The table below gives the number of hours ten randomly selected students spent studying and their corresponding midterm exam grades. using this data, consider the equation of the regression line, y = bo + b1x, for predicting the midterm exam grade that a student will earn based the number of hours spent studying. keep in mind, the correlation coefficient may or may not be statistically significant for the data given. remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
hours studying 0 1 1.5 2 2.5 3 4.5 5 5.5 6
midterm grades 65 70 77 79 83 91 92 94 95 98
a. find the estimated slope. round your answer to three decimal places.
b. find the estimated y-intercept. round your answer to three decimal places.
c. find the estimated value of y when x=5. round your answer to three decimal places.
d. find the error prediction when x=2. round your answer to three decimal places.

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?