Can't see the graph, but it should look something like this:
What is the intersection of the given lines AE and DE?
1 answer:
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Answer:
See the attached figure.
Step-by-step explanation:
Modeling each part as a function.
Let x is hours of the working day
The company packs 80 boxes of toys every hour for the first 3 hours of the day. ⇒ y₁ = 80 x , x ∈ [0,3]
At the end of the 3 hours The company packs = 80 * 3 = 240
They stop packaging for the next 2 hours in order to carry out a training session. ⇒ y₂ = 240 , x ∈ [3,5]
Then, for the next 4 hours, they pack 20 boxes of toys every hour
y₃ = 20x + c , x ∈ [5,9]
To find c, y₂ = y₃ at x =5
∴ 240 = 20 * 5 + c
∴ c = 240 - 20 * 5 =240 - 100 = 140
∴ y₃ = 20x + 140 , x ∈ [5,9]
So,
y₁ = 80 x , x ∈ [0,3]
y₂ = 240 , x ∈ [3,5]
y₃ = 20x + 140 , x ∈ [5,9]
The graph models the piecewise function for the given situation is as shown in the attached figure.
Answer: The required number of passwords that can be created is 175760.
Step-by-step explanation: Given that a company needs temporary passwords for the trial of a new payroll software.
Each password will have one digit followed by three letters and the letters can be repeated.
We are to find the number of passwords that can be created using this format.
For the one digit in the password, we have 10 options, 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Since there are 26 letters in English alphabet and letters can be repeated, so the number of options for 3 letters is
26 × 26 × 26 = 17576.
Therefore, the total number of ways in which passwords can be created using the given format is
Thus, the required number of passwords that can be created is 175760.