Part 1: Graph piecewise functions from tables and equations. Isabel sells new and used mystery novels online. Her customers are
primarily in the United States. She sends up to 10 pounds of books in one shipment. She uses the United States Postal Service’s Media Mail service because it is inexpensive for her customers. Current Media Mail shipping prices for book shipments weighing 10 pounds or less appear below.
How much would it cost to ship a package weighing 3.2 pounds? Explain how you arrived at your answer. (3 points) What type of graph is needed to represent the Media Mail shipping prices as a function of the weight of the books shipped? Explain your thinking. (3 points)
Graph the Media Mail shipping prices as a function of the weight of the books shipped. (10 points)
1 answer:
A) The cost to send a package that weighs 3.2 pounds is $4.13. Since this weight exceeds 3 pounds but remains below 4 pounds, we have to refer to the pricing that applies to 4-pound packages (see the attached document for pricing details).
b) To illustrate the Media Mail shipping costs based on the weight of the books, a line graph is appropriate. In this graph, the weight in pounds is represented on the x-axis and the shipping costs on the y-axis.
c) The graph depicting the Media Mail shipping costs as a function of book weight will be represented by the equation: f(x) = 2.69 + 0.48(x-1)
b) To illustrate the Media Mail shipping costs based on the weight of the books, a line graph is appropriate. In this graph, the weight in pounds is represented on the x-axis and the shipping costs on the y-axis.
c) The graph depicting the Media Mail shipping costs as a function of book weight will be represented by the equation: f(x) = 2.69 + 0.48(x-1)
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Answer:
To measure 1.25 mL of dye solution, use 5 mL of dye combined with 3 mL of water
Consequently, the total solution volume reaches 8 mL.
Next,
This 8 mL solution consists of
part dye and part water.In the following step, extract 2 mL of this solution.
Thus,
The dye content in the 2 mL solution is
or
The 2 mL solution contains 1.25 mL of dye
Hence,
the required 1.25 mL of dye is now accurately measured.
Step-by-step explanation:Given:
A 10-mL graduated cylinder calibrated in 1-mL increments
The dye solution to be measured = 1.25 mL
Now,
Combine 5 mL of dye with 3 mL of water
This creates a total solution volume of 8 mL.
Next,
This 8 mL solution comprises
part dye and part water.Then, extract 2 mL from this solution.
Thus,
The concentration of dye in the 2 mL solution measures
or
1.25 mL of dye per 2 mL solution
Therefore, 1.25 mL of dye has been accurately determined.