Question 1) Find a counterexample to the following universally quantified statements, where the domain for all variables consist of all integers. ∀x, x^2 ≤ x^3Question 2) What can you conclude from the following series of statements? Explain the rules of inference used.”I am either hungry or angry.””I am not hungry.””If I am angry I will go for a walk.”

John makes $2,800 per month and has an opportunity to invest $150 per month at an APR of 4.5% in

John makes $2,800 per month and has an opportunity to invest $150 per month at an APR of 4.5% in a 401K plan through work. He plans to retire in 30 years. Type in the EXACT formula you would use in excel (no spaces) to find the amount in the account after he has invested for 30 years.Using excel, what is the answer to the formula from the previous part?How much money will he deposit into the 401K over the 30 years?How much total interest will he earn on his 401K over the 30 years?

A patient/client weighs 152 lb. Available is 20,000 units of heparin in 1000 mL of D5W. The physician orders the

A patient/client weighs 152 lb. Available is 20,000 units of heparin in 1000 mL of D5W. The physician orders the following: heparin sodium IV bolus of 40 units/kg and start the drip at 10 units/kg/hour. What is the correct IV rate in milliliter per hour? Round to the nearest whole number.A.20B.30C.25D.35

Suppose you have a complete, weighted graph with 6 vertices.How many Hamilton Circuits are there in this graph? How many

Suppose you have a complete, weighted graph with 6 vertices.How many Hamilton Circuits are there in this graph? How many Hamilton Circuits are there through this graph if you start at vertex A? If you were to use the Brute Force Method to determine the optimal circuit, how many Hamilton Circuits will you have to check? .

Roger has to place cookies in plastic bags for a bake sale. He has 84 sugar cookies and 66 chocolate

Mathematics Assignment Writing ServiceRoger has to place cookies in plastic bags for a bake sale. He has 84 sugar cookies and 66 chocolate chip cookies. He wants to place the same number of cookies in each bag, wants to make sure that only one type of cookie goes into each bag, and wants to put the most cookies he can in each bag. How many cookies should be in each bag?

The accumulated value just after the last payment under a 12-year annuity-immediate of 1000 per year, paying interest at the

The accumulated value just after the last payment under a 12-year annuity-immediate of 1000 per year, paying interest at the rate of 5% per annum effective, is to be used to purchase a perpetuity at an interest rate of 6%, withfirst payment to be made 1 year after the last payment under the annuity. Determine the size of the payments under the perpetuity.Calculate k if a deposit of 1 will accumulate to 2.7183 in 10 years at a force of interest given by:

-Stephen Curry’s free throw percentage in basketball is around 90%, meaning a probability of 9/10. At one point in

-Stephen Curry’s free throw percentage in basketball is around 90%, meaning a probability of 9/10. At one point in a game, he has made 9/9 free throws. Is he “due for a miss” and guaranteed to miss the next free throw? Explain why or why not. -What is the probability of rolling three dice in a row and none of them show a 1? What is the probability that at least one of them shows a 1? -The standard license plate in the United States begins with a digit 0-9, followed by 3 letters, then followed by 3 more digits. How many different license plates are there of this form?

max z(x1,x2)=17×1 11×2-9subject tog1(x1,x2)=2×1 x2<=32=b1g2(x1,x2)=x1 x2<=20=b2g3(x1,x2)=x1 2×2=0Find the limits of each of b1,b2,b3, within which the original dual solution remains valid. That is, max z(x1,x2)=17×1 11×2-9subject tog1(x1,x2)=2×1 x2<=32=b1g2(x1,x2)=x1 x2<=20=b2g3(x1,x2)=x1 2×2=0Find the limits of each of b1,b2,b3, within which the original dual solution remains valid. That is, find the max and min of b1 when b2=20

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