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2 days ago

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Claire is a manager at a toy packaging company. The company packs 80 boxes of toys every hour for the first 3 hours of the day.

They stop packaging for the next 2 hours in order to carry out a training session. Then, for the next 4 hours, they pack 20 boxes of toys every hour. Which graph models the piecewise function for the given situation?

2 answers:

Svet_ta [4.3K]2 days ago

8 0

Response:

Refer to the figure attached.

Step-by-step explanation:

Each portion is treated as a function.

Let x represent the hours worked in a day

The company packs 80 boxes of toys each hour during the first three hours. Thus, y₁ = 80x, for x ∈ [0,3]

After three hours, the total boxes packed = 80 * 3 = 240

They pause packaging for two hours for a training session. Therefore, y₂ = 240, for x ∈ [3,5]

Next, for the subsequent four hours, they pack 20 boxes of toys hourly

y₃ = 20x + c, for x ∈ [5,9]

To determine c, equate y₂ and y₃ at x = 5

∴ 240 = 20 * 5 + c

∴ c = 240 - 20 * 5 = 240 - 100 = 140

∴ y₃ = 20x + 140, for x ∈ [5,9]

Consequently,

y₁ = 80x, for x ∈ [0,3]

y₂ = 240, for x ∈ [3,5]

y₃ = 20x + 140, for x ∈ [5,9]

The graph plotting the piecewise function that depicts the described situation is shown in the attached illustration.

babunello [3.6K]2 days ago

6 0

Response: D

Step-by-step explanation:

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According to our problem, the initial investment is <span>$30,000 with a duration of ten years, thus </span> $P=30000$ and $t=10$ . Interest is compounded annually, so $n=1$ . To convert the percentage interest rate into decimal, we divide it by 100%
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Substituting the known values,

60° + m∠B + 45° = 180.

This gives us m∠B = 75°.

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Using the law of sines,

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

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