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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Let X U(4) find Var(3x) and distribution function.
- Let m(t) =(1/6)e^t+(2/6)e^2t+(3/6)e^3t Find E(y) Find V(y) Find the distribution of y2.(22) let h(x)Let f(x,0) = ex-1 06. If X is t-distributed, show that X² is F-distributed.Let X and Y be independent and distributed as N(, 1). Is T = X-Y sufficient?4. Find the value of c that satisfy the equation f (b)- f (a) _ != f'(c) b-a in the conclusion of Mean Value Theorem for functions and intervals in : a. f(x)=x² + 2x=1, [0,1] b. f(x) = x³, [0,1] 1 c. S (4) =x+. [;,2] d. f(x)= /x-1, [1,3]Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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