Consider the following functions from ℤ × ℤ → ℤ. Which
functions are onto? Justify your...
Consider the following functions from ℤ × ℤ → ℤ. Which
functions are onto? Justify your answer by proving the function is
onto or providing a counterexample and explaining why it is a
counterexample.
(a) f(x,y) = xy + 3
(b) f(x,y) = |xy| + 10
(c) f(x,y) = ⌊(x+y)/5⌋
Consider the following ordered data. 8 11 11 12 13 13 14 15
16
(a) Find...
Consider the following ordered data. 8 11 11 12 13 13 14 15
16
(a) Find the
low,
Q1,
median,
Q3,
and high. (For each answer, enter a number.)
(b) Find the interquartile range. (Enter a number.)
1) Show that ∀a, b, c ∈ ℤ, a|b ∨ a|c =⇒
a|bc.
2) Consider the...
1) Show that ∀a, b, c ∈ ℤ, a|b ∨ a|c =⇒
a|bc.
2) Consider the integers 3213 and 1386.
a) Show the steps of the Euclidean Algorithm for 3213 and
1386.
b) Show the steps of the Exended Euclidean Algorithm for 3213
and 1386.
3) Notice that as we compute the solution to a
set of congruences with Chinese Remainder Theorem, our moduli
increase in size at each step. This means that each computation
will require numbers of greater...
14. For each of the following sets, show whether it is convex or
not.
(a) ?...
14. For each of the following sets, show whether it is convex or
not.
(a) ? = {(?1, ?2 ) ? ∈ ? 2 : ?1 + ?2 ≤ 2, ?1 ≥ 0, ?2 ≥ 0}
(b) ? = {(?1, ?2 ) ? ∈ ? 2 : ?2 − ?1 2 = 0}
1. Consider the following situation: The universal set U
is given by: U = {?|? ?...
1. Consider the following situation: The universal set U
is given by: U = {?|? ? ? , ? ≤ 12}
A is a proper subset of U, with those numbers that are
divisible by 4.
B is a proper subset of U, with those numbers that are
divisible by 3.
C is a proper subset of U, with those numbers that are
divisible by 2
a) Using Roster Notation, list the elements of sets U, A, B and
C....
Consider the following data from a random sample: 23 12 26 14 20
25 14 11...
Consider the following data from a random sample: 23 12 26 14 20
25 14 11 21 14 25 21 22 21 8 19 17 22 17 16
a.) Construct a stem-and-leaf plot and specify the five-number
index (min, Q1, Q2, Q3, & max)
b.) Compute the mean and the standard deviation
c.) Find a 95% confidence interval for the population mean.
Consider the following 14 independent measurements from
a normal distribution:
Independent measurements
11
14
1
18...
Consider the following 14 independent measurements from
a normal distribution:
Independent measurements
11
14
1
18
6
12
10
10
20
19
11
16
15
13
1) What is the standard error of the sample mean?
7.0193
5.1248
1.3697
1.4214
2) Calculate a 99% confidence interval for the population
mean.
[8.9413,16.2016]
[9.2637,15.8791]
[8.4455,16.6973]
[-0.8786,26.0215]
Find min, max, range, median and mode for the following
data:
9 16 11
14 11 ...
Find min, max, range, median and mode for the following
data:
9 16 11
14 11 6
13 5
17 7
8 15
22 16
Put your answers in the following table:
Min=
Max=
Range=
Ascending order:
Median=
Ascending order:
Mode=
b. Given the three sets A = {Kim, Tom, John}, B =
{biology-major, arts-major, CS-major}, C...
b. Given the three sets A = {Kim, Tom, John}, B =
{biology-major, arts-major, CS-major}, C = {$40K, $20K, $70k},
{biology-major, arts-major, CS-major}, show that the following
subset is a relation of the Cartesian product A × B × C, and show
the relation in tabular form. (2 points) {(Kim, CS-major, $70K),
(Tom, arts-major, $20K), (John, biology-major, $40K)}
c. For the table derived in problem 6B, give the projections
P({1, 3}) in a tabular form (2 points)
d. Given the...