Determine whether the equation defines y as a function of x. 22. Зх — 5у %3D7 23. Зх2 -
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- A downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that. Which equation(s) describes the total cost y as a function of the hours x? Y = 5x + 2.5x Y = 5x + 2.5(x-2) Y = 5x for 2 hours or less, then Y =10 + 2.5(x-2) for over 2 hours Y = 5x up to 2 hours then Y = 5x + 2.5x for over 2 hoursThe US Department of Health conducted a survey for the years 1985-2018 regarding the use of cigarettes. Datafrom those years indicate that the linear function y = −0.47x + 47.1 gives an estimate of the 18-25 age group using cigarettes. The variable x represents the number of years since 1985 and y represents the percentage of 18-25 year old individuals using cigarettes. Explain what the −0.47 represents in terms of time and the percentage of 18-25 year old individuals using cigarettes.The relation between the cost of a diamond and its weight is linear. In looking at two diamonds, we find that one of the diamonds weighs 0.7 carats and costs $3,340, while the other diamond weighs 0.8 carat and costs $4,065. Find a linear function that relates the price of a diamond, C, to its weight, x, treating weight as the independent variable.Predict the price of a diamond that weighs 0.77 carat.If a diamond costs $5300, what do you think it should weigh?
- After 1000 mL of a solution is given to a patient via an IV, then 20 mL per minute was given this follows a function represented as M=1000+20t which answer best identifies the independent variable and the dependent variable?A 400-room hotel can rent every one of its rooms at $120 per room. For each $1 increase in rent, two fewer rooms are rented. a. Express the number of rooms rented, N, as a function of the rent, x. b. Express the hotel’s revenue, R, as a function of the rent, x.Determine whether the equation defines y as a function of x : lxl - y = 5
- A farmer finds there is a linear relationship between the number of bean stalks, n, she plants and the yield, y, each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Is the function from part (a) increasing or decreasing? How do you know?The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of the year, t. When will less than 6,000 people be afflicted?The price of 1 gallon of unleaded gasoline at the pump dropped to $2.19 on January 1, 2015, and continued to fall at the rate of 4 cents per month for the next 9 months. Express the price of 1 gallon of unleaded gasoline as a function of time for the period starting January 1, 2015. What was the price of 15 gallons of gasoline on April 1, 2015? On September 1, 2015?
- Student Loans Data for selected years from 2011and projected to 2023 can be used to show that thebalance of federal direct student loans y, in billions ofdollars, is related to the number of years after 2010,x, by the function y = 130.7x + 699.7.a. Graph the function for x-values corresponding2010 to 2025.b. Find the value of y when x is 13.c. What does this function predict the balance offederal direct student loans will be in 2029?(Source: U.S. Office of Management and Budget)A concert hall has a maximum capacity of 4050. When the ticket price is $31.00 the average attendance per concert has been 1900. When the price dropped to $23.00, the average attendance rose to 2700. Assume that attendance is linearly related to ticket price. Find a function that models the per concert revenue in terms of the attendance xThe value of a car decreases each year. The rate at which the value decreases is called depreciation and is a represented by a percentage. For Alina buys a car for $25,000, and the depreciation rate is 25%. That means that her car’s value goes down by 25% each year. The value can be represented by the function V(y)=25000(0.75)^v, where V represents the value of her car and y represents the number of years that she owns a car. Find the depreciated value of her car if she keeps it for 5 years. In other words, evaluate: V(5)=25000(0.75)^5, rounding to the proper decimal place for money.