Consider the theorem and its proof below. Theorem: If the product of two positive real numbers is greater than 25, then at least one of the numbers is greater than 5. Proof: For all positive real numbers a and b, If a ≤ 5 and b ≤ 5, then ab ≤ 25. If a ≤ 5, then ab ≤ 5b. Since b ≤ 5, then ab ≤ 25. Therefore, if ab > 25, then a > 5 or b > 5. Is the proof valid, and which type of proof is used?

The proof is valid, and it is a direct proof.

The proof is not valid, and it is a direct proof.

The proof is valid, and it is proof by contrapositive.

The proof is not valid, and it is proof by contrapositive.

A vehicle moves along a straight road. The vehicle's position is given by $f(t)$, where $t$ is measured in seconds since the vehicle starts moving. During the first 10 seconds of the motion, the vehicle's acceleration is proportional to the cube root of the time since the start. Which of the following differential equations describes this relationship, where $k$ is a positive constant? A $\frac{d f}{d t}=k \sqrt[3]{t}$ (B) $\frac{d f}{d t}=k \sqrt[3]{f}$ C $\frac{d^{2} f}{d t^{2}}=k \sqrt[3]{t}$ (D) $\frac{d^{2} f}{d t^{2}}=k \sqrt[3]{f}$

Using LC-3 Programming Exercise 1 Use .BLKW to set up a remote array of 10 values, starting at memory location x4000, as in lab 3. Now programmatically populate the array with the numbers 0 through 9 (note - NOT the characters '0' through '9'!) – i.e. hard-code just the first value (0), then calculate the rest one at a time, storing them in the array as you go. Remember the proper way of setting a register to 0! After you've stored them all, grab the seventh value (i.e. 6) and store it in R2. Clearly, you can't access this location via a label, so you'll need its actual address. How will you obtain that? And how will you use that address to get the value stored there? As always, step through your program and examine the values as they are stored in the array, and examine the final value stored in R2, to make sure your program works as expected. Exercise 2 You'll notice that Exercise 1 didn't ask you to output to console the array you built. Why not? Because as you know by now, numbers are not characters! So now copy your exercise 1 code into lab4_ex2.asm, and add an output loop, making it output the characters corresponding to the numbers stored in your array. Exercise 3 Let's try another modification of our well-used array program from Exercise 1: This time, instead of calculating and storing the numbers from 0 to 9 in the array, calculate and store the first ten powers of 2, starting with 20 = 1 in array index 0. Finally, grab the seventh value (26) from the array, and store it in R2. In order to do this, you will have to figure out how to calculate powers of 2. Some hints: Mathematically speaking: How do I obtain 2n+1 if I know 2n? What LC-3 operation could I use to multiply a number by 2? As always, place a breakpoint in your program, and step through it, examining the values as they are being stored in the array, and examine the final value stored in R2,  to make sure your program works as expected. Pay attention to both the decimal and hex representations of the values being stored. You already understand that you can't simply output the values in the array to the console “as is”, so we have to manipulate them somehow to turn them into characters. But this time all but the first four are multi-digit numbers when represented as decimal values, so our trick from the last exercise won't work – it can only convert the numbers from 0 to 9 into the single-digit ascii characters '0' through '9'.  Exercise 4 For now, we will instead observe what happens if we attempt to do what we just said can't be done - output the contents of the array "as is", i.e. as if they were ascii codes (which they are not!). Copy your exercise 3 code into your lab4_ex4.asm file, and add a second loop that loads the content of each element of the array into R0 and outputs it to the console using OUT. Now place a breakpoint at the start of your display loop and step through it: You will need to keep an eye on the Console to understand what is going on!! Please add comments!!!

7. The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with mean of 0.04 flaws per square foot of plastic panel. Assume automobile interior contains 10 square feet of plastic panel.(a) What is the probability that there are no surface flaws in an auto's interior?(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?(c) If 10 cars are sold to a rental company, what is the probability that at most two cars have any surface flaws?

QN ; Compare [ a construction company ] against TEN of the requirements of the audit standard given in supporting document below. [ 30 marks ] 1.0 PlanningRequirements:1.1Establish audit programme.1.2Selection of and checks on competence of audit lead.1.3Establish the scope of the audit.1.4Set procedures for the

I need answer in C++. Thank You!!! Project on pharmacy management system in c++ with oop concepts classes (medicine type, administration, cashier, manager, customer, owner) for software engineering mapping abstract class encapsulation inheritance friend function polymorphism association

Please DO NOT respond to this question by copy/pasting the code provided elsewhere on the site, none of those work. Thanks. Virtual Memory Lab This lab project addresses the implementation of page-replacement algorithms in a demand-paging system. Each process in a demand-paging system has a page table that contains a list of entries. For each logical page of the process, there is an entry in the table that indicates if the page is in memory. If the page is in memory, the memory frame number that page is resident in is indicated. Also, for each page, the time at which the page has arrived in memory, the time at which it has been last referenced, and the number of times the page has been referenced since the page arrived in memory are maintained. The page table data structure is a simple array of page-table entries (PTEs). Each PTE contains five fields as defined below: struct PTE { int is_valid; int frame_number; int arrival_timestamp; int last_access_timestamp; int reference_count; } Each process in the system has a page table that is simply an array of PTEs. Each process also has a pool of frames that is allocated. The frame pool for a process is represented as an array of integers, where each Integer represents the frame number of a frame that is free and is available for use by the process. Note that in order to get the frame number in the pool, you first need to access the integer in the array. This lab project aims to exercise the various policies for page replacement. In particular, we study the following three page-replacement policies: First-In-First-Out (FIFO) Least-Recently-Used (LRU) Least-Frequently-Used (LFU) In order to implement the above policies, we need to develop corresponding functions that process page accesses for a process. That is, for each process, given its page table, a logical page number being referenced and the free frame pool of the process, the functions should determine the memory frame number for the logical page. Also, the functions should modify the page table and the free frame pool appropriately. The details of the functions with respect to the different policies are described below. You need to develop code for these functions that implement the specifications. Place the code in a file called virtual.c. You should include the oslabs.h file.