Singh works at a restaurant where he is paid by the hour plus time-and-a-half for his hours over 40. last week he worked 3 hours overtime and his gross pay was $380.48. what is his hourly wage?

The hourly wage is $8.55 per hour

Step-by-step explanation:

Step 1: Determine the expression for the gross pay

Total gross pay=(Unit rate per hour×number of hours(≤40))+(Overtime rate×number of overtime hours)

where;

Total gross pay=$380.48

Unit rate per hour=x

Number of hours=40 hours

Overtime rate=x×(1 1/2)=1.5 x

Number of overtime hours=3 hours

Step 2: Replace to solve for hourly wage

380.48=(x×40)+(1.5 x)×3

40 x+4.5 x=380.48

44.5 x=380.48

x=380.48/44.5

x=8.55

The hourly wage is $8.55 per hour

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places