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solve question 1 please, functions
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- If the relationship between y and x is given by the equation y = 1.57 − 0.0407 x, the slope coefficient 0.0407 means this: __________. for every unit increase in x, y decreases by 0.0407 for every unit increase in x, y increases by 0.0407 for every unit increase in x, y increases by 1.5293 for every unit increase in x, y decreases by 1.5293An employee at a particular company can expect to get a $1,500 raise each year. If Jeff has been working at this company for 7 years and makes $32,500, find a formula that relates his salary to the number of years worked, then use the formula to determine how long he’ll have to work there until he makes $100,000 per year. Find a linear function that models the relationship between the two variables and describe the slope and intercept (For example, if gives weekly pay P, as a function of number of units sold s, then the slope of 7.5 is the pay per unit sold and the intercept of 80 is the amount of the employees base pay each week.)Marissa must decide between one of two companies as her long-distance phone provider. Company A charges a monthly fee of $7.00 plus $0.06 per minute,while Company B does not have a monthly fee,but charges $0.08 per minute. (a) Find a linear function that relates cost, C, to total minutes on the phone,x,for each company. (b) Determine the number of minutes x for which the bill from Company A will equal the bill from Company B. (c) Over what interval of minutes x will the bill from Company B be less than the bill from Company A?
- Suppose it costs $8750 for a public health nurse to provide a prenatal education program to 25 pregnant women, but it costs 12,500 to provide to 40 women. If x represents the number of women served by the program and y the cost, assuming a linear relationship, how much would it cost to provide the program to 150 women?find the equation of the specified line with slope 1/4 crossing 3x+y=12 at its x-interceptThe 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?
- Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 6p^3+x^2= 234,375 .Determine the rate at which sales are changing at a time when x= 375 ,p= 25 ,and the price is falling at the rate of $.60 per week. The rate at which sales are changing is ______thousand units per week.If f(x) is the equation of a line with slope 5 that goes through the point (2,3), what is f(0) ?Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2,500 when the price is $5.50 each but that the demand is 3,700 when the price is $5.26 each. Assuming that the demand function is linear, write its equation. Use p for price (in dollars) and q for quantity.
- A large department store is prepared to buy 3950 of your tie-dye shower curtains per month for $5 each, but only 3700 shower curtains per month for $10 each. a) Determine a linear expression for demand, q(x), where x is the price charged for each shower curtain. b) Give the unit of measure and interpretation of the slope. c) Determine the revenue function for the company’s shower curtain sales. d) What price should be charged to maximize revenue?The 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.Suppose a mining company will supply 120000 tons of ore per month if the price is 70 dollars per ton but will supply 75000 tons per month if the price is 25 dollars per ton. Assuming the supply function is of the form y = mx + b, find the slope, m and y-intercept, b.