Determine whether a conclusion can be drawn about the existence of uniqueness of a solution of the differential equation (7 minus t )y double prime plus 5 t y prime minus 7 y equals sine t, given that y (0 )equals 7 and y prime (0 )equals 7. If a conclusion can be drawn, discuss it. If a conclusion cannot be drawn, explain why.

When turned about its axis of rotation, which shape could have created this three-dimensional object?

(05.03 mc) part a: explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points) part b: make tables to find the solution to 4x = 2x−2. take the integer values of x between −3 and 3. (4 points) part c: how can you solve the equation 4x = 2x−2 graphically? (2 points)

The birth weights of newborn babies in the unites states follow in a normal distrubution with a mean of 3.4 kg and standard deviation of 0.6 kg. reaserches interested in studying how. children gain weights decide to take random samples of 100 newborn babies and calculate the sample mean birth weights for each sample