Question

1. the cost y (in dollars) of a cell phone plan is given by y = 30x, where x is the number of phones on the plan.

a) identify the independent and dependent variables.
b) you can have up to 4 phones on the plan. identify the domain and range.

1. samantha is saving money to buy a new bicycle. she already has $50 and plans to save an additional $15 each week. let x represent the number of weeks samantha saves and y represent her total money. y = 15x + 50 models this situation.

a) identify the independent and dependent variables.
b) if samantha works 6 weeks, identify the domain and range.

1. the function s(p) = 40p - 15 gives the total cost in dollars of buying p pairs of shoes during a sale where $15 is taken off the total. what is the cost to buy 4 pairs of shoes?
2. the function e(h) = 8.5h represents the amount earned (in dollars) by working h hours at a job that pays $8.50 per hour. how much will you earn after working 6 hours?
3. the table shows the number of hours you rent a bicycle and the total cost of the rental. the points represented by the table lie on a line. find and interpret the slope of the line.

Explanation:

Step1: Substitute \(p = 4\) into \(S(p)=40p - 15\)

$$S(4)=40\times4-15$$

Step2: Calculate \(40\times4\)

$$40\times4 = 160$$

Step3: Calculate \(160-15\)

$$160 - 15=145$$

Step1: Substitute \(h = 6\) into \(E(h)=8.5h\)

$$E(6)=8.5\times6$$

Step2: Calculate \(8.5\times6\)

$$8.5\times6=(8 + 0.5)\times6=8\times6+0.5\times6=48 + 3=51$$

Step1: Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Take \((x_1,y_1)=(1,12)\) and \((x_2,y_2)=(2,18)\)

$$m=\frac{18 - 12}{2 - 1}$$

Step2: Calculate the numerator and denominator

$$18-12 = 6,2 - 1=1$$

Step3: Find the slope

$$m=\frac{6}{1}=6$$
The slope \(m = 6\) means that for each additional hour of renting the bicycle, the cost increases by \(\$6\).

Answer:

The cost to buy 4 pairs of shoes is \(\$145\).