Answer:
Length of the rectangle = 16 inches
Width of the rectangle = 12 inches
Step-by-step explanation:
Let the length of the rectangle be represented by x.
Then width can be expressed as ![\[\frac{x}{2}+4\] ](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7Bx%7D%7B2%7D%2B4%5C%5D%0A)
Perimeter of a rectangle is the sum of four sides of the rectangle.
This can be expressed as 2*(length + breadth)
= ![\[2* (x + \frac{x}{2}+4)\]](https://tex.z-dn.net/?f=%5C%5B2%2A%20%28x%20%2B%20%5Cfrac%7Bx%7D%7B2%7D%2B4%29%5C%5D)
= ![\[2* (\frac{3x}{2}+4)\]](https://tex.z-dn.net/?f=%5C%5B2%2A%20%28%5Cfrac%7B3x%7D%7B2%7D%2B4%29%5C%5D)
= ![\[3x + 8\]](https://tex.z-dn.net/?f=%5C%5B3x%20%2B%208%5C%5D)
But perimeter is given as 56.
So, ![\[3x + 8 = 56\] ](https://tex.z-dn.net/?f=%5C%5B3x%20%2B%208%20%3D%2056%5C%5D%0A)
=> ![\[3x = 48\]](https://tex.z-dn.net/?f=%5C%5B3x%20%3D%2048%5C%5D)
=> ![\[x = 16\]](https://tex.z-dn.net/?f=%5C%5Bx%20%3D%2016%5C%5D)
Hence length of the rectangle = 16 inches
Width of the rectangle =
= 12 inches
Answer:
c
Step-by-step explanation:
d=2r=2X3=6
<h2>
Hello!</h2>
The answer is:
The second option,
b.) 
<h2>
Why?</h2>
We are given the functions E(x) and K(x), since they both are function of the same variable, we need to add them in order to find the correct option.
From the statement we know the functions:

and

So, adding the functions we have:




Hence, the answer is the second option,
b.) 
Have a nice day!
Answer:
The answer is c.) 0.6 and 0.14
Step-by-step explanation:
Given population has a size of 320.
The proportion of population = 0.6
The mean of population, p = 0.6
The mean of sample,
= 0.6
Therefore
= 1 -
= 1 - 0.6 = 0.4
The sample size = 12
Therefore the standard deviation of the sample,

The mean and the standard deviation for a sample size of 12 are 0.6 and 0.14 respectively.
The answer is c.) 0.6 and 0.14
Answer: 2343 / 256
Explanation
I will do this for you in two forms: 1) adding each term, and 2) using the general formula for the sum of geometric series.
1) Adding the terms:
4
∑ 3 (3/4)^i = 3 (3/4)^0 + 3 (3/4)^1 + 3 (3/4)^2 + 3 (3/4)^3 + 3 (3/4)^4
i=0
= 3 + 9/4 + 27/16 + 81/64 + 243/256 = [256*3 + 27*16 + 64*9 + 4*81 + 243] / 256 =
= 2343 / 256
2) Using the formula:
n-1
∑ A (r^i) = A [1 - r^(n) ] / [ 1 - r]
i=0
Here n - 1 = 4 => n = 5
r = 3/4
A = 3
Therefore the sum is 3 [ 1 - (3/4)^5 ] / [ 1 - (3/4) ] =
= 3 [ 1 - (3^5) / (4^5) ] / [ 1/4 ] = 3 { [ (4^5) - (3^5) ] / (4^5) } / {1/4} =
= (3 * 781) / (4^5) / (1/4) = 3 * 781 / (4^4) = 2343 / 256
So, no doubt, the answer is 2343 / 256