Verify Property 2 of the definition of a probability density function over the given interval. f(x) = 48 -X, [5,11] . . . What is Property 2 of the definition of a probability density function? O A. The area under the graph of f over the interval [a,b] is 1. O B. The area under the graph of f over the interval [a,b] is a. O C. The area under the graph of f over the interval [a, b] is b. Identify the formula for calculating the area under the graph of the function y = f(x) over the interval [a,b]. Choose the correct answer below. OA. b OB. b | +( x ) ax = [F(x)1 2 = F(a)-F(b ) |f ( x ) dx = [F ( x ) 1 2 = F (b ) - F ( a ) a a O c. a OD. a f ( x ) dx = [F ( x ) 1 = = F (a ) - F ( b ) F ( x ) dx = [F ( x ) 13 = F (b ) - F ( a ) b b Substitute a, b, and f(x) into the left side of the formula from the previous step. area = Q X dxA company determines that its marginal revenue per day is given by R'(t), where R(t) is the total accumulated revenue, in dollars, on the tth day. The company's marginal cost per day is given by C'(t), where C(t) is the total accumulated cost, in dollars, on the tth day. R'(t) = 806, R(O) = o; C'(t) = so 0.41, 0(0) = o a) Find the total prot P(T) from t= 0 to t= 10 (the rst 10 days). T P(T) = R(T) ' 00') = Io [R'(t) - C'(t)] dt The total profit is $ . (Round to the nearest cent as needed.) b) Find the average daily prot for the first 10 days. The average daily prot is $ . (Round to the nearest cent as needed.) Find the average value of the function f(x) = x2 - 17 on [0,9]. The average value of the function f(x) =x2 - 17 on [0,9] is In 20 years, Maggie Beechwood is to receive $200,000 under the terms of a trust established by her grandparents. Assuming an interest rate of 5.4%, compounded continuously, what is the present value of Maggie's legacy? The present value of the legacy is 58 (Round to the nearest cent as needed.)