The answer is 30
we expect that in every 50 people, 1 will have free admission.
so:
The square root of 192 is 13.856. so the answer is more than likely 14 or 13.85
Answer:
B
Step-by-step explanation:
The equation of a line parallel to the x- axis is
y = c ← standard form
Where c is the value of the y- coordinates the line passes through
here the line passes through (1, 4) with y- coordinate of 4, hence
y = 4 ← is the equation of the horizontal line
Answer:
![r = \±\sqrt{14](https://tex.z-dn.net/?f=r%20%3D%20%5C%C2%B1%5Csqrt%7B14)
![Product = -14](https://tex.z-dn.net/?f=Product%20%3D%20-14)
Step-by-step explanation:
Given
![\frac{1}{2x} = \frac{r - x}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2x%7D%20%3D%20%5Cfrac%7Br%20-%20x%7D%7B7%7D)
Required
Find all product of real values that satisfy the equation
![\frac{1}{2x} = \frac{r - x}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2x%7D%20%3D%20%5Cfrac%7Br%20-%20x%7D%7B7%7D)
Cross multiply:
![2x(r - x) = 7 * 1](https://tex.z-dn.net/?f=2x%28r%20-%20x%29%20%3D%207%20%2A%201)
![2xr - 2x^2 = 7](https://tex.z-dn.net/?f=2xr%20-%202x%5E2%20%3D%207)
Subtract 7 from both sides
![2xr - 2x^2 -7= 7 -7](https://tex.z-dn.net/?f=2xr%20-%202x%5E2%20-7%3D%207%20-7)
![2xr - 2x^2 -7= 0](https://tex.z-dn.net/?f=2xr%20-%202x%5E2%20-7%3D%200)
Reorder
![- 2x^2+ 2xr -7= 0](https://tex.z-dn.net/?f=-%202x%5E2%2B%202xr%20%20-7%3D%200)
Multiply through by -1
![2x^2 - 2xr +7= 0](https://tex.z-dn.net/?f=2x%5E2%20-%202xr%20%2B7%3D%200)
The above represents a quadratic equation and as such could take either of the following conditions.
(1) No real roots:
This possibility does not apply in this case as such, would not be considered.
(2) One real root
This is true if
![b^2 - 4ac = 0](https://tex.z-dn.net/?f=b%5E2%20-%204ac%20%3D%200)
For a quadratic equation
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
By comparison with ![2x^2 - 2xr +7= 0](https://tex.z-dn.net/?f=2x%5E2%20-%202xr%20%2B7%3D%200)
![a = 2](https://tex.z-dn.net/?f=a%20%3D%202)
![b = -2r](https://tex.z-dn.net/?f=b%20%3D%20-2r)
![c =7](https://tex.z-dn.net/?f=c%20%3D7)
Substitute these values in ![b^2 - 4ac = 0](https://tex.z-dn.net/?f=b%5E2%20-%204ac%20%3D%200)
![(-2r)^2 - 4 * 2 * 7 = 0](https://tex.z-dn.net/?f=%28-2r%29%5E2%20-%204%20%2A%202%20%2A%207%20%3D%200)
![4r^2 - 56 = 0](https://tex.z-dn.net/?f=4r%5E2%20-%2056%20%3D%200)
Add 56 to both sides
![4r^2 - 56 + 56= 0 + 56](https://tex.z-dn.net/?f=4r%5E2%20-%2056%20%2B%2056%3D%200%20%2B%2056)
![4r^2 = 56](https://tex.z-dn.net/?f=4r%5E2%20%3D%2056)
Divide through by 4
![r^2 = 14](https://tex.z-dn.net/?f=r%5E2%20%3D%2014)
Take square roots
![\sqrt{r^2} = \±\sqrt{14](https://tex.z-dn.net/?f=%5Csqrt%7Br%5E2%7D%20%3D%20%5C%C2%B1%5Csqrt%7B14)
![r = \±\sqrt{14](https://tex.z-dn.net/?f=r%20%3D%20%5C%C2%B1%5Csqrt%7B14)
Hence, the possible values of r are:
or ![-\sqrt{14](https://tex.z-dn.net/?f=-%5Csqrt%7B14)
and the product is:
![Product = \sqrt{14} * -\sqrt{14}](https://tex.z-dn.net/?f=Product%20%3D%20%5Csqrt%7B14%7D%20%2A%20-%5Csqrt%7B14%7D)
![Product = -14](https://tex.z-dn.net/?f=Product%20%3D%20-14)
You do 35 divide by 18 = 1.94 repeating