See

,See media-d37-d37d5c1c-ed90-40ff-8ee8-8a59ef31e2b5-phprLUrJE-3.png,Write a function that models the difference between the female U.S. population and the male U.S. population for the years shown in the bar graph.,b. Use the function from part (a) to find how many more women than men there were in the U.S. population in 2005.,c. Does the result in part (b) overestimate or underestimate the actual difference between the female and male population in 2005 shown by the bar graph? By how much?,

Problem 1: Let V and W be vector spaces over a field F, and let T

Problem 1: Let V and W be vector spaces over a field F, and let T : V ? W be a linear transformation. Suppose that ker(T) and im(T) are both finite dimensional, that {v1,…vn} is a basis for ker(T), and that {w1,…wm} is a basis for im(T).,For each i ? {1, . . . m}, consider the vector wi. Since wi is in the image of T, there is a vector ui in V with T(ui) = wi. Pick such a vector, for each i.,Now think about the set of vectors {v1,…vn,u1,…um} in V.,a) Show that this set of vectors is linearly independent.,b) Let v be a vector in V. Show that there is some vector u in V, where u is a linear combination of the vectors u1, . . . um, such that T (v) = T (u).,c) Explain why v?u can be expressed as a linear combination of the vectors v1,…vn.,d) Now explain why v can be expressed as a linear combination of the vec- tors v1,…vn,u1,…um.,This shows that {v1,…vn,u1,…um} is a basis for V. Therefore: dim(V ) = n + m = dim(ker(T )) + dim(im(T )).,This result is called the Rank-Nullity Theorem. So, good job proving the Rank- Nullity Theorem.

To monitor the proportion of green M&M’s in packages of M&M’s, a

To monitor the proportion of green M&M’s in packages of M&M’s, a quality control manager picked at random 20 M&M packages, each with 300 M&M’s in them. The manager computed the proportion of green M&M’s across all these packages as 0.15. What is the standard deviation of the sampling process? Note: Each package represents a randomly selected sample. Round the final answer to three decimal places.,Select one:,a. 0.021,b. 0.079,c. 0.005,d. 0.357

1. Find the vertex, the focus, and the directrix. Then draw the

,1.  Find the vertex, the focus, and the directrix.  Then draw the graph.,     x,2 ,= 12y,2.  Find the equation of the parabola determined by the given information.,     Focus (3,0), directrix x = -3,3.  Find the vertex, the focus, and the directrix.  Draw the graph of ,     y,2, – 3y – x + 4 = 0,4.  Find the center and the radius of the circle with the given equation.  Then draw the graph.,    x,2, + y,2, + 2x – 10y = 0,5.  Find the vertices and the foci of the ellipse with the given equation.  Then draw the graph.,   4x,2, + 9y,2, = 36,6.  Find the equation of an ellipse satisfying the given conditions.,     Foci: (-2,0) and (2,0); length of major axis: 12,7.  Find the center, the vertices, and the foci of the ellipse.  Then draw the graph.,9x,2, + 25y,2, – 54x + 100y – 44 = 0,8.  Find the equation of a hyperbola satisfying the given conditions.,    Vertices at (0,3) and (0,-3); foci at (0,5) and (0,-5),9.  Determine the foci and the equations of the asymptotes.,   ,(,y – 1),2, / 9 – (x – 1),2, / 4 = 1,

A maintenance group aims to improve the effectiveness of its

A maintenance group aims to improve the effectiveness of its repair work. The group therefore monitors the number of maintenance requests that require a second visit to complete the repair. On any given week the maintenance group responds to 200 maintenance requests. The following table summarizes the number of those maintenance requests that required a second visit in the last five weeks.,Week Number 1 2 3 4 5,Number of those maintanance requests,that required a second visit,6 8 9 7 3,What type of control chart should be used here?,Select one:,a. mean chart,b. range chart,c. p-chart,d. c-chart,e. run test,,,An automobile manufacturer wishes to control the number of nonconformities (defects) in a subassembly area, producing manual transmissions. The inspection unit is a single transmission and the data for 10 samples are shown below:,Transmission Number 1 2 3 4 5 6 7 8 9 10,Number of Nonconformities (defects) 1 5 2 0 1 1 3 4 3 2,What type of control chart should be used here?,Select one:,a. mean chart,b. range chart,c. p-chart,d. c-chart,e. run test