Answer:
4 are playing at the sand table
Step-by-step explanation:
There were 9 kids at Kenneth's preschool and 3 were playing, thats one third of the kids(3x3=9). One third of 12 is 4(3x4=12) Basically since there were 9 total kids, and 3 at the sand table, they are divided equally in groups of three so you just divide 12 by 3 too and thats how you get 4
Answer
x/3 and 2 1/3
Step-by-step explanation:
Given,
The expression is,
![P(x)=x^3-7x^2+15x-9](https://tex.z-dn.net/?f=P%28x%29%3Dx%5E3-7x%5E2%2B15x-9)
If x- 3 is the factor of the given polynomial function, then on substituting the value of x = 3 in the polynomial function, it become zero.
Thus subsituting the value of x in the polynomial,
![\begin{gathered} P(3)=3^3-7\times3^2+15\times3-9 \\ =27-7\times9+45-9 \\ =27+45-63-9 \\ =72-72 \\ =0 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%283%29%3D3%5E3-7%5Ctimes3%5E2%2B15%5Ctimes3-9%20%5C%5C%20%3D27-7%5Ctimes9%2B45-9%20%5C%5C%20%3D27%2B45-63-9%20%5C%5C%20%3D72-72%20%5C%5C%20%3D0%20%5Cend%7Bgathered%7D)
Here, the obtained value of polynomial is 0.
Hence, x-3 is a factor of the given polynomial.
Thus, option A(true) is correct.
a. Notice that
1/(1*2) = 1/2 = 1 - 1/2
1/(2*3) = 1/6 = 1/2 - 1/3
1/(3*4) = 1/12 = 1/3 - 1/4
and so on, which suggests the n-th term of the sum can be written as
![\dfrac1{n(n+1)}=\dfrac1n-\dfrac1{n+1}](https://tex.z-dn.net/?f=%5Cdfrac1%7Bn%28n%2B1%29%7D%3D%5Cdfrac1n-%5Cdfrac1%7Bn%2B1%7D)
Then the sum itself is telescoping:
![\dfrac1{1\cdot2}+\dfrac1{2\cdot3}+\dfrac1{3\cdot4}+\cdots+\dfrac1{n(n+1)}](https://tex.z-dn.net/?f=%5Cdfrac1%7B1%5Ccdot2%7D%2B%5Cdfrac1%7B2%5Ccdot3%7D%2B%5Cdfrac1%7B3%5Ccdot4%7D%2B%5Ccdots%2B%5Cdfrac1%7Bn%28n%2B1%29%7D)
![=\left(1-\dfrac12\right)+\left(\dfrac12-\dfrac13\right)+\left(\dfrac13-\dfrac14\right)+\cdots+\left(\dfrac1n-\dfrac1{n+1}\right)](https://tex.z-dn.net/?f=%3D%5Cleft%281-%5Cdfrac12%5Cright%29%2B%5Cleft%28%5Cdfrac12-%5Cdfrac13%5Cright%29%2B%5Cleft%28%5Cdfrac13-%5Cdfrac14%5Cright%29%2B%5Ccdots%2B%5Cleft%28%5Cdfrac1n-%5Cdfrac1%7Bn%2B1%7D%5Cright%29)
![=1-\dfrac1{n+1}](https://tex.z-dn.net/?f=%3D1-%5Cdfrac1%7Bn%2B1%7D)
b. The proof is trivial:
![\dfrac1n-\dfrac1{n+1}=\dfrac{n+1}{n(n+1)}-\dfrac n{n(n+1)}=\dfrac{n+1-n}{n(n+1)}=\dfrac n{n+1}](https://tex.z-dn.net/?f=%5Cdfrac1n-%5Cdfrac1%7Bn%2B1%7D%3D%5Cdfrac%7Bn%2B1%7D%7Bn%28n%2B1%29%7D-%5Cdfrac%20n%7Bn%28n%2B1%29%7D%3D%5Cdfrac%7Bn%2B1-n%7D%7Bn%28n%2B1%29%7D%3D%5Cdfrac%20n%7Bn%2B1%7D)
so the formula found in (a) is correct.
Answer:
scatter plot A: -0.90
scatter plot B: 0.89
scatter plot C: -0.76
scatter plot D: 0.55
Step-by-step explanation:
if the line is going down, it's negative and if it goes up it's positive. The closer the points are <em>the higher the number</em>.
HOPE THIS HELPS!!