Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN: 9781133382119

Author: Swokowski

Publisher: Cengage

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2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food?
Table 2.7
Bacteria Strain I Bacteria Strain II Bacteria Strain III
Food A 1 2 0
Food B 2 1 3
Food C 1 1 1

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There are X-Mart and Y-Mart convenience stores. It is assumed that each customer purchases once a week at one of the two supermarkets (but not both). In a study, a sample of 100 buyers was taken for 10 weeks. From this research it is known that if buyers go to X-mart store one week, 85 people will still buy at X-mart store the following week and if buyers go to Y-mart store one week, 70 people will still buy at Y-mart store. mart the following week.
1. Make a table and matrix of transition probabilities.
2. If John purchases at X-mart in the first week, what is the probability that Bob purchases at X-store in the third and fourth weeks?

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Suppose Martin is a very talented used-car salesman. Whenever Martin talks to a new customer, there is a 90% chance that he convinces the customer to purchase one of his used cars. Brian, Martin's boss, is envious that Martin sells many more cars than he does. Because of his jealousy, Brian institutes a new rule that Martin is only allowed to talk to 35 customers per day. Thus, Martin continues to work each day until he speaks to 35 customers, at which point Brian sends him home. Let ? represent the number of used cars that Martin sells on a given day.
What are the mean, ?, and variance, ?^2, of ?? Please round your answers to the nearest two decimal places.
?=_______?
?^2=_________?

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A health researcher studying child birth is interested in the possible effect that smoking by the mother during pregnancy has on the baby's birth weight. To investigate, the researcher conducts an observational study by reviewing 400 records of women in their twenties who have recently given birth for the first time. For each record, he notes whether or not the woman smoked during pregnancy and the baby's birth weight, in addition to the woman's education level, and age. From the data, the researcher creates two groups: women in their twenties who smoked during pregnancy and women in their twenties who did not smoke during pregnancy. Then he compares the average birth weight between the two groups.
(a)Why might the researcher have chosen to perform an observational study (by gathering information from past records) and not a randomized experiment (by assigning pregnant women to either the smoking or nonsmoking group at random)? Choose the best answer from the choices below.
In a…

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The management of a company know that in the past, 38% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 17% of their sales were from people who are over 50 years old. A sample of 225 customers was taken to see if these market shares had changed. In the sample, 75 people were under 30 years old, 100 people were between 30 and 50 years old, and 50 people were over 50 years old.
What is the expected counts under the null for people over 50 years old? (round to 2 decimals)
The value of the test statistic χ2 is: (round to 4 decimals)
The p-value is: (round to 4 decimals)
The conclusion is:

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Is there a link between dark chocolate and weight loss when compared to milk chocolate? A nutritionist gathers 60 people, selected at random, then randomly assigns half of the group to eat a single dark chocolate bar after dinner each night and the other half to eat a single milk chocolate bar after dinner each night for 6 months. Everyone is to keep track of the other food they eat in an app provided. The nutritionist then compares each person’s weight after the 6 months to their weight before eating the different chocolates accounting for the other calories consumed.
12) What type of study does this describe?
a)
Survey
b)
Observational study
c)
Experimental study

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A Gallup survey showed that in March
2011
,
8
of every
25
employers in the United States were adding more workers to their workforce,
9
of
50
were reducing their workforce, and
1
of
2
were keeping it the same. In a metropolitan area there are
1250
employers and of those who will hire, they will hire an average of seven new employees. If the employers who were cutting their workforce in that area were planning on letting go an average of nine workers, what would the net change in jobs for the area be?
This metropolitan area would see a ▼net decrease or increase of
jobs.

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Suppose we are interested in analyzing the market share and customer loyalty for Murphy's Foodliner and Catalina's Supermarket, the only two grocery stores in a small town. We focus on the sequence of shopping trips of one customer and assume that the customer makes one shopping trip each week to either Murphy's Foodliner or Catalina's Supermarket, but not both. The data shows that of all customers who shopped at Murphy's in a given week, 90% shopped at Murphy's the following week while 10% switched to Catalina's. The data shows that of all customers who shopped at Catalina's in a given week, 80% shopped at Catalina's the following week while 20% switched to Murphy's. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at Murphy's (State 1) and a 0.5 probability that the customer shopped at Catalina's…

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A large family travelling on the road in convoy decided to stop at a bed and breakfast since it was getting pretty late. However, there were too many people so they decided to split up to 3 nearby bed and breakfasts. 40% of the family members stayed at B&B 1, 35% stayed at B&B 2, and 25% stayed at B&B 3. According to feedback, 6% of the rooms in B&B 1 have lights that do not work, 9% of rooms in B&B 2 have lights that do not work, and 7% of rooms in B&B 3 have lights that do not work. 1) Given the data above, make a venn diagram.2) Determine the probability that a family member will have a room with functional lights. 3) Determine the probability that a family member whose room lights do not work was assigned to B&B A.

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In a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation.
(a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters.
P A
T
=
P
A
(b) Find the initial distribution vector for this Markov chain.
X0
=
(c) What percentage of the commuters are expected to use public transportation 6 months…

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Suppose we are interested in analyzing the market share and customer loyalty for Murphy's Foodliner and Ashley's Supermarket, the only two grocery stores in a small town. We focus on the sequence of shopping trips of one customer and assume that the customer makes one shopping trip each week to either Murphy's Foodliner or Ashley's Supermarket, but not both. The data shows that of all customers who shopped at Murphy's in a given week, 90% shopped at Murphy's the following week while 10% switched to Ashley's. The data shows that of all customers who shopped at Ashley's in a given week, 80% shopped at Ashley's the following week while 20% switched to Murphy's. Suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at Murphy's (State 1) and a 0.5 probability that the customer shopped at Ashley's (State 2) at…

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A car agency has offices in Phoenix, Denver and Chicago. The agency allows one- or two-way rentals so that cars rented in one location may end up in another. Statistics show that at the end of each week 70% of all rentals are twoway. As for the one-way rentals: from Phoenix, 40% go to Denver, and the rest to Chicago; from Denver, 60% go to Chicago and the rest to Phoenix; from Chicago, 40% go to Denver and the rest to Phoenix;
(a) Express the situation as s Markov chain.
(b) If the agency starts the week with 100 cars in each location, what will the distribution be like in two weeks (two-step transition probability matrix)?
(c) If each location is designed to handle a maximum of 120 cars, would there be a long run space availability problem in any of the location?

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