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- Suppose the relationship between Y and X is given by: Y = 50 + 3X + error By how much does the expected value of Y change if X decreases by 2 units?In a chemical manufacturing plant, a certain type of chemical B is producedthrough reactions in chemical A. Through observation, the officers on duty have noted that the rate of conversion from chemical A to B in proportion to the amount of chemical A present at any time, further investigation has revealed that 10% amount has been converted in first five minutes.a) The plant manager wishes to know the percentage of chemical A that will be converted in 20 minutes.b) The plant manager wishes to know the time it will take to convert 60minutes of chemical A.For time series data on sales (y) and advertisement cost (X) the fitted trend equation is y^=-43.80+35.950x. When the advertising cost is 5.5 million the corresponding actual sales is 153. Find the residual value when the advertisement cost is 5.5 million.
- Suppose the relationship between Y and X is given by: Y = 25 - 3X + error By how much does the expected value of Y change if X decreases by 1 unit?a car sells for $12,500 and one year later it is valued at $11,375. find the decay rate of the carIn a chemical reaction, a certain compound changes into another compound at a rate proportional to the unchanged amount. There is 40 grams of the original compound initially and 35 grams after 1 hour. When will 75 percent of the compound be changed?
- A.F.D.C. was intended to provide mothers with enough to get by — barely — while raising their children. In 1970 three-person families on A.F.D.C. received, on average, $194 a month. Adjusting for inflation, that’s the equivalent of around $15,000 a year today, compared with the $6,000 a family with two children over age 6 ($7,200 if they’re under 6) will receive under the new plan. In 1970, an A.F.D.C. family of three received about 25 percent of median income for three-person families — hardly a generous allowance, but maybe, just, enough to live on. The new American Rescue Plan will give a single parent of two children less than 7 percent of median income c. What is median family income today (2021)? How much will the new relief bill give to a single parent with two children annually?A bacterial population B is known to have a rate of growth proportional to B itself. If between noon and 2 P.M. the population triples, at what time, no controls being exerted, should B become 100 times what it was at noon?Two pumps capable of delivering 100 hp to an agricultural application are being evaluated in a present economy study. The selected pump will only be utilized for one year, and it will have no market value at the end of the year. Pertinent data are summarized as given follows. If electric power costs $0.10 per kWh and the pump will be operated 4,000 hours per year, which pump should be chosen? Recall that 1 hp = 0.746 kW.
- The decay of radioactive elements can sometimes be used to date events from Earth’s past. In a living organism, the ratio of radioactive carbon, carbon-14, to ordinary carbon stays fairly constant during the lifetime of the organism, being approximately equal to the ratio in the organism’s atmosphere at the time. After the organism’s death, however, no new carbon is ingested, and the proportion of carbon-14 in the organism’s remains decreases as the carbon-14 decays. Scientists who do carbon-14 dating often use a figure of 5730 years for its half-life. Find the age of a sample in which 10% of the radioactive nuclei originally present have decayed.What’s the initial value and what’s the elimination rate?A hat manufacturer is planning to expand its workforce. It estimates thatthe number of hats produced by hiring x new workers is given byT(x) = – 0.25 x4 + 6 x3 0 ≤ x ≤ 18a) When is the rate of change of hat production increasing and when is itdecreasing?b) What is the point of diminishing returns (Hint: inflection point) and themaximum rate of change of hat production?
