your roommate who wished they had taken ECH 3301 modeled a process in her/his lab class and obtained the following ODE that s/he did not know how to solve. S/he approached you for help after hearing you are taking ECH 3301 and doing well in it. Show your prowess with the general solution of the ODE, with details, to convince her/him that what s/he heard and her/his decision to come to you were both right! y” + 4 y’ + 4 y = 4x + 3ex
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your roommate who wished they had taken ECH 3301 modeled a process in her/his lab class and
obtained the following ODE that s/he did not know how to solve. S/he approached you for help after hearing
you are taking ECH 3301 and doing well in it. Show your prowess with the general solution of the ODE, with
details, to convince her/him that what s/he heard and her/his decision to come to you were both right!
y” + 4 y’ + 4 y = 4x + 3ex
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- A researcher for a cereal company wanted to demonstrate the health benefits of eating oatmeal. A sample of 9 volunteers was obtained each participant ate a fixed diet without any oatmeal for 30 days. At the end of the 30 days period cholesterol was measured for each individual. Then the participants begin a second 30 day period in which they repeated exactly the same diet except that they added 2 cups of oatmeal each day. After the second 30 day period, cholesterol levels were measured again and the researchers recorded the difference between the two scores for each participant. For this sample, cholesterol score averaged Md= 16 points lower with the oatmeal diet with SS=538 for the difference scores. A) Are the data sufficient to indicate a significant change in cholesterol levels? use a two-tail test with alpha=0.01A media personality argues that global temperatures are not rising, because every year an increase is reported such as 0.08 degrees C. The difference from the previous year is less than the margin of error of about 0.15 degrees C, so that difference should be ignored. What is a strong counterarguement? A. Even 0.08 degrees is a lot and thus should be considered. B. The margin of error is just extra information and thus can be ignored. C. The difference with any previous decade is much greater than the margin of error. D. 0.15 - 0.08 is 0.07, which is still an increase and thus should be considered.A machine to manufacture fasteners has a setup cost of $1,500 and a unit cost of $0.003 for each fastener manufactured. A newer machine has a setup cost of $1,750 but a unit cost of only $0.0025 for each fastener manufactured. Find the break point. (Round your answer to the nearest whole unit.)
- An allergy pill contains 180 mg of medicine. 10% of the medicine is eliminated from the patient's body every hour. To be effective, 70 mg of the medicine needs to be in the patient's body. If the patient takes one pill at 8 am, should they still be allergy-free at 5 pm?A media personality argues that global temperatures are not rising, because every year an increase is reported such as 0.08 degrees C. The difference from the previous year is less than the margin of error of about 0.15 degrees C, so that difference should be ignored. What is a strong counterargument? a) Even 0.08 degrees is a lot and thus should be considered b) the margin of error is just extra information and thus can be ignored c) the difference with any previous decade is much greater than the magin of error d) 0.15-0.08 is 0.07, which is still an increase and thus should be consideredA media personality argues that global temperatures are not rising, because every year an increase is reported such as 0.08 degrees C. The difference from the previous year is less than the margin of error of about 0.15 degrees C, so that difference should be ignored. What is a strong counterargument? A. Even 0.08 degrees is a lot and thus should be considered. B. The margin of error is just extra information and thus can be ignored. C. The difference with any previous decade is much greater than the margin of error. D. 0.15 - 0.08 is 0.07, which is still an increase and thus should be considered.
- A building contractor has a contract which will expire in 30 days. He has 80 men on the job and can finish the work in 50 days. The wage per day of 40 men is P20 and that of the other 40 men is P18 each for 8 hours of work per day. The fine or liquidated damages for the delay in work is P400 per day. How many more men should the contractor add in order to enable him to complete the work on time? Assuming that the additional men will have a wage of P20 each per day, will the contractor save money by employing enough men to enable him to complete the work on time or not adding men and paying the liquidated damages? How much is the saving if any? No overtime.The KLM Christmas tree Farm owns a plot of land with 5000 evergreen trees.Each year KLM allows retailers of Christmas trees to select and cut trees for sale to individualcustomers. KLM protects small trees (usually less than 4 feet tall) so that they will be availablefor sale in future years. Currently, 1500 trees are classified as protected trees, while theremaining 3500 are available for cutting. However, even though a tree is available for cuttingin a given year, it may not be selected for cutting until future years. Most trees not cut in agiven year live until the next year, but some diseased trees are lost every year. In viewing the KLM Christmas tree operation as a Markov process with yearly periods, we define thefollowing four states:A store is currently offering a 60% discount on all items Your cashier is trying to convince you to open a store credit card and says to you, "In addition to the 60% discount you are receiving for purchasing these items on sale today, you will get an additional 20% off for opening a credit card account. That means you are getting 105% off!" What is the mistaken assumption here? Why is that assumption incorrect? If you did truly have 80% discount, explain what should happen when you go to the counter to buy $500 worth of items? show calculation If you got your 60% discount and opened up the card for an additional 20%, what is the actual % discount you would receive? show calculation Is it better to apply the 60% discount first or the 20% discount first? show calculation
- You go to the doctor and he gives you 12 milligrams of radioactive dye. After 16 minutes, 4.5 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute.You will spend ____ minutes at the doctor's office.The past records of a supermarket show that its customers spend an averageof $95 per visit at this store. Recently the management of the store initiated a promotionalcampaign according to which each customer receives points based on the total moneyspent at the store, and these points can be used to buy products at the store. Themanagement expects that as a result of this campaign, the customers should beencouraged to spend more money at the store. To check whether this is true, the managerof the store took a sample of 14 customers who visited the store. The following data givethe money (in dollars) spent by these customers at this supermarket during their visits. 109 136 107 116 101 109 110 94 101 97 104 83 67 120Assume that the money spent by all customers at this supermarket has a normaldistribution. Using a 5% significance level, can you conclude that the mean amount ofmoney spent by all customers at this supermarket after the campaign was started is morethan $95?The Pine Christmas Tree Farm owns a plot of land with 5000 evergreen trees. Each year, the owner allows retailers of Christmas trees to select and cut trees for sale to individual customers. The farm protects small trees (usually less than 4 feet tall) so that they will be available for sale in future years. Currently, 1500 trees are classified as protected trees, while the remaining 3500 are available for cutting. However, even though a tree is available for cutting in a given year, it may not be selected for cutting until future years. Most trees not cut in a given year live until the next year, but some diseased trees are lost every year. In viewing the Christmas tree operation as a Markov process with yearly periods, we define the following four states: (1) Cut and sold, (2) Lost to disease, (3) Too small for cutting, (4) Available for cutting but not cut and sold.The following transition matrix is appropriate: States (1) (2) (3) (4) (1) 1 0 0 0 (2) 0 1 0 0 (3) 0.1 0.15…