A paint company is trying to recycle unpopular paint colours by mixing them together to create better colours. All paints are composed of four pigments (A,B,C,D). The current paints are composed of pigments (in percent) according to the following equations: are p₁ = 80A + 16C + 4D, P2 = 80B + 20C, P3 = 30A + 10B + 60C, P4 = 10A + 10B + 72C + 8D. The better colour say p; is composed as follows: ps = 40A + 27B + 31C + 2D. How much of the paints P₁, P2, P3, and p4 should be used to make one gallon of ps. Hint: use (Ax=b).
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- In a hypothetical study of population dynamics, scientists have been tracking the number of rabbits and foxes on an island. The number of rabbits and foxes are determined once a year using high resolution infrared cameras and advanced computer vision methods.Each year, the number of rabbits and foxes are found to change by the following equations: $$ {\Delta}R = round( kr*R - krf*R*F ) $$ $$ {\Delta}F = round( -kf*F + kfr*R*F ) $$ where $ {\Delta}r $ and $ {\Delta} f $ are the changes in number of rabbits and foxes by the end of that year; and R and F are the population sizes at the end of the previous year. kr, krf, kf, kfr are coefficients that depend on the species of rabbits and foxes.With these dynamics, the scientists realize that one or both species can become extinct on the island. At the end of each year, if there are fewer than 2 animals of a kind, the scientists transfer rabbits and/or foxes to make sure there are at least 2 of each kind.Write a function…Given X = {1, 2, 5, 8, 9}, Y = {3, 4, 6, 7, 8}, Z = {1, 2, 4, 6, 8} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Findthe following: 1. (X -Z̅) ∪ Y2. (X̅ ∪ Z) ∩ Y3. (Y ∩̅Z) ∩ X4. (X ∩ Z) - (X ∪ Y)5. Z̅ – (Y ∩ X)You and your friends decided to hold a “Secret Santa” gift exchange, where each person buys a gift for someone else. To see how this whole thing works, let’s consider the following example. Suppose there are 7 people A, B, C, D, E, F, and G. We denote x → y to mean “x gives a gift to y.” If the gift exchange starts with person A, then they give a gift to E. Then E gives a gift to B. And it is entirely possible that B gives a gift to A; in such a case we have completed a “cycle.” In case a cycle occurs, the gift exchange resumes with another person that hasn’t given their gift yet. If the gift exchange resumes with person D, then they give a gift to G. Then G gives a gift to F. Then F gives a gift to C. Then finally C gives a gift to D, which completes another cycle. Since all of the people have given their gifts, the giftexchange is done, otherwise the gift exchange resumes again with another person. All in all, there are two cycles that occurred during the gift exchange: A → E → B → A…
- You are given a grid having N rows and M columns. A grid square can either be blocked or empty. Blocked squares are represented by a '#' and empty squares are represented by '.'. Find the number of ways to tile the grid using L shaped bricks. A L brick has one side of length three units while other of length 2 units. All empty squares in the grid should be covered by exactly one of the L shaped tiles, and blocked squares should not be covered by any tile. The bricks can be used in any orientation (they can be rotated or flipped). Input Format The first line contains the number of test cases T. T test cases follow. Each test case contains N and M on the first line, followed by N lines describing each row of the grid. Constraints 1 <= T <= 501 <= N <= 201 <= M <= 8Each grid square will be either '.' or '#'. Output Format Output the number of ways to tile the grid. Output each answer modulo 1000000007. Sample Input 3 2 4 .... .... 3 3 ...…Given the following linear programming model; Who are the basic variables on the initial board? MAX Z = 5 X1 + 5 X2 Hold it: 12 X1 + 8X2 <= 96 6 X1 + 12X2 <= 72 X1 <= 2 X1, X2> = 0 Select one: a.All b.h1; h2 c.X1; X2 d.None e.h1; h2; h3A library must build shelving to shelve 200 4-inch high books, 150 8-inch high books, 300 10-inch high books and 180 12-inch high books. Each book is 0.5 inch thick. The library has several ways to store the books. For example, an 8-inch high shelf may be built to store all books of height less than or equal to 8 inches, and a 12-inch high shelf may be built for the 12-inch books. Alternatively, a 12-inch high shelf might be built to store all books. The library believes it costs $2,300 to build a shelf and that a cost of $5 per square inch is incurred for book storage. (Assume that the area required to store a book is given by height of storage area times book’s thickness.) Formulate and solve a shortest-path problem that could be used to help the library determine how to shelve the books at minimum cost. (Hint: Have nodes 0, 4, 8, 10 and 12, with cij being the total cost of shelving all books of height >i and ≤ j on a single shelf.)
- Bruno gives his son P100 on one day, P50 on the second day, P25 on third day and so on. What will be total amount given by Ram to his son starting from the first day, if he lives forever?We examine a problem in which we are handed a collection of coins and are tasked with forming a sum of money n out of the coins. The currency numbers are coins = c1, c2,..., ck, and each coin can be used as many times as we want. What is the bare amount of money required?If the coins are the euro coins (in euros) 1,2,5,10,20,50,100,200 and n = 520, we need at least four coins. The best option is to choose coins with sums of 200+200+100+20.How make simulation Aquarium Automatic Care (AOC) system (incl. coding) with Arduino. AOC is simulated using Tinkercad based on below conditions? Conditions: 1. Water must be replaced when -Water level (T) < 41 mm -Discard water and fill 30% of Aquarium water volume when high Acidic pH (pH> 9)2. Fish food (pellets): 1 x 4.5 mL/day at 6am in the morning, the machine only contains 100 mL (warning on D-day is over)3. To save electricity, the aquarium lights are on at night (8 hours)
- Recall Pigou’s example discussed in class, where there are two roads that connect a source, s, and destination, t. The roads have different travel costs. Fraction x1 of the traffic flow on route 1, and the remainder x2 on route 2. Here consider the following scenario. • The first road has “infinite” capacity but is slow and requires 1 hour travel time, T1 = 1. • The second road always requires at least 15 mins, which then increases as a function of traffic density, T2 = 0.25 + 0.75x2. If drivers act in a “selfish” manner – the user optimal scenario – all the traffic will flow on the second path, as one is never worse off. Worst case scenario for path 2, both paths take one hour. So no one is incentivized to change their behavior. 1. Assume user optimal behavior, and calculate τ the expected travel time per car. 2. If instead we could control the flows, we could minimize the expected travel time. Using the expression in part (a), calculate the optimal allocation of flows x¯1 and ¯x2…I don't need a code for these questions. I just need them answered Nine steel specimens were submerged in seawater at various temperatures, and the corrosion rates were measured. The results are presented in the following table:Temperature (OC)Corrosion(mm/yr.)26.6 1.5826 1.4527.4 1.1321.7 0.9614.9 0.9911.3 1.0515 0.828.7 0.688.2 0.59a. Construct a scatterplot of corrosion (y) vs. temperature (x). Verify that a linear model is appropriate.b. What is the least-square line (trendline/regression line) for predicting corrosion from temperature?c. Two steel specimens whose temperatures differ by 10OC are submerged in seawater. By how much would you predict their corrosion rates differ?d. Predict the corrosion rate for steel submerged in seawater at a temperature of 20OC.e. Construct a table with predicted values from the original dataset.f. Compute the residuals. Which point has the residual with the largest magnitude?g. What is the correlation between temperature and corrosion rate? What…Suppose we have a nice young couple who borrow $700000 from the bank, at an annual interest rate of3.124%. The mortgage is a 30 year loan, so they need to pay it off within 360 months total. Our happycouple decide to set their monthly mortgage payment at $2000 per month. Will they pay off the loan intime or not?Note that the monthly balance will be calculated asbalance = (im × previous balance) - monthly paymentwhere the convert annual interest to a monthly multiplier im is calculated as im = (1 +i)1/12 and i = annualinterest rate.Write a loop for track the total payment in 360 months so that we can evaluate if the couple can pay off theloan. Write in R Please and thank you.