Concept explainers
(a)
To calculate: The product of matrix A and matrix B.
Where,
(b)
The number of males who are sick in the city.
Where,
(c)
The number of female carriers in the city.
Where,
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Finite Mathematics & Its Applications (12th Edition)
- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.arrow_forwardSatellite Television: Two competing companies offer satellite television to a city with 100,000 households. Gold Satellite System has 25,000 subscribers and Galaxy Satellite Network has 30,000 subscribers. (The other 45,000 households do not subscribe.) The matrix shows the percent changes in satellite subscriptions each year. FromGoldFromGalaxyFromNon-subscriberPercentChangesPercentChanges{ ToGoldToGalaxyToNonsubscriber [ 0.700.150.150.200.800.150.100.050.70 ] (a) Find the number of subscribers each company will have in 1 year using matrix multiplication. Explain how you obtained your answer. (b) Find the number of subscribers each company will have in 2 years using matrix multiplication. Explain how you obtained your answer. (c) Find the number of subscribers each company will have in 3 years using matrix multiplication. Explain how you obtained your answer. (d) What is happening to the number of subscribers to each company? What is happening to the number of nonsubscribers?arrow_forwardCompleting the transition to adulthood is measured by one or more of the following: leaving home, finishing school, getting married, having a child, or being financially independent.The bar graph shows the percentage of Americans, ages 20 and 30, who had completed the transition to adulthood in 1960 and in 2000. b. Use a 2 X 2 matrix to represent the data for 1960. Call this matrix B. c. Find B - A. What does this matrix represent?arrow_forward
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- A social media app is conducting a study on the amount of time users spend on the app. They collect the following variables. Age Years: How old they are in years? Income: Monthly Income Location: What country do they live in? Device: Do they use an iPhone, Samsung, other? Service: Who provides their mobile phone service? For example: T-Mobile, At&t, Verizon, ect Hours: How many hours do they spend on the app per week. A) Which variable could the research construct a one proportion z-interval for? B) The social media app just launched a new algorithm that suggest content in an effort to increase the amount of time the user spends on the app. The researchers want to use the survey results to see if there is statistically significant evidence that on average users spend more than 10 hours per week on the social media app. The researchers found in their sample of 44 users, the mean hours spent on the app is 10.5 hours with a standard deviation of 5.675 hours. Which type of hypothesis test…arrow_forwardA company produces handmade shawls and afghans. They spin the yarn, dye it, and then weave it. A shawl requires 1 hour of spinning, 1 hour of dyeing, and 1 hour of weaving. An afghan requires 1 hour of spinning, 2 hours of dyeing, and 4 hours of weaving. There are at most 8 hours available each day for spinning, 10 hours for dyeing, and 16 hours for weaving. Summarize the data in a table. Use the table to write a system of inequalities. Then graph the feasible region. Complete the table. Hours Hours Number Spinning Dyeing Shawls x Afghans y Maximum Number of Hours Available 8 10 Hours Weaving 16arrow_forwardInsurance (Life Expectancy). Insurance companies base their premiums on many factors, but basically all the factors are variables that predict life expectancy. Life expectancy varies from place to place. The following variables are from a data set on various measures obtained from the 50 US states (around 2009) Murder: rate per 100,000 HS Graduation: recorded as a percentage Income: per capita income in dollars Illiteracy: rate per 1,000 Life Expectancy: recorded in years 2008 Electoral vote state color: red / blue State electoral vote color coded: red = 1 / blue = 0 Multiple linear regression results: See Attachments please Write the multiple linear regression equation, use this equation to predict the Life expectancy for Pennsylvania and calculate the residual. Data: State Name Life Expectancy Murder HS Grad Income Illiteracy ColorCode Color Alabama 69.05 15.1 41.3 3624 2.1 1 red Alaska 69.31 11.3 66.7 6315 1.5 1 red Arizona 70.55 7.8 58.1 4530 1.8 1 red Arkansas…arrow_forward
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