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2 months ago

The table lists the results from a survey (of questionable accuracy) of adults and how much they spend on a night out.

Mathematics

2 answers:

PIT_PIT [12.4K]2 months ago

7 0

The correct answer is:

The appropriate scatter plot is shown.

The data suggest a negative correlation between an individual's age and how much they spend on a night out.

Explanation:

Plot age on the x-axis as the independent variable, and cost of a night out on the y-axis as the dependent variable.

Ages span from 20 up to 45. Begin the x-axis at 0 and label in increments of 5 up to 45.

Night out costs range between 38 and 58. Start the y-axis at 0 and use increments of 5, extending to 60.

Mark each data point using coordinates in the form (age, amount spent).

After plotting, the pattern shows a downward trend: as age goes up, spending tends to go down.

PIT_PIT [12.4K]2 months ago

3 0

Create a graph with age on the x-axis and money spent on a night out on the y-axis. Plot the ordered pairs as a scatter plot. After placing all points, state the relationship, for example: "the older someone is, the less money they spend on a night out," ensuring the description matches the plotted data. (:

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Read 2 more answers

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Answer:

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Part 2) When x=40 m, the area of the schoolyard is A=2,800 m^2

Part 3) The valid domain consists of all real numbers exceeding zero and below 75 meters

Step-by-step explanation:

Part 1) Formulate an expression for A(x)

Let

x -----> the length of the rectangular school yard

y ---> the width of the rectangular school yard

It is known that

The perimeter for the fencing (taking the school wall as one side) is

$P=2x+y$

$P=150\ m$

thus

$150=2x+y$

$y=150-2x$ -----> this is equation A

The area of the rectangular school yard is

$A=xy$ ----> this is equation B

Substituting equation A into equation B yields

$A=x(150-2x)$

$A=150x-2x^2$

Change to function notation

$A(x)=150x-2x^2$

Part 2) What is the area when x=40?

With x equal to 40 m

substitute the value into the expression from Part 1 to determine A

$A(40)=150(40)-2(40^2)$

$A(40)=2,800\ m^2$

Part 3) What would be a suitable domain for A(x) in this scenario?

We understand that

A signifies the area of the rectangular school yard

x characterizes the length of the rectangular school yard

It follows that

$A(x)=150x-2x^2$

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The vertex indicates a maximum point

The x-coordinate of the vertex corresponds to the length that maximizes the area

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The vertex corresponds to (37.5, 2812.5)

Refer to the accompanying figure

Consequently,

The peak area achieved is 2,812.5 m^2

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The domain for A is the range -----> (0, 75)

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