For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. if the random variable x has mean mu subscript xμx and standard deviation sigma subscript xσx, then the mean, variance and standard deviation of y are given by the following formulas. mu subscript y baseline equals a plus b mu subscript xμy=a+bμx sigma squared subscript y baseline equals b squared sigma squared subscript xσ2y=b2σ2x sigma subscript y baseline equals |b| sigma subscript xσy=|b|σx the mean annual salary for employees at a company is $31 comma 00031,000. at the end of the year, each employee receives a $40004000 bonus and a 44% raise (based on salary). what is the new mean annual salary (including the bonus and raise) for the employees?

Afinancial institution, the thriftem bank, is in the process of formulating its loan policy for the next quarter. a total of $12 million is allocated for that purpose. being a full-service facility, the bank is obligated to grant loans to different clientele. the following table provides the types of loans, the interest rate charged by the bank, and the possibility of bad debt as estimated from past experience.type of loaninterest rateprobability of bad debtpersonal.140.10car.130.07home.120.03farm.125.05commercial.100.02 bad debts are assumed unrecoverable and hence produce no interest revenue either. competition with other financial institutions in the area requires that the bank allocate at least 40% of the total funds to farm and commercial loans. to assist the housing industry in the region, home loans must equal at least 50% of the personal, car, and home loans. the bank also has a stated policy specifying that the overall ratio for bad debts on all loans may not exceed .04. formulate this problem as a linear program. define your variables clearly and write all the constraints explaining the significance of each.

Apharmaceutical packaging company (ppc) has decided to reorganize its processes into cells. the company has four different production operations, each requiring a unique piece of equipment. the names and functions of the four pieces of equipment are sort, count, place, and package. the company packages five different families of products (a, b, c, d, and e). the tables below indicate the demand (total units/day by product family), required operations, and operation cycle times for each product family. assume that any individual piece of equipment is available to operate 16 hours/day, but 2 hours (in total) are lost each day on each piece of equipment due to breaks and meetings when operators are not available to operate the equipment. how many minutes/day are available for production

Ajewelry direct sales company pays its consultants based on recruiting new members. question 1 options: the company is running a pyramid scheme, which is illegal. the company is running a pyramid scheme, which is legal. the company has implemented a legal and ethical plan for growth. the company uses this method of compensation to reduce the fee for the product sample kit.