Conclusion:
Please refer to the explanation provided.
Detailed explanation:
Starting with these facts:
Total revenue = $250
Fee charged = $70 per car
Tips received = $50
Equation 1 representing the above:
(Fee per car × number of cars) + tips = total revenue
Let the number of cars be c.
Thus, we have:
$70c + $50 = $250
Part B:
Total revenue = $250
Fee charged = $75 per car
Tips received = $35
Supplies cost per car washed = $5
Equation 2:
(Fee per car × number of cars) + tips - (supplies cost × number of cars) = total revenue
$75c + $35 - $5c = $250
$70c + $35 = $250
Part C:
Equation 1 does not factor in costs associated with washing the car, while equation 2 does incorporate costs, which are deducted from the amount charged per car. Additionally, tips in equation 1 total $50 compared to a $35 fee in equation 2.
Answer:
9 minutes
Step-by-step explanation:
By dividing 45 by 5, we find that the result equals 9
<span>As the restaurant owner,
The likelihood of hiring Jun is 0.7 => p(J)
The likelihood of hiring Deron stands at 0.4 => p(D)
The chance of hiring at least one of them is 0.9 => p(J or D)
We can formulate the probability equation:
p(J or D) = p(J) + p(D) - p(J and D) => 0.9 = 0.7 + 0.4 - p(J and D)
p(J and D) = 1.1 - 0.9 = 0.2
Thus, the probability that both Jun and Deron are hired is 0.2.</span>
1. Selected Case B. 2. 9 cm³. 3. 20 cm. 4. 4.5 m³. Explanation: In question 1, we need to fit a drum with a volume of 14,000 cm³. The volume of a cylinder can be calculated via the formula πr²h. For Case A, with r = 100 mm (10 cm) and h = 300 mm (30 cm), the total volume is approximately 9424.78 cm³, insufficient for the given drum. Case B, with r = 200 mm (20 cm) and h = 30 cm, gives a volume of approximately 37699.11 cm³. Case C with r = 32 cm and h = 250 mm (25 cm) results in a volume of about 80424.77 cm³. The smallest volume among Cases B and C is Case B at 37699.11 cm³, thus it is the correct choice. For question 2, the dimensions of the speaker are Length = 45 cm = 0.45 m, Width = 0.4 m, Height = 50 cm = 0.5 m, leading to a volume of 0.09 m³ or 9 cm³. Question 3 involves a speaker with a volume of 30,000 cm³ with Length = 30 cm = 0.45 m and Height = 500 mm = 50 cm, requiring to find its Width: 30,000 = 30 × W × 50, hence W = 20 cm. For question 4, with dimensions of Base = 2 m, Length = 3 m, Height =1.5 m, the volume of the prism is calculated as 4.5 m³.
Answer:
We have defined functions:
f(x) = IxI + 1
g(x) = 1/x^3.
Currently, it is evident that the composite functions are not commutative.
How can we demonstrate this?
To determine if two composite functions are commutative, the following must hold true:
f(g(x)) = g(f(x))
One could apply brute force (simply substituting values to see if the composite functions commute),
but I will opt for a more sophisticated approach.
There are two notable observations:
g(x) has a point of discontinuity at x = 0.
Thus:
f(g(x)) = I 1/x^3 I + 1
remains discontinuous at x = 0, whereas:
g(f(x)) = 1/(IxI + 1)^3
shows that the denominator IxI + 1 can never reach zero.
At this point, there is no discontinuity.
Consequently, the composite functions cannot be commutative.
