<h2>
Answer:</h2>
The ratio of the area of region R to the area of region S is:
![\dfrac{24}{25}](https://tex.z-dn.net/?f=%5Cdfrac%7B24%7D%7B25%7D)
<h2>
Step-by-step explanation:</h2>
The sides of R are in the ratio : 2:3
Let the length of R be: 2x
and the width of R be: 3x
i.e. The perimeter of R is given by:
![Perimeter\ of\ R=2(2x+3x)](https://tex.z-dn.net/?f=Perimeter%5C%20of%5C%20R%3D2%282x%2B3x%29)
( Since, the perimeter of a rectangle with length L and breadth or width B is given by:
)
Hence, we get:
![Perimeter\ of\ R=2(5x)](https://tex.z-dn.net/?f=Perimeter%5C%20of%5C%20R%3D2%285x%29)
i.e.
![Perimeter\ of\ R=10x](https://tex.z-dn.net/?f=Perimeter%5C%20of%5C%20R%3D10x)
Also, let " s " denote the side of the square region.
We know that the perimeter of a square with side " s " is given by:
![\text{Perimeter\ of\ square}=4s](https://tex.z-dn.net/?f=%5Ctext%7BPerimeter%5C%20of%5C%20square%7D%3D4s)
Now, it is given that:
The perimeters of square region S and rectangular region R are equal.
i.e.
![4s=10x\\\\i.e.\\\\s=\dfrac{10x}{4}\\\\s=\dfrac{5x}{2}](https://tex.z-dn.net/?f=4s%3D10x%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cs%3D%5Cdfrac%7B10x%7D%7B4%7D%5C%5C%5C%5Cs%3D%5Cdfrac%7B5x%7D%7B2%7D)
Now, we know that the area of a square is given by:
![\text{Area\ of\ square}=s^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%5C%20of%5C%20square%7D%3Ds%5E2)
and
![\text{Area\ of\ Rectangle}=L\times B](https://tex.z-dn.net/?f=%5Ctext%7BArea%5C%20of%5C%20Rectangle%7D%3DL%5Ctimes%20B)
Hence, we get:
![\text{Area\ of\ square}=(\dfrac{5x}{2})^2=\dfrac{25x^2}{4}](https://tex.z-dn.net/?f=%5Ctext%7BArea%5C%20of%5C%20square%7D%3D%28%5Cdfrac%7B5x%7D%7B2%7D%29%5E2%3D%5Cdfrac%7B25x%5E2%7D%7B4%7D)
and
![\text{Area\ of\ Rectangle}=2x\times 3x](https://tex.z-dn.net/?f=%5Ctext%7BArea%5C%20of%5C%20Rectangle%7D%3D2x%5Ctimes%203x)
i.e.
![\text{Area\ of\ Rectangle}=6x^2](https://tex.z-dn.net/?f=%5Ctext%7BArea%5C%20of%5C%20Rectangle%7D%3D6x%5E2)
Hence,
Ratio of the area of region R to the area of region S is:
![=\dfrac{6x^2}{\dfrac{25x^2}{4}}\\\\=\dfrac{6x^2\times 4}{25x^2}\\\\=\dfrac{24}{25}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B6x%5E2%7D%7B%5Cdfrac%7B25x%5E2%7D%7B4%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B6x%5E2%5Ctimes%204%7D%7B25x%5E2%7D%5C%5C%5C%5C%3D%5Cdfrac%7B24%7D%7B25%7D)
Answer:
what i cant see
Step-by-step explanation:
Answer:
2 : 3
Step-by-step explanation:
bananas to apples = 8 : 12
simplify by dividing both values by highest common factor of 4:
8 ÷ 4 : 12 ÷ 4 = 2 : 3
Answer:
81.86%
Step-by-step explanation:
We have been given that final exam scores are normally distributed with a mean of 74 and a standard deviation of 6.
First of all we will find z-score using z-score formula.
Now let us find z-score for 86.
Now we will find P(-1<Z) which is probability that a random score would be greater than 68. We will find P(2>Z) which is probability that a random score would be less than 86.
Using normal distribution table we will get,
![P(-1](https://tex.z-dn.net/?f=P%28-1%3CZ%29%3D%20.15866)
We will use formula
to find the probability to find that a normal variable lies between two values.
Upon substituting our given values in above formula we will get,
![P(-1](https://tex.z-dn.net/?f=P%28-1%3CZ%3C2%29%20%3D%20P%28Z%3C2%29%20-%20P%28Z%3C-1%29)
![P(-1](https://tex.z-dn.net/?f=P%28-1%3CZ%3C2%29%20%3D%200.97725-0.15866%3D0.81859)
Upon converting 0.81859 to percentage we will get
![0.81859*100=81.859\approx 81.86](https://tex.z-dn.net/?f=0.81859%2A100%3D81.859%5Capprox%2081.86)
Therefore, 81.86% of final exam score will be between 68 and 86.
Answer:
216in2
step-by-step
cause i said so