week 8 final

/in /by
If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?

Let .

Are the events F and G mutually exclusive?


If a merchant deposits $1,500 annually at the end of each tax year in an IRA account paying interest at the rate of 10%/year compounded annually, how much will she have in her account at the end of 25 years? Round your answer to two decimal places.

4.

Maximize

P= 10x + 12y

subject to

5.
Find the simple interest on a $400 investment made for 5 years at an interest rate of 7%/year. What is the accumulated amount?

6.
Find the present value of $40,000 due in 4 years at the given rate of interest 8%/year compounded monthly.

7.

Write the following set in builder notation form

8.
Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9

y = x +

 


y = x –

 


y = –x –

 


y = –x +

 

9.

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

one and only one solution


one and only one solution


one and only one solution


infinitely many solutions

10.
What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?

 

11.

Solve the system of linear equations using the Gauss-Jordan elimination method.

12.

In a poll conducted among 180 active investors, it was found that 100 use discount brokers, 122 use full-service brokers, and 54 use both discount and full-service brokers. How many investors use only discount brokers?

13.

Write the equation in the slope-intercept form and then find the slope and y-intercept of the corresponding line.

14.
Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 4 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent.

15.

Metro Department Store’s annual sales (in millions of dollars) during 5 years were

Annual Sales, y

5.8

6.1

7.2

8.3

9

Year, x

1

2

3

4

5

Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.



 

16.

Solve the linear programming problem by the simplex method.

17.
A system composed of two linear equations must have at least one solution if the straight lines represented by these equations are nonparallel.

18.

Solve the linear system of equations

Unique solution:


Unique solution:


Infinitely many solutions:

19.

The following breakdown of a total of 18,686 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT).

Mode of Transportation

Car

Train

Bicycle

Plane

Number of Fatalities

16,525

842

698

538

What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a train or a plane accident? Round answer to two decimal places.

20.

Check that the given simplex tableau is in final form. Find the solution to the associated regular linear programming problem.

21.
An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event “A head is tossed and an odd number is rolled.”

22.

Indicate whether the matrix is in row-reduced form.

23.

Use Venn diagrams to illustrate the statement.

24.
A survey of 900 subscribers to the Los Angeles Times revealed that 700 people subscribe to the daily morning edition and 400 subscribe to both the daily and the Sunday editions.How many subscribe to the Sunday edition?

25.

Find the pivot element to be used in the next iteration of the simplex method.
 

(3 points) On an exam with a mean of M = 82, you obtain a score of X =86. a. Would you prefer a standard deviation of s = 2 or s = 10? (Hint: Sketch each distribution and find the location of your score.) b. If your score were X = 78, would y

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Assignment 2

1.    (3 points) On an exam with a mean of M = 82, you obtain a score of X =86.

a.    Would you prefer a standard deviation of s = 2 or s = 10? (Hint: Sketch each distribution and find the location of your score.)

b.    If your score were X = 78, would you prefer s = 2 or s = 10? Explain your answer.

 

 

2.  (3 points)   A student was asked to compute the mean and standard deviation for the following sample of n = 5 scores: 81, 87, 89, 86, and 87.  To simplify the arithmetic, the student first subtracted 80 points from each score to obtain a new sample consisting of 1, 7, 9, 6, and 7.  The mean and standard deviation for the new sample were then calculated to be M = 6 and x = 3.  What are the values of the mean and standard deviation for the original sample?

3.  (3 points)   

Calculate SS, variance, and standard deviation for the following population of N = 7 scores: 8, 1, 4, 3, 5, 3, 4. (Note: The definitional formula works well with these scores.)

 

 

4.  (3 points) For the following population of N = 6 scores: 5, 0, 9, 3, 8, 5

 

a.    Sketch a histogram showing the population distribution.

 

 

a.    Locate the value of the population mean in your sketch, and make an estimate of the standard deviation (as done in Example, 4.2).

 

b.    Compute SS, variance, and standard deviation for the population.  (How well does your estimate compare with the actual value of σ?)

 

 

5.  (3 points) A distribution has a standard deviation of σ = 12.  Find the z-score for each of the following locations in the distribution.

a.    Above the mean by 3 points.   

b.    Above the mean by 12 points.  

c.    Below the mean by 24 points.  

d.    Below the mean by 18 points.   

 

6.  (5 points) For a population with a mean of µ = 100 and a standard deviation of 12

a.    Find the z-score for each of the following X values.

X = 106    X = 115    X = 130   

X = 91     

X = 88     

X = 64     

b.    Find the score (X value) that corresponds to each of the following z-scores.

z = – 1.00   

z = – 0.50   

z = 2.00      z = 0.75     

z = 1.50     

z = – 1.25   

 

7.  (3 points) Find the z-score corresponding to a score of X = 60 for each of the following distributions.

a. µ = 50 and σ = 20                 

b. µ = 50 and σ = 10                 

c. µ = 50 and σ = 5                   

d. µ = 50 and σ = 2                    

 

8.  (1 point) A score that is 6 points below the mean corresponds to a z-score of z = – 0.50.  What is the population standard deviation?

 

 

9.  (3 points) For each of the following, identify the exam score that should lead to the better grade.  In each case, explain your answer.

a.    A score of X = 56, on an exam with µ = 50 and σ = 4, or a score of X = 60 on an exam with µ = 50 and σ = 20.

 

b.    A score of X = 40, on an exam with µ = 45 and σ = 2, or a score of X = 60 on an exam with µ = 70 and σ = 20.

 

c.    A score of X = 62, on an exam with µ = 50 and σ = 8, or a score of X = 23 on an an exam with µ = 20 and σ = 2.

 

 

Assignment 1

1.  For the following set of scores, find the value of each expression.  (5 points)

X
-4
-2
0
-1
-1

 

2.  Construct a frequency distribution table for= the following set of scores.  Include columns for proportion and percentage in your table. (5 points)

Scores: 5, 7, 8, 4, 7, 9, 6, 6, 5, 3, 9, 6, 4, 7, 7, 8, 6, 7, 8, 5

       
       
       
       
       
       
       
       
       
       
       

 

3.  The following scores are the ages for a random sample of n = 30 drivers who were issued speeding tickets in New York during 2008.  Determine the best interval width and place the scores in a grouped frequency distribution table.  From looking at your= table, does in appear the tickets are issued equally across age groups? (5= points)

17,  30,  45,  20,  39,  53,28,  19

24,  21,  34,  38,  22,  29, 64

22,  44,  36,  16,  56,  20, 23,  58

32,  25,  28,  22,  51,  26, 43

         
       
         
         
         
         
         
         
         
         
         

 

No the tickets are not distributed equally among all age groups.

 

4.  Find the mean, median, and mode for the scores in the following frequency distribution table. (5 points)

_____

  X       f      f*X       cf

 

10    1      10      15

  9    2      18      14

  8    3      24      12

  7    3      21      9

  6    4      24      6

  5    2      10      2

 

Another Multi. Choice Problem

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Question 1 of 20
 0.0/ 5.0 Points
Graph the function by making a table of coordinates.

f(x) = x
A.  
B.  
C.  
D.  

Question 2 of 20
 0.0/ 5.0 Points
Use the graph of log5x to obtain the graph of f(x) = 2log5x.
A.  
B.  
C.  
D.  

Question 3 of 20
 0.0/ 5.0 Points
The long jump record, in feet, at a particular school can be modeled by  where x is the number of years since records began to be kept at the school. What is the record for the long jump 14 yearsafter record started being kept? Round your answer to the nearest tenth.
A. 20.3 feet  
B. 23.7 feet  
C. 24.1 feet  
D. 23.9 feet  

Question 4 of 20
 0.0/ 5.0 Points
The rabbit population in a forest area grows at the rate of 7% monthly. If there are 180 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use .
A. 402  
B. 408  
C. 428  
D. 415  

Question 5 of 20
 0.0/ 5.0 Points
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. ln (x – 6) + ln (x + 1) = ln (x – 15)
A. {3, -3}  
B. {-3}  
C. {3}  
D. Ø  

Question 6 of 20
 5.0/ 5.0 Points
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

log6x2 = log6(5x + 36)
A.  
B. {9}  
C. Ø  
D. {9, -4}  

Question 7 of 20
 0.0/ 5.0 Points
Evaluate or simplify the expression without using a calculator. log 1000
A. 3  
B. 30  
C.  
D.  

Question 8 of 20
 5.0/ 5.0 Points
Use the graph of f(x) = log x to obtain the graph of g(x) = log x + 5.
A.  
B.  
C.  
D.  

Question 9 of 20
 0.0/ 5.0 Points
The logistic growth function f(t) = models the number of people who have become ill with a particular infection tweeks after its initial outbreak in a particular community. How many people were ill after 9 weeks?
A. 88,450 people  
B. 87,000 people  
C. 84,502 people  
D. 540 people  

Question 10 of 20
 5.0/ 5.0 Points
Use the graph of f(x) = ln x to obtain the graph of g(x) = -4 – ln x.
A.  
B.  
C.  
D.  

Question 11 of 20
 0.0/ 5.0 Points
The formula S = A models the value of a retirement account, where A = the number of dollars added to the retirement account each year, r = the annual interest rate, and S = the value of the retirement account after t years. If the interest rate is 11%, how much will the account be worth after 15 years if $2200 is added each year? Round to the nearest whole number.
A. $86,218  
B. $168,418  
C. $11,675  
D. $35,200  

Question 12 of 20
 0.0/ 5.0 Points
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

ln (x – 8) – ln (x + 7) = ln (x – 10) – ln (x + 8)
A.  
B.  
C. {-2}  
D.  

Question 13 of 20
 0.0/ 5.0 Points
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

log6(5x – 5) = log6(3x + 7)
A. {1}  
B. {6}  
C. Ø  
D. {2}  

Question 14 of 20
 0.0/ 5.0 Points
Write the equation in its equivalent logarithmic form.

23= x
A. log2x = 3  
B. log23 = x  
C. logx2 = 3  
D. log3x = 2  

Question 15 of 20
 0.0/ 5.0 Points
Use Newton’s Law of Cooling, T = C + (T0 – C.ekt, to solve the problem A cup of coffee with temperature 102°F is placed in a freezer with temperature 0°F. After 8 minutes, the temperature of the coffee is 52.5°F. What will its temperature be 13 minutes after it is placed in the freezer? Round your answer to the nearest degree.
A. 32°F  
B. 29°F  
C. 35°F  
D. 27°F  

Question 16 of 20
 0.0/ 5.0 Points
Use the compound interest formulas A = P nt and A = Pertto solve. Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?
A. Both investment plans yield the same return.  
B. $11,000 invested at 6.3% compounded semiannually over 10 years yields the greater return.  
C. $11,000 invested at 6.25% compounded continuously over 10 years yields the greater return.  

Question 17 of 20
 0.0/ 5.0 Points
The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = -logx where x represents the concentration of the hydrogen ions in the solution in moles per liter. Find the pH if the hydrogen ion concentration is 1 x 10-1
A. 13  
B. 1  
C. -13  
D. -1  

Question 18 of 20
 0.0/ 5.0 Points
A fossilized leaf contains 15% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14. Solve the problem.
A. 35,828  
B. 15,299  
C. 1311  
D. 21,839  

Question 19 of 20
 0.0/ 5.0 Points
Use the graph of log5x to obtain the graph of f(x) = 2 + log5x.
A.  
B.  
C.  
D.  

Question 20 of 20
 5.0/ 5.0 Points
Graph the functions in the same rectangular coordinate system.

f(x) = x and g(x) = log1/4 x
A.  
B.  
C.  
D.  

Multi Choice Problems

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Question 1 of 20
 0.0/ 5.0 Points
Find the slope of the tangent line to the graph of f at the given point.

f(x) = at ( 36, 6)
A.  
B. 12  
C. 3  
D.  

Question 2 of 20
 5.0/ 5.0 Points
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.
A. 16  
B. does not exist  
C. -16  
D. 0  

Question 3 of 20
 0.0/ 5.0 Points
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

(2x2 + 2x + 3)2
A. -9  
B. 9  
C. does not exist  
D. 1  

Question 4 of 20
 0.0/ 5.0 Points
Complete the table for the function and find the indicated limit.
A. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = -1  
B. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0  
C. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0.1  
D. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 1  

Question 5 of 20
 0.0/ 5.0 Points
Use the definition of continuity to determine whether f is continuous at a.

f(x) = 5x4 – 9x3+ x – 7a = 7
A. Not continuous  
B. Continuous  

Question 6 of 20
 0.0/ 5.0 Points
Find the slope of the tangent line to the graph of f at the given point.

f(x) = x2+ 5x at (4, 36)
A. 13  
B. 21  
C. 9  
D. 3  

Question 7 of 20
 0.0/ 5.0 Points
Use the definition of continuity to determine whether f is continuous at a.

f(x) = a = 4
A. Not continuous  
B. Continuous  

Question 8 of 20
 0.0/ 5.0 Points
Graph the function. Then use your graph to find the indicated limit. f(x) = 7ex , f(x)
A. 0  
B. 7  
C. 1  
D. -7  

Question 9 of 20
 0.0/ 5.0 Points
The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or function value does not exist.

a. f(x)
b. f(1)
A. a.  f(x) = 1
b. f(1) = 0		  
B. a. f(x) does not exist
b. f(1) = 2		  
C. a. f(x) = 2
b. f(1) = 2		  
D. a. f(x) = 2
b. f(1) = 1		  

Question 10 of 20
 0.0/ 5.0 Points
Choose the table which contains the best values of x for finding the requested limit of the given function.
A.  
B.  
C.  
D.  

Question 11 of 20
 5.0/ 5.0 Points
Choose the table which contains the best values of x for finding the requested limit of the given function.

(x2+ 8x – 2)
A.  
B.  
C.  
D.  

Question 12 of 20
 0.0/ 5.0 Points
Determine for what numbers, if any, the given function is discontinuous.

f(x) =

A. 5  
B. None  
C. 0  
D. -5, 5  

Question 13 of 20
 0.0/ 5.0 Points
Complete the table for the function and find the indicated limit.
A. -1.22843; -1.20298; -1.20030; -1.19970; -1.19699; -1.16858 limit = -1.20  
B. -2.18529; -2.10895; -2.10090; -2.09910; -2.09096; -2.00574 limit = -2.10  
C. -4.09476; -4.00995; -4.00100; -3.99900; -3.98995; -3.89526 limit = -4.0  
D. 4.09476; 4.00995; 4.00100; 3.99900; 3.98995; 3.89526 limit = 4.0  

Question 14 of 20
 0.0/ 5.0 Points
The function f(x) = x3describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, find the average rate of change of the volume with respect to x as x changes from 1 inches to 1.1 inches.
A. 2.33 cubic inches per inch  
B. -3.31 cubic inches per inch  
C. 23.31 cubic inches per inch  
D. 3.31 cubic inches per inch  

Question 15 of 20
 0.0/ 5.0 Points
The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or function value does not exist.

a. f(x)
b. f(3)
A. a. f(x) = 3
b. f(3) = 5		  
B. a. f(x) = 5
b. f(3) = 5		  
C. a. f(x) = 4
b. f(3) does not exist		  
D. a. f(x) does not exist
b. f(3) = 5		  

Question 16 of 20
 0.0/ 5.0 Points
Use the definition of continuity to determine whether f is continuous at a.

f(x) = 
a = -5
A. Not continuous  
B. Continuous  

Question 17 of 20
 0.0/ 5.0 Points
Use the graph and the viewing rectangle shown below the graph to find the indicated limit.

( x2 – 2)

[-6, 6, 1] by [-6, 6, 1]
A. (x2 – 2) = -6  
B. (x2 – 2) = 2  
C. (x2 – 2) = -2  
D. (x2 – 2) = 6  

Question 18 of 20
 5.0/ 5.0 Points
Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

5
A. -5  
B. 0  
C. 5  
D. 2  

Question 19 of 20
 0.0/ 5.0 Points
Find the derivative of f at x. That is, find f ‘(x). f(x) = 7x + 8; x = 5
A. 40  
B. 8  
C. 35  
D. 7  

Question 20 of 20
 0.0/ 5.0 Points
Graph the function. Then use your graph to find the indicated limit.

f(x) = , f(x)
A. 6  
B. -2  
C. -6  
D. 2  

complete

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Fill the blank:

 

The following data were collected on the study of the relationship between a company’s retail sales and advertising dollars:

Retail Sales ($)

Advertising ($)

31,312

16,468

35,990

17,563

40,659

20,780

43,771

23,658

47,252

26,372

49,353

28,012

51,281

32,167

56,470

35,305

56,655

37,199

59,636

38,002

 

a.             Obtain a linear regression line for the data. (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
Retail Sales = http://edugen.wiley.com/edugen/art2/common/pixel.gif_______ + http://edugen.wiley.com/edugen/art2/common/pixel.gif_________ (advertising)

 

b.            Compute a correlation coefficient and determine the strength of the linear relationship. (Round your answer to 2 decimal places, the tolerance is +/-0.01.)
Correlation coefficient is http://edugen.wiley.com/edugen/art2/common/pixel.gif______________. It indicates http://edugen.wiley.com/edugen/art2/common/pixel.gif__________(No, a moderate positive, or a strong positive) linear relationship. (Use not rounded amounts to answer this question.)

 

c.             Using the linear regression equation, develop a forecast of retail sales for advertising dollars of $40,108. (Round your answer to 2 decimal places, the tolerance is +/-0.01. Do not round intermediate results used to achieve this answer.)
Forecast = http://edugen.wiley.com/edugen/art2/common/pixel.gif________________$

 

Just put Exclusive for Homework Help 1234

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Find the mean of the data summarized in the given frequency distribution. Also, compare the computed means to the actual means obtained by using th eoriginal list of data values, which are as follow: (Exercise 29) 35.9 year; (Exercise 30)44.1 years; (Exercise31)84.4;(exercise32)15.0 years

 

age of best actor                                                                Frequency

when oscar was won

20-29                                                                                        1

30-39                                                                                       26

40-49                                                                                       35

50-59                                                                                       13

60-69                                                                                         6

70-79                                                                                         1

Lesson 3 (Mulit. Choice Questions)

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Question 1 of 20
 0.0/ 5.0 Points
Halley’s comet has an elliptical orbit with the sun at one focus. Its orbit shown below is given approximately by In the formula, r is measured in astronomical units. (One astronomical unit is the average distance from Earth to the sun, approximately 93 million miles.) Find the distance from Halley’s comet to the sun at its greatest distance from the sun. Round to the nearest hundredth of an astronomical unit and the nearest million miles.
A. 12.13 astronomical units; 1128 million miles  
B. 91.54 astronomical units; 8513 million miles  
C. 5.69 astronomical units; 529 million miles  
D. 6.06 astronomical units; 564 million miles  

Question 2 of 20
 0.0/ 5.0 Points
Use the center, vertices, and asymptotes to graph the hyperbola.

(x – 1)2 – 9(y – 2)2= 9
A.  
B.  
C.  
D.  

Question 3 of 20
 0.0/ 5.0 Points
Find the standard form of the equation of the ellipse and give the location of its foci.
A. + = 1
foci at (- , 0) and ( , 0)		  
B. – = 1
foci at (- , 0) and ( , 0)		  
C. + = 1
foci at (- , 0) and ( , 0)		  
D. + = 1
foci at (-7, 0) and ( 7, 0)		  

Question 4 of 20
 0.0/ 5.0 Points
Rewrite the equation in a rotated x’y’-system without an x’y’ term. Express the equation involving x’ and y’ in the standard form of a conic section.

31x2 + 10xy + 21y2-144 = 0
A. x‘2 = -4 y’  
B. y‘2 = -4x’  
C. + = 1  
D. + = 1  

Question 5 of 20
 0.0/ 5.0 Points
Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5
A. + = 1  
B. + = 1  
C. + = 1  
D. + = 1  

Question 6 of 20
 0.0/ 5.0 Points
Find the vertices and locate the foci for the hyperbola whose equation is given.

49x2 – 100y2= 4900
A. vertices: ( -10, 0), ( 10, 0)
foci: (- , 0), ( , 0)		  
B. vertices: ( -10, 0), ( 10, 0)
foci: (- , 0), ( , 0)		  
C. vertices: ( -7, 0), ( 7, 0)
foci: (- , 0), ( , 0)		  
D. vertices: (0, -10), (0, 10)
foci: (0, – ), (0, )		  

Question 7 of 20
 5.0/ 5.0 Points
Write the equation in terms of a rotated x’y’-system using θ, the angle of rotation. Write the equation involving x’ and y’ in standard form. xy +16 = 0; θ = 45°
A. +  = 1  
B. y‘2 = -32x’  
C. + = 1  
D. – = 1  

Question 8 of 20
 0.0/ 5.0 Points
Write the appropriate rotation formulas so that in a rotated system the equation has no x’y’-term.

10x2 – 4xy + 6y2– 8x + 8y = 0
A. x = -y’; y = x’  
B. x = x’ – y’; y = x’ + y’  
C. x = (x’ – y’); y = (x’ + y’)  
D. x = x’ – y’; y = x’ + y’  

Question 9 of 20
 0.0/ 5.0 Points
Find the location of the center, vertices, and foci for the hyperbola described by the equation.

– = 1
A. Center: ( -4, 1); Vertices: ( -10, 1) and ( 2, 1); Foci: and
(		  
B. Center: ( -4, 1); Vertices: ( -9, 1) and ( 3, 1); Foci: ( -3 + , 2) and ( 2 + , 2)  
C. Center: ( -4, 1); Vertices: ( -10, -1) and ( 2, -1); Foci: ( -4 – , -1) and ( -4 + , -1)  
D. Center: ( 4, -1); Vertices: ( -2, -1) and ( 10, -1); Foci: and  

Question 10 of 20
 0.0/ 5.0 Points
Sketch the plane curve represented by the given parametric equations. Then use interval notation to give the relation’s domain and range.

x = 2t, y = t2+ t + 3
A. Domain: (-∞, ∞); Range: -1x, ∞)

  
B. Domain: (-∞, ∞); Range: [ 2.75, ∞)

  
C. Domain: (-∞, ∞); Range: [ 3, ∞)
  
D. Domain: (-∞, ∞); Range: [ 2.75, ∞)
  

Question 11 of 20
 0.0/ 5.0 Points
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.

y = ±
A. Asymptotes: y = ± x
  
B. Asymptotes: y = ± x

  
C. Asymptotes: y = ± x
  
D. Asymptotes: y = ± x
  

Question 12 of 20
 0.0/ 5.0 Points
Graph the ellipse.

16(x – 1)2 + 9(y + 2)2= 144
A.  
B.  
C.  
D.  

Question 13 of 20
 0.0/ 5.0 Points
Is the relation a function?

y = x2+ 12x + 31
A. Yes  
B. No  

Question 14 of 20
 5.0/ 5.0 Points
Determine the direction in which the parabola opens, and the vertex.

y2= + 6x + 14
A. Opens upward; ( -3, 5)  
B. Opens upward; ( 3, 5)  
C. Opens to the right; ( 5, 3)  
D. Opens to the right; ( 5, -3)  

Question 15 of 20
 0.0/ 5.0 Points
Match the equation to the graph.

x2= 7y
A.  
B.  
C.  
D.  

Question 16 of 20
 0.0/ 5.0 Points
y2= -2x
A.  
B.  
C.  
D.  

Question 17 of 20
 0.0/ 5.0 Points
Convert the equation to the standard form for a hyperbola by completing the square on x and y.

x2 – y2+ 6x – 4y + 4 = 0
A. (x + 3)2 + (y + 2)2 = 1  
B. – = 1  
C. (x + 3)2 – (y + 2)2 = 1  
D. (y + 3)2– (x + 2)2 = 1  

Question 18 of 20
 0.0/ 5.0 Points
Eliminate the parameter t. Find a rectangular equation for the plane curve defined by the parametric equations.

x = 6 cos t, y = 6 sin t; 0 ≤ t ≤ 2π
A. x2 – y2 = 6; -6 ≤ x ≤ 6  
B. x2 – y2 = 36; -6 ≤ x ≤ 6  
C. x2 + y2 = 6; -6 ≤ x ≤ 6  
D. x2 + y2 = 36; -6 ≤ x ≤ 6  

Question 19 of 20
 5.0/ 5.0 Points
Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate.

y2+ 2y – 2x – 3 = 0
A. (y + 1)2 = 2(x + 2)  
B. (y – 1)2 = -2(x + 2)  
C. (y + 1)2 = 2(x – 2)  
D. (y – 1)2 = 2(x + 2)  

Question 20 of 20
 0.0/ 5.0 Points
Convert the equation to the standard form for a hyperbola by completing the square on x and y.

y2 – 25x2+ 4y + 50x – 46 = 0
A. – (x – 2)2 = 1  
B. – (y – 1)2 = 1  
C. (x – 1)2 – = 1  
D. – (x – 1)2 = 1