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?

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.

43

step-by-step explanation:

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!