ROBLEM 13. [TIME ALLOWED = 5 MINUTES] Give the contrapositive, converse, and inverse of the following proposition: “If the number is positive, then its square is positive.”
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- PROBLEM 12. [TIME ALLOWED = 5 MINUTES] Give the contrapositive and converse of the following proposition: “If it is sunny, then I will go swimming.”PROBLEM 2. [TIME ALLOWED = 5 MINUTES] Is the following sentence a proposition? If it is a proposition, determine whether it is true or false.PROBLEM 14. [TIME ALLOWED = 5 MINUTES] Let p and q be the propositions: p : I bought a lottery ticket this week. q : I won the million dollar jackpot on Friday. The proposition (p q) as an English sentence is: (a) I did not buy a lottery ticket this week, and I did not win the million dollar jackpot on Friday. (b) Either I bought a lottery ticket this week or I won the million dollar jackpot on Friday. (c) Not better than good beer. (d) None of the above.
- (Oceanography) The pressure, P, exerted on an underwater object can be determined by this formula: P=gh is the density of water, which is 1.94slug/ft3 . g is the acceleration caused by Earth’s gravity, which is 32.2ft/sec2. h is the object’s depth in the water in feet. a. Determine the units of P by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for pressure listed in Table 1.1. b. Determine the pressure on a submarine operating at a depth of 2500 feet.Problem 5 (#2.1.36).Find the truth set of each of these predicates where the domain is the set of integers. a) P(x) : “x3≥1” b) Q(x) : “x2= 2” c) R(x) : “x < x2”PROBLEM 11. [TIME ALLOWED = 5 MINUTES] Express the contrapositive in English of the following sentence: “I will buy the tickets only if you call.”
- PROBLEM 3. [TIME ALLOWED = 5 MINUTES] Is the following sentence a proposition? If it is a proposition, determine whether it is true or false. “Enter your password.”4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result..Problem 1: The monthly payment M of a loan amount P for y years and with interest rate r can be calculated by the formula: P(r/12) M = 1-(1+r/12)-12y Calculate the monthly payment and the total payment for a $100,000 loan for 10, 11, 12, ..., 29, 30 years with an interest rate of 4.85%. Display the results in a three-column table where the first column is the number of years, the sec- ond is the monthly payment, and the third is the total payment.
- - For all the employees supervised by KING, give them a salary increase, which is equal to the 2% of the company’s average salary(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.a)A thief robbing a store finds 5 items; the items are worth 8,10,7,20 and 11 dollars and weights 2,3,2,7 and 7 pounds. He wants to take as valuable a load as possible, but he can carry at most 9 pounds in his knapsack. What is the maximum worth of items that he can take? b) What if the thief somehow managed to increase the capacity of his knapsack by 2 pounds? What will be the maximum worth of items that he can take then?
