Answer:
The equation of the line that passes through the points (0, 3) and (5, -3) is 
.
Step-by-step explanation:
From Analytical Geometry we must remember that a line can be formed after knowing two distinct points on Cartesian plane. The equation of the line is described below:
(Eq. 1)
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Slope, dimensionless.
- y-Intercept, dimensionless.
If we know that 
and 
, the following system of linear equations is constructed:
(Eq. 2)
(Eq. 3)
The solution of the system is: , 
. Hence, we get that equation of the line that passes through the points (0, 3) and (5, -3) is .
Here you go, hope this kinda helps you out :)
Answer:
The volume of the water in the tank is 112 m³
Step-by-step explanation:
The volume of the rectangular prism V = L × W × H, where
∵ A rectangular tank has a length of 4 m, a width of 12 m, and
a height of 3.5 m
∴ L = 4 m
∴ W = 12 m
∴ H = 3.5 m
∵ V = L × W × H
∴ The volume of the tank = 4 × 12 × 3.5
∴ The volume of the tank = 168 m³
∵ The tank is filled with water 
of its capacity
→ That means the volume of the water is the volume of the tank
∵ The volume of the water = the volume of the tank
∴ The volume of the water = × 168
∴ The volume of the water = 112 m³
∴ The volume of the water in the tank is 112 m³
Let
denote the random variable for the weight of a swan. Then each swan in the sample of 36 selected by the farmer can be assigned a weight denoted by
, each independently and identically distributed with distribution
.
You want to find
Note that the left side is 36 times the average of the weights of the swans in the sample, i.e. the probability above is equivalent to
Recall that if
, then the sampling distribution
with
being the size of the sample.
Transforming to the standard normal distribution, you have
so that in this case,
and the probability is equivalent to
