Answer:
See the attached image for the answers and the working out.
Step-by-step explanation:
Answer:
y = 6.5 units
Step-by-step explanation:
Let L be the length of sides of the square.
Given the following data;
Perimeter of square = 8y - 12
Area of square = 100 square units
To find the value of y;
Area of a square = L²
Substituting into the formula, we have;
100 = L²
L = √100
L = 10 units
Mathematically, the perimeter of a square is given by the formula;
Perimeter of a square = 4L
Substituting into the formula, we have;
8y - 12 = 4*10
8y - 12 = 40
8y = 40 + 12
8y = 52
y = 52/8
y = 6.5 units
Answer:
r² = 0.5652 < 0.7 therefore, the correlation between the variables does not imply causation
Step-by-step explanation:
The data points are;
X, Y
0.7, 1.11
21.9, 3.69
18, 4
16.7, 3.21
18, 3.7
13.8, 1.42
18, 4
13.8, 1.42
15.5, 3.92
16.7, 3.21
The correlation between the values is given by the relation
Y = b·X + a


Where;
N = 10
∑XY = 499.354
∑X = 153.1
∑Y = 29.68
∑Y² = 100.546
∑X² = 2631.01
(∑ X)² = 23439.6
(∑ Y)² = 880.902
From which we have;


![r = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{\sqrt{\left [N\sum X^{2} - \left (\sum X \right )^{2} \right ]\times \left [N\sum Y^{2} - \left (\sum Y \right )^{2} \right ]}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7BN%5Csum%20XY%20-%20%5Cleft%20%28%5Csum%20X%20%20%5Cright%20%29%5Cleft%20%28%5Csum%20Y%20%20%5Cright%20%29%7D%7B%5Csqrt%7B%5Cleft%20%5BN%5Csum%20X%5E%7B2%7D%20-%20%5Cleft%20%28%5Csum%20X%20%20%5Cright%20%29%5E%7B2%7D%20%5Cright%20%5D%5Ctimes%20%5Cleft%20%5BN%5Csum%20Y%5E%7B2%7D%20-%20%5Cleft%20%28%5Csum%20Y%20%20%5Cright%20%29%5E%7B2%7D%20%5Cright%20%5D%7D%7D)

r² = 0.5652 which is less than 0.7 therefore, there is a weak relationship between the variables, and it does not imply causation.
Answer:
A-a rectangle with two 12-ft sides and two 2-ft sides
Step-by-step explanation:
Got it right on edge
Answer:
The following two equations model this relationship.
Step-by-step explanation:
We know that when 'y' varies inversely with 'x', we get the equation
y ∝ 1/x
y = k / x
k = yx
where 'k' is called the 'constant of proportionality'.
In our case, it is given that the cube root of 'r' varies inversely with the square of 's', then
∝ 
![\:\sqrt[3]{r}=\:\frac{k}{s^2}](https://tex.z-dn.net/?f=%5C%3A%5Csqrt%5B3%5D%7Br%7D%3D%5C%3A%5Cfrac%7Bk%7D%7Bs%5E2%7D)
or
∵ ![\sqrt[3]{r}=r^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Br%7D%3Dr%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
Therefore, the following two equations model this relationship.