Answer:
[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]
Where [tex]C[/tex] is the integration constant.
Step-by-step explanation:
We use integration by substitution to obtain the integral, where:
[tex]u = \sin 3x[/tex], [tex]du = 3\cdot \cos 3x\,dx[/tex]
[tex]I = \int {\sin 3x\cdot \cos 3x} \, dx[/tex]
[tex]I = \frac{1}{3} \int {u} \, du[/tex]
[tex]I = \frac{1}{6}\cdot u^{2} + C[/tex]
[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]
Where [tex]C[/tex] is the integration constant.
PLEASE HELP ME I DESPERATE
Answer:
A and C
Step-by-step explanation:
5+(-5) is the same thing as 5-5 so the answer is 0. If you went to the right of number five you would get ten. The answer is 0 so you have to go left of 5 to get to zero.
Find the sum of the series if n = 6, r = 1/4, a = 2.
Given =
n=6,
r=1/4
a=2
Sn = a+ar+ar²+ar³+ar⁴+ar⁵= 2+0.5+0.125+0.03125+0.0078125+0.00195~ 2.67
Wilcox, chief executive officer and chairman of the board of directors, owned 60 percent of the shares of Sterling Corporation. When the market price of Sterling’s shares was $22 per share, Wilcox sold all of his shares in Sterling to Conrad for $29 per share. The minority shareholders of Sterling brought suit against Wilcox demanding a pro rata share of the amount Wilcox received in excess of the market price. a. What are the arguments to support the minority shareholders’ claim for a pro rata share of the amount Wilcox received in excess of the market price? b. What are the arguments to reject the minority shareholders’ claim for a pro rata share of the amount Wilcox received in excess of the market price? c. Which side should prevail?
Answer:
Sterling Corporation
a. Arguments to support the minority shareholders' claim include:
1. If there is a provision to this effect in the Shareholders' agreement,
2. If the minority shareholders can prove that Wilcox oppressed the minority shareholders by selling off his shares in the corporation, and
3. If the Shareholders' agreement forbids Wilcox from selling off his shareholdings.
b. The arguments to reject the minority shareholders' claim include:
1. As the majority shareholder, Wilcox dictates the direction of firm until the sale-off.
2. Wilcox is within his rights to sell his shares to Conrad.
3. Wilcox does not oppress the minority shareholders with the sale to Conrad.
c. Wilcox should prevail. Apparently, he did not act illegally or contrary to agreement.
Step-by-step explanation:
Shareholding of Wilcox (chief executive officer and chairman of the BOD) = 60%, which is > 50%.
Shareholding of Minority shareholders = 40%, which is <50%
Market price per share of Sterling Corporation = $22
Selling price of Wilcox's shares = $29
Excess of the market price = $7 ($29 - $22)
Suppose that a large mixing tank initially holds 500 gallons of water in which 60 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 5 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine a differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)
Answer:
The answer is "[tex]\frac{dA}{dt}+ \frac{A}{100}=0\ \ and \ \A(0)=60[/tex]"
Step-by-step explanation:
[tex]A(0)=60\\\\ \frac{dA}{dt}=Rin-Rout\\\\Rin=0\\\\Rout=\frac{A(t)}{500} \times (5)\\\\ =\frac{A}{100}\\\\ so,\\\\\frac{dA}{dt}=Rin-Rout\\\\\frac{dA}{dt}=0- \frac{A}{100}\\\\\frac{dA}{dt}+ \frac{A}{100}=0\\\\A(0)=60[/tex]
You roll a six-sided number cube and flip a coin. What is the probability of rolling a number greater than 4 and flipping heads? Write your answer as a fraction in simplest form.
Answer:
1/6
Step-by-step explanation:
the options greater than 4 on a six-sided dice are 5 and 6 so 2 out of the 6 options so that simplifies to 1/3 and then heads or tails for the coin is 1/2 so then multiply 1/3 times 1/2 to get the probability of those both happening and the answer is 1/6
Convert.
2 mi = _ yd
Answer: 2 mi = 3520.00 yd
Answer:
2 mi= 3520 yd
Step-by-step explanation:
To convert a mile measurement to a yard measurement, multiply the length by the conversion ratio.
1 mile is equal to 1,760 yards
multiply the length value by 1760 to get your answer
2 x 1760 = 3520
A van travels 150 miles on 6 gallons of gas. How many gallons will it need to travel 325 miles?
A.12 gallons
B.2.8 gallons
C.13 gallons
D.25 gallons
plss help no link im giving brainless i need it Asap
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Work Shown:
(150 miles)/(6 gallons) = (325 miles)/(x gallons)
150/6 = 325/x
150*x = 6*325 .... see note below
150x = 1950
x = 1950/150 .... divide both sides by 150
x = 13 gallons is the final answer
-----------
Note: in this step, I cross multiplied. The general template for cross multiplication is that we go from A/B = C/D to A*D = B*C. As the name implies, the "cross" refers to the "X" shape that forms when you multiply the terms.
a number p divided by 22
Answer:
a number p, 14 - p
Step-by-step explanation:
A rectangular lawn has an area of 1624 square metres. Its perimeter is 170 metres. What are the dimensions of the lawn?
GIVEN
L×B = 1624. ---1)
2(L+B) = 170
(L+B) = 85
L= 85- B
Substitute value of L in eq 1)
(85-B)B = 1624
B²-85B+1624 = 0
B²-56B-29B+1624 = 0
B(B-56)-29(B-56) = 0
(B-29)(B-56) = 0
B= 29 OR B= 56
IF B = 29, L = 56
IF B = 56, L = 29
The dimension of lawn is 56×29 cm²
Draw a square with one vertex on the origin (-3, 5) and a perimeter of 20.
Answer:
Coordinates:
(-3, 5)
(2, 5)
(-3, 10)
(2, 10)
Step-by-step explanation:
Perimeter formula:
length + width + length + width
Insert known value(s):
l + w + l + w = 20
Squares must have the same value for all 4 sides, so what number × 4 will equal 20? 5.
5 + 5 + 5 + 5 = 20
This means coordinates will be 5 units apart:
(-3 + 5, 5) = (2, 5)
(-3, 5 + 5) = (-3, 10)
Mark these coordinates on your grid as you go to double check the shape turns becomes a square:
(2, 5 + 5) = (2, 10)
Counting between them should equal 5 units for each side: I checked using the desmos graphing calculator online.
SOMEONE PLEASE HELP!!
Answer:
It's the first one I think
Step-by-step explanation:
Compound inequalities :A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements .
THE CORRECT ANSWER IS THE LAST ONE ..
An envelope is 6 cm longer than it is wide. The area is 72 cm squared, find the length and the width.
Answer:
full length would be 56 and width 42
Step-by-step explanation:
The required length and width of the envelope are given as 12cm and 6cm respectively.
Given that,
An envelope is 6 cm longer than it is wide. The area is 72 cm squared.
Surface area is defined as the measure of a region or surface is called as surface area.
Here,
Let the width of the envelope be x,
According to the question,
Length of the envelope = x + 6
Area of the envelope = (x + 6)x
(x + 6)x = 72
x² + 6x -72 = 0
(x + 12)(x - 6) = 0
x = 6 and x = -12
We consider x = 6 because the measure of length is always positive,
Length = x + 6 = 6 + 6 = 12
Thus, the required length and width of the envelope is given as 12cm and 6cm.
Learn more about the surface area here: https://brainly.com/question/2835293
#SPJ2
Do you think credit cards want customers to pay off their balances?
Answer: 12 THE ANSWER IS 12 FOR SURE
Step-by-step explanation: Did I get it right!?!??!
f(x) = x^2. what is g(x)?
Answer:
Option C
Step-by-step explanation:
I just graphed on my TI-84
Hope this helps!
Find the value of x that makes m || n
Answer:
x = 23
Step-by-step explanation:
7x - 11 = 4x + 58
(7x - 4x) - 11 = (4x - 4x) + 58
3x - 11 = 58
3x (- 11 + 11) = 58 + 11
3x = 69
3x/3 = 69/3
x = 23
What does it mean by And,Or in probability?
Answer:
In probability, there's a very important distinction between the words and and or. And means that the outcome has to satisfy both conditions at the same time. Or means that the outcome has to satisfy one condition, or the other condition, or both at the same time.
Step-by-step explanation:
thank me later
Please help me I need this asap
Answer:
its b i had this same thing in classkick
Step-by-step explanation:
What is the diameter of a hemisphere with a volume of 651 m^3, to the nearest tenth
of a meter?
Answer: 13.5 m, hope this helps :)
If the volume of the sphere is 651 m³. Then the diameter of the sphere will be 10.75 meters.
What is the volume of the sphere?If the given sphere is of radius r units, then its volume is given as:
V = 4/3 πr³ unit³
The volume of the sphere is 651 m³.
Then the diameter of the sphere will be
We know the formula in the form of diameter.
V = 1/6 πd³ unit³
Then we have
651 = 1/6 πd³
πd³ = 3906
d³ = 1243.31
d = 10.75 m
Learn more about the volume of a sphere here:
https://brainly.com/question/381274
#SPJ2
21/100 = k/10 + 1 /100 what number is k?
Use the graph of f(x) to write its equation. y! X
Answer:
y = |x + 2|
Step-by-step explanation:
given the straight shape, it must be a linear function, but the "bend" in it indicates that an absolute value is being used.
So to start we can say: y = |x|
But that's not sufficient, as it would show that bend being at 0, 0. Instead, we need to translate it two units to the left, giving us:
y = |x + 2|
A company's sales force makes 400 sales calls, with 0.25 probability that a sale will be made on a call. What is the probability that between 75 (inclusive) and 95 (inclusive) sales will be made? Enter your answer as a decimal value, rounded to 4 decimal places.
Answer:
0.8629
Step-by-step explanation:
Given :
Number of trials, n = 400
p = 0.25
q = 1 - p = 1 - 0.25 = 0.75
With the information given, we could use a binomial probability relation to solve :
Recall : P(x = x) = nCx * p^x * q^(n-x)
Therefore, the probability that between 75 (inclusive) and 95 (inclusive) can be interpreted as :
P(75≤X≤90) = P(X ≥ 75) - P(X ≤ 90)
Using a binomial probability calculator :
P(X ≥ 75) = 0.9987
P(X ≤ 90) = 0.1358
0.9987 - 0.1358 = 0.8629
Ct+7m. If C=5,t=2, and m=2
Answer:
24
Step-by-step explanation:
5(2) + 7(2) = 10+14 = 24
You choose a letter at random from the alphabet. What is the probability you choose one of the letters in “Math”?
A. 0
B.100
C. 4/26
D. 1/13
E. 22/26
Answer:
Option c is correct one
C. 4/26
Bcz word MATH contains 4 words and total alphabet is 26
what is the value of x??? please help me easy math question
Answer:
x = 30
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
60 + x+3x = 180
60 + 4x = 180
Subtract 60 from each side
60+4x-60 = 180-60
4x = 120
Divide by 4
4x/4 = 120/4
x = 30
Thank you for the help I need it for a test so if I could have ASAP thank you
Express in simplest form: (3x^2 + 4x - 8) - (-2x^2 + 4x + 2)
Answer:
5x² - 10
Step-by-step explanation:
Step 1:
( [tex]3x^{2}[/tex] + 4x - 8 ) - ( [tex]-2x^{2}[/tex] + 4x + 2 ) Equation
Step 2:
3x² + 4x - 8 + 2x² - 4x - 2 Open Parenthises
Answer:
5x² - 10 Simplify
Hope This Helps :)
Answer:
5x² + 10
Step-by-step explanation:
Given Equation :-
( 3x² + 4x - 8 ) - ( -2x² + 4x + 2)
Solution :-
( 3x² + 4x - 8 ) - ( -2x² + 4x + 2)Step 1:- Remove unnecessary parantheses.
3x² + 4x - 8 + 2x ² - 4x - 2Step 2 :- arranging like terms.
3x² + 5x² + 4x - 4x -8 - 2Step 3 :- Calculate like terms.
5x² + 10A math recap workshop is provided to the first year students entering a city college. To evaluate the workshop effectiveness, a study is conducted as following: 20 students with similar math backgrounds are randomly selected for the study. Of the 20 students, 10 of them are selected to attend the workshop and the other 10 do not attend the workshop. After the workshop has taken place a test is given to all 20 students. What is the appropriate inference test to use in this situation
Answer:
Independent sample t test
Step-by-step explanation:
The Independent sample t test could be explained as a statistical test carried out in other to establish or examine if significant difference exists between two independent samples. That is the outcome of the samples do not depend on one another. Using the scenario described above, the difference between the same variable is measured for two different groups which is the ideal set up for an independent sample t test. The difference between test score for two independent samples (those who attended the workshop and those who did not) is being compared.
Write a function rule for the area A(h) of a parallelogram whose base is 3 units more than its height h.
A. A(h) = h2 + 3
B. A(h) = h2 + 3h
C. A(h) = h2 + 3h + 3
D. A(h) = h + 3h
===================================================
Work Shown:
height = h
base = h+3, since the base is 3 more than the height
area = base*height
area = h*(h+3)
area = h*h + h*3
area = h^2+3h
Find the area of the sector formed by a central angle of 45 degrees in a circle of radius 2.1
meters. Round to the hundredth.
Answer:
1.731 meters squared
Step-by-step explanation:
Look at the image for reasoning
You buy milk at $3.48 per gallon. One portion of oatmeal requires 5 ounces of milk. How much does the milk for one portion cost? Round to the nearest cent.
Answer: $0.1359375
Step-by-step explanation:
First and foremost, we should note that 1 gallon = 128 ounce. Therefore, $3.48 per gallon simply means $3.48 for 128 ounce. Therefore, the cost per ounce will be:
= $3.48 / 128
= $0.0271875
Therefore, the amount for the the milk for one portion cost which requires 5 ounces of milk will be:
= $0.0271875 × 5
= $0.1359375