Answer:
<em>The width is 4 cm</em>
<em>The length is 12 cm.</em>
Step-by-step explanation:
<u>Area of a rectangle</u>
Given a rectangle of width W and length L, its area is calculated as follows:
![A=W\cdot L](https://tex.z-dn.net/?f=A%3DW%5Ccdot%20L)
The area of the given rectangle is 48 cm^2, and the length is three times the width, thus:
L = 3W
Substituting into the formula of the area:
![W\cdot L=48](https://tex.z-dn.net/?f=W%5Ccdot%20L%3D48)
![W\cdot 3W=48](https://tex.z-dn.net/?f=W%5Ccdot%203W%3D48)
Simplifying:
![3W^2=48](https://tex.z-dn.net/?f=3W%5E2%3D48)
Solving:
![W^2=48/3=16](https://tex.z-dn.net/?f=W%5E2%3D48%2F3%3D16)
![W=\sqrt{16}=4](https://tex.z-dn.net/?f=W%3D%5Csqrt%7B16%7D%3D4)
The width is 4 cm. Find the length:
L=3W=3*4= 12
The length is 12 cm.
The image attached shows the rectangle on the centimeter grid
Answer:
a. 25
Step-by-step explanation:
Sₙ = n/2 * (2 * a₁ + (n-1) * d)
Sₙ = 500 a₁ = -4 d = 2
500 = n/2 * (-8 + (n-1) * 2) = n/2 * (-8 + 2n - 2) = n/2 * (2n - 10) = n² -5n
n² - 5n -500 = 0
(n - 25) (n + 20) = 0
n > 0
n = 25
Answer:
what
Step-by-step explanation:
Answer:
0.1606 = 16.06% probability that the number of births in any given minute is exactly five.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
In this question:
We only have the mean during an interval, and this is why we use the Poisson distribution.
The mean number of births per minute in a given country in a recent year was about 6.
This means that ![\mu = 6](https://tex.z-dn.net/?f=%5Cmu%20%3D%206)
Find the probability that the number of births in any given minute is exactly five.
This is P(X = 5). So
![P(X = 5) = \frac{e^{-6}*6^{5}}{(5)!} = 0.1606](https://tex.z-dn.net/?f=P%28X%20%3D%205%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B5%7D%7D%7B%285%29%21%7D%20%3D%200.1606)
0.1606 = 16.06% probability that the number of births in any given minute is exactly five.