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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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- A new process to produce synthetic diamonds can be operated at a profitable level only if their average weight is greater than 0.5 carats. To evaluate the profitability of the process, six diamonds are generated with weights of 0.46, 0.61, 0.52, 0.48, 0.57 and 0.54 carats. Do these six measurements present enough evidence to indicate that the average weight of the diamonds produced by the process is more than 0.5 carats? Calculate the lower limit for µ of 95% using a lower confidence limit.ment Pla x 6 0 [ Q A Player A education.wiley.com/was/ui/v2/assessment-player/index.html?launchId=51278b39-ea18-4374-abf9-4ec63a4de8eb#/question/13 Question 14 of 20 View Policies Current Attempt in Progress 2 t X WP Videoplayer A a. The initial amount is Fill in a table of values for the amount A = 70 1.051¹ for values of the time period t of 0, 1, 10, 15, and 20, and then complete the following statements. Round answers to three decimal places. 0 F2 i c. The first of the time periods in the table in which the population is at least doubled is d. The first integer time period in which the population is at least doubled is D S4 X $ 1 a F4 R חד Earth system notes #1 X M Inbox (3,313) - agyem XM Update - Kellogg's ca X % 5 16 F5 IM T G Mi 10 6 MacBook Air c F6 Y & 7 H Jud i F7 U * 8 J ] IN 15 DII F8 Attempts: 0 of 3 used Submit Answer ( 9 K 8 F9 0 -/5 = : 20 ) L VCU F10 P University Counseling X + = 0 H 111 ? Update V deleteAn experiment has been conducted to evaluate a new process for producing syntheticdiamonds. A number of diamonds have been generated by the new process with recordedweights of 0.46, 0.61, 0.52, 0.48, 0.57, and 0.54 carat. A study of the process costsindicates that the actual average weight of the diamonds must exceed 0.5 in order that theprocess be operated at a profitable level.a). Based on a 95% confidence level, estimate the actual mean weight of syntheticdiamonds using the new process.b). Carefully interpret this interval estimation.c). Explain carefully whether or not there is sufficient evidence to conclude that theprocess is operating at a profitable level using the estimation in part (a)
- An experiment has been conducted to evaluate a new process for producing syntheticdiamonds. A number of diamonds have been generated by the new process with recordedweights of 0.46, 0.61, 0.52, 0.48, 0.57, and 0.54 carat. A study of the process costsindicates that the actual average weight of the diamonds must exceed 0.5 in order that theprocess be operated at a profitable level. a). At 5% level of significance, is there sufficient evidence to conclude that the process isoperating at a profitable level? Your conclusion must be in terms of the P-Value aswell as setting up a Rejection Region. You must show all necessary work. b). Which statistical distribution should be applied in this situation and why? Explaincarefully. c). What type of error is possible and describe this error in terms of the problemAn experiment has been conducted to evaluate a new process for producing syntheticdiamonds. A number of diamonds have been generated by the new process with recordedweights of 0.46, 0.61, 0.52, 0.48, 0.57, and 0.54 carat. A study of the process costsindicates that the actual average weight of the diamonds must exceed 0.5 in order that theprocess be operated at a profitable level.a). At 5% level of significance, is there sufficient evidence to conclude that the process isoperating at a profitable level? Your conclusion must be in terms of the P-Value aswell as setting up a Rejection Region. You must show all necessary work.b). Which statistical distribution should be applied in this situation and why? Explaincarefully.c). What type of error is possible and describe this error in terms of the problem.d). Based on a 95% confidence level, estimate the actual mean weight of syntheticdiamonds using the new process.e). Carefully interpret this interval estimation.f). Explain carefully whether…Solar energy generation along highways. The potential of using solar panels constructed above national highways to generate energy was explored in the International Journal of Energy and Environmental Engineering (December 2013). Two-layer solar panels (with 1 meter separating the panels) were constructed above sections of both east-west and north-south highways in India. The amount of (kilowatt-hours) supplied to the country's grid by the solar panels above the two types of highways was determined each month. The data for several randomly selected months are provided in the table. The researchers concluded that the "two-layer solar panel energy generation is more viable for the north-south oriented highways as compared to east- west oriented roadways." Compare the mean solar energy amounts generated for the two types of highways using a 95% confidence interval. Does the interval support the re- energy searchers' conclusion? Month East-West North-South February April July September…
- Assuming an M/M/1 system setup with a service rate of 25 entities per hour and an idling ratioof 4% Define the system’s birth rate. Define at least two ways of arriving at the number of entities in the system. Define the ratio of the time an entity spends waiting and the time the entity spends in thesystem?The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the independent variable and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portionof the hours worked. The intercept for the sample regression line that the owner has computed is -2.24 and the slope is 0.03. What is the predicted number of labor hours for moving 484 cubic feet? Hint: Provide your answer accurate to 2 decimal places.3. The time it takes an employee to package the components of a certain product is normally distributed with H=8.5 minutes and o=1.5minutes. To boost productivity, management has decided to give special training to the 34% of employees who took the greatest amount of time to package the components. Find the amount of time taken to package components that will indicate that an employee should get special training. [5 points]
- 9. State the null hypothesis and the alternative hypothesis for this situation: "The level of a pollutant in a river adjacent to a chemical plant is regularly monitored. Over a period of years, the normal level of the pollutant of 0.5 ppm has been established by chemical analyses. Recently, the company has made several changes to the plant that appear to have increased the level of the pollutant. The company wants proof that the pollutant level has not increased." 10. State the null hypothesis and the alternative hypothesis for this situation: "Sewage and industrial pollutants dumped into a body of water can reduce the dissolved oxygen concentration and adversely affect aquatic species. In one study, weekly readings are taken from the same location in a river over a two-month period. The mean dissolved oxygen obtained from the analysis is 4.5 ppm. Some scientists think that 5.0 ppm is a dissolved oxygen level that is marginal for fish to live. They want to proof whether the mean…2. A medicine company has manufactured and claimed that their medicine pill contains an average of 14mg of active ingredient. Null Hypothesis: Alternative Hypothesis: Parameter: average Claim: average of 14mg RUBRICThe owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the independent variable and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portion of the hours worked. If the sum of squares Y is 1,513.32 and the sum of squares error is 176.22. What proportion of variation in labor hours is explained by the number of cubic feet moved? Hint: Provide answer accurate to 4 decimal places.