Answer:
(2, 1/4)
Step-by-step explanation:
Try each x and see if its y matches the function:
(1/2)^0 = 1 not 1/2
(1/2)^0 = 1 not 0
(1/2)^2 = 1/4 so this is correct as we have (2, 1/4)
Answer: $187 will be in the account after 6 years.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $100
r = 11% = 11/100 = 0.11
n = 1 because it was compounded once in a year.
t = 6 years
Therefore,.
A = 100(1 + 0.11/1)^1 × 6
A = 100(1 + 0.11)^6
A = 100(1.11)^6
A = $187
Answer:
![\sum_{n=10}^{15}(n+\frac{3}{n})=\sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D10%7D%5E%7B15%7D%28n%2B%5Cfrac%7B3%7D%7Bn%7D%29%3D%5Csum_%7Bn%3D10%7D%5E%7B15%7D%20n%20%2B%20%5Csum_%7Bn%3D10%7D%5E%7B15%7D%20%5Cfrac%7B3%7D%7Bn%7D)
Step-by-step explanation:
Given expression : ![\sum_{n=10}^{15}(n+\frac{3}{n})](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D10%7D%5E%7B15%7D%28n%2B%5Cfrac%7B3%7D%7Bn%7D%29)
Solving further:
![\sum_{n=10}^{15}(n+\frac{3}{n})](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D10%7D%5E%7B15%7D%28n%2B%5Cfrac%7B3%7D%7Bn%7D%29)
![\Rightarrow \sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csum_%7Bn%3D10%7D%5E%7B15%7D%20n%20%2B%20%5Csum_%7Bn%3D10%7D%5E%7B15%7D%20%5Cfrac%7B3%7D%7Bn%7D)
So,![\sum_{n=10}^{15}(n+\frac{3}{n})=\sum_{n=10}^{15} n + \sum_{n=10}^{15} \frac{3}{n}](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D10%7D%5E%7B15%7D%28n%2B%5Cfrac%7B3%7D%7Bn%7D%29%3D%5Csum_%7Bn%3D10%7D%5E%7B15%7D%20n%20%2B%20%5Csum_%7Bn%3D10%7D%5E%7B15%7D%20%5Cfrac%7B3%7D%7Bn%7D)
So, Option A is true
Hence the given expression is equivalent to Option A
Answer:
Point of x-intercept: (2,0).
Point of y-intercept: (0,6).
Step-by-step explanation:
1. Finding the x-intercept.
This point is where the graph of the function touches the x axis. It can be found by substituting the "y" for 0. This is how you do it:
![y=-3x+6\\ \\-3x+6=0\\ \\-3x=-6\\\\x=\frac{-6}{-3} \\ \\x=2](https://tex.z-dn.net/?f=y%3D-3x%2B6%5C%5C%20%5C%5C-3x%2B6%3D0%5C%5C%20%5C%5C-3x%3D-6%5C%5C%5C%5Cx%3D%5Cfrac%7B-6%7D%7B-3%7D%20%5C%5C%20%5C%5Cx%3D2)
Hence, the point of x-intercept: (2,0).
2. Finding the y-intercept.
This point is where the graph of the function touches the y axis. It can be found by substituting the "x" for 0. This is how you do it:
![y=-3(0)+6\\ \\y=6](https://tex.z-dn.net/?f=y%3D-3%280%29%2B6%5C%5C%20%5C%5Cy%3D6)
Hence, the point of y-intercept: (0,6).