Answer:
The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Step-by-step explanation:
Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.
The random variable <em>X</em> is exponentially distributed with mean 7 minutes.
Then the parameter of the distribution is,
.
The probability density function of <em>X</em> is:

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

![=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148](https://tex.z-dn.net/?f=%3D%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7B%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7Be%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5B-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%5D%5E%7B9%7D_%7B6%7D%5C%5C%5C%5C%3De%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%206%7D-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%209%7D%5C%5C%5C%5C%3D0.424373-0.276453%5C%5C%5C%5C%3D0.14792%5C%5C%5C%5C%5Capprox%200.148)
Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
2.8 meter= 2800cms
To solve this, we can create a simple algebraic equation:
45x=2800
Divide both sides by 45.
(45x)/45=(2800)/45
x=62.222
You can make 62 full pieces.
To find the waste, multiply the numbers of pieces by the length of each.
62*45
=2790
2800-<span>2790
=10 centimeters
There would be 10 centimeters of wasted linen.
Hope this helps!
-Benjamin</span>
Answer: width = 5 units
Step-by-step explanation:
Let L represent the length of the rectangle.
The width of a rectangle is the length minus 2 units. It means that the width of the rectangle is (L - 2) units.
The formula for determining the area of a rectangle is expressed as
Area = length × width
The area of the rectangle is 35 units. It means that
L(L - 2) = 35
L² - 2L = 35
L² - 2L - 35 = 0
L² + 5L - 7L - 35 = 0
L(L + 5) - 7(L + 5) = 0
L - 7 = 0 or L + 5 = 0
L = 7 or L = - 5
Since the length cannot be negative, then
L = 7 units
Width = 7 - 2 = 5 units
The time it takes to install 1 insulator would be 1.25 hours