<span>Notice that this slope will be the same if the points (1,3) and (2, 5) are used for the calculations. For straight lines, the rate of change (slope) is constant (always the same). For every one unit that is moved on the x-axis, two units are moved on the y-axis. This is true at any location on the line.</span>
Answer:

Step-by-step explanation:
The midpoint formula is:

where (x₁, y₁) and (x₂, y₂) are the points are the endpoints.
We are given the points: (2,4) and (6,8). Therefore,

Substitute the values into the formula.

Find the x coordinate first.
- Add 2 and 6: 2+6=8
- Divide by 2: 8/2=4

Find the y-coordinate next.
- Add 4 and 8: 4+8= 12
- Divide by 2: 12/2=6

The midpoint of EF is (4,6)
Answer:
If n = 1000000, then
![P(h E [495000, 505000]) = \int\limits^{50500}_{495000} {\frac{2}{\sqrt{2000000\pi}} e^{\frac{-(k-500000)^2}{500000} }} \, dk](https://tex.z-dn.net/?f=P%28h%20E%20%5B495000%2C%20505000%5D%29%20%3D%20%5Cint%5Climits%5E%7B50500%7D_%7B495000%7D%20%7B%5Cfrac%7B2%7D%7B%5Csqrt%7B2000000%5Cpi%7D%7D%20e%5E%7B%5Cfrac%7B-%28k-500000%29%5E2%7D%7B500000%7D%20%7D%7D%20%5C%2C%20dk)
If n = 10400, then
![P(h E [495000, 505000]) = \int\limits^{50500}_{495000} {\frac{2}{\sqrt{2000000\pi}} e^{\frac{-(k-500000)^2}{500000} }} \, dk](https://tex.z-dn.net/?f=P%28h%20E%20%5B495000%2C%20505000%5D%29%20%3D%20%5Cint%5Climits%5E%7B50500%7D_%7B495000%7D%20%7B%5Cfrac%7B2%7D%7B%5Csqrt%7B2000000%5Cpi%7D%7D%20e%5E%7B%5Cfrac%7B-%28k-500000%29%5E2%7D%7B500000%7D%20%7D%7D%20%5C%2C%20dk)
If N = 102, then

Step-by-step explanation:
Since the coin is fair, then the probability that a filp is heads is 1/2. Given N tries, the amount of heads can be approximated with a Normal distribution with mean μ = N *1/2 = N/2 and standard deviation σ = √(N*1/2 * 1/2) = √N/ 2
The density function of that random variable is given by de following formula

If n = 1000000, then
![P(h E [495000, 505000]) = \int\limits^{50500}_{495000} {\frac{2}{\sqrt{2000000\pi}} e^{\frac{-(k-500000)^2}{500000} }} \, dk](https://tex.z-dn.net/?f=P%28h%20E%20%5B495000%2C%20505000%5D%29%20%3D%20%5Cint%5Climits%5E%7B50500%7D_%7B495000%7D%20%7B%5Cfrac%7B2%7D%7B%5Csqrt%7B2000000%5Cpi%7D%7D%20e%5E%7B%5Cfrac%7B-%28k-500000%29%5E2%7D%7B500000%7D%20%7D%7D%20%5C%2C%20dk)
If n = 10400, then
![P(h E [495000, 505000]) = \int\limits^{50500}_{495000} {\frac{2}{\sqrt{2000000\pi}} e^{\frac{-(k-500000)^2}{500000} }} \, dk](https://tex.z-dn.net/?f=P%28h%20E%20%5B495000%2C%20505000%5D%29%20%3D%20%5Cint%5Climits%5E%7B50500%7D_%7B495000%7D%20%7B%5Cfrac%7B2%7D%7B%5Csqrt%7B2000000%5Cpi%7D%7D%20e%5E%7B%5Cfrac%7B-%28k-500000%29%5E2%7D%7B500000%7D%20%7D%7D%20%5C%2C%20dk)
If N = 102, then

Answer: d
Step-by-step explanation: