How many 4-digits number can be formed out of 0,1,2,3,5,7 and 8. If: the number must be even with no repetition, then with repetition

Below in bold.

Step-by-step explanation:

No repetition.

There are a total of 7 numbers.

For the number to be even it must end in 0,  2 or 8.

The other 3 numbers will be the number of permutations of 3 from  the 6 other numbers.

Number of 4 digit numbers ending in 0

= 6P3 = 6! / 6-3!

= 120.

Now the number could also end in 2 or 8,

so there are 3*120 = 360 4-digit even numbers (no repetition).

With repetition.

There are 3 * 7^3 = 1029  with repetition.

when studying polynomials, you often hear the terms zeros, roots, factors and x x the multiplicity of a zero is important because it tells us how the graph of the let's look at the graph of a function that has the same zeros

step-by-step explanation:

- "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."