How much profit was generated by the sales of gold label and black label combined?

You can utilize the Pythagorean theorem expressed as a^2 + b^2 = c^2... if b is unknown, you can rearrange the formula. Hence, c^2 - a^2 = b^2. Squaring 47 gives 2209 and squaring 13 yields 169... Subtracting gives you 2209-169, which results in 2040. Taking the square root of that yields approximately 45.166359, which can be rounded to 45 or as 45.167 when expressed to two decimal places. I hope this helps!:)

Answer:

Part a) Your budget is $40.

Part b) The price for one gallon of gasoline is $3.55, while a car wash costs $8.

Part c)

Part d) Refer to the explanation below.

Step-by-step explanation:

Please see the complete question in the attached image.

Part a) The budget is expressed by the equation

y = 40

therefore,

Your budget amounts to $40.

Part b) In terms of costs, how much is a gallon of gasoline and what is the car wash price?

Let

y ------> denote the total cost for a gallon of gasoline along with a car wash

x -----> define the volume of gasoline in gallons

We can express the relationship as

y = 3.55x + 8

For calculations, when x = 0, we have:

y = 3.55(0) + 8 = 8

The y-intercept signifies the cost of the car wash, being $8.

Now, to identify the price of one gallon of gasoline:

We know the slope of the linear function is

m = $3.55 per gallon

This confirms that a gallon of gasoline costs $3.55.

Part c) Formulate an inequality representing the potential quantity of gasoline you can purchase:

We have:

Now, solve for x:

Part d) Utilize the graph to determine the solution of the inequality from part c)

We can set up the system:

y = 40

y = 3.55x + 8

The solution lies at the intersection of both graphs. By observing the graph, the intersection appears to be around (9, 40).

This indicates that the maximum volume of gasoline purchasable within your budget is approximately 9 gallons.

Answer:

Step-by-step explanation:

Aligning each vocabulary term with its relevant example:

(1). All Americans = f. Population (a collective of items or subjects studied, e.g., residents of an area, the number of vehicles in a city, or employees in a workplace)

(2). The percentage of all Americans who strongly believe prisoners with life sentences who develop Alzheimer's should be released = c. Parameter (the figure summarizing a characteristic of a population)

(3). The percentage of the 85 surveyed Americans who strongly feel that prisoners with life sentences who have Alzheimer's should be released = d. Statistic (the characteristic of a sample that corresponds to a population parameter used for statistical inference)

(4). The responses being 'Strongly Agree', 'Agree', 'Disagree', or 'Strongly Disagree' = b. Variable (any measurable quality or characteristic)

(5). The 85 individuals surveyed = e. Sample (a subset of a population chosen based on certain criteria)

(6). The array of responses provided by the 85 participants = a. Data (the collected pieces of information meant for analysis)

Response:

Refer to the figure attached.

Step-by-step explanation:

Each portion is treated as a function.

Let x represent the hours worked in a day

The company packs 80 boxes of toys each hour during the first three hours. Thus, y₁ = 80x, for x ∈ [0,3]

After three hours, the total boxes packed = 80 * 3 = 240

They pause packaging for two hours for a training session. Therefore, y₂ = 240, for x ∈ [3,5]

Next, for the subsequent four hours, they pack 20 boxes of toys hourly

y₃ = 20x + c, for x ∈ [5,9]

To determine c, equate y₂ and y₃ at x = 5

∴ 240 = 20 * 5 + c

∴ c = 240 - 20 * 5 = 240 - 100 = 140

∴ y₃ = 20x + 140, for x ∈ [5,9]

Consequently,

y₁ = 80x, for x ∈ [0,3]

y₂ = 240, for x ∈ [3,5]

y₃ = 20x + 140, for x ∈ [5,9]

The graph plotting the piecewise function that depicts the described situation is shown in the attached illustration.