Jake, Rob, Sarah, and Becky each conducted surveys on the number of pets people have in their homes. Then they each answered the question below: “Must all measures of central tendency (mean, median, mode) appear as a number in the set of data collected?”

Which student’s statement is true?

A.
Sarah says this is sometimes true because the mean and median may or may not be in the set of data, but the mode is always in the set of data.

B.
Rob says this is never true because all the measures of central tendency are never numbers
in the set of data.

C.
Becky says this is sometimes true because the mean and mode may or may not be in the set
of data, but the median is always in the set of data.

D.
Jake says this is always true because all the measures of central tendency also have to be
numbers in the set of data.

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

Find the length of the normal and the angle it makes with the positive x-axis. (see pictured below)