Answer:
The number line is shown below.
Step-by-step explanation:
We need to represent number that is less than 3 on a number line.
Let x be numbers.
So,
.
Now, we have a number which represents x<3. Here 3 is not included in the solution set, so there is an open circle on 3 and left side of 3 are in the solution set.
The number line is shown below.
Yes. Parallel means same slope as original line. So it’s 2
27 (circumference) ➗ 3.14 (pi) = 8.59 (diameter)
Distance across (diameter) would be closest to 9.
Let us denote the smaller even integer by
![N](https://tex.z-dn.net/?f=N)
.
Then, the next even integer must be
![N+2](https://tex.z-dn.net/?f=N%2B2)
.
To verify, set
![N](https://tex.z-dn.net/?f=N)
as any even number, say
![174](https://tex.z-dn.net/?f=174)
.
Then, the next even integer must be 2 more than this number, i.e.
![174+2=176](https://tex.z-dn.net/?f=174%2B2%3D176)
.
The sum of these two consecutive even integers can be expressed as:
![N+(N+2)=2N+2](https://tex.z-dn.net/?f=N%2B%28N%2B2%29%3D2N%2B2)
We are told that this sum divided by four is 189.5, i.e.
![(2N+2)\div4=189.5](https://tex.z-dn.net/?f=%282N%2B2%29%5Cdiv4%3D189.5)
Multiplying both sides by 4 will reverse the division:
![(2N+2)\times1=758](https://tex.z-dn.net/?f=%282N%2B2%29%5Ctimes1%3D758)
Subtracting 2 from each side will reverse the addition:
![2N=756](https://tex.z-dn.net/?f=2N%3D756)
Dividing both sides by 2 will reverse the multiplication:
![N=378](https://tex.z-dn.net/?f=N%3D378)
Therefore, the two consecutive integers must be
378 and
380.
Check this:
The formula for N choose K is given as:
C(n, k)= ![\frac{n!}{[k!(n-k)!] }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bn%21%7D%7B%5Bk%21%28n-k%29%21%5D%20%20%7D)
Where,
n is the total numbers.
k is the number of the selected item.
Options C is correct.