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- Use the Binomial Theorem to expand (3x+12y)6Find y" by implicit diferentiation 3x2+y2=3RJ&M Company manufactures furniture such as sofas and tables. In theircurrent inventory, a total of 48 planks of wood are left. Each sofa needs four planks of wood to be made while each table needs two planks of wood to be made. The company earns a profit of P hundred pesos where P(x, y) = (6x^2)y for selling x units of sofas and y units of tables. With their current inventory of woods, how many sofas and tables are needed to be produced to maximize their profit?
- Determine the uncertainties in x2 and y2 using the rule for propagating uncertainties when multiplying two numbers. x=80, y=60, ∆x= ∆y=5.A Company is planning a Children’s Christmas party for their 750 employees.Base on the survey responses they have 526 who indicated that they have girls and342 indicating that that have boys.From the survey how many possible employees have both boys and girls,if 75 employees did not do the survey?Find the expliciy general solution.
- The television show Lett3rs has been successful for many years. That show recently had a share of 19, which means, that among the TV sets in use, 19% were tuned to Lett3rs. An advertiser wants to verify that 19% share value by conducting its own survey, and a pilot survey begins with 10 households have TV sets in use at the time of a Lett3rs broadcast. If at most one household is tuned to Lett3rs, does it appear that the 19% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?) A. no, it is not wrongB. yes, it is wrongSuppose you are going to randomlysample 1 individual from a population of160 people. In the population, there are50 children younger than 12, 70teenagers, and 40 adults. What is theprobability the individual you select willbe a teenager or an adult? Show solution.evaluate nCx px qn-x for n=5 x=2 p= 1/2
- When Alexa takes her 1st free throw in a game, she has a 40 percent chance to score.She has a 70 percent chance of scoring on her next throw if she scored on the earlierone, but only a 20 percent chance if she didn't score on the previous one. Assumeshe needs to make 3 free throws in a row, the first of which she misses. What is theprobability that she will score at least once on one of the following two throws?Maximize B=5xy^2, where x and y are positive numbers such that x+y^2=5.The inventor of a new game believes that the variable cost for producing the game is $0.95 per unit and the fixed cost are $4,700. The inventor sells each game for $1.99. Let c be the number of games produced