Let
s--------> denote the cube's side length
We know that
the volume of a cube is calculated as
if the side length s measures
then
and thus, the volume is defined as
This leads us to conclude
the correct option is
D. A cube with side lengths of 2 feet has a volume of 8 cubic feet.
Answer:
1) (2.2, -1.4)
2) (1.33, 1)
Detailed solution:
Question 1)
We are provided with two linear equations representing lines, and we need to find the intersection point that solves the system.
The lines given are:
Line 1 equation:
This line passes through points (0, 2.5) and (2.2, -1.4).
Line 2 equation:
The second line goes through (0, -3) and (2.2, -1.4).
According to the graph and data, the solution to the system is the coordinate where both lines intersect.
The solution to a system of linear equations is the coordinate pair common to both lines, i.e., the intersection point.
Here, both lines share the point (2.2, -1.4), indicating it is their intersection and the solution.
Therefore, the solution for question 1 is (2.2, -1.4).
Question 2)
The equations given are:
y = 1.5x - 1 Equation 1
y = 1 Equation 2
The method of substitution can be used to find the solution.
Replacing y from Equation 2 into Equation 1 gives:
1 = 1.5x - 1
Add 1 to both sides:
2 = 1.5x
Dividing both sides by 1.5 yields:
x = 2/1.5
x = 1.33
y = 1
Thus, the solution of the system is (1.33, 1).
1) 4.55
2) Short hit
Step-by-step explanation:
1)
The score and corresponding probabilities are shown in the following table:
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Let us define
X = Miguel's score on the Water Hole
The expected value of the variable X can be represented as:
where
represents the different possible outcomes of X
denotes the associated probabilities
Accordingly, the expected value of Miguel's score is calculated as follows:
2)
Here, we will again consider:
X = Miguel's score on the Water Hole
In this case:
- For a successful long hit, the expected value of X is
- Conversely, if the long hit isn't successful, the expected value of X becomes
We also know that the likelihood of succeeding with a long hit is
Consequently, the chance of failure in a long hit is
Thus, the expected value of X when opting for the long hit strategy is:
In the first part of this question, we calculated the expected value using the short hit strategy, yielding:
Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.