Solve the following questions of probability and Algebra.
11:06 Lab manuals Putting it All Together Following the same format as the examples, write text descriptions for the algebra needed to arrive at each of the simplified derivatives below. It will likely help to work out the problems on a piece of paper. Algebra: Algebra: (x3. ex . (13 + 3x - 1) STEP 1 (the product of the first two factora): Algebra: STEP 2 ( the product of the third factor with the rest of the function): Algebra: (x - 2x+ 1) dx x - 1 Algebra: dx \\c + do Algebra:Definition 4.4 (Algebraic Closure). An algebraic closure of a field K is a field extension K C F such that F is algebraic over K and F is algebraically closed. M311 F20 FINAL PROJECT 5 Observation 4.5. We have R C C is an algebraic closure of R. We have C is algebraically closed. the field C is R(i) and i is a root of r' + 1 so C is algebraic over R. Definition 4.6 (Relative Algebraic Closure). Given a field extension K C F we have the set {o ( F : a is algebraic over K ). Corollary 6.2.8 of BB states that this set is a subfield of K. We denote this set by Kp. It is called the relative algebraic closure of K in F. (4) Problem Show that if K C F is a field extension and F is algebraically closed then Ky is an algebraic closure of K. We know it Kpis a field. By definition it is algebraic over K. The problem is to show it is algebraically closed. Definition 4.7. The field Q = Qc is an algebraic closure of Q. The field Qc is called the field of algebraic numbers.24. An isomorphism from the Boolean algebra with set B = {0, 1, a, a'} to the Boolean algebra with set p(1 1, 2}) was defined in this section. Because the two Boolean algebras are essentially the same, an opera- tion in one can be simulated by mapping to the other, operating there, and mapping back. a. Use the Boolean algebra on p({1, 2}) to simulate the computation 1 . a' in the Boolean algebra on B. b. Use the Boolean algebra on p( {1, 2}) to simulate the computation (a)' in the Boolean algebra on B. ". Use the Boolean algebra on B to simulate the computation {1} U (2) in the Boolean algebra on (( ( 1 , 2 }).20. The average price for a gallon of gasoline is $3.73 in the United States and $3.40 in Russia (Bloomberg Businessweek, March 5-March 11, 2012). Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $.25 in the United States and a standard deviation of $.20 in Russia. a. What is the probability that a randomly selected gas station in the United States charges less than $3.50 per gallon? b. What percentage of the gas stations in Russia charge less than $3.50 per gallon? c. What is the probability that a randomly selected gas station in Russia charges more than the mean price in the United States?QUESTION 7 a) According to a constructor, the probability that a building will need repairs during a ten-year period is 0.10. Does the statement fall under classical probability, empirical probability, or subjective probability? Classical probability Empirical probability Subjective probability b) A financial analyst projects that the value of the dollar will fall after the results of the USA presidential elections are announced. Does the statement fall under classical probability, empirical probability, or subjective probability? Classical probability Empirical probability Subjective probability c) Of the ISO 9000 family of standards which ones can a company be certified for? ISO 9000:2015 ISO 9001:2015 ISO 9004:2018
