In a study of the effect of cooling rate on the hardness of welded joints, 50 welds cooled at a rate of 10oC/s had an average Rockwell (B) hardness of 91.1 and a standard deviation of 6.62, and 40 welds cooled at a rate of 30oC/s had an average hardness of 90.7 and a standard deviation of 4.62. Ten more welds will be made in order to increase the precision of the confidence interval. Which would increase the precision the most, cooling all 10 welds at the rate of 10oC/s, cooling all 10 welds at the rate of 30oC/s, or cooling 5 welds at 10oC/s and 5 at 30oC/s

Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above

Afair die is cast four times. calculate the probability of obtaining exactly two 6's round to the nearest tenth of a percent

First work with stencil one. use a combination of reflections, rotations, and translations to see whether stencil one will overlap with the original pattern. list the sequence of rigid transformations you used in your attempt, noting the type of transformation, the direction, the coordinates, and the displacement