Let X = {1, 2, 3, 4}, Y = {a, b, c}.
(1) Give an example for f : X → Y so that ∀y ∈ Y, ∃x ∈ X, f(x) = y. 1 2
(2) Give an example for f : X → Y so that ∃y ∈ Y, ∀x ∈ X, f(x) = y.
(3) Give an example for f : X → Y and g : Y → X so that f ◦ g = IY
In: Advanced Math
A, B, C, D are all matricies
A = 2x3
1 2 −3
−1 4 5
,
B = 2x3
3 0 −1
1 2 1
, C = 2x2
2 5
1 2
,
D = 3x3
1 −1 1
2 −1 2
4 −3 4
Find each of the following or explain why it does not exist.
1) A + B,
2) 2A − 3B,
3) A + C,
4) A − C,
5) AC,
6) CA,
7) AD,
8) DA,
9) C
10) D−1
.
11) Solve the matrix equation CX = B
In: Math
In: Finance
1) Define the sets X ={ 1, 2, 3} and Y = {4, 5, 6}. Now, define the relation R from X to Y by xRy if and only if x − y is even. Find all of the elements in R.
2) Define the relation R on ℤ by mRn if and only if 2|(m − n). Show that R is an equivalence relation.
In: Advanced Math
For the following exercises, given v, draw v, 3v and 1/2 v.
⟨−1, 4⟩
In: Math
In: Chemistry
. (1) A man has a 4-sided (tetrahedral) die, with four faces, 1, 2, 3, and 4. He rolls it 12 times. (a) Given that for each roll of the die, the probability of rolling a 4 is 1/4 and the probability of not doing so is 3/4, compute the following probabilities P(x = x0),where x is the number of times that the man rolls a 4 among the 12 trials. (b) What is the average value of x? What is the standard deviation? (c) Which possible value of x has the highest likelihood of occurring? (2) IQ scores in America, by definition, are normally distributed, with 100 points being the mean IQ and the standard deviation being 10 points. (a) Suppose a person has an IQ of 115. What percentage of the population is expected to have a higher IQ than this person? (b) Now suppose a person has an IQ of 75. What percentage of the population is expected to have a lower IQ than this person? (c) An individual’s IQ was claimed to have jumped from 83 to 212 after a procedure. (An IQ of 212 is not possible, given that most tests only can assign scores of at most 170.) What percentage of the population, were the claim not false, would be between the first score and the second?
In: Statistics and Probability
On October 15, 2020, the board of directors of Ensor Materials
Corporation approved a stock option plan for key executives. On
January 1, 2021, 30 million stock options were granted, exercisable
for 30 million shares of Ensor's $1 par common stock. The options
are exercisable between January 1, 2024, and December 31, 2026, at
80% of the quoted market price on January 1, 2021, which was $15.
The fair value of the 30 million options, estimated by an
appropriate option pricing model, is $5 per option. Ensor chooses
the option to recognize forfeitures only when they occur.
Ten percent (3 million) of the options were forfeited when an
executive resigned in 2022. All other options were exercised on
July 12, 2025, when the stock’s price jumped unexpectedly to $30
per share.
Required:
1. When is Ensor’s stock option measurement
date?
2. Determine the compensation expense for the
stock option plan in 2021. (Ignore taxes.)
3. Prepare the journal entries to reflect the
effect of forfeiture of the stock options on Ensor’s financial
statements for 2022 and 2023.
5. Prepare the journal entry to account for the
exercise of the options in 2025.
In: Accounting
On October 15, 2020, the board of directors of Ensor Materials
Corporation approved a stock option plan for key executives. On
January 1, 2021, 32 million stock options were granted, exercisable
for 32 million shares of Ensor's $1 par common stock. The options
are exercisable between January 1, 2024, and December 31, 2026, at
80% of the quoted market price on January 1, 2021, which was $30.
The fair value of the 32 million options, estimated by an
appropriate option pricing model, is $6 per option. Ensor chooses
the option to recognize forfeitures only when they occur.
Ten percent (3.2 million) of the options were forfeited when an
executive resigned in 2022. All other options were exercised on
July 12, 2025, when the stock’s price jumped unexpectedly to $34
per share.
Required:
1. When is Ensor’s stock option measurement
date?
2. Determine the compensation expense for the
stock option plan in 2021. (Ignore taxes.)
3. Prepare the journal entries to reflect the
effect of forfeiture of the stock options on Ensor’s financial
statements for 2022 and 2023.
5. Prepare the journal entry to account for the
exercise of the options in 2025.
In: Accounting
On October 15, 2020, the board of directors of Ensor Materials
Corporation approved a stock option plan for key executives. On
January 1, 2021, 30 million stock options were granted, exercisable
for 30 million shares of Ensor's $1 par common stock. The options
are exercisable between January 1, 2024, and December 31, 2026, at
80% of the quoted market price on January 1, 2021, which was $15.
The fair value of the 30 million options, estimated by an
appropriate option pricing model, is $5 per option. Ensor chooses
the option to recognize forfeitures only when they occur.
Ten percent (3 million) of the options were forfeited when an
executive resigned in 2022. All other options were exercised on
July 12, 2025, when the stock’s price jumped unexpectedly to $33
per share.
Required:
1. When is Ensor’s stock option measurement
date?
2. Determine the compensation expense for the
stock option plan in 2021. (Ignore taxes.)
3. Prepare the journal entries to reflect the
effect of forfeiture of the stock options on Ensor’s financial
statements for 2022 and 2023.
5. Prepare the journal entry to account for the
exercise of the options in 2025.
In: Accounting