Austin is arranging 14 cans of food in a row on a shelf. he has 5 cans of corn, 1 can of olives, and 8 cans of beans. in how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?

18018

Step-by-step explanation:

Given:

Number of cans = 14

Number of cans of corn = 5

Number of cans of olives = 1

Number of cans of beans = 8

When there are objects to be arranged in order, out of which   objects are of one kind, objects are of another and so on, then the number of different arrangements is given as:

Here,

Therefore, the distinct orders in which the cans can be arranged is

answer: 12

step-by-step explanation:

because yes

- "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."