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Concept explainers
E. Practical Applications
Sports and Leisure In baseball analytics, a statistic known as FIP, or fielding independent pitching, is a measurement of a pitcher’s performance that removes the role of defense and luck. The formula is defined as follows:
where HR = home runs yielded, BB = number of batters walked, HBP = number of batters hit by a pitch, K = strikeouts, and IP = innings pitched. A lower FIP indicates a better pitching performance. In 2015, Jake Arrieta of the Cubs and Zack Greinke of the Dodgers were both contending for the Cy Young Award, given to the outstanding pitcher in each major league. Here are their stats:
Determine each pitcher’s FIP rounded to two decimal places. Based on this statistic, who should have gotten the Cy Young Award?
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Chapter 7 Solutions
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
- Given the following set X = {2, 4, 6, 8} and Y = {1, 2, 3}, explicitly give (e.g., write down the sets with numerical entries) of the outputs of the following requested set operations: (a) [2 points] XUY (Union) (b) [2 points] XY (Intersection) (c) [3 points] X\Y (Difference) (d) [3 points] XAY (Symmetric Difference)arrow_forward4.2 Product and Quotient Rules 1. 9(x)=125+1 y14+2 Use the product and/or quotient rule to find the derivative of each function. a. g(x)= b. y (2x-3)(x-1) c. y== 3x-4 √xarrow_forward4.2 Product and Quotient Rules 1. Use the product and/or quotient rule to find the derivative of each function. 2.5 a. g(x)=+1 y14+2 √x-1) b. y=(2x-3)(x-:arrow_forward
- For what values of k will the equation (k + 1)x² + 6kx + 2k² - x = 0 have: a) one root equal zero b) one root the reciprocal of the other c) roots numerically equal but of opposite signarrow_forward3. The total profit (in dollars) from selling x watches is P(x)=0.52x²-0.0002x². Find and interpret the following. a) P(100) b) P'(100)arrow_forward3. Find the slope and the equation of the tangent line to the graph of the given function at the given value of x. -4 f(x)=x-x³;x=2arrow_forward
- 2. Find the equation of the tangent line to the graph of the given function at the given point. f(x)=(x+3)(2x²-6) at (1,-16)arrow_forward6. Researchers who have been studying the alarming rate at which the level of the Dead Sea has been dropping have shown that the density d (x) (in g per cm³) of the Dead Sea brine during evaporation can be estimated by the function d(x)=1.66 0.90x+0.47x², where x is the fraction of the remaining brine, 0≤x≤1. a) Estimate the density of the brine when 60% of the brine remains. b) Find and interpret the instantaneous rate of change of the density when 60% of the brine remains.arrow_forward5. If g'(5) 10 and h'(5)=-4, find f'(5) for f(x)=4g(x)-2h(x)+3.arrow_forward
- 2. Find each derivative. Write answers with positive exponents. a) Dx 9x -3 [97] b) f'(3) if f(x) = x²-5x² 8arrow_forwardT3.2: Prove that if the Graceful Tree Conjecture (every tree has a graceful labeling) is true and T' is a tree with m edges, then K2, decomposes into 2m - 1 copies of T. Hint - Delete a leaf to get 7" and apply the decomposition of K2(m-1)+1 = K2m-1 into T'. Then explain how the decomposition allows the pendant edge to be added to a new vertex to obtain a decomposition of K2m into copies of T.arrow_forwardUse the matrix tree theorem to determine the number of spanning trees of the graphs Kr∨sK1.These are the graphs formed by by adding all edges between a complete graph on r vertices and atrivial graph (no edges) on s vertices.arrow_forward
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