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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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- An analyst in the real estate business is interested in the relationship between the cost of the monthly rent of an apartment and the size of an apartment, in big cities. She gathers data for apartment buildings in 12 cities in 12 different states. In each city, she gets the numbers for at least 5 different buildings and at least 40 apartments in each building. She reaches the following conclusion: the rental cost of a 2-bedroom apartment is 50% more than the rental cost of a 1-bedroom apartment, and the rental cost of a 3-bedroom apartment is 50% more than the rental cost of a 2-bedroom apartment. Based on the paragraph, what is the minimum number of apartments she collected data on? Do you think her sample was large enough to be statistically valid? Based on the paragraph, are there any apartments or apartment buildings that she would have excluded from her study? Do you see any bias in how she selected apartments for her study? Based on the paragraph, is there a positive…As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatically. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be N(t) = 0.00525t2 + 0.075t + 4.7 (0 ≤ t ≤ 4) million in decade t, where t = 0 corresponds to 2010.† (a)What is the projected number of people with Alzheimer's disease in the United States age 65 years and over in 2040? (Round your answer to four decimal places.) million (b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2040? million per decade (c)How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study? million per decade per decadeA media personality argues that global temperatures are not rising, because every year an increase is reported, such as 0.09 degrees C. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument? a. The change of 0.09 is not a lot and thus should be ignored b. the difference is only 0.04, but that is still a significant change c. the margin of error is larger than the increase, so we should consider it an issue of just extra information and thus can be ignored d. the margin of error is quite small compared to the change year over year, so it is a significant issue
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- A researcher wants to determine if the exam scores of the students are dependent on the length of time spent in studying the subject. Ten students in a certain class were taken and the results are shown in the table below where X is the time spent in studying the subject in hours and Y is the examination scores.Which of the following statements is true? If a student spend 2 hours and 45 minutes in studying the subject, then his estimated examination score (in whole number) is 84. For every hour increase in the time spent in studying the subject, its examination score will increase by 7. The time spent in studying the subject and the examination score are not associated at all. There is an inverse linear relationship between the time spent in studying the subject and the examination score.The purchased cost of a shell-and-tube heat exchanger (floating-head and carbon-steel tubes) with A m^2 of the heating surface was OMR B in 2015.(a) What will be the 2015 purchased cost of a similar heat exchanger with C m^2 of the heating surface if the purchased cost capacity exponent is 0.65 for surface areas ranging from 10 to 50 m^2?(b) If the purchased cost capacity exponent for this type of exchanger is 0.83 for surface areas ranging from 50 to 200 m^2, what will be the purchased cost of a heat exchanger with A m^2 of heating surface in 2018? [15 Marks] Use suitable Marshall & Swift or Chemical engineering plant cost index data values with proper referencing. where A=7728 m^2 B=7728 OMR C=28 m^2The task I am struggling with: La Villa is a village in the Italian Alps. Given its enormous popularityamong Swiss, German, Austrian, and Italian skiers, all of its beds are always booked in the winter season and there are on average 1200 skiers in the village. On average skiers stay in La Villa for 10 days.a) How many new skiers are arriving on average in La Villa every day?b) A study done by the largest hotel in the village has shown that skiers spend on average $50 per person on the first day and $30 per person on each additional day in local restaurants. The study also forecasts that due to increased hotel prices the average length of stay for 2003/2004 season will be reduced to five days. What will be the percentage change in revenues of local restaurants compared to last year when skiers still stayed for 10 days? Assume that hotels continue to be fully booked! Thank you very much for your help.
- The following question is on statistics. An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that 30 minutes before closing time, 5 cars are in line. If the car wash is in continuous use until closing time, is it likely anyone will be in line at closing time?Have you ever agreed to give up your airplane ticket in return for a free ticket? Have you ever searched for the cheapest flight so that you could visit a special friend? This example provides some of the analysis that leads to results such as overbooked flights and reduced fares on certain flights. Suppose that you are in charge of marketing airline seats for a major carrier. Four days before the flight date you have 16 seats remaining on the plane. You know from past experience data that 80% of the people that purchase tickets in this time period will actually show up for the flight. a. If you sell 20 extra tickets, what is the probability that you will overbook the flight or have at least 1 empty seat? b. If you sell 18 extra tickets, what is the probability that you will overbook the flight or have at least 1 empty seat?(a)Consider a flight with a seating capacity of 160 seats. This flight is always full and there is a chance to be overbooked. The actual no-show rate (NSR) of the flight is 3.5% and the estimated NSR is 6.3%. If this flight is oversold according to the estimated NSR, what is the number of excess/extra passengers that will show up and there will be no seats for them on the day of departure? (b)Consider a flight with a seating capacity of 160 seats. This flight is always full and there is a chance to be overbooked. The actual no-show rate (NSR) of the flight is 3.5% and the estimated NSR is 6.3%. If the one-way fare of this flight is $300. If this flight is oversold according to the estimated NSR, what is the additional revenue that this flight will generate due to overbooking?