Jing jing works in a store and she spends some of her time organizing the stationary section. If there are nine different items on the rack, how many ways can she organize the rack so that the two most expensive items are not together?

282240 ways

Step-by-step explanation:

number of items = 9 different items

Ranking based on worth

determine number of ways to arrange the 9 items such that the 2 most expensive are apart

first step: consider the 2expensive items as 1

∴ number of permutation = [ ( 9 - 2 ) + 1 ]!  * 2!

                                          = [ 8 ] ! * 2!  = 80640

Total number of permutation/arrangement = 9! = 362880

hence to arrange the 9 items without having the two most expensive items together

= 362,880 - 80640

= 282240 ways

the equation for this situation is y=122+45. to solve the equation you would add 45 and 122 to get a total of 167lbs. in conclusion, grace's weight eight weeks ago was 167lbs.  

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."