Question

1105 = 5 × 13 × 17. Find three diﬀerent ways of writing 1105 as
the sum of two squares. (Here I do not consider b^{2} +
a^{2} to be diﬀerent from a^{2} +
b^{2}.)

Answer #1

Consider the following two-person zero-sum game. Assume the two
players have the same three strategy options. The payoff table
below shows the gains for Player A.
Player B
Player A
Strategy b1
Strategy b2
Strategy b3
Strategy a1
3
2
?4
Strategy a2
?1
0
2
Strategy a3
4
5
?3
Is there an optimal pure strategy for this game? If so, what is it?
If not, can the mixed-strategy probabilities be found
algebraically? What is the value of the game?

Questions 1-17 are related to the following
Below are the values for two variables
x and y obtained from a sample of size 5. We want to
build a regression equation based the sample data.
ŷ = b₀ + b₁x
y
x
18
5
25
10
9
5
30
15
46
18
12
Sum of squares total (SST) is,
a
753.9
b
761.5
c
769.2
d
776.9
13
Sum of
squares regression (SSR) is,
a
676.50
b
683.37
c
690.20
d...

The Scholastic Aptitude Test (SAT) contains three sections:
critical reading, mathematics and writing. Each part is scored on a
500-point scale. Information on test scores for the 2018 version of
SAT is available at the College Board website. A sample of SAT
scores for 5 students follow:
SAT scores - 2017
Student
Reading
Math
Writing
1
453
458
465
2
456
458
459
3
454
460
457
4
458
455
461
5
454
454
463
mean
455
457
461
ANOVA...

(7pt) The Scholastic Aptitude Test (SAT) contains three
sections: critical reading, mathematics and writing. Each part is
scored on a 500-point scale. Information on test scores for the
2018 version of SAT is available at the College Board website. A
sample of SAT scores for 5 students follow:
ANOVA Table
Source of variation
Sum of Squares (SS)
Degrees of freedom
Mean Square (MS)
F
Treatment
93.3
2.0
46.67
8.75
Error
64.0
12.0
5.33
Total
157.3
14
SAT scores...

a. Find the number of ways to arrange the three letters in the
word CAT in different two-letter groups where CA is different from
AC and there are no repeated letters.
b. Three members from the group of 12 on the board of directors
at Belford Community Hospital will be selected to go to a
convention with all expenses paid. How many different groups of 3
are there?

5 molecules have speeds 11, 17, 42, 13, 94 m/s. Find the
difference between the root mean square value and the mean (i.e.
Vrms - Vmean) in m/s

13. (5 pts) Find the resultant of 33 m at 74o and 52 m at
-35o.
A) Calculate the sum of the displacements in the x-direction. Keep
six sf.
B) Calculate the sum of the displacements in the x-direction. Keep
six sf.
C) What is the magnitude of the resultant of the displacement? Keep
two sf.
D) What is the angle of the resultant in degrees? Keep two sf.
(SF means significant figures)

12, 16, 21, 14, 21, 20, 17, 13, 18, 22
Find a 95% CI for the population mean assuming the population
variance is 12.
From your CI above do you think the population mean could be 24?
State Yes or No and why.
Find a 90% CI for the population mean assuming the population
standard deviation is unknown.
From your CI above do you think the population mean could be
18?
State Yes or No and why.
Find a 90%...

#13
There is an archaeological study area located in southwestern
New Mexico. Potsherds are broken pieces of prehistoric Native
American clay vessels. One type of painted ceramic vessel is called
Mimbres classic black-on-white. At three different sites,
the number of such sherds was counted in local dwelling
excavations.
Site I
Site II
Site III
64
26
17
39
10
38
24
58
72
11
62
22
81
18
52
13
28
(b) Find SSTOT,
SSBET, and
SSW and check that...

2. There is a famous problem in computation called Subset Sum:
Given a set S of n integers S = {a1, a2, a3, · · · , an} and a
target value T, is it possible to find a subset of S that adds up
to T? Consider the following example: S = {−17, −11, 22, 59} and
the target is T = 65. (a) What are all the possible subsets I can
make with S = {−17, −11, 22,...

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