The following table shows some data from a study on substance use among 10th graders in the United States and Europe. Smoked Cigarettes Cigarette-Free Totals U.S. x y 12,000 Europe z w 98,000 Total 65,210 110,000 (a) The table leads to a linear system of four equations in four unknowns. What is the system? x + y = 12,000 y + w = 98,000 z + w = 65,210 x + w = 110,000
The following table shows some data from a study on substance use among 10th graders in the United States and Europe. Smoked Cigarettes Cigarette-Free Totals U.S. x y 12,000 Europe z w 98,000 Total 65,210 110,000 (a) The table leads to a linear system of four equations in four unknowns. What is the system? x + y = 12,000 y + w = 98,000 z + w = 65,210 x + w = 110,000
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 4CE
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Question
The following table shows some data from a study on substance use among 10th graders in the United States and Europe.
| Smoked Cigarettes | Cigarette-Free | Totals | |
|---|---|---|---|
| U.S. | x | y | 12,000 |
| Europe | z | w | 98,000 |
| Total | 65,210 | 110,000 |
(a)
The table leads to a linear system of four equations in four unknowns. What is the system?
| x | + | y | = | 12,000 | ||||
| y | + | w | = | 98,000 | ||||
| z | + | w | = | 65,210 | ||||
| x | + | w | = | 110,000 | ||||
|
|
| x | + | y | = | 12,000 | ||||
| z | + | w | = | 98,000 | ||||
| y | + | w | = | 65,210 | ||||
| x | + | w | = | 110,000 | ||||
|
|
| x | + | y | = | 12,000 | ||||
| z | + | w | = | 98,000 | ||||
| y | + | w | = | 65,210 | ||||
| x | + | y | + | z | + | w | = | 110,000 |
|
|
| x | + | y | = | 12,000 | ||||
| y | + | w | = | 98,000 | ||||
| z | + | w | = | 65,210 | ||||
| x | + | y | + | z | + | w | = | 110,000 |
|
|
Does it have a unique solution?
This system has one solution.This system has no solution. This system has infinitely many solutions.This system has a finite number of solutions.
What does this indicate about the missing data?
The given data is sufficient to obtain the missing data (x, y, z and w).The given data is insufficient to obtain the missing data (x, y, z and w).
(b)
Given that 41,510 more European 10th graders smoked cigarettes than U.S. 10th graders, find the missing data.
(x, y, z, w) =
1640,10360,40150,57850
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