Mathematics: Functions and Cost Calculations

Questions and Answers

What is the total length of a line of 3 grocery carts?

12 feet

13 feet

12.5 feet (correct)

12.75 feet

Which variable represents the independent variable in the scenario?

Total length of the carts

Length of an individual cart

Length added for each cart

Number of grocery carts (correct)

If there are zero grocery carts, what is the length of the line?

3.5 feet

4 feet

2 feet

0 feet (correct)

Which statement is true regarding the total length of the line of carts?

The total length can be represented by a linear function. Signup and view all the answers

How is the additional length added for each extra cart expressed mathematically?

$rac{1}{2}$ foot Signup and view all the answers

What is the equation representing the length of the line of carts for $n$ carts?

Length = $4n + 0.5(n - 1)$ Signup and view all the answers

What is the total cost for two hours of repair according to the function rule C(h) = 35h + 35?

$105 Signup and view all the answers

Which function rule represents Tim's total savings after m months, given that he saves $20 a month and saved $35 last month?

t(m) = 35 + 20m Signup and view all the answers

If you have 5 grocery carts, what is the total length of the line?

22.5 feet Signup and view all the answers

What would the length be for a line of 10 grocery carts?

42 feet Signup and view all the answers

If the entrance fee to the amusement park is $25 and each ride ticket costs $2, how much would it cost for a visit with 5 ride tickets?

$45 Signup and view all the answers

Which graph best represents the cost of visiting the amusement park with respect to the number of ride tickets purchased?

Graph B Signup and view all the answers

What is the correct interpretation of the term 'h' in the mechanic's cost function C(h) = 35h + 35?

The hours the mechanic has to bill Signup and view all the answers

If Tim wants to save at least $300 for his game system, how many months must he save if he saved $35 last month?

14 months Signup and view all the answers

How does the cost function for the amusement park change if the entrance fee is increased to $30?

t(x) = 2x + 30 Signup and view all the answers

Which of the following statements correctly describes the slope of the function modeling ride costs at the amusement park?

$2 per ride ticket Signup and view all the answers

Which function represents a linear equation with a negative slope?

f(x) = x - 6 Signup and view all the answers

What does the variable 'x' represent in the shipping cost function?

The weight of the package in ounces Signup and view all the answers

Which equation correctly represents the total shipping cost for a package weighing x ounces?

c(x) = 0.85x + 5.50 Signup and view all the answers

If the weight of a package is 10 ounces, what would be the total shipping cost using the correct cost function?

$10.35 Signup and view all the answers

Which of the following functions has the smallest y-intercept?

f(x) = x - 6 Signup and view all the answers

What is the relationship between shipping cost and weight as described by the function?

Cost increases linearly with weight Signup and view all the answers

Which function shows an increase in cost for every ounce over 0.85?

c(x) = 0.85x + 5.50 Signup and view all the answers

What characterizes a function rule that would not represent shipping costs?

c(x) = 5.50 * x Signup and view all the answers

How much additional money does Anna plan to save each month?

$50 Signup and view all the answers

How long will it take Anna to save enough for the television?

3 months Signup and view all the answers

What is the total amount Anna wants to have saved to buy the television?

$1,225 Signup and view all the answers

Which equation represents Anna's total savings as a function of the number of months she will save?

s(m) = 525 + 50*m Signup and view all the answers

If Anna saves for 6 months, how much will she have saved in total?

$675 Signup and view all the answers

What is the daily rental charge for Ms. Kai's moving truck?

$85 Signup and view all the answers

What is the formula that models the rental cost for Ms. Kai as a function of miles driven?

c(m) = 85 + 0.25*m Signup and view all the answers

If Ms. Kai drives 400 miles, what will be her total rental cost?

$300 Signup and view all the answers

Study Notes

Grocery Carts

Each grocery cart measures 4 feet in length.
Total length of a line of carts includes 1 cart length plus an additional 0.5 feet for each extra cart.
The number of carts is the independent variable while the total length is the dependent variable.
No carts in line have a total length of 3.5 feet.

Function Rules and Graphing

For functions like f(x)=x−6 and f(x)=2x+1, the equations represent direct relationships.
Shipping cost function for shipping a package will be c(x)=5.50 + 0.85x, where x stands for weight in ounces.
Amusement park charges $25 for entry plus $2 per ride, illustrating a linear cost model.

Cost Calculations

Repair cost function: C(h)=35h+35, where h represents hours of work.
If a mechanic works for 2 hours, the total repair cost can be calculated using this function.

Savings and Budgeting

Tim's savings approach models income over time as a function of months saved.
Anna saves $50 monthly towards a flat-screen TV costing $1,225, starting with $525 in savings.
There's an equation s(m)=525 + 50m which depicts her savings function over months.

Truck Rental

Truck rental cost function: c(m)=85 + 0.25m, covering daily rental and mileage charges.
Ms. Kai aims to keep her rental spending under $300, which relates to mileage and daily rental constraints.

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Description

This quiz explores various mathematical functions related to real-world scenarios such as grocery cart lengths, shipping costs, and repair costs. Test your understanding of direct relationships and budgeting strategies through practical applications. Gain insights into how functions can model everyday financial situations.