cam6877

17.06.2020 •

Mathematics

Consider the equation , where x represents the number of basketball players that have signed up for a new league. What is a possible scenario that would be modeled by this equation? Consider how many teams in the league and the number of players on each team this equation could describe

Solved

Show answers

Ответ:

edgartorres5123

26.10.2020

Mathematics

E. cm to 200 Km

F. in to 100 mi

G. cm to 1,000 Km

Step-by-step explanation:

Verify each case

case A) in to mi

In this part the scale is equal to

$\frac{1}{1}\frac{in}{mi}$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{1}\frac{in}{mi}=\frac{x}{210}\frac{in}{mi}\\ \\x=210\ in$

$\frac{1}{1}\frac{in}{mi}=\frac{x}{410}\frac{in}{mi}\\ \\x=410\ in$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case A) is not the solution

case B) cm to Km

In this part the scale is equal to

$\frac{1}{1}\frac{cm}{Km}$

Convert the dimensions of the book to cm

$1\ in=2.54\ cm$

$5\ in=5*2.54=12.70\ cm$

$8\ in=8*2.54=20.32\ cm$

Convert the actual dimensions of Kansas to Km

$1\ mi=1.609344\ Km$

$210\ mi=210*1.609344=337.96\ Km$

$410\ mi=410*1.609344=659.83\ Km$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{1}\frac{cm}{km}=\frac{x}{337.96}\frac{cm}{km}\\ \\x=337.96\ cm$

$\frac{1}{1}\frac{cm}{km}=\frac{x}{659.83}\frac{cm}{km}\\ \\x=659.83\ cm$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case B) is not the solution

case C) in to mi

In this part the scale is equal to

$\frac{1}{10}\frac{in}{mi}$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{10}\frac{in}{mi}=\frac{x}{210}\frac{in}{mi}\\ \\x=210/10=21\ in$

$\frac{1}{10}\frac{in}{mi}=\frac{x}{410}\frac{in}{mi}\\ \\x=410/10=41\ in$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case C) is not the solution

case D) ft to 100 mi

In this part the scale is equal to

$\frac{1}{100}\frac{ft}{mi}$

Convert the dimensions of the book to ft

$1\ ft=12\ in$

$5\ in=5/12=0.42\ ft$

$8\ in=8/12=0.67\ ft$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{100}\frac{ft}{mi}=\frac{x}{210}\frac{ft}{mi}\\ \\x=210/100=2.1\ ft$

$\frac{1}{100}\frac{ft}{mi}=\frac{x}{410}\frac{ft}{mi}\\ \\x=410/100=4.1\ ft$

The dimensions of Kansas on a map is greater than the dimensions of the page

therefore

case D) is not the solution

case E) cm to 200 Km

In this part the scale is equal to

$\frac{1}{200}\frac{cm}{Km}$

Convert the dimensions of the book to cm

$1\ in=2.54\ cm$

$5\ in=5*2.54=12.70\ cm$

$8\ in=8*2.54=20.32\ cm$

Convert the actual dimensions of Kansas to Km

$1\ mi=1.609344\ Km$

$210\ mi=210*1.609344=337.96\ Km$

$410\ mi=410*1.609344=659.83\ Km$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{200}\frac{cm}{km}=\frac{x}{337.96}\frac{cm}{km}\\ \\x=337.96/200=1.69\ cm$

$\frac{1}{200}\frac{cm}{km}=\frac{x}{659.83}\frac{cm}{km}\\ \\x=659.83/200=3.30\ cm$

The dimensions of Kansas on a map is less than the dimensions of the page

therefore

case E) could be a scale on the map

case F) in to 100 mi

In this part the scale is equal to

$\frac{1}{100}\frac{in}{mi}$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{100}\frac{in}{mi}=\frac{x}{210}\frac{in}{mi}\\ \\x=210/100=2.1\ in$

$\frac{1}{100}\frac{in}{mi}=\frac{x}{410}\frac{in}{mi}\\ \\x=410/100=4.1\ in$

The dimensions of Kansas on a map is less than the dimensions of the page

therefore

case F) could be a scale on the map

case G) cm to 1,000 Km

In this part the scale is equal to

$\frac{1}{1,000}\frac{cm}{Km}$

Convert the dimensions of the book to cm

$1\ in=2.54\ cm$

$5\ in=5*2.54=12.70\ cm$

$8\ in=8*2.54=20.32\ cm$

Convert the actual dimensions of Kansas to Km

$1\ mi=1.609344\ Km$

$210\ mi=210*1.609344=337.96\ Km$

$410\ mi=410*1.609344=659.83\ Km$

Convert the actual dimensions of Kansas to the model dimensions on a map and compare with the dimensions of the page of the book

By proportion

$\frac{1}{1,000}\frac{cm}{km}=\frac{x}{337.96}\frac{cm}{km}\\ \\x=337.96/1,000=0.34\ cm$

$\frac{1}{1,000}\frac{cm}{km}=\frac{x}{659.83}\frac{cm}{km}\\ \\x=659.83/1,000=0.66\ cm$

The dimensions of Kansas on a map is less than the dimensions of the page

therefore

case G) could be a scale on the map

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice