On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio.

Which expression correctly uses the formula (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 to find the location of point R?

(StartFraction 3 Over 3 + 5 EndFraction) (2 minus (negative 14)) + (negative 14)

(StartFraction 3 Over 3 + 5 EndFraction) (negative 14 minus 2) + 2

(StartFraction 3 Over 3 + 5 EndFraction) (2 minus 14) + 14

StartFraction 3 Over 3 + 5 EndFraction (negative 14 minus 2) minus 2

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

Which spreadsheet would be used to compute the first nine terms of the geometric sequence a^n=32•(1/2)n-1

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution