Question

Help please

Answer 1

Help please

Answer 2

3. A local store owner pays her employees time-and-a-half for overtime. That means for every hour an employee works more than 40 hours per week, the store will pay 1.5 times the regular hourly wage of 14.50.

Part I: Write a function, P(x), that defines the weekly pay for employees who work up to but not more than 40 hours in a week.


Part II: Suppose an employee works overtime (more than 40 hours per week). What is the hourly wage for the overtime hours?

Part III: Follow these steps to write a function, P(x), that defines the total weekly pay for employees who work more than 40 hours in a week.

a. How much does an employee make working the first 40 hours at $14.50 an hour?


b. If an employee works x > 40 hours per week, write an expression for the overtime pay.
Hint:
The employee works (x-40) overtime hours.
overtime pay = (overtime hourly wage) • (number of overtime hours)

c. Use your answer from parts (a) and (b) to write the function P(x), that defines the total weekly pay for employees who work more than 40 hours in a week.

Part IV: Use the functions from Part I and Part III to write the piecewise function for how much an employee will be paid if he or she were to work less than or equal to 40 hours, or more than 40 hours.


Part V: Use the function from Part III to determine how much an employee will be paid if he or she were to work 50 hours in a week.

Answer 3

part I) since they're working less than overtime, you only need to consider the normal wage

so write a function that describes total wage, given hourly wage and number of hours (x)

Answer 4

it's just total wage = P(x) = (hourly wage)(number of hours) then plug in the hourly wage and number of hours (in this case, we will use x for number of hours, since we just want the general function)

Answer 5

total wage = P(x) = (hourly wage)(number of hours)
(14.50)(40)

Answer 6

580

Answer 7

*** (in this case, we will use x for number of hours, since we just want the general function) ***

Answer 8

(14.50)(x)

Answer 9

good, P(x) = 14.50x

Answer 10

part II)

overtime wage is just 1.5 * regular hourly wage = ?

Answer 11

overtime wage is just 1.5 * 14.50 =$21.75

Answer 12

good

part III) a)

a. How much does an employee make working the first 40 hours at $14.50 an hour?

it's just number of hours * hourly wage = ?

Answer 13

$580

Answer 14

awesome

then for part III) b)

b. If an employee works x > 40 hours per week, write an expression for the overtime pay.
Hint:
The employee works (x-40) overtime hours.
overtime pay = (overtime hourly wage) • (number of overtime hours)

you are given the overtime hourly wage from part III)a, and the "number of overtime hours" is also given as (x-40), just perform the appropriate substitution, don't distribute or simplify yet

Answer 15

overtime pay = (overtime hourly wage) • (number of overtime hours)
overtime pay= 1.5*40
= 60

Answer 16

number of overtime hours is given as (x-40) not 40

Answer 17

also the overtime hourly wage is not 1.5, it's $21.75 as we determined in IIIa

Answer 18

overtime pay = (overtime hourly wage) • (number of overtime hours)
overtime pay= 1.5*x-40
= 1.5x-40
=

Answer 19

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
also the overtime hourly wage is not 1.5, it's $21.75 as we determined in IIIa
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 20

overtime pay = (overtime hourly wage) • (number of overtime hours)
overtime pay= 21.75*x-40
= 21.75x-40
=

Answer 21

good just be careful about your parentheses

overtime pay = 21.75(x-40)

Answer 22

IIIc

c. Use your answer from parts (a) and (b) to write the function P(x), that defines the total weekly pay for employees who work more than 40 hours in a week.

just add the parts a and part b together

P(x) = 580 + 21.75(x-40) = your ans

Answer 23

Part IV: Use the functions from Part I and Part III to write the piecewise function for how much an employee will be paid if he or she were to work less than or equal to 40 hours, or more than 40 hours.

your piecewise function will have 3 parts (one for less than 40 hours, one for equal to 40 hours, one for more than 40 hours)

for less than 40 hours --> (14.50)(x) as we determined in part I
equal to 40 hours --> 580 from part IIIa
more than 40 hours --> 580 + 21.75(x-40) from part IIIc

then write this in piecewise function notation

Answer 24

wait so it is just graphed right

Answer 25

it is not asking for a graph, it is asking for a piece wise function

Answer 26

Like this

Answer 27

yes

Answer 28

\[g(x)=\left\{ 580 + 21.75(x-40) \right\} if x=0\]

Answer 29

the function should have three rows

also the function in our problem is P(x) not g(x)

Answer 30

let's start with the first row

P(x) = (14.50)(x) for "less than 40 hours worked" so x < 40

P(x) = 14.50x, x < 40 is the first row

then keep going for the other two rows

Answer 31

the function is P(x) not F(x)

also you need to include the actual functions not just the domains

Answer 32

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
Part IV: Use the functions from Part I and Part III to write the piecewise function for how much an employee will be paid if he or she were to work less than or equal to 40 hours, or more than 40 hours.

your piecewise function will have 3 parts (one for less than 40 hours, one for equal to 40 hours, one for more than 40 hours)

for less than 40 hours --> (14.50)(x) as we determined in part I
equal to 40 hours --> 580 from part IIIa
more than 40 hours --> 580 + 21.75(x-40) from part IIIc

then write this in piecewise function notation
\(\color{#0cbb34}{\text{End of Quote}}\)

^ these are the functions + their domains, each row should have the function + its domain

Answer 33

row 1: 14.50x, x < 40
row 2: 580, x = 40
row 3: 580 + 21.75(x-40), x > 40

Answer 34

good (just change that F(x) to a P(x)

then for part V) x = 50, use the appropriate row of the function to calculate the total wage for 50 hours

Answer 35

Wait so this is different than the previous function

Answer 36

?

so you just wrote a piecewise function that will determine the value of the function for any x value

each row of the function corresponds to a particular type of x value

since x = 50, which is greater than 40, simply use the third row of your piecewise function to determine the value of the function for x = 50

Answer 37

so just x-50?

Answer 38

x = 50

plug this into the function

Answer 39

580+21.75 ((x-50-40)), 50>40

Answer 40

580 + 21.75(x-40)

replace "x" with "50"

580 + 21.75(50-40) = ?

Answer 41

797.5

Answer 42

good, that's it for part V