Week 8

course Mth 152

xQ_M˯恓assignment #019

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

019. `query 19

Liberal Arts Mathematics II

07-23-2007

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18:04:40

query problem 13.6.9 wt vs ht 62,120; 62,140; 63,130; 65,150; 66,142; 67,13068,175; 68,135; 70,149; 72,168. Give the regression equation and the predicted weight when height is 70.

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RESPONSE -->

Y = 3.35X - 78.4

Y = 3.35 (70) - 78.4

Y = 156.1

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18:05:41

** The equation is obtained by substituting the weights for y and the heights for x in the formula for the regression line.

You get

y = 3.35 x - 78.4.

To predict weight when height is 70 you plug x = 70 into the equation:

y = 3.35 * 70 - 78.4.

You get

y = 156,

so the predicted weight for a man 70 in tall is 156 lbs. **

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RESPONSE -->

Ok.

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18:14:03

**** query problem 13.6.12 reading 83,76, 75, 85, 74, 90, 75, 78, 95, 80; IQ 120, 104, 98, 115, 87, 127, 90, 110, 134, 119

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RESPONSE -->

A = [10*(90437) - ((811)*(1104))] / [10*(66225) - (811^2)]

A = [9026] / [4529]

A = 1.99

B = [1104 - ((1.99)*(811))] / 10 = -50.99

Y = 1.99X - 50.99

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18:16:05

**

n = 10

sum x = 811

sum x ^2 = 66225

sum y = 1104

sum y^2 = 124060

sum xy = 90437

a = [10(90437) - (811)(1104)] / [10(66225) - (811^2)] = 1.993

a = 1.99

b = [1104 - (1.993)(811) / 10 = -51.23

y' = 1.993x - 51.23 is the eqation of the regression line.

**

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RESPONSE -->

Ok.

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18:38:50

**** query problem 13.6.15 years 0-5, sales 48, 59, 66, 75, 80, 89

What is the coefficient of correlation and how did you obtain it?

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RESPONSE -->

X Y XY X^2 Y^2

0 48 0 0 2304

1 59 59 1 3481

2 66 132 4 4356

3 75 225 9 5626

4 80 320 16 6400

5 90 450 25 8100

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15, 418, 1186, 55, 30266

R = 6(1186) - 15(418) / Sqrt (330) - (225) * Sqrt (181596) - (174724) = 846 / Sqrt (105) * (6872) = 846 / Sqrt (721560) = 846 / 849.4 = .996

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18:39:12

**STUDENT SOLUTION:

X Y XY X^2 Y^2

0 48 0 0 2304

1 59 59 1 3481

2 66 132 4 4356

3 75 225 9 5626

4 80 320 16 6400

5 90 450 25 8100

Sums=

15 418 1186 55 30266

The coefficient of the correlation: r = .996

I found the sums of the following:

x = 15, y = 418, x*y = 1186, x^2 = 55

n = 6 because there are 6 pairs in the data

I also had to find Ey^2 = 30266

I used the following formula:

r = 6(1186) - 15(418) / sq.root of 6(55) - (15)^2 * sq. root of 6(30266) - (418)^2 =

846 / sq. root of 105 * 6872 = 846 / sq. root of 721560 = 846 / 849.4 = .996 **

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RESPONSE -->

Ok.

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18:42:52

**** query problem 13.6.24 % in West, 1850-1990, .8% to 21.2%

What population is predicted in the year 2010 based on the regression line?

What is the equation of your regression line and how did you obtain it?

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RESPONSE -->

Y = 1.44(16) - .39 = 22.65

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18:43:02

** STUDENT SOLUTION:

Calculating sums and regression line:

n = 8

sum x = 56

sum x^2 = 560

sum = 77.7

sum y^2 = 1110.43

sum xy = 786.4

a = 1.44

b = -.39

r = .99

In the year 2010 the x value will be 16.

y' = 1.44(16) - .39 = 22.65.

There is an expected 22.65% increase in population by the year 2010. **

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RESPONSE -->

Ok.

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TЂۉNԈÇmޤ~֭

assignment #020

020. `query 20

Liberal Arts Mathematics II

07-23-2007

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19:19:56

query 9.1.36 Ray MO U ray OM **** How do you express the intersection of the two rays?

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RESPONSE -->

MO

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19:20:33

** STUDENT SOLUTION:

The intersection of the two rays consists of the elements common to both sets, which would be MO.

However, a union symbol is used in the question and a union is composed of all the elements found in atleast one of the two sets, which would also be MO. **

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RESPONSE -->

Ok.

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19:22:28

**** query 9.1.54 lines SR and TP intersecting at Q **** What are the names of the pairs of vertical angles for this figure?

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RESPONSE -->

PQR, SQT, TQR, SQP

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19:23:03

** STUDENT SOLUTION:

The vertical angles are SQT and PQR; SQP and TQR **

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RESPONSE -->

Ok.

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19:26:17

**** query 9.1.60 5x - 129 vert with 2x - 1 **** What is the value of x and how did you obtain it?

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RESPONSE -->

5X - 129 = 2X - 21

3X - 129 = -21

3X = 108

X = 36

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19:27:08

*&*& Starting with 5x - 129 = 2x - 21 to get

3x - 129 = -21. Add 129 to both sides to get

3x = 108. Divide both sides by 3 to get

x = 36.

To check substitute 36 in for x in the equation and simplify, getting 51 = 51.

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RESPONSE -->

Ok.

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19:28:27

**** What equation did you solve to obtain x, and how did you get the equation?

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RESPONSE -->

All the angles are equal to each other, so you would set the equation equal to each other.

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19:28:36

Since the angles are vertical angles, they are equal to eachother, therefore, I set them up to be equal to eachother and then solved.To check myself, I then substituted my answer in for x on both sides of the equation to make sure they were equal.

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RESPONSE -->

Ok.

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19:34:05

**** query 9.1.72 complement 10 deg less that 1/5 of suppl **** What is the measure of the angle and how did you get it?

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RESPONSE -->

90 - X = 1/5(180-X) - 10

450 - 5X = 180 - X - 50

450 - 5X = 130 - X

-4X = -320

X = 80

Complement: 10 Deg

Supplement: 100 Deg

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19:34:40

** Let x be the degree measure of the angle. Then the supplement is 180 x; 10 deg less than 1/5 the supplement is 1/5(180 - x) 10. The complement is 90 - x.

So the equation is

90 - x = 1/5(180 - x) 10. Multiplying both sides by 5 we get

450 5 x = 180 x 50 so that

450 5 x = 130 x. Adding x 450 to both sides we get

-4x = -320 so thatx = 80.

The complement of 80 deg is 10 deg.

The supplement of 80 deg is 100 deg; 1/5 the supplement is 1/5 * 100 deg = 20 deg, so the complement 10 deg is 10 deg less than the supplement 20 deg. **

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RESPONSE -->

Ok.

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19:36:41

**** What equation did you solve to obtain the measure of the angle?

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RESPONSE -->

90 - X = 1/5(180-X) - 10

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19:37:13

Student Response: I determined which equations represented the degree measure of the angle, complement, and supplement. I then substituted those in the equation using the worded problem.

90 - x (complement) = 10 (10 less than) - 1/5 (1/5 of the supplement) 180 - x (supplement).

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RESPONSE -->

Ok.

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19:37:46

**** Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

None.

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19:37:56

The query was basically what I expected it to be.

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RESPONSE -->

Ok.

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ؽ|tl|D~Yӟ

assignment #021

021. `query 21

Liberal Arts Mathematics II

07-23-2007

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20:01:53

**** query 9.2.6 sq must be rhombus **** Is the statement true or false and why?

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RESPONSE -->

True; a rhombus does not have to have right angles such as a square.

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20:03:24

** This statement is true.

A parallelogram is a quadrilateral with two pairs of parallel sides and a rhombus is a parallelogram with all sides having equal length. All sides of a square have equal length. If a square were not a rhombus then all sides would not be of equal length.

It is not true that a rhombus must be a square. The angles of a rhombus do not have to be right angles, while the angles of a square do. **

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RESPONSE -->

Ok.

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20:04:53

**** query 9.2.10 parallelogram must be rect and rect must be parallelogram **** Is the statement true or false and why?

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RESPONSE -->

False; a parallelogram does not have to be a rectangle.

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20:05:04

** A rectangle is a parallelogram but a parallelogram is not necessarily a rectangle, so the statement is false. **

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RESPONSE -->

Ok.

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20:07:26

**** query 9.2.18 rb with 4 loops **** Is the curve simple, closed, both or neither?

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RESPONSE -->

Closed

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20:08:52

This is only a closed curve because its starting point and ending point are the same and it can be drawn without lifting the pencil from the paper. It is not simple because some points are passed through twice.

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RESPONSE -->

Ok.

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20:15:00

**** query 9.2.24 ellipse **** Is the region inside the curve convex or not, and why?

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RESPONSE -->

Convex; any line would be inside the curve.

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20:17:37

The region inside is convex because the line segment connecting any two points is completely inside the figure.

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RESPONSE -->

Ok.

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20:25:21

**** query 9.2.48 A 30 deg more than B which equals C **** What are the measures of the three angles?

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RESPONSE -->

X + (X+30) + X = 180

3X + 30 = 180

3X = 150

X = 50

A = 80

B = 50

C = 50

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20:25:52

Angle A + Angle B + Angle C = 180 deg. If x is the degree measure of B then angle A has measure x + 30 degrees and angle C has measure x degrees. So we have

x + x +30 + x = 180

3x + 30 = 180

3x = 150

x = 50

Angle B and Angle C are both equal to x, i.e., to 50 deg.

Angle A = 50 deg + 30 deg = 80 deg

To check, 80 + 50 + 50 = 180.

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RESPONSE -->

Ok.

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20:30:49

**** What equation did you solve to obtain your answer, and how did you use the solution to determine all angles?

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RESPONSE -->

X + (X+30) + X = 180

Angles B and C are equal to X (50).

Angle A is equal to X + 30 (80).

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20:32:08

Student Response: The definition for the angle sum of a triangle says the sum of the measures of the angles of any triangle is 180 deg.

I used x to represent angles B and C and x + 30 to represent angle A since it is 30 deg higher than the other two. All this equaled 180 deg. I solved for x to get the degree measure of angles B and C and then added 30 on to x to get the degree measure for angle A.

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RESPONSE -->

Ok.

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20:32:18

**** Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

None.

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20:32:26

There were no really big surprises.

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RESPONSE -->

Ok.

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Very good work. Let me know if you have any questions.