Define the following propositions: j: Sally got the job. l: Sally was late for her interview r: Sally updated her resume. Express each pair of sentences using logical expressions. Then prove whether the two expressions are logically equivalent. (a) If Sally did not get the job, then she was late for her interview or did not update her resume. If Sally updated her resume and did not get the job, then she was late for her interview. (b) If Sally did not get the job, then she was late for her interview or did not update her resume. If Sally updated her resume and was not late for her interview, then she got the job. (c) If Sally got the job then she was not late for her interview. If Sally did not get the job, then she was late for her interview. (d) If Sally updated her resume or she was not late for her interview, then she got the job. If Sally got the job, then she updated her resume and was not late for her interview.

Why there has to be two lines in a plane

Suppose that jim plans to borrow money for an education at texas a& m university. jim will need to borrow $25,000 at the end of each year for the next five years (total=$125,000). jim wishes his parents could pay for his education but they can’t. at least, he qualifies for government loans with a reduced interest rate while he is in school. he has a special arrangement with aggiebank to lend him the money at a subsidized rate of 1% over five years without having to make a payment until the end of the fifth year. however, at the end of the fifth year, jim agrees to pay off the loan by borrowing from longhorn bank. longhorn bank will lend him the money he needs at an annual interest rate of 6%. jim agrees to pay back the longhorn bank with 20 annual payments and the payments will be uniform (equal annual payments including principal and interest). (i) calculate how much money jim has to borrow at the end of 5 years to pay off the loan with aggiebank. a. $121,336 b. $127,525 c. $125,000 d. $102,020 e. none of the above

If a country is looking to increase economic growth quickly, it should: choose the correct answer from the following choices, and then select the submit answer button. answer choices focus on natural resources and develop physical capital. make investments from domestic savings and adopt new technology. increase spending on human capital and start a new political approach. develop new technologies funded by the public sector.