Two suppliers manufacture a plastic gear used in a laser printer. the impact strength of these gears measured in foot-pounds is an important characteristic. a random sample of 10 gears from supplier 1 results in x1 = 290 and s1 = 12, while another random sample of 16 gears from the second supplier results in x2 = 321 and s2 = 22.(a) is there evidence to support the clain that supplier 2 provides gears with higher mean impact strength? use α = 0.05, and assume that both populations are normally distributed but the variances are not equal. what is the p-value for this test? (b) do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot - pounds higher than that of supplier 1? make the same assumptions as in part () construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences. show all work and correct answers .

Find the slope and the y-intercept if there's one and the equation of the line given these two points( 3, 2) and( 3, -4)

Describe the symmetry of the figure. identify lines of symmetry, if any. find the angle and the order of any rotational symmetry.

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?