Before this class, I had previously taken statistics classes however most of the topics and the
formulas had withered out of my mind. After looking at the instructions on how to do most of the work it all
came back to me. So overall I think that I have im
1. Find the equation of the regression line for the given data. What is the predicted value of Y when X = -2? What is the predict
X
Y
-7
-12
X
-7
-2
5
1
-1
-2
0
2
3
-3
-2
-8
5
9
1
1
-1
-5
F
115.16
p-value
5.00E-06
-2
-6
0
-1
Y
-12
-8
9
1
-5
-6
-1
4
7
-8
R
Here is the data that I collected from the earlier SLP.
11
8
15
11
13
7
8
9
10
11
Mean: 10.3, added them all up and divided by 10
Median: 10.5, put them all in order and determined the middle two numbers, added them
together, and divided that value by 2.
1) In this problem there were 177 respondents that reported that they had been in a car accident,
and 107 respondents that reported that they had not been in an accident.
Adding the two numbers together, shows that there were a total of 284 total responde
1.) After looking at all eight of the numbers, it is clear that the standard deviation is 77.4.
2.)
Wendys
The highest number in the data set was 198 and the lowest was 110, so the range is 78. After
finding the average, subtracting the average from each
Question 1:
Excel output is shown below:
Anova: Single Factor
SUMMARY
Groups
First 8
Last 7
ANOVA
Source of Variation
Between Groups
Within Groups
Count
8
7
SS
Total
Sum
38
28
df
Average
4.75
4
MS
2.1
167.5
1
13
169.6
14
2.1
12.88461538
Variance
21.64286
DAY
Number Of Phone Calls Per Day
1
11
2
8
3
15
4
11
5
13
6
7
7
8
8
9
9
10
10
11
The data that I have started collecting is ten days of the number of phone calls that I
received from the time I woke up in the morning until the time I went to bed at night.
1. 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes
with 496, 348, and 481 students respectively. Identify which type of sampling is used and
why.
The sampling used here is stratified random sampling because the number o
1/19/2016
Philip Gaddy
Homework 4 Solutions
Section 11.2
27. First, we note that
is equivalent to the sequence cfw_ n
n < n + 1,
n=1 . First, since
this sequence
it follows that n + 1 < n, and as a result, that this sequence is decreasing. Now, since n i
2/23/2017
Philip Gaddy
Homework 15 Solutions
Section 13.5
0
23. The line will intersect the xy-plane when z = 0. Then, we see that xx
= dz03 , meaning that
d1
x = x0 dd1 3z0 . Similar, we see that y = y0 dd2 3z0 . Therefore, the point this line intersects
2/12/2017
Philip Gaddy
Homework 11 Solutions
Section 13.3
11. (a)
ab=61=5
ac=8
b c = 12 + 6 = 18
(b) First, note that kak = 5, kbk = 14, and kck = 5. Then, we see that the cosine of the angle
between a and b, a and c, and b and c, respectively, are given
1/24/2016
Philip Gaddy
Homework 5 Solutions
Section 12.2
n
n
P
19. In this case, we want to show that the series n=0 32 diverges. To see this, note that limn 32
diverges (in particular it does not equal zero). Therefore, since the previous limit is not 0,
2/21/2017
Philip Gaddy
Homework 14 Solutions
Section 13.5
13. Note that, since the direction vectors of these lines are not parallel. To see if they are intersecting, we
attempt to solve the following system of equations
t+3=1
1t=4+u
5 + 2t = 2 + u
Lookin
1/25/2016
Philip Gaddy
Homework 7 Solutions
Section 12.4
18. In order to see that
3
1
P
3
n(ln 2 n)
converges, we will use the integral test. Since n(ln n) 2 is a strictly in-
creasing sequence, it follows that the sequence defining the above series is st
1/24/2016
Philip Gaddy
Homework 6 Solutions
Section 12.3
18. To see that
P
7n+2
n=1 2n5 +7
converges, note that
1
n4
n 7n+2
2n5 +7
lim
=
2
7
P
Therefore, since this P
limit exists and is non zero, and n=1 n14 converges, it follows from the limit
7n+2
comp
1/18/2016
Philip Gaddy
Homework 3 Solutions
Section 11.1
12. First, note that the least upper bound of this sequence is given by the least upper bound of the
sequence cfw_2, 2.1, 2.11, . . ., which is given by 2.1 = 19
9 . Similarly, the greatest lower bo
3/10/2017
Philip Gaddy
Homework 20 Solutions
Section 15.6
26. (a) To see that this limit cannot exist, note that, along the line y = 0, f (x, 0) = 1, so limx0 f (x, 0) =
1. However, along the path y = x, we see that this limit is 0. Therefore, since these
1/11/2016
Philip Gaddy
Homework 1 Solutions
Section 11.3
2. Let > 0 be given. Then, choosing N N sufficiently large such that N >
since the natural numbers are unbounded). Then, we see that, for n > N ,
2 2
< <
n N
2
(this can always be done
as requi
1/11/2016
Philip Gaddy
Homework 2 Solutions
Section 11.2
5. In this case, notice that, for n N
an =
n2 + 1
n
9. First, in order to see that this sequence must be bounded, note that since n 1, it follows that n1 1,
which means that this sequence is bounded
1/25/2016
Philip Gaddy
Homework 8 Solutions
Section 13.1
4. First, we find the length. This is given by
p
(4 + 2)2 + 32 + 62 = 81 = 9
Furthermore, we see that the midpoint is given by
42 3 6
3
, ,
= 1, , 3
2
2 2
2
Here is the required picture.
11. The e
2/21/2017
Philip Gaddy
Homework 16 Solutions
Section 15.1
2. The domain of this function is given by the inequality 1 xy 0, and therefore consists of all points
such that xy 1. Furthermore, the range of this function is given by [0, ) (for any r R+ , choo
3/10/2017
Philip Gaddy
Homework 21 Solutions
Chapter 15 Review
2. Since the domain of ex is R, we see that the domain of f is R2 . Furthermore, since x2 + y 2 0, we
2
2
see that e(x +y ) e0 = 1. Furthermore, since ex > 0 for any x, it follows that the ran
3/10/2017
Philip Gaddy
Homework 18 Solutions
Section 15.3
19. Here, the level surface is given by x + 2y + 3z = 0. This surface is given below
20. Here, the level surface is given by x2 + y 2 = 4, This surface is given below (this should be a cylinder)
31
2/12/2017
Philip Gaddy
Homework 12 Solutions
Section 13.3
1
13. This vector is given by (cos( 3 ), cos( 4 ), cos( 2
3 ) = ( 2 ,
2
1
2 , 2)
17. First, note that the norm of this vector is 2. Then, we see that the direction angles are given by
1
=
arccos
2/21/2017
Philip Gaddy
Homework 17 Solutions
Section 15.3
2. Notice that, for any c, f (x, y) = c is equivalent to y = 2xc, and therefore these level curves correspond
to lines with slope 2.
6. For any c, we see that f (x, y) = c is equivalent to y = cx2
2/12/2017
Philip Gaddy
Homework 13 Solutions
Section 13.5
1. Letting t = 0, we see that r(t) = (1, 2, 0), so this point is on the line. Furthermore, letting t = 1, we
see that r(1) = (5, 1, 5), so this point is also on the line. Finally, note that (1, 2,
2/5/2017
Philip Gaddy
Homework 9 Solutions
Section 13.2
15. Here, the norm is given by
22 + 12 + 22 =
9=3
19. (a) Since c = 3a and 2a = d, we have that a, c, and d are parallel.
(b) a and c have the same direction.
(c) a and c have a direction opposite th
3/10/2017
Philip Gaddy
Homework 19 Solutions
Section 15.4
3.
13.
= sin sin
= e+ sin( ) + e+ cos( )
= cos cos
= e+ sin( ) + e+ cos( )
31. First, we see that
y
f
x+yx
=
=
2
x
(x + y)
(x + y)2
This means that fx (1, 2) =
33.
2
9
f
x
=
y
(x + y)2
and fy (1,
2/12/2017
Philip Gaddy
Homework 10 Solutions
Section 13.3
1.
a b = 2(2) + 0(3) + 1(3) = 4 + 3 = 1
5.
a b = 2(1) + 1(1) 2(2) = 2 + 1 4 = 1
7.
(3a b) (a 2b) = 3(a b) 2(a b) = a b
10.
a (a + 2c) + (2b a) (a + 2c) 2b (a + 2c) = (a + 2c) (a + 2b a 2b) = 0
15.