calculations.
Determine the exchange table for this economy, where the columns describe how the output of each sector is exchanged among the three sectors.
For f (x) = 3/x: Find f'(x). Find f'(2). Find an equation of the tangent line to the curve at x = 2
David has a rectangular garden that measures 11 feet by 13 feet. He wants to plant peas in hisgarden. Dad said that one seed packet will be enough to fill a space 10 feet on a side. Will David's garden have enough space to plant 2 seed packets?
what angle does the wire make with the ground?
that catalyst or temperature or their interaction affects the percentage of byproduct?
what will be the value of her retirement account?
Hiro is in the spirit club. There are 29 students in the club. Three of them will be picked at random to go on a retreat. What is the probability he will not be selected? Put your answer as a fraction.
A key in the Vigenère cryptosystem is a string of English letters, where the case of the letters does not matter. How many different keys for this cryptosystem are there with three, four, five, or six letters?
The surface area of this pyramid is 189cm squared.The area of the square base is 49cm squared. What is the area of one triangular face of the lateral surface? Show the steps of your solution and explain your work.
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