In a horse race, how many different finishes among the first 3 places are possible if 7 horses are running? (Exclude ties) There are a possible___different finishes.

7 x 6 x 5 = 210

Step-by-step explanation:

its a combination's problem.

7 horses are eligible for first place.

6 of those are eligible for 2nd given that one of the 7 finished first.

similarly 5 of the remaining are eligible for 3rd place given 2 horses have taken the first 2 spots.

therefore 7 x 6 x 5 possible combinations = 210 combinations.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

the perimeter is increased by a factor of 2