Jeremy likes to paint. He estimates the number of paintings he completes using the function, P(w) = 1/3w + 4, where w is the number of weeks he spends painting. The function J(y) represents how many weeks per year he spends painting. Which composite function would represent how many paintings Jeremy completes in a year?

a.) P[J(y)] = J(1/3w + 4)
b.) J[P(w)] = 1/3 ⋅ J + 4
c.) P[J(y)] = 1/3 ⋅ J(y) + 4
d.) J[P(w)] = J(1/3w + 4)

9514 1404 393

  c.)  P[J(y)] = 1/3 ⋅ J(y) + 4

Step-by-step explanation:

The function P takes a number of weeks as an argument and returns the number of paintings.

The function J takes some argument (unspecified) and returns a number of weeks per year.

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The composite function that will give the number of paintings per year will be P(weeks per year) = P(J(y)).

  P(J(y)) = 1/3·J(y) +4 . . . . . matches choice C

Additional comment

Looking at the units of the input and output of each of the functions is called "units analysis." It is a good way to solve many problems.

c > -10.55

step-by-step explanation:

none.

step-by-step explanation:

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find the slope and y-intercept of the second equation.

tap for more

m

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b

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b=-6

compare the slopes

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compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

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m

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m1=5,m2=0