The volume of the rectangular prism is 1120 yd³.
<h3>What is a prism?</h3>
A prism is a solid geometric figure whose two ends are similar, equal, and parallel rectilinear figures, and whose sides are parallelograms.
To calculate the volume of the rectangular prism, we use the formula below.
Formula:
- V = LWH.......... Equation 1
Where:
- V = Volume of the rectangular prism
- L = Length of the prism
- W = Width of the prism
- H = Height of the prism.
From the question,
Given:
- L = 14 yards
- W = 8 yards
- H = 10 yards.
Substitute thee values into equation 1
Hence, The volume of the rectangular prism is 1120 yd³.
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Using it's concept, it is found that there is a 0.8 = 80% probability that the learner is a senior or a male.
<h3>What is a probability?</h3>
A probability is given by the <u>number of desired outcomes divided by the number of total outcomes</u>.
In this problem, there is a total of 6 + 4 + 5 = 15 students. Of those, there are 6 seniors, and 6 male non-seniors, hence there are 12 desired outcomes, and the probability is given by:
p = 12/15 = 0.8 = 80%.
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Answer:
Part 1) 
Part 2) The slope is undefined
Step-by-step explanation:
we know that
The formula to calculate the slope between two points is equal to
Part 1
we have
Substitute the values
----> is a horizontal line (parallel to x-axis)
Part 2
we have
Substitute the values
----> is a vertical line (parallel to y-axis)
The slope is undefined
The value of -(5 - 3)² + (8 - -2) - 3(4 + -1)² is -21
Step-by-step explanation:
Let us revise some notes about the positive and negative numbers
- a - b = + value if a > b
- a - b = - value if a < b
- a + (-b) = a - b
- a - (-b) = a + b
- a(-b) =-a(b) = -ab
Let us evaluate -(5 - 3)² + (8 - -2) - 3(4 + -1)²
∵ 5 - 3 = 2 ⇒ 1st note above
∵ 8 - (-2) = 8 + 2 = 10 ⇒ 4th note above
∵ 4 + (-1) = 4 - 1 = 3 ⇒ 3rd note above
- Substitute them in the expression above
∴ -(5 - 3)² + (8 - -2) - 3(4 + -1)² = -(2)² + (10) - 3(3)²
∵ -(2)² = -(4) = -4 ⇒ 5th note above
∵ -3(3)² = -3(9) = -27
∴ -(2)² + (10) - 3(3)² = -4 + 10 - 27
∵ -4 + 10 - 27 = (-4 + -27) + 10 = -31 + 10 = -21
∴ -(2)² + (10) - 3(3)² = -21
∴ -(5 - 3)² + (8 - -2) - 3(4 + -1)² = -21
The value of -(5 - 3)² + (8 - -2) - 3(4 + -1)² is -21
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