Math Help

profileMDK88
Section5.4Homework.pdf

1.

Student: Kiare Mays Date: 06/15/20

Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)

Assignment: Section 5.4 Homework

The percentages of dentistry degrees earned by women are shown in the table for various years.

Year Percent 1970 3 1980 15 1990 28 2000 41 2002 40

Let p be the percentage of dentistry degrees earned by women at t years since 1970. For example, t = 0 represents 1970 and t = 10 represents 1980.

a. Create a scattergram of the data. Choose the correct scattergram below.

A.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

B.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

C.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

D.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

b. Draw a line that comes close to the points in your scattergram. Choose the correct scattergram below.

A.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

B.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

C.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

D.

0 10 20 30 40 0

10 20 30 40 50 60

t

p

c. Predict the percentage of dentistry degrees that will be earned by women in 2010.

The percentage of dentistry degrees earned by women in 2010 will be about %.

d. Estimate when women earned 20% of dentistry degrees.

Women earned 20% of dentistry degrees in .

2. If there are too many ticketed passengers for a flight, a person can volunteer to be "bumped" onto another flight. The voluntary bumping rates for large U.S. airlines (number of bumps per 10,000 passengers, January through September) are shown in the table for various years. Let r be the voluntary bumping rate (number of bumps per 10,000 passengers) at t years since 2000.

Year Bumping Rate 2000 23 2001 21 2002 20 2003 15 2004 14 2005 12

a. Create a scattergram of the data. Choose the correct graph below.

A.

0 5 10 15 20 25 0

1

2

3

4

5

Years since 2000

Bu m

pi ng

R at

e

t

r

B.

0 1 2 3 4 5 0

5

10

15

20

25

Years since 2000

Bu m

pi ng

R at

e

t

r

C.

0 1 2 3 4 5 0

5

10

15

20

25

Years since 2000

Bu m

pi ng

R at

e

t

r

b. Draw a line that comes close to the points in your scattergram.

Choose the correct graph below.

A.

0 5 10 15 0

5

10

15

20

25

Years since 2000

Bu m

pi ng

R at

e

t

r

B.

0 5 10 15 0

5

10

15

20

25

Years since 2000

Bu m

pi ng

R at

e

t

r

C.

0 5 10 15 20 25 0

5

10

15

Years since 2000

Bu m

pi ng

R at

e

t

r

c. What is the r-intercept of the line in part b.?

(Round to the nearest integer. Type an ordered pair.)

What does it mean in this situation?

A. According to the model, the average bumping rate will be 0 per passengers in the year 20 .

10,000 23

B. According to the model, the average bumping rate per passengers was decreasing by in the year 2000.

10,000 23

C. According to the model, the average bumping rate was per passengers in the year 2000.

23 10,000

d. Predict when the voluntary bumping rate will be bumps per 10,000 passengers using the line in part b.5

(Round to the nearest year.)

e. What is the t-intercept of the line in part b.?

(Round to the nearest integer. Type an ordered pair.)

What does it mean in this situation?

A. According to the model, the average bumping rate was per passengers in the year 2000. This seems reasonable, since the airlines cannot eliminate bumping completely.

10 10,000

B. According to the model, the average bumping rate will be 0 per passengers in the year . Since this prediction implies that the airlines will eliminate bumping completely, it is not

plausible, and therefore model breakdown has occurred.

10,000 2010

C. According to the model, the average bumping rate will be 0 per passengers in the year . Since this prediction implies that the airlines will eliminate bumping completely, it is not

plausible, and therefore model breakdown has occurred.

10 2010

3. The percentages of people who are satisfied with the way things are in their country are shown in the table on the right for various years.

Year Percent Year Percent 1992 16 1996 40 1993 24 1997 45 1994 28 1998 52 1995 37 1999 51

Let p be the percentage of people at t years since 1990 who are satisfied with the way things are.

a. Create a scattergram of the data. Choose the correct answer below.

A.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

B.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

C.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

D.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

b. Draw a line that comes close to the data points. Choose the correct answer below.

A.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

B.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

C.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

D.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

c. Use your line to estimate the percentage of people who were satisfied in .2003

The percentage of people who were satisfied in is %.2003

d. Data for the years 2000-2004 are shown in the table on the right.

Year Percent Year Percent 2000 52 2003 43 2001 48 2004 41 2002 46

Create a scattergram of the data for the years 1992-2004. Choose the correct answer below.

A.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

B.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

C.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

D.

0 3 6 9 12 15 0

15 30 45 60 75 90

t

p

e. Compute the error in the estimation for that you made in part (c). (The error is the difference between the estimated percentage and the actual percentage.)

2003

The error in the estimation for is %.2003

4.

5.

The windchill is a measure of how cold you feel as a result of being exposed to wind. The table below provides some data on windchills for various temperatures for a certain wind speed.

Temperature (oF) Windchill (oF) − 15 − 31 − 12 − 26 − 5 − 20 4 − 11 10 − 3 13 5 18 10 25 13

Let w be the windchill (in degrees Fahrenheit) corresponding to a temperature of t degrees Fahrenheit.

(a) Without graphing, estimate the coordinates of the t-intercept for a line that comes close to the data points. Choose the correct answer below.

( ,0)13

( ,0)− 13

( ,0)10

( ,0)12

(b) Without graphing, estimate the coordinates of the w-intercept for a line that comes close to the data points.Choose the correct answer below.

(0, )12

(0, )− 11

(0, )− 13

(0, )− 20

Consider the scattergram of data and the graph of the model y = mx + b in the indicated figure. Sketch the graph of a linear model that describes the data better.

0 14 0

14

x

y

Choose the correct answer below.

A.

0 14 0

14

x

y

B.

0 14 0

14

x

y

C.

0 14 0

14

x

y

D.

0 14 0

14

x

y

6. The table lists College record times for the men's 400-meter run.

Year 1900 1916 1928 1932 1941 1950 1961 1968 1988 1999 Record Time

(seconds) 54.6 54.2 53.8 52.9 52.7 52.6 51.5 50.35 49.71 49.64

a. Let r be the record time (in seconds) at t years since 1900. Use a graphing calculator to draw a scattergram of the data. Choose the correct answer below.

A.

0 120 40

60

B.

0 120 40

60

C.

0 120 40

60

D.

0 120 40

60

b. Find an equation of a linear model to describe the data. Choose the equation below that best represents the data.

A. r = 0.062t + 55.192 B. t = − 0.062r + 55.192 C. r = − 0.05t + 57.173 D. r = − 0.062t + 55.192

c. Draw your line and the scattergram in the same viewing window. Verify that the line passes through the two points you chose in finding the equation in part (b) and that it comes close to all of the data points. Choose the correct answer below.

A.

0 120 40

60

B.

0 120 40

60

C.

0 120 40

60

D.

0 120 40

60

7. The market shares (percentages of vehicle sales) of an automobile company are shown in the table to the right for various years. Use the table to answer parts (a) through (e). Year

Market Share (%)

1998 26 2000 23 2002 20 2004 19 2006 15 2008 14

a. Let s f(t) be the company's market share (in percent) at t years since 1995. Find an equation of f using the data points for the years 2000 and 2008. Does the model fit the data well?

=

f(t) = (Round to three decimal places as needed.)

Does the model fit the data well?

Yes

No

b. Find f( ). What does it mean in this situation?4

f( )4 = (Round to three decimal places as needed.)

Intepret the result.

According to the model, % of the market share belongs to the automobile company in the year .

(Round to the nearest year as needed.)

c. Find t when f(t) . What does it mean in this situation?= 6

t = (Round to two decimal places as needed.)

Interpret the result.

According to the model, % of the market share belongs to the automobile company in the year .

(Round to the nearest year as needed.)

d. Find the t-intercept. What does it mean in this situation?

The t-intercept is . (Type an ordered pair. Round to two decimal places as needed.)

Interpret the t-intercept.

According to the model, % of the market share belongs to the automobile company in the year .

(Round to the nearest year as needed.)

e. Find the s-intercept. What does it mean in this situation?

The s-intercept is . (Type an ordered pair. Round to three decimal places as needed.)

Intepret the s-intercept.

8.

According to the model, % of the market share belongs to the automobile company in the year .

(Round to the nearest year as needed.)

An equation models the percentage p of births outside marriage in a country at t years since 1900 (see table on the right.) Use the equation to answer parts (a) through (e).

p = 0.77t − 43.18 Year Percent of Births Outside Marriage 1970 10.7 1975 14.6 1980 18.4 1985 22.3 1990 26.1 1995 30.0 2000 33.8 2005 37.7

a. Rewrite the equation with the function name f. Choose the correct answer below.p = 0.77t − 43.18

A. f(t) = 0.77p − 43.18 B. f(p) = 0.77p − 43.18 C. f(p) = t D. f(t) = 0.77t − 43.18

b. Find f( ). What does the result mean in this situation?114

f( ) (Type an integer or a decimal.)114 =

Interpret the result.

According to the model, about % of births in the year will be outside marriage. (Round to the nearest year as needed.)

c. Find the value of t so that f(t) . What does the result mean in this situation?= 55

t (Round to two decimal places as needed.) =

Interpret the result.

According to the model, % of births around the year will be outside marriage. (Round to the nearest year as needed.)

d. According to the model, in what year will all births be outside marriage?

All births will be outside marriage in the year . (Round to the nearest year as needed.)

e. Estimate the percentage of births outside marriage in 1997. The actual percentage is 32.4%. What is the error in the estimate? (The error is the difference between the estimated value and the actual value.)

According to the model, % of births were outside of marriage in 1997. (Round to one decimal place as needed.)

Find the error.

The error is percentage point(s). (Type an integer or a decimal. Use the answer from the previous step to find this answer.)

9.

10.

11.

The number of commercial airline boardings on domestic flights increased steadily during the 1990s. Let f(t) be the number of commercial airline boardings on domestic flights (in millions) for the year that is t years since 1990.

Year Number of Boardings(millions) 1991 452 1993 481 1995 548 1997 597 1999 634 2000 667

a. Use a graphing calculator to draw a scattergram of the data. Choose the correct graph below.

A. B.

C. D.

The viewing window for all graphs is Xmin 0, Xmax 11, Xscl 1, Ymin 430, Ymax 680, Yscl 25.

= = = = = =

b. Find an equation of f. Does your model fit the data well? Choose the correct answer below.

A. f(t) t= 24.32 + 421.33 B. f(t) t= 421.33 + 24.32 C. f(t) f= 421.33 − 24.32 D. f(t) f= 24.32 − 421.33

Does your model fit the data well?

no

yes

c. Use your model f to estimate the number of boardings in .2004

The model predicts that the number of boardings in is million.

2004

(Round to the nearest integer as needed.)

The actual number was million. What is the error in your estimate?

694

The error is million. (Round to the nearest integer as needed.)

The percentage of female workers who prefer a female boss over a male boss increased approximately linearly from % in 1975 to % in 2006. Predict when % of female workers will prefer a female boss.

11 25 31

% of female workers will prefer a female boss in year .31 (Round to the nearest whole number as needed.)

You can not print this question until you complete the required media.

12. You can not print this question until you complete the required media.