When the cutting speed increased from low to high level, the tool age increases. This can be observed from the plot where the tool age values at higher cutting speeds are higher compared to the lower cutting speeds. The coefficient of the metal hardness is positively related to the output of tool age, which is evident as the metal hardness values increase, the tool age also increases. The coded coefficient is lower for cutting speed than the cutting angle related to the output of tool age, which can be understood by comparing the slopes or differences in means between changing levels of cutting speed and cutting angle.

In a 2-level factorial design with 5 factors, the total number of possible combinations is 2^5 = 32. If the design is using 16 experimental runs, it indicates a half-fractional factorial design. Therefore, Statement A is correct. Main effects in half-fractional designs are typically confounded with higher-order interactions depending on the design, so Statement B and C can be correct under such circumstances. However, Statement D is incorrect because, in a half-fractional design, each level of a factor should appear equally often across runs. Hence, it is impossible for 8 experimental runs to have the first factor consistently at the high level without skewing the design balance.

The Pareto Chart of the Standardized Effects is used to identify and prioritize the factors that have significant effects in a Design of Experiments (DOE) analysis. From the chart, we can determine that the effects of B, BD, DE, D, and E are significant as their bars cross the vertical line indicating the threshold for significance (standardized effect greater than 2.06, which relates to an alpha risk of 0.05). Therefore, the correct statements are that it is unknown from this graph how many factors were in the experimental design, and the effects to keep in the mathematical model are E, D, DE, BD, and B with an alpha risk equal to 0.05.