Answer: 0.271
Step-by-step explanation:
Probability of complement of an even is 1 decreased by the probability of the event
P(At least one) =1 - P(none)
The probability that of testing negative is 0.9 because the probability of testing positive is 0.1
P( at least one) = 1 - P(none) = 1 - (0.93^3) = 0.271
The dimensions of the bulletin board is 2 ft and 9 ft.
Let the width of board = x
Then, the length of board = 7+x
Area of board = 18 ft²
Area of rectangle = L×W
so, (7+x) × x = 18 ft²
7x + x² = 18 ft²
7x + x² + 18 = 0
x² + 9x -2x -18 = 0
x(x+9) -2(x+9) = 0
(x+9) (x-2) = 0
x+9 =0, x -2 = 0
Dimension can not be in negative number, so
x = 2, Width = 2 ft
Length = 2+7 = 9 ft
Hence, the dimensions of board will be:
The width of board = 2 ft
And, the length of bard = 9 ft.
Answer:
x = 10 and x = -10
Step-by-step explanation:
Given the function
![f(x)=\dfrac{5x^2+3x+6}{x^2-100}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B5x%5E2%2B3x%2B6%7D%7Bx%5E2-100%7D)
This function is undefied when the denominator equals to 0. Find these values for x:
![x^2-100=0\\ \\(x-10)(x+10)=0\\ \\x-10=0\ \ \text{or}\ \ x+10=0\\ \\x=10\ \ \text{or}\ \ x=-10](https://tex.z-dn.net/?f=x%5E2-100%3D0%5C%5C%20%5C%5C%28x-10%29%28x%2B10%29%3D0%5C%5C%20%5C%5Cx-10%3D0%5C%20%5C%20%5Ctext%7Bor%7D%5C%20%5C%20x%2B10%3D0%5C%5C%20%5C%5Cx%3D10%5C%20%5C%20%5Ctext%7Bor%7D%5C%20%5C%20x%3D-10)
This means that vertical lines x = 10 and x = -10 are vertical asymptotes (the graph of the function f(x) cannot meet these lines because this function is undefined at x = 10 and x = -10)
Here are the examples for
1. a normal line to a line
The corner of a photo frame, or the corner of a note book
2. A normal line to a circle
A circular plate balanced on a scale
3. A normal line to a plane
The pole standing on a plain ground