answer:The existence of a pseudo-polynomial time algorithm for counting the total number of feasible schedules in this scheduling problem is an open question. As mentioned in [Ber09], the problem becomes #P-complete when the input numbers are in binary, implying the difficulty of finding a pseudo-polynomial time algorithm for this variant. However, there is no known result specifically addressing the case with unary input. For more information, consult the referenced paper: [Ber09] Gerardo Berbeglia. The counting complexity of a simple scheduling problem. Operations Research Letters, 37(5):365–367, September 2009. http://dx.doi.org/10.1016/j.orl.2009.05.004

answer:The least squares vector is given by left( begin{array}{c} -0.177 -0.304 end{array} right) This vector minimizes the sum of squared differences between the predicted and actual values in the given system.

answer:Alfred Wegener's theory of continental drift, initially met with skepticism, proposed that the Earth's continents were once part of a single supercontinent called "Pangea" and have since drifted apart. He provided several key lines of evidence to support his theory: 1. **Fossil Correlation**: Wegener observed similar fossil species on different continents that are not found elsewhere, suggesting that these landmasses were once connected. 2. **Mountain Range Alignments**: The matching mountain ranges on different continents, such as the Appalachian Mountains in North America and the Caledonides in Europe, indicated that they were once connected. 3. **Geological Fit**: Wegener demonstrated that the continents fit together like puzzle pieces, implying they were once joined. 4. ** Paleoclimatic Evidence**: The presence of ice age glacial deposits in regions far from the current polar latitudes (like tropical South America) suggested a different arrangement of landmasses in the past. Wegener's theory laid the groundwork for the modern understanding of plate tectonics, which explains how continents move and interact due to the motion of the Earth's lithospheric plates.

answer:The projection of vector vec{v} onto vector vec{u}, denoted as text{proj}_{vec{u}}(vec{v}), can be calculated using the formula: [ text{proj}_{vec{u}}(vec{v}) = frac{vec{v} cdot vec{u}}{|vec{u}|^2} cdot vec{u} ] First, calculate the dot product of vec{v} and vec{u}: [ vec{v} cdot vec{u} = left(frac{1}{2}right)left(-frac{5}{2}right) + left(frac{1}{4}right)left(-frac{3}{2}right) + left(frac{9}{4}right)left(-frac{5}{2}right) + 2left(-frac{3}{2}right) + left(-frac{3}{4}right)left(-frac{3}{4}right) + left(-frac{5}{2}right)left(-frac{5}{4}right) ] [ = -frac{5}{4} - frac{3}{8} - frac{45}{8} - 3 + frac{9}{16} + frac{25}{8} ] [ = -frac{40}{16} - frac{6}{16} - frac{90}{16} - frac{48}{16} + frac{9}{16} + frac{50}{16} ] [ = frac{-40 - 6 - 90 - 48 + 9 + 50}{16} ] [ = frac{-125}{16} ] Next, find the magnitude of vec{u}: [ |vec{u}|^2 = left(-frac{5}{2}right)^2 + left(-frac{3}{2}right)^2 + left(-frac{5}{2}right)^2 + left(-frac{3}{2}right)^2 + left(-frac{3}{4}right)^2 + left(-frac{5}{4}right)^2 ] [ = frac{25}{4} + frac{9}{4} + frac{25}{4} + frac{9}{4} + frac{9}{16} + frac{25}{16} ] [ = frac{100}{16} + frac{36}{16} + frac{100}{16} + frac{36}{16} + frac{9}{16} + frac{25}{16} ] [ = frac{286}{16} ] [ = frac{143}{8} ] Finally, calculate the projection: [ text{proj}_{vec{u}}(vec{v}) = frac{vec{v} cdot vec{u}}{|vec{u}|^2} cdot vec{u} = frac{-frac{125}{16}}{frac{143}{8}} cdot left(-frac{5}{2}, -frac{3}{2}, -frac{5}{2}, -frac{3}{2}, -frac{3}{4}, -frac{5}{4}right) ] [ = -frac{125}{16} cdot frac{8}{143} cdot left(-frac{5}{2}, -frac{3}{2}, -frac{5}{2}, -frac{3}{2}, -frac{3}{4}, -frac{5}{4}right) ] [ = frac{125}{143} cdot left(frac{5}{2}, frac{3}{2}, frac{5}{2}, frac{3}{2}, frac{3}{4}, frac{5}{4}right) ] [ = left{frac{625}{286}, frac{187.5}{286}, frac{625}{286}, frac{187.5}{286}, frac{37.5}{286}, frac{312.5}{572}right} ] So, the components of the projection vector are: [ text{proj}_{vec{u}}(vec{v}) = left{frac{625}{286}, frac{187.5}{286}, frac{625}{286}, frac{187.5}{286}, frac{37.5}{286}, frac{312.5}{572}right} ]