6. josie wants to buy internet access. one service provider charges a flat - rate of $34.95/month. a second…

1. Let the number of hours of Internet - use per month be (h).
   • For the first service provider, the cost (C_1) is a flat - rate of (C_1 = 34.95) dollars per month.
   • For the second service provider, the cost (C_2) is given by the equation (C_2=25 + 0.33h), where (25) is the fixed charge per month and (0.33) is the charge per hour.
2. We want to find when (C_1<C_2).
   • Set up the inequality (34.95<25 + 0.33h).
   • First, subtract (25) from both sides of the inequality:
     • (34.95−25<25 + 0.33h−25).
     • (9.95<0.33h).
   • Then, divide both sides of the inequality by (0.33) to solve for (h):
     • (h>\frac{9.95}{0.33}\approx30.15).

So Josie should choose the flat - rate when she uses more than approximately (30.15) hours of Internet per month.

Explanation:

Step1: Define cost functions

Let (C_1 = 34.95) (first provider cost), (C_2=25 + 0.33h) (second provider cost).

Step2: Set up inequality

Set (34.95<25 + 0.33h).

Step3: Simplify inequality

Subtract 25 from both sides: (9.95<0.33h).

Step4: Solve for (h)

Divide by 0.33: (h>\frac{9.95}{0.33}\approx30.15).

Answer:

Josie should choose the flat - rate when she uses more than approximately (30.15) hours of Internet per month.