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- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.If we know the average speed (s1) for an unknown distance, d, and the average speed (s2) of a second journey across the same distance, d, how can we calculate the average speed of the two journeys? {Values of time and distance are not known}Determine the best (according to sum-of-squares-measure) curve y = Aebx , through the data above. Transformed equation ln(y) = ln(A) + bx or Y = a + bx.
- If a ball is thrown into the air with an initial velocity of 42 ft/s, its height in feet after t seconds is given by y = 42t − 16t2. (a) Find the average velocity of the ball (in ft/s) for the time interval beginning at t = 2 and lasting for each of the following. (i) 0.5 seconds ft/s (ii) 0.1 seconds ft/s (iii) 0.05 seconds ft/s (iv) 0.01 seconds ft/s (b) Use your answers from part (a) to estimate the instantaneous velocity (in ft/s) when t = 2. ft/sRound off to one decimal place where applicable The table time (xi) 1 2 3 4 5 6infections (yi = f(xi)) 32 37 34 48 53 69 depicts the number of newly infected individuals with a contagious, airborne disease atintervals of 1 day over a period of 6 days. Here i = 0, 1, 2, . . . , 5 and the quantities x0 = 1and y0 = 32, respectively, represent the end of the first day of testing for the disease, andnumber of positive tests conducted by the end of that day.(Note: xi represents the end of a testing day, where the values of xi are as tabulated, whileyi represents the number of positive tests conducted by the end of day xi.) (b) (i) Use the table presented in (a), along with Newton’s forward difference formula, toapproximate f(7) with a polynomial of degree 3, P3(x). Start with x0 = 1. (ii) Estimate the error in the approximation in (b)(i).If a ball is thrown into the air with a velocity of 42 ft/s, its height in feet t seconds later is given by y = 42t − 16t2. (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. (i) 0.5 seconds _____ft/s (ii) 0.1 seconds _____ft/s (iii) 0.05 seconds _____ft/s (iv) 0.01 seconds _____ft/s (b) Estimate the instantaneous velocity when t = 2. _____ft/s
- If a ball is thrown into the air with a velocity of 50 ft/s, its height in feet t seconds later is given by y = 50t − 16t2. (a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. (i) 0.5 seconds_________ ft/s(ii) 0.1 seconds_______ ft/s(iii) 0.05 seconds _____ft/s(iv) 0.01 seconds________ ft/s (b) Estimate the instantaneous velocity when t = 2.__________ ft/sThe table shows data collected on the relationship between the average number of minutes spent exercising per day and math test scores. The line of best fit for the data is yˆ=0.44x+65.2. Minutes 25303540 Test Score 76798083 (a) According to the line of best fit, the predicted test score for someone who spent 42 minutes exercising is 83.68. (b) Is it reasonable to use this line of best fit to make the above prediction? Select the correct answer below: The estimate, a predicted test score of 83.68, is both reasonable and reliable. The estimate, a predicted test score of 83.68, is unreliable but reasonable. The estimate, a predicted test score of 83.68, is both unreasonable and unreliable. The estimate, a predicted test score of 83.68, is reliable but unreasonable.Accountants at the Tucson firm, Larry Youdelman,CPAs, believed that several traveling executives were submittingunusually high travel vouchers when they returned from businesstrips. First, they took a sample of 200 vouchers submitted from the past year. Then they developed the following multiple-regres-sion equation relating expected travel cost to number of days on the road ( x1 ) and distance traveled ( x2 ) in miles:yn = +90.00 + +48.50x1 + +.40x2The coefficient of correlation computed was .68.a) If Donna Battista returns from a 300-mile trip that took herout of town for 5 days, what is the expected amount she shouldclaim as expenses?b) Battista submitted a reimbursement request for $685. Whatshould the accountant do?c) Should any other variables be included? Which ones? Why?