[tex] \displaystyle \int \bf \: \frac{2 \: tan \: x. {sec}^{2} \: x }{1 + {tan}^{2} \: x } \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 2 \displaystyle \int \bf \: \frac{tan \: x \: . \: \cancel{ {sec}^{2} \: x}}{ \cancel{ {sec}^{2} \: x}} \: \: dx \: \: \: \: \pink{ \{ \because \: {sec}^{2} \: x - {tan}^{2} \: x = 1 \}} \\ \\ = 2 \displaystyle \int \bf \: tan \: x \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = 2 \displaystyle \int \bf \: \frac{sin \: x}{cos \: x} \: \: dx \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = - 2 \displaystyle \int \bf \: \frac{ - \: sin \: x}{ \: cos \: x} \: \: dx\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ = \bf \: - 2 \ln \: |cos \: x| + c\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \green{ \{ \because \: \displaystyle \int \bf \: \frac{ {f}^{′} (x)}{f(x)} \: dx = \ln \: |f(x)| + c \}}[/tex]
Hey guys please help me please and thank you
Answer:
Option B, 5/16
Step-by-step explanation:
f(4) = 5•(1/2)⁴
= 5•(1/2⁴)
= 5•(1/16)
= 5/16
The procluct of q and y digided by the sum of 8 and X
Answer: do you have any of the values?
Step-by-step explanation:
?
Given: Measure of arc AB = measure of arc BC,
Measure of angle x = 60°, measure of angle y = 15°
Find: Measure of arc AC
9514 1404 393
Answer:
100°
Step-by-step explanation:
The relevant relation for angle x is ...
x = (AB +DE)/2
and for angle y, it is ...
y =(AC -DE)/2
Using the second relation to write an expression for DE, we have ...
DE = AC -2y
In the first equation, this lets us write ...
x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2
2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2
(2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3
AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values
AC = 100°
(b) In a company, out of 20 candidates 14 men and 6 women apply for two vacancies. What is the probability that (1) both men are selected ? (ii) both women are selected ? (iii) one man and one woman are selected ?
i hope my answer helps you and you will give me the best answer
A recipe calls for 4 cups of flour and 6 cups of sugar. How many cups of sugar per cup of flour does the recipe require?
Answer:
3 cups of sugar per 2 cups of flour
Step-by-step explanation:
just flip and simplify the fraction
4/6 = 6/4 = 3/2
Andre owns a computer backup service. He charges his customers $2.50 for each backup CD. His expenses include $875 for the CD recording equipment and $0.35 for each blank CD. Which equation could Andre use to calculate his profit p for the recording of n CDs?
Answer:
[tex]p =2.15n - 875[/tex]
Step-by-step explanation:
Given
[tex]CD_s= n[/tex]
[tex]Charges = 2.50[/tex] per CD
Expenses
[tex]E_1 = 875[/tex]
[tex]E_2 = 0.35[/tex] per CD
Required
The profit (p)
First, calculate the total income on n CDs
[tex]Total = Charges * n[/tex]
[tex]Total = 2.50 * n[/tex]
[tex]Total = 2.50n[/tex]
Next, the expenses on n CDs
[tex]Expenses = E_1 + E_2 * n[/tex]
[tex]Expenses = 875 + 0.35 * n[/tex]
[tex]Expenses = 875 + 0.35n[/tex]
The profit (p) is:
[tex]p = Total - Expenses[/tex]
[tex]p =2.50n - (875 + 0.35n)[/tex]
Open bracket
[tex]p =2.50n - 875 - 0.35n[/tex]
Collect like terms
[tex]p =2.50n - 0.35n - 875[/tex]
[tex]p =2.15n - 875[/tex]
Professor Iron always gives two exams in his communications class. He only uses the lower of the two scores that a student gets on the exams when he calculates the course grade. Put the grade on the first exam on the horizontal axis and the grade on the second exam on the vertical axis. What kind of preference a student should have for these two grades. Group of answer choices Perfect Complements Perfect Substitutes Cobb-Douglas Preference Neutral Preference
Answer:
Perfect complements
Step-by-step explanation:
Since minimum score of tests is to be considered. It is a case of perfect complements.
Correct option is
Perfect complements
You decide to determine, once and for all, which chocolate brownies are best-- yours or your sister-in-law's Yolanda-- by devising a test of hypothesis. She is a superb baker and she mocks your baking as inferior. Undaunted, you decide to randomly select 100 names from the NYC phone book. You contact each selected individual and they agree to participate in your study. Then, you send your brownies with instructions for rating the taste and one week later you send Yolanda's brownies with the same instructions. Each group rates the brownies on a 10 point ordinal scale--10 implies exquisite and 1 implies inedible. True or False: This test is performed on paired or matched samples.
Answer:
Ture
Step-by-step explanation:
The rates of the same participatant are paired.
please help me with geometry
Answer:
x = 7
Explaination:
ABC = 40°
and BD bisects the angle so ABD = 20°
so 3x-1=20
solving for x gets us
x = 7
Hi there!i am confused about this equation. Please help to solve this.
Answer:
Step-by-step explanation:
Short of taking 3 hours to type out the way that I did this, let me just tell you the process. Square both sides and multiply to distribute. You end up with radicals still, so square both sides again and multiply to distribute. What you end up with is a 6th degree polynomial that has to be factored. What I got in the end were these zeros:
x = 21.41917943
x = 1.306542114+/-7186864435i
x = -1.066667927
x = 1.28038353
x = 1.28038353
x = -.2459792634
An analyst has developed the following probability distribution for the rate of return for a common stock.
Scenario Probability Rate of Return
10 0.34 -19%
20 0.48 8%
30 0.18 26%
a. Calculate the expected rate of return. Round your answer to 2 decimal places.
b. Calculate the variance and the standard deviation of this probability distribution. Use the percentage values for your calculations (for example 10% not 0.10). Round intermediate calculations to 4 decimal places.
Answer:
a) 2.06
b) variance = 270.90 , std = 275.14
Step-by-step explanation:
a) Determine Expected rate of return
attached below is the calculated table for the solution provided
∴ Expected rate of return = ∑ Xp(x) = -6.46 + 3.84 + 4.68 = 2.06
b) Determine the variance and standard deviation
Variance ( Vx ) = E(x)^2 - [ Expected rate of return ]^2
= 275.14 - ( 2.06 )^2 ≈ 270.90
standard deviation = √ variance = √270.90 = 16.459
note : E(x)^2 = ∑ x^2 p(x) = 275.14
The point of a square pyramid is cut off, making each lateral face of the pyramid a trapezoid with the dimensions shown. A trapezoid has a base of 3 inches, height of 1 inches, and top side length of 1 inch:
What is the area of one trapezoidal face of the figure?
A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answer:
Easy, all you ha
Step-by-step explanation:
Having just turned 16 years old, your friend has their mind set on buying a new car by the time they turn 20 years old. They can afford to save $440 per month. They place the money into an annuity that pays 5.5% per year, compounded monthly. How much will they have to spend on a car after 4 years?
Answer:
$26,179.82
Step-by-step explanation:
FVA = PMT * n * (1 + i) ^ (n - 1)
FVA = 440 * 48* (1.00458)^(47)
Fill in the blank by performing the indicated elementary row operation(s).
6
1
5
-6R2+R
1
-5
0
Answer 7 Points
Keybo
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Prev
In this question, we are given a matrix, and we have to perform the given operation.
The matrix is:
[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]
The following operation is given:
[tex]R_1 \rightarrow -6R_2 + R_1[/tex]
In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.
Updating the first line:
[tex]R_{1,1} = -6*1 + 6 = 0[/tex]
[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]
[tex]R_{1,3} = -6*0 + 5 = 5[/tex]
Thus, the filled matrix will be given by:
[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]
For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657
An Arabian camel can travel 20 miles in 8 hours, carrying a 300-pound load on its back. At this rate, how far can the camel travel in 10 hours?
Answer:
25 miles
Step-by-step explanation:
Given that:
Cammel can travel 20 miles in 8 hours;
The traveling rate or speed = distance / time
Rate = 20 miles / 8 hours = 2.5 miles per hour
The distance traveled in 10 hours at this rate will be :
Distance = speed or rate * time
Distance = 2.5 mph * 10 hours
Distance traveled = 25 miles
HELP ME PLSSS SUMMER SCHOOL A HARD
Answer:
y=2x+8
Step-by-step explanation:
Hope this helps
Factorise 2x3+9x2+10x+3
Answer:
Hello,
Answer is (x+1)(x+3)(2x+1)
Step-by-step explanation:
[tex]p(x)=2x^3+9x^2+10x+3\\p(-1)=2*(-1)^3+9*(-1)^2+10*(-1)+3=-2+9-10+3=0\\p(x)\ is\ divisible\ by\ (x+1)We\ arrange\ to\ put\ a\ factor\ of\ x+1\\\\2x^3+9x^2+10x+3\\\\=2x^3+2x^2+7x^2+7x+3x+3\\\\=2x^2(x+1)+7x(x+1)+3(x+1)\\\\=(x+1)(2x^2+7x+3)\\\\=(x+1)(2x^2+6x+x+3)\\\\=(x+1)(2x(x+3)+1(x+3))\\\\=(x+1)(x+3)(2x+1)\\[/tex]
Write the following as an expression: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol? The answer is an EXPRESSION, not an actual answer!! WILL MARK BRAINLIST!!!
Answer: [tex]\dfrac{11}{9}I[/tex]
Step-by-step explanation:
Given
There is [tex]l[/tex] liter of pure alcohol
Suppose [tex]x[/tex] liters of water is added
After addition of water, alcohol becomes 45% in concentration
[tex]\Rightarrow \dfrac{l}{x+l}=45\%\\\\\Rightarrow \dfrac{I}{0.45}=x+I\\\\\Rightarrow \dfrac{20}{9}I-I=x\\\\\Rightarrow x=\dfrac{11}{9}I[/tex]
Thus, [tex]\dfrac{11}{9}I[/tex] of water is added to the pure alcohol.
Find the length of BC
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we want to find the opposite side and we know the hypotenuse. Therefore, we should use sine.
sin(51) = BC / 58
BC = 58 x sin(51)
BC = 45.1 units
Hope this helps!
Step-by-step explanation:
Hey there!
From the above given figure;
Angle CAB = 51°
AB = 58
Taking Angle CAB as reference angle we get;
Perpendicular (p) = BC= ?
Hypotenuse (h) = 58
Now;
Taking the ratio of sin we get;
[tex] \sin( \alpha ) = \frac{p}{h} [/tex]
[tex] \sin(51) = \frac{bc}{58} [/tex]
Simplify it;
0.7771459*58 = BC
Therefore, BC = 45.0744.
Hope it helps!
In performing a one-way ANOVA, ________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response and its corresponding treatment mean.
Answer: SS Error
Step-by-step explanation:
The SS Error refers to the sum of the squares of the deviations of the observations, from their mean. It is simply the total variance from the observations on the study.
In performing a one-way ANOVA, the SS Error measures the variability of the observed values around their respective means and this is done through the summation of the squared differences between each observed value of the response and its corresponding treatment mean.
If a drug has a concentration of 8.22 mg per 3.039 mL, how many mL are needed to give 7.469 gram of the drug? Round to 1 decimal.
Answer:
2.8 litres
Step-by-step explanation:
8.22 mg per 3.039 mL
2.704 mg per 1 mL
7.469 gram = 7469 milligrams
7469 milligrams per 2,761.34927mL
= 2.761 litres = 2.8 litres
An environmentalist wants to find out the fraction of oil tankers that have spills each month.
Suppose a sample of 1036 tankers is drawn. Of these ships, 777 did not have spills. Using the data, estimate the proportion of oil tankers that had spills. Write your answer as a fraction or a decimal number rounded to three decimal places.
Answer:
The estimate of the proportion of oil tankers that had spills is 0.25.
Step-by-step explanation:
Proportion of oil tankers that had spills:
1036 tankers.
777 did not have spills.
So 1036 - 777 = 259 had spills.
The proportion is:
[tex]p = \frac{259}{1036} = 0.25[/tex]
The estimate of the proportion of oil tankers that had spills is 0.25.
The diameter of a regulation soccer ball is about 8 and three-fifths inches. This number was graphed on a number line.
A number line going from negative 9 to positive 9. Point A is between negative 9 and negative 8, point B is between negative 7 and negative 6, point C is between 6 and 7, point D is between 8 and 9.
Which point could be the point representing the graph of the diameter of the ball?
A
B
C
D
Answer:
D
Step-by-step explanation:
8 and 3/5 = 8.2 and 8.2 is between 8 and 9 so the answer is D.
Marie's backyard deck cost $68.29 per square meter to build. The deck is 9 meters wide and 9 meters long. How much did it cost to build the deck?
$5531.49
(9×9)×$68.29
With one alarm clock, we have a 0.875 probability of being awakened. What is the probability of being awakened if we are using two alarm clocks?(
The probability will be the same for both clocks.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
With one alarm clock, we have a 0.875 probability of being awakened.
The probability for the two clocks will be the same because both the clocks will ring at the same time.
To know more about probability follow
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What is the solution set of the
equation?
(3x – 5)(2x – 10) = 0
Answer:
Step-by-step explanation:
3x - 5 = 0
3x = 5
x = 5/3
2x - 10 = 0
2x = 10
x = 10/2 = 5
A mid-sized company has decided to implement an enterprise resource planning (ERP) system, and management suspects that many of its employees are concerned about the planned implementation. Managers are considering holding informational workshops to help decrease anxiety levels among employees. To determine whether such an approach would be effective, they randomly select 16 employees to participate in a pilot workshop. These employees were given a questionnaire to measure anxiety levels about ERP before and after participating in the workshop. Do the data indicate that anxiety levels about ERP decreases as a result of the workshop
Answer:
From the data The anxiety levels decreases as a result of the workshop
given that the mean value of the differences = -1.1125
Step-by-step explanation:
Number of randomly selected employees = 16
From the data It can be noticed that the difference in anxiety levels decrease ( Tends towards values below 0 )
To determine this we have to determine the mean value of the differences
(-3) + (-3) + (-2) +(-2) +(-2) + (-2 ) + (-1) + (-1) + (-1) + (-1) + (-1 ) + 0 + 0 + 0 + 0 + 1 / 16
= -18 / 16 = - 1.1125
mean value = -1.1125.
Suppose that a population begins at a size of 100 and grows continuously at a rate of 200% per year. Give the formula for calculating the size of that population after t years.
A) A = 100 + te^2
B) A = 100 + e^2t
C) A = 100e^2t
D) A = 100 + 2e^t
Answer:
D)
Step-by-step explanation: Im not so sure ok i sorry if Im wrong
A piece of wire 11 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area
Answer:
11 meters
Step-by-step explanation:
First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).
The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is
(√3/4)((11-4x)/3)²
= (√3/4)(11/3 - 4x/3)²
= (√3/4)(121/9 - 88x/9 + 16x²/9)
= (16√3/36)x² - (88√3/36)x + (121√3/36)
The total area is then
(16√3/36)x² - (88√3/36)x + (121√3/36) + x²
= (16√3/36 + 1)x² - (88√3/36)x + (121√3/36)
Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)
When x=0, each side of the triangle is 11/3 meters long and its area is
(√3/4)a² ≈ 5.82
When x=2.75, each side of the square is 2.75 meters long and its area is
2.75² = 7.5625
Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters
The length of the square must be 4 m in order to maximize the total area.
What are the maxima and minima of a function?When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.
We have,
Length of the wire = 11 m
Let the length of the wire bent into a square = x.
The length of the wire bent into an equilateral triangle = (11 - x)
Now,
The perimeter of a square = 4 side
4 side = x
side = x/4
The perimeter of an equilateral triangle = 3 side
11 - x = 3 side
side = (11 - x)/3
Area of square = side²
Area of equilateral triangle = (√3/4) side²
Total area:
T = (x/4)² + √3/4 {(11 -x)/3}² _____(1)
Now,
To find the maximum we will differentiate (1)
dT/dx = 0
2x/4 + (√3/4) x 2(11 - x)/3 x -1 = 0
2x / 4 - (√3/4) x 2(11 - x)/3 = 0
2x/4 - (√3/6)(11 - x) = 0
2x / 4 = (√3/6)(11 - x)
√3x = 11 - x
√3x + x = 11
x (√3 + 1) = 11
x = 11 / (1.732 + 1)
x = 11/2.732
x = 4
Thus,
The length of the square must be 4 m in order to maximize the total area.
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