Prove that for every n ∈ N:
a) (10^n + 3 * 4^(n+2)) ≡ 4 mod 19, [note that 4^3 ≡ 1 mod
9]
b) 24 | (2*7^(n) + 3*5^(n) - 5),
c) 14 | (3^(4n+2) + 5^(2n+1) [Note that 3^(4n+2) + 5^(2n+1) =
9^(2n)*9 + 5^(2n)*5 ≡ (-5)^(2n) * 9 + 5^(2n) *5 ≡ 0 mod 14]
A bar with an equilateral triangle cross section experienced a
strain of 6.5983 x 10-4 due to an axial load of 2 kN. The
dimensions of the cross section is 5 mm and the length is 300 mm.
Assume that the poisson’s ratio is 0.28.
What is the value of the modulus of elasticity in GPa? Ans =
280 GPa
What is the value of the modulus of rigidity in GPa? Ans =
109.38 GPa
What is the bulk modulus...
set
Hypothesis
u^
μ0
o^
n
α
a)
μ ≠
μ0
14.2
10
4
29
0.05
b)
μ >
μ0
98.3
99.3
6.8
21
0.10
c)
μ <
μ0
19.1
20
9.1
23
0.01
a)
Compute the appropriate test statistic(s) to make a decision about
H0.
critical value = ________ ; test statistic = __________
Decision:--Select---Reject H0 or Fail to reject H0
Compute the corresponding effect size(s) and indicate
magnitude(s).
d = ______ ; Magnitude:--Select---na, trivial effect,
small effect, medium...
(a) The population 3, 4, 9, 14, and 20 has a mean of 10 and a
standard deviation of 6.356. The z-scores for each of the
five data values are
z3 ≈ −1.101,
z4 ≈ −0.944,
z9 ≈ −0.157,
z14 ≈ 0.629,
and z20 ≈ 1.573.
Find the mean and the standard deviation of these
z-scores.
mean
standard deviation
(b) The population 2, 6, 12, 17, 22, and 25 has a mean of 14 and a
standard deviation of 8.226....
4. Refer to Table 10-1, which is based on bonds paying 10
percent interest for 20 years. Assume interest rates in the market
(yield to maturity) decline from 16 percent to 6 percent.
a. What is the bond price at 16 percent?
Bond
price
b. What is the bond price at 6 percent?
Bond
price
c. What would be your percentage return on
investment if you bought when rates were 16 percent and sold when
rates were 6 percent? (Do...
QUESTION 4 Regression Analysis
Guide to marks: 20 marks – 5 for a, 10 for b, 3 for c, 2 for
d
Belinda, the accountant at Murray Manufacturing Company wants to
identify cost drivers for support overhead costs. She has the
impression that the staff spend a large part of their time ensuring
that the equipment is correctly set up and checking the first units
of production in each batch. Deborah has collected the following
data for the past 12...
y
x1
x2
13
20
3
1
15
2
11
23
2
2
10
4
20
30
1
15
21
4
27
38
0
5
18
2
26
24
5
1
16
2
A manufacturer recorded the number of defective items (y)
produced on a given day by each of ten machine operators and also
recorded the average output per hour (x1) for each operator and the
time in weeks from the last machine service (x2).
a. What is the...
1. Suppose an industry has 4 firms and the firms have 40%, 30%,
20% and 10% of the market share, what is the HHI index for this
industry?
2. If the third and fourth firms in the industry above merge,
what is the new HHI index for this industry?
3.What is the largest possible number for HHI index?
4. What is the HHI for the cellular wireless industry?