1. Let f(n) = 2n^3 −n^2 10n−7. Prove that f(n) is O(n^3). Show all work. 2. Prove by contradiction

1. Let f(n) = 2n^3 −n^2 10n−7. Prove that f(n) is O(n^3). Show all work. 2. Prove by contradiction that 6^n is not O(2^2n). 3. Suppose that f(n) is O(g(n)). Does it follow that 2^f(n) is O(2^g(n))? Justify your answer.4. Consider the following pseudocode for an algorithm called “Algorithm,” which reads procedure Algorithm(a1, a2, …, an: integers) x := a1 for i := 2 to n x := x ai return x Suppose a list a1,a2,…,an of integers is given as an input. a) Describe what Algorithm(a1, a2, …, an) returns as output. b) How many times would the expression x := x ai be executed? c) Give a Θ estimate for the runtime of this algorithm.5. [3 marks] Consider the following pseudocode for an algorithm called “Algorithm,” which reads procedure Algorithm(a1, a2, …, an: integers) set L as the empty list sum := 0 i := 1 while i ≤ n if ai > sum then append ai to L end if sum := sum ai i := i 1 return L Suppose a list a1,a2,…,an of integers is given as an input. a) Describe what Algorithm(a1, a2, …, an) returns as output. b) How many times would the expression i ≤ n be executed? c) Give a Θ estimate for the runtime of this algorithm.

Solve all the question with proper information
a) One number is five less than another number. If the sum of
Question Solve all the question with proper information
a) One number is five less than another number. If the sum of these numbers is seventy-three, find the larger number. Clearly define the variable that you use. b) A vet needs to calculate the dosage of a painkiller given to dogs after surgery. The standard dose for a dog weighing up to 10 kilograms is 5 milligrams, after this an extra 0.5 milligrams of the drug is needed for each additional kilogram of weight. (i) Complete the equation below to show how the vet should calculate the dose (in milligrams) to be given to a dog weighing 10 kg or more. Clearly define the variable that you use. Variable: jQuery22408972030165615359_1592797283161?? = (ii) Use your equation to find the weight of dog given a dose of 17 milligrams of painkiller. Give your answer to the nearest milligram. c) A local fitness centre has two payment options. (i) OPTION 1: You pay $15 for each class you attend. Using ? to represent the number of classes attended, write anexpression for the total you would pay in a month using this option: (ii) OPTION 2: You can pay $80 for a monthly pass plus $5 for each class you attend. Using ? to represent the number of classes attended, write anexpression for the total you would pay in a month using this option: (iii) How many classes would you attend in a month to pay the same using either option?

1. On July 1, 2015, Janet purchased a corporate bond with a face
Question 1. On July 1, 2015, Janet purchased a corporate bond with a face value of $10,000 and coupon rate of 4% compounded semi-annually. Interest rate for similar bonds at the time when she made the purchased was J2=4.5%.(a) If Janet purchased the bond at a fair market value of $9758.77, in how many months from July 1 2015 will the bond matures or redeemable? Also, Five years ago, you paid $2,000 to purchase 50 preferred shares of Starz Coffee that pays quarterly dividend of $0.25 per share. The current interest rate is 2.5% effective, how much would you expect to gain or lose if you sell all your shares today? Note: the next dividend is due in 3 months.

1. Terry Schiavo was removed from life support after a years-long
Question 1. Terry Schiavo was removed from life support after a years-long court battle. CNN used a graph similar to the one below to show who agreed with the decision to remove the feeding tube.What is misleading about this particular graph?2. Global Warming out of control!!! What seems to be the problem with this misleading graph?

Solve all the question with proper information a) Given the exponential model: ? = 75(0.60)^ ?
Mathematics Assignment Writing ServiceQuestion Solve all the question with proper information a) Given the exponential model: ? = 75(0.60)^ ? (i) Does this model represent an exponential growth or decay? Justify your answer. (ii) What is the percent rate of change? b) Given the right environmental conditions desert locusts in East Africa can form giant swarms that destroy crops. At the peak of the swarm the population can grow at the incredible rate of 1900% during each 3-month breeding cycle. (i) If a swarm starts with 100 locusts, writean equation that models the growth of the locust population with respect to time. Clearly define any variables you use. (ii) According to this model, how many locusts will be in the swarm in 9 months’ time? Give your answer to the nearest whole number.c) To help explain the risks of these swarms to farmers it is useful to talk about the ‘doubling time’. On average, how many breeding cycles does it take for the locust population to double? Give you answer to 2 decimal places.

Solve the all the question.
1. A hospital used a 70%
Question Solve the all the question.
1. A hospital used a 70% Isopropyl Alcohol solution as a disinfectant. To make this solution hospital workers mix together a 60% solution and a 90% solution. How many litres of each solution need to be mixed to make 16.5 litres of the 70% solution? Use algebraic techniques to support your answer and clearly define any variables that you use. 2. a) Plot the equations below on the same set of axes. Use the space to find suitable coordinates to plot. = − 2 2 4 = 2b) Use the graph to find the simultaneous solution(s). Indicate the location of the solution(s) on the graph and state your solution(s) below.c) Verify (check) your -coordinates in part b) by solving the equations simultaneously

I have 2 questions for mathematical modeling. Please check attachment for info and I will need it done pretty fast.
I have 2 questions for mathematical modeling. Please check attachment for info and I will need it done pretty fast. 1. Consider the following population model: dx/dt=2−x/1 x, where x(t) is the population density attime t.(a) Sketch the phase line for this model. Use the phase line to identify the fixed points, and indicate thetype of stability for each fixed point.(b) Suppose we incorporate a constant harvest h to this population, where h is any positive number.(i) Write a new differential equation that incorporates the harvest into the original model.(ii) Sketch the phase line for this model. You only need to show the phase line for x > 0. Includedifferent cases to show all types of possibilities for different numbers of fixed points and typesof stability.(iii) In each case you described in (ii), identify the non-negative fixed points, and indicate the typeof stability for each fixed point.(iv) Find the critical harvest level. That is, find the number such that the population approaches 0for any initial condition if h is above this number.(c) Suppose we incorporate a percentage harvest Hx to the original model, where 0 0). Use the phaseline to identify the positive fixed points, and indicate the type of stability.(b) Suppose we incorporate a constant harvest h to this population, where h is any positive number.(i) Write a new differential equation that incorporates the harvest into the original model.(ii) Sketch the phase line for this model. You only need to show the phase line for x > 0. Includedifferent cases to show all types of possibilities for different numbers of fixed points and typesof stability.(iii) In each case you described in (ii), identify the non-negative fixed points, and indicate the typeof stability for each fixed point.(iv) Find the critical harvest level. That is, find the number such that the population approaches 0for any initial condition if h is above this number.(c) Suppose we incorporate a percentage harvest Hx to the original model, where 0