Find the length of  if ​A​ = (-3, 5) and ​B​ = (2, 1). Round to the nearest tenth, if necessary.a. 6.4b. 4.1c. 8.1d. 5Find the length of  if ​P​ = (8, -­4) and ​Q​ = (­-3, ­-4). Round to the nearest tenth, if necessary.a. 13.6b. 11c. 5d. 9.4On the number line below, find the coordinates of point ​U​ such that the length of  is  the length of  from ​R​ to ​T​.a. 8b. -2c. 2d. 0On the number line below, find the coordinates of ​P​ such that the length of  ​ is  the length of   ​from ​L​ to ​N.a. -2b. 1c. 8d. 4Points ​X​(6, 4) and ​Y​(-4, -16) are the endpoints of . What are the coordinates of point ​Z​ on   such that ​XZ ​is  the length of ?a. (-2, -12)b. (14, 20)c. (4, 0)d. (-12, -32)Find the coordinates of ​O​ on the number line below such that ​O​ partitions   such that ​MO​:​MN​ is in a 3:4 ratio.a. 3b. 2c. 8d. 5.25On the coordinate plane below, find the coordinates of ​S​ such that  ​is  the length of .a. (3,2)b. (-3, 4)c. (0,3)d. (9,0)Find the coordinates of ​P​ along the directed line segment of ​AB​ so that the ratio of AP​:​PB ​is 3:2. a. (1.4, 1.2)b. c. (0.6, -0.2)d. On the coordinate plane below, find the coordinates of ​R​ such that   ​is  the length of   from ​Q​ to ​T​.a. (-1, -1)b. (3.2, 1.8)c. (-2.2, -1.8)d. (-5.8, -4.2)

1. To determine whether a new sleeping pill has an effect that varies with dosage, a researcher randomly assigns adult insomniacs, in equal numbers, to receive either 4 or 8 grams of the sleeping pill. The amount of sleeping time is measured for each subject during an 8-hour period after the administration of the dosage. What type of design is this, and what type of statistic is needed to analyze the data?2. Dr. Bill Board designs a 2 X 2 between-subjects factorial design, where Factor A is word frequency (low or high) and Factor B is category cues (no cues or cues). Assume that the data are interval. What type of statistic is needed to analyze the data.

hello,Please see attached the questions . kindly show the working on excel and word document.regards