Question 1

Determine whether the lines through the given pairs of points are perpendicular. Answer yes or no.

Accepted Answer

The answer of Determine whether the lines through the given...

Question 2

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​
If the data consist of two distinct points, then the least-squares line is just the line that passes through the two points.
​

Accepted Answer

A)  It is true.
Suppose that we are given two data points  
If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amounts d1, d2, respectively.
​  
The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares  
Be made as small as possible. In this case the smallest sum is zero.   , when   and   .
Therefore, the required least-squares line is just the line that passes through the two points. 
B)  It is false.
Example: Find the least-squares line for the data   Solution: Here, we have n = 2 and  
The least-squares line for the data is given by linear equation y = f(x) = mx + b
Where the constants m and b satisfy the normal equations       Then, we obtain the normal equations   Solving them, we found   Therefore, the required least-squares line is y = x + 0.4. The scatter diagram and the least-squares line are shown in the figure. We can see that the line does not pass through any data point.   
A)  It is true.
Suppose that we are given two data points  
If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amounts d1, d2, respectively.
​  
The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares  
Be made as small as possible. In this case the smallest sum is zero.   , when   and   .
Therefore, the required least-squares line is just the line that passes through the two points. 
B)  It is false.
Example: Find the least-squares line for the data   Solution: Here, we have n = 2 and  
The least-squares line for the data is given by linear equation y = f(x) = mx + b
Where the constants m and b satisfy the normal equations       Then, we obtain the normal equations   Solving them, we found   Therefore, the required least-squares line is y = x + 0.4. The scatter diagram and the least-squares line are shown in the figure. We can see that the line does not pass through any data point.

Question 3

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
The point (1, k) lies on the line with equation 3x + 8y = 24 if and only if   .

Accepted Answer

A) True 
 B)False

Question 4

Assume that a certain commodity's demand equation has the form p = ax + b, where x is the quantity demanded and p is the unit price in dollars. Suppose the quantity demanded is 1,000 units when the unit price is $19.00 and 7,000 when the unit price is $13.00. What is the quantity demanded when the unit price is $18.50?

Accepted Answer

A)  6,000 units 
B)  1,500 units 
C)  6,500 units 
D)  8,000 units 
A)  6,000 units 
B)  1,500 units 
C)  6,500 units 
D)  8,000 units

Question 5

Find an equation of the line that has slope   and y-intercept   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

The demand equation for the Schmidt-3000 fax machine is   , where x is the quantity demanded per week and p is the unit price in dollars. The supply equation is   , where x is the quantity the supplier will make available in the market when the unit price is p dollars. Find the equilibrium quantity and the equilibrium price for the fax machines.   __________   $ __________

Accepted Answer

The answer of The demand equation for the Schmidt-3000 fax...

Question 7

Sketch a set of coordinate axes and plot the given point. (7, -10)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the point of intersection of the pair of straight lines. 3x - 4y = 9
4x + 12y = 25

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Find the slope of the line that passes through the pair of points.   and

Accepted Answer

The answer of Find the slope of the line that...

Question 10

Find an equation of the line that passes through the point (3, - 4) and has the slope m = 2.

Accepted Answer

A)  y - 2x = 10 
B)  y = 2x - 4 
C)  y = 2(x + 3) - 4 
D)  y = 2x - 10 
A)  y - 2x = 10 
B)  y = 2x - 4 
C)  y = 2(x + 3) - 4 
D)  y = 2x - 10

Question 11

What are the coordinates of point B?

Accepted Answer

The answer of What are the coordinates of point B?...

Question 12

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Sketch a set of coordinate axes and plot the given point. (3, -6)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Which point has a negative x-coordinate and a negative y-coordinate?

Accepted Answer

A)  B 
B)  C 
C)  A 
A)  B 
B)  C 
C)  A

Question 16

College admissions officers estimate that 65% of the students who are offered admission to the freshman class at the university will actually enroll.Find an equation that expresses the relationship between the number of students who actually enroll (y) and the number of students who are offered admission to the university (x).If the desired freshman class size for the upcoming academic year is 1,300 students, how many students should be admitted?

Accepted Answer

A)    2,000 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300. 
B)    2,200 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300. 
C)    6,500 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300. 
D)    1,846 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300. 
A)    2,000 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300. 
B)    2,200 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300. 
C)    6,500 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300. 
D)    1,846 students should be admitted, if the desired freshman class size for the upcoming academic year is 1,300.

Question 17

Find the distance between the given points.
(1, 3) and (5, 6)

Accepted Answer

The answer of Find the distance between the given points.
(1,...

Question 18

Which point has a negative x-coordinate and a negative y-coordinate?

Accepted Answer

A)  B 
B)  C 
C)  A 
A)  B 
B)  C 
C)  A

Question 19

Refer to the accompanying figure and determine the coordinates of the given point and the quadrant in which it is located.

Accepted Answer

A)  (   1,   1); Quadrant III 
B)  (1, 1); Quadrant I 
C)  (1,   1); Quadrant IV 
D)  (   1, 0); Quadrant II 
E)  (   1, 1); Quadrant II 
A)  (   1,   1); Quadrant III 
B)  (1, 1); Quadrant I 
C)  (1,   1); Quadrant IV 
D)  (   1, 0); Quadrant II 
E)  (   1, 1); Quadrant II

Question 20

Find an equation of the line that passes through the points.   and

Accepted Answer

The answer of Find an equation of the line that...

Determine whether the lines through the given pairs of points are perpendicular. Answer yes or no.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If the data consist of two distinct points, then the least-squares line is just the line that passes through the two points.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The point (1, k) lies on the line with equation 3x + 8y = 24 if and only if .

Find an equation of the line that has slope and y-intercept .

Sketch a set of coordinate axes and plot the given point. (7, -10)

Find the point of intersection of the pair of straight lines. 3x - 4y = 9 4x + 12y = 25

Find the slope of the line that passes through the pair of points. and

Find an equation of the line that passes through the point (3, - 4) and has the slope m = 2.

What are the coordinates of point B?

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

Sketch a set of coordinate axes and plot the given point. (3, -6)

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

Which point has a negative x-coordinate and a negative y-coordinate?

Find the distance between the given points. (1, 3) and (5, 6)

Which point has a negative x-coordinate and a negative y-coordinate?

Refer to the accompanying figure and determine the coordinates of the given point and the quadrant in which it is located.

Find an equation of the line that passes through the points. and

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Exam 1: Straight Lines and Linear Functions

Determine whether the lines through the given pairs of points are perpendicular. Answer yes or no.

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. ​ If the data consist of two distinct points, then the least-squares line is just the line that passes through the two points. ​

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. The point (1, k) lies on the line with equation 3x + 8y = 24 if and only if .

Find an equation of the line that has slope and y-intercept .

Sketch a set of coordinate axes and plot the given point. (7, -10)

Find the point of intersection of the pair of straight lines. 3x - 4y = 9 4x + 12y = 25

Find the slope of the line that passes through the pair of points. and

Find an equation of the line that passes through the point (3, - 4) and has the slope m = 2.

What are the coordinates of point B?

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

Sketch a set of coordinate axes and plot the given point. (3, -6)

Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.

Which point has a negative x-coordinate and a negative y-coordinate?

Find the distance between the given points. (1, 3) and (5, 6)

Which point has a negative x-coordinate and a negative y-coordinate?

Refer to the accompanying figure and determine the coordinates of the given point and the quadrant in which it is located.

Find an equation of the line that passes through the points. and

Systems of Linear Equations and Matrices

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false. If the data consist of two distinct points, then the least-squares line is just the line that passes through the two points.