5. Solve the following problem using a Venn diagram: Consider the following data among 110 students in the college dormitory: 30 students are on a list A (taking Accounting);: 35 students are on a list B (taking Biology); and 20 students are on both lists. Find the number of students: AVERSI a. on list A orB b. on exactly one of the two lists С. on neither list 6. Let g(x) = Find the domain of g(x). x-4" 2x2-3x+7 7. Let f(x) = Find f(3). %3D 5x2-2x
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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 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 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 10% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more interesting and profitable items on the shelves. Before making a final decision she decides to keep track of the total number of customers for a day, and whether they purchase specialty clothes for their pet. a) Assuming the pet store owner is correct in thinking that only 10% of her customers purchase specialty clothes for their pets, how many customers should she expect before someone buys a garment for their pet? b) What is the probability that she does not sell a garment until the 5th customer? c) What is the probability that exactly 4 of the first 10 customers buy specialty clothes for their pet? d) What is the probability that at least 3 of the first 35 customers buy specialty clothes for their pet?…1. a car rental company conducted a survey among 380 customers to gain ideas about a vehicle. The survey showed that 200 customers prioritized vehicle safety above all other features, 160 customers prioritized vehicle size above all other features, and 40 were not interested in either features. a)recreate the information detailed above in a venn diagram in order to show the number of customers that preferred vehicle safety and vehicle size equally. b) Solve for x, to determine the number of people who consider both features equally important c) determine the probability that a customer would consider both features equally important.
- A gender psychologist is interested in studying whether children, when left on their own, actually show more interest in toys associated with their assigned gender. The psychotherapist allows the participants (n = 16) to move freely back and forth for 40 minutes between two rooms, one of which contains toys traditionally associated with girls and another which contains toys traditionally associated with boys. She collects the data and finds that on average the children spend 23 minutes in the room (M = 23) with the toys associated with their assigned gender, with a standard deviation of s = 9. She conducts a one-tailed test and sets the alpha at .05.A gender psychologist is interested in studying whether children, when left on their own, actually show more interest in toys associated with their assigned gender. The psychotherapist allows the participants (n = 16) to move freely back and forth for 40 minutes between two rooms, one of which contains toys traditionally associated with girls and another which contains toys traditionally associated with boys. She collects the data and finds that on average the children spend 23 minutes in the room (M = 23) with the toys associated with their assigned gender, with a standard deviation of s = 9. She conducts a one-tailed test and sets the alpha at .05. The alternative hypothesis is μ > ______ What is the critical t? _________ Calculate the t value and round to 2 decimals: _______ With alpha = .05. can she reject the null (type yes or no)? _______ch 13. 5: Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force who call on existing customers and look for new business. The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined: The amount earned in commissions last month (y) The number of miles driven last month (x1) The number of sales calls made last month (x2) The information is reported below. Commissions ($000) Calls Driven Commissions ($000) Calls Driven 29 139 2,371 27 146 3,290 26 132 2,226 25 144 3,103 28 144 2,731 29 147 2,122 26 142 3,351 25 144 2,791 29 142 2,289 25 149 3,209 28…
- The dependencies between the 10 activities listed in the table above are as follows:• The project starts with two activities—A, and B—which can be done concurrently.• When activity A is finished, activity C can start• When activity B is finished, activities D and E can start• When both activities C and D are finished, activity F can start• When activity E is finished, activity G can start• When activity F is finished, activity H can start• When both activities G and H are finished, activity I can start• When activity G is finished, activity J can start• The project is complete when activities I and J are finished Questions1. Organize the information above in an activity precedence table showing the activity, precedent and duration (calculated using the PERT weighted average formula and round to the nearest integer).2. Draw an AON network diagram and calculate its early start, early finish, late start and late finish times, floats (Free and total) for each activity. Make sure you…Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computerized wheel alignment and balancing machine. Managers feel that maintenance expense is related to usage of the machine, and they have collected the following information on weekly usage of the machine (in hours) and annual maintenance expense (in hundreds of dollars) from 10 other companies that own the machine.Company Weekly Usage(hours) Annual maintenance Expense(hundreds of dollars)A 13 17.0B 10 22.0C 20 30.0D 28 37.0E 32 47.0F 17…In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 40 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 40-minute interval) one otter initiates social grooming of another. Lambda = 6.8 (b) Find the probabilities that in your 40 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.) P(4) = P(5) = P(6) =
- In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 30 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another. a) What is ?? b) Write out the formula for the probability distribution of the random variable r. P(r) = _________ c) Find the probability that one otter will initiate social grooming four or more times during the 30-minute observation period. (Round your answer to four decimal places.)In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group of river otters under study had a frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing river otters for 30 minutes. Let r = 0, 1, 2, ... be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another. a) Find the probabilities that in your 30 minutes of observation, one otter will initiate social grooming four times, five times, and six times. (Round your answers to four decimal places.) P(4) = P(5) = P(6) = b) Find the probability that one otter will initiate social grooming less than four times during the 30-minute observation period. (Round your answer…1. a car rental company conducted a survey among 580 customers to gain ideas about a vehicle. The survey showed that 200 customers prioritized vehicle safety above all other features, 160 customers prioritized vehicle size above all other features, and 40 were not interested in either features. a)recreate the information detailed above in a venn diagram in order to show the number of customers that preferred vehicle safety and vehicle size equally. b) Solve for x, to determine the number of people who consider both features equally important c) determine the probability that a customer would consider both features equally important. 2. a) determine the probability that a customer would chose a vehicle based on it's safety.