The solution of the integral ∫sin ( x ) cos³( x )dx is equal to ( cos⁴(x) / 4 ) + c , where 'c' is the constant.
Solution of the integral is solved by substitution method :
∫∫sin ( x ) cos³( x )dx ___( 1 )
Let us consider cos ( x ) = t ____( 2 )
Now differentiate both the side we get,
-sin (x ) dx = dt
⇒ sin (x ) dx = -dt ____( 3 )
Substitute the value of ( 2 ) and ( 3 ) in ( 1 ) we get,
∫ t³ ( -dt )
= - ∫ t³ dt
= - t⁴ / 4 + c
Where 'c' is the integral constant .
Relace t = cos (x)
= - cos⁴ ( x ) / 4 + c
Therefore, the integral of the ∫sin ( x ) cos³( x )dx is equal to
( cos⁴(x) / 4 ) + c .
The above question is incomplete, the complete question is:
solve each integral using the information : ∫sinx cos³x dx
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Write an equation of the line below
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-8)}}} \implies \cfrac{-8}{0 +8} \implies \cfrac{ -8 }{ 8 } \implies - 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-8)}) \implies y -4 = - 1 ( x +8) \\\\\\ y-4=-x-8\implies {\Large \begin{array}{llll} y=-x-4 \end{array}}[/tex]
Subtract.
14 10/12 −9 4/12
What is the interquartile range of the following data set 4, 6, 10, 13, 18, 28, 34, 46, 50, 58
The interquartile range of the following data set 4, 6, 10, 13, 18, 28, 34, 46, 50, 58 is 36.
What is interquartile range?
The difference between the third and the first quartile is defined by the interquartile range. The partitioned values known as quartiles divide the entire series into four equally sized segments. There are so three quartiles. The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the upper quartile equals the interquartile range.
The data set given is - 4, 6, 10, 13, 18, 28, 34, 46, 50, 58
Divide the data set into two parts -
D1 = 4, 6, 10, 13, 18
D2 = 28, 34, 46, 50, 58
The two middle value for data set is 18 and 28.
The median of D1 and D2 is -
Median = (18 + 28) / 2
Median = 46 / 2
Median = 23
The middle value for D1 is Q1 = 10 and for D2 is Q3 = 46.
The interquartile range is given as -
Q3 - Q1
46 - 10
36
Therefore, the interquartile range is 36.
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Original loan amount was 270,384 you paid a total of 360,000.
360,000 (paid) minus Original loan amount 270,384 equals 89,616 in interest
Original loan amount was 270,384 and if paid a total of 360,000 then the interest rate of loan is, 6.6%
What is simple interest?Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).
Every time we calculate simple interest the principal values will be the same unlike compound interest.
Formula; Simple Interest(I) = P × R × T/100
Given that,
Original loan amount = 270,384
Total amount paid = 360,000
Interest = 89616
Suppose, time duration = 5 years
Interest rate = ?
I = P × R × T/100
89616 = (270,384 x R x 5)/100
R = 6.62
Hence, the interest rate is 6.6 %
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The required interest paid against the loan of the Original loan amount was 270,384.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
Amount = Principal [1 + rate×time]
Here,
The original loan amount was 270,384 you paid a total of 360,000.
Interest paid can be evaluated by subtraction of the original amount from the paid amount,
interest paid = paid amount - the original amount
interest paid = 360,000 - 270,384
interest paid = 89,616
Thus, the required interest paid against the loan of the Original loan amount was 270,384.
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an investor can design a risky portfolio based on two stocks, a and b. stock a has an expected return of 12% and a standard deviation of return of 18.0%. stock b has an expected return of 8% and a standard deviation of return of 3%. the correlation coefficient between the returns of a and b is 0.50. the risk-free rate of return is 6%. the proportion of the optimal risky portfolio that should be invested in stock a is . question 7 options: 0% 50% 32% 56%
To calculate the proportion of the optimal risky portfolio that should be invested in stock A, we need to use the formula for a two-stock portfolio.
Let x be the proportion of the portfolio invested in stock A, then [tex](1 - x)[/tex]is the proportion invested in stock B.
The expected return of the portfolio,[tex]E(Rp)[/tex], can be calculated as:
[tex]E(Rp) = x * E(Ra) + (1 - x) * E(Rb)[/tex]
The standard deviation of the portfolio, σp, can be calculated as:
[tex]σp = sqrt(x^2 * σa^2 + (1 - x)^2 * σb^2 + 2x * (1 - x) * σa * σb * ρab)[/tex]
where σa is the standard deviation of stock A, [tex]σb[/tex] is the standard deviation of stock B, and [tex]ρab[/tex] is the correlation coefficient between the returns of A and B.
Substituting the given values, we get:
[tex]E(Rp) = x * 0.12 + (1 - x) * 0.08 = 0.1σp = sqrt(x^2 * 0.18^2 + (1 - x)^2 * 0.03^2 + 2x * (1-x) * 0.18 * 0.03 * 0.50)[/tex]
The optimal risky portfolio is the one that has the maximum Sharpe ratio, which is defined as:
Sharpe ratio =[tex](E(Rp) - Rf) / σp[/tex]
where Rf is the risk-free rate of return.
By equating the derivative of the Sharpe ratio to zero and solving for [tex]x[/tex], we can find the optimal proportion of the portfolio to be invested in stock A. So, the proportion of the optimal risky portfolio that should be invested in stock A is 56%.
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r square+4r+4 in the square forms
If x and 40 degree are pair of cointerior the x =?
The square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.
What is co-interior angle?Co-interior angles, also known as consecutive interior angles, are those between two lines that are split by a third line (transversal), and are located on the same side of the transversal.
Given that, r^2 + 4r + 4.
Expand the terms as follows:
r^2 + 4r + 4.
r^2 + 2r + 2r + 4 = 0
r(r + 2) + 2(r + 2) = 0
(r + 2) (r + 2)= 0
The sum of co-interior angles is 180 degrees:
x + 40 = 180
x = 140 degrees.
Hence, the square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.
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a box containing 8 shock absorbers and 10 brake pad sets weighs 101.6 lb
Answer:
10.16 lb
Step-by-step explanation:
This is a classic example of a problem that can be solved using dimensional analysis. To find the weight of a single shock absorber or brake pad set, you need to divide the total weight by the number of items in the box.
Weight of a single shock absorber = Total weight of shock absorbers / Number of shock absorbers in the box
= 101.6 lb / 8
= 12.7 lb
Weight of a single brake pad set = Total weight of brake pad sets / Number of brake pad sets in the box
= 101.6 lb / 10
= 10.16 lb
Therefore, a single shock absorber weighs 12.7 lb and a single brake pad set weighs 10.16 lb.
write an equation to represent the number of points receieved by the winning team on one day of the competition. remember to define your variables
An equation representing the number of points received by the winning team on one day of the competition is P = winning team's points on one day.
Here is an equation to represent the number of points received by the winning team on one day of the competition:
Let's call the number of points received by the winning team on one day of the competition "P".
Then, the equation to represent this would be:
P = winning team's points on one day of the competition
Note: This equation is only a representation, and the actual calculation of the winning team's points would depend on various factors such as the rules of the competition, the performance of the players, etc.
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Please help me with this question.
If S = {a, b}, then S will be C. not an integral domain.
What is an integral domain?A nonzero commutative ring known as an integral domain is one in which the product of any two nonzero components is nonzero.
A nonzero commutative ring that belongs to an integral domain has nonzero elements that are all cancellable when multiplied. A ring that has a nonzero element set that is a commutative monoid under multiplication is known as an integral domain.
If S = {a, b}, then S is not an integral domain, as the product of a and b is undefined, and it is not a field because it does not have a multiplicative identity element. It is also not a commutative ring without unity, as it does not have an additive identity element.
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Of digoxin has a half life of 35hrs, how long will it take for a toxic plasma concentration of 8ng/ML to decline to a therapeutic plasma concentration of 2ng/ML?
70hrs, 5 hrs, 130hrs,180hrs ?
Digoxin has a half-life of 35 hours, so it takes 70 hours for the toxic plasma concentration to decline to a therapeutic plasma concentration of 2ng/ML.
What is digoxin?Digoxin has a half-life of 35 hours, which means it takes 35 hours for the quantity of digoxin in the body to be decreased by half. The dangerous plasma concentration of 8ng/ML must be decreased to a therapeutic plasma concentration of 2ng/ML in this circumstance.
To calculate how long this will take, we need to use the formula:
Time = (Toxic Concentration - Therapeutic Concentration) / (0.5 x Half-Life)
Time = (8ng/ML - 2ng/ML) / (0.5 x 35hrs)
Time = 6ng/ML / (17.5hrs)
Time = 0.342hrs
Time = 70hrs
As a result, the dangerous plasma concentration of 8ng/ML will take 70 hours to decrease to a therapeutic plasma concentration of 2ng/ML.
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PLEASE HELP!!!! A rectangle has sides measuring (3x + 5) units and (6x + 11) units.
Part A: What is the expression that represents the area of the rectangle?
The expression that represents the area of the rectangle is 18x² + 63x + 55.
What is the multiplication of polynomials?
Multiplying polynomials is a basic concept in algebra. Multiplication of two polynomials will include the product of coefficients to coefficients and variables to variables.
The area is just length times width:
(3x + 5)(6x + 11) = 18x² + 63x + 55
The degree of the expression is the highest power which is in 18x²
Above we multiplied 2 polynomials (3x + 5) and (6x + 11) and obtained another polynomial. This demonstrated the closure property of polynomials
Hence, the expression that represents the area of the rectangle is 18x² + 63x + 55.
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A survey asked people of different ages wether they get their news by reading the paper. what is the probability that a person surveyed is under 40 given that he or she gets the news by reading the paper if necessary, round .
The probability that a person surveyed gets the news by reading the paper, given that he or she is under 40 is 10%. The Option A is correct.
How do we arrive at 10% as our probability?We are given that number of people who read paper and under 40 is 4 and number of people who are under 40 is 40.
We need to find the probability that a person surveyed gets the news by reading the paper given that he or she is under 40.
We will use the "Conditional probability": P (Person that read the paper given that he or she is under 40) is given by:
= P(read the paper and under age 40) / P(person who are under age 40)
= 4 / 40
= 0.1
= 10%
Full questions"A survey asked people of different ages whether they get their news by reading the paper. What is the probability that a person surveyed gets the news by reading the paper, given that he or she is under 40? If necessary, round your answer to the nearest percent. A.10% B.14% C.5% D.90%
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Please help me with this question.
The solution to the initial value problem using the method of Laplace transforms is y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t
How to determine the initial value problemFrom the question, we have the following parameters that can be used in our computation:
y" - 3y' - lOy = 0, y(0) = 1, y'(0) = 12
Let L{y(t)} = Y(s),
Take the Laplace transform of both sides, we have:
s^2Y(s) - sy(0) - y'(0) - 3sY(s) + 3y(0) + 10Y(s) = 0
Using initial conditions y(0) = 1 and y'(0) = 12, we get:
s^2Y(s) - s - 12 - 3sY(s) + 3 + 10Y(s) = 0
Solving for Y(s), we have:
Y(s) = (s + 12)/(s^2 + 3s + 10)
Taking inverse Laplace transform of Y(s), we have:
y(t) = L^-1{Y(s)}
y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t
Hence, the solution is y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t
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Find the x-value at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.
f(x) =
1 + x2 if x ≤ 0
2 − x if 0 < x ≤ 2
(x − 2)2 if x > 2
x =
continuous from the right continuous from the left neither
On the basis of x-value at x = 0 function is left continuous and at x = 2 function is continuous from left and right both.
Function 'f' is continuous from the right, or from the left, or neither:
x = 0 (smaller value )
[tex]\lim_{x \to 0-} f(x)[/tex]
= [tex]\lim_{x \to 0-}[/tex] ( 1 + x² )
= 1+ 0
= 1
[tex]\lim_{x \to 0+} f(x)[/tex]
= [tex]\lim_{x \to 0+}[/tex] ( 2 - x)
= 2 - 0
= 2
[tex]\lim_{x \to 0} f(x)[/tex]
= f(0)
= 1 + 0²
= 1
[tex]\lim_{x \to 0-} f(x)[/tex] = f(0)
It is left continuous.
x = 2 (larger value )
[tex]\lim_{x \to 2-} f(x)[/tex]
= [tex]\lim_{x \to 2-}[/tex] ( 2 - x )
= 2 - 2
= 0
[tex]\lim_{x \to 2+} f(x)[/tex]
= [tex]\lim_{x \to 2+}[/tex] ( x - 2)²
= ( 2- 2)²
= 0
[tex]\lim_{x \to 2} f(x)[/tex]
= f(2)
= 2 - 2
= 0
[tex]\lim_{x \to 2-} f(x) = \lim_{x \to 2+} f(x)[/tex] = f(2)
It is continuous from both right and left.
Therefore, the function is continuous from left at x= 1 and x = 2 it is continuous from both left and right side.
The above question is incomplete ,the complete question is:
Find the x-value at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.
f(x) = 1 + x² if x ≤ 0
2 − x if 0 < x ≤ 2
(x − 2)² if x > 2
x = (smaller value)
continuous from the right, or continuous from the left, or neither
x = (larger value)
continuous from the right, or continuous from the left, or neither.
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consider an experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre. the yield is assumed to be between
The corresponding sample space is S = {x|150 ≤ x ≤ 150}.
An experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre.
The yield is assumed to be between 150 and 250 bushels.
A sample space is a collection of probable outcomes from a random event. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.
Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
Then the sample space should be
S = {x|150 ≤ x ≤ 150}
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The complete question is:
Consider an experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre. The yield is assumed to be between 150 and 250 bushels.
Determine the corresponding sample space.
A water tank already contains 55 gallons of water when Baxter begins to fill it.
Water flows into the tank at a rate of 8 gallons per minute. Write a linear equation to model this situation. Find the volume of water in the tank 25 minutes after Baxter begins filling the tank.
Answer: 55+ (8* M)
Step-by-step explanation: I think that's the answer
helpp !!!!! giving brainlest!!
Answer: x= 90
Step-by-step explanation:
expand (2x2^+3)(4x+5)-8x(x2^-2)
Answer: Expanding the expression:
(2x * 2^+3) * (4x + 5) - 8x * (x^2^-2)
Start with the first set of parentheses:
2x * 2^+3 = 2x * 8 = 16x
Next, the second set of parentheses:
16x * (4x + 5) = 16x * 4x + 16x * 5 = 64x^2 + 80x
Finally, the third set:
-8x * (x^2^-2) = -8x * x^2^-2 = -8x * (1/x^2) = -8/x
So the final expanded form is:
64x^2 + 72x - 8/x
Step-by-step explanation:
a bicycle with 20-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. the cyclist pedals at 190 rpm.
The linear speed of the bicycle is 20891.59 inches / min
The bike moving in 19.78 mph
As per the given data:
A bicycle with 20-in.-diameter wheels
Determine the speed that needs to be determined either angular or linear. Determine the given speed and radius.
Determining the linear speed is the task at hand. The indicated angular speed is 190 rpm.
To find the linear speed when the angular speed and the radius of the circular object are given, k revolutions per minute [tex]$ =\frac{k \text { revolutions }}{1 \text { minute }} \times \frac{2 \pi}{1 \text { revolution }} \\[/tex]
[tex]$=\frac{2 \pi k}{\text { minute }}[/tex]
For every cycle of the 7-inch sprocket, the 4-inch goes around
[tex]$\frac{7}{4}$[/tex] = 1.75 times.
Therefore 190 × 1.75+ π × 20 = 20891.59 inches / min
Therefore the linear speed of the bicycle is 20891.59 inches / min
Now, determine how fast the bike is moving in mph.
[tex]$\frac{20891.59}{12} \times \frac{60}{5280}$[/tex]
= 19.78 mph
Bike moving in 19.78 mph.
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A bicycle with 20-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. the cyclist pedals at 190 rpm.
Find the linear speed of the bicycle (correct to at least two decimal places) in/min
How fast is the bike moving in mph (to two decimal places)?
Pablo is solving the system of equations shown and says that the first step is to add the equations together to eliminate the y variables.
a. describe Pablo's error
b. What is a possible first step Pablo could take?
c. Find the solution to the system of equations?
3x + 4y =26
2x + 4 = 28 <<
Pablo's error was that he added the equations.
A possible first step is to subtract the equations.
The solution of the system is x = -2 and y = 8.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
We have s system of equations,
3x + 4y = 26 {equation 1}
2x + 4y = 28 {equation 2}
Pablo is solving the system of equations shown and says that the first step is to add the equations together to eliminate the y variables.
To eliminate the y-variable:
Subtract equation 2 to equation 1.
3x - 2x = 26 - 28
x = -2
Then y = 8.
Therefore, the solution of the system is x = -2 and y = 8.
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I really really need help understanding this geomtry packet.
Based on the definition of congruent triangles, the measures are:
4. m<R = 75°
5. XY = 6
6. m<X = 55°
7. m<S = 50°
What are Congruent Triangles?Congruent triangles are two triangles that have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal in measure.
Since triangles QRS are congruent to each other, therefore, their corresponding parts will be equal. Thus:
4. m<R = 180 - 55 - 50
m<R = 75°
5. XY = QR = 6
6. m<X = m<Q
m<X = 55°
7. m<S = m<Z
m<S = 50°
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The equation of the least-squares regression line for predicting icicle length, in centimeters, from time, in minutes, is
icicle length=-1.93 +0.173xtime
There are 2.54 centimeters in an inch. If length were measured in inches, what would the slope of the new regression line be?
Enter your answer to three decimal places.
The slope of the new regression line with length measured in inches would be 0.068 inches/minute.
Calculating slope of the new regression lineThe slope of the regression line for predicting icicle length, in centimeters, from time, in minutes, is 0.173 cm/minute.
To convert this to inches, we need to multiply the slope by the conversion factor from centimeters to inches, which is 2.54 cm/inch:
0.173 cm/minute x (1 inch/2.54 cm) = 0.068 inches/minute
So, the slope of the new regression line with length measured in inches would be 0.068 inches/minute.
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Recall the definition of covariance for two random variables, X and W: Cov(X,W) =
E(X − E(X))(W − E(W)).
Prove or disprove
Cov(aX + b, cW) = ac Cov(X,W)
where a, b, and c are constants. Start with applying the covariance definition to Cov(aX +
b, cW), proceed by applying appropriate properties of expectation operator, and see if your
simplified expression is the same as ac Cov(X,W).
Answer:
The statement Cov(aX + b, cW) = ac Cov(X,W) is true.
Step-by-step explanation:
Starting with the definition of covariance:
Cov(aX + b, cW) = E((aX + b) - E(aX + b))(cW - E(cW))
Using linearity of expectation:
Cov(aX + b, cW) = E(a(X - E(X)) + (b - E(b)))(c(W - E(W)))
Expanding and rearranging the product:
Cov(aX + b, cW) = acE(X - E(X))(W - E(W)) + E(b - E(b))E(c(W - E(W)))
Since the expectation of a constant is the constant itself and E(b - E(b)) = 0, the above expression simplifies to:
Cov(aX + b, cW) = ac Cov(X,W)
can someone help me whit this factor[tex](\frac{2x}{7}- \frac{1}{4})^{2}[/tex]
The simplified expression (2x/7 - 1/4)² is given as follows:
(2x/7 - 1/4)² = 4x²/49 - x/7 + 1/16.
How to simplify the expression?The expression for this problem is defined as follows:
(2x/7 - 1/4)².
The square of a subtracted binomial notable product is given as follows:
(a - b)² = a² - 2ab + b².
The parameters for this problem are given as follows:
a = 2x/7.b = 1/4.Hence the terms of the expression are given as follows:
a² = (2x/7)² = 4x²/49.2ab = 2 x 2x/7 x 1/4 = x/7.b² = (1/4)² = 1/16.Hence the simplified expression is defined as follows:
(2x/7 - 1/4)² = 4x²/49 - x/7 + 1/16.
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HELP !!!!!!!! Jahaksgshshshshshsgshhaehhehee
On using the formula for compound interest the amount of time it will take until the account of Gracie has a balance of $0 is 4 years.
What is Compound Interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
The initial deposit made by Gracie is P = $30,000
The rate at which the interest is earned r = 3.1% = 3.1/100 = 0.031
The withdrawal amount is W = $150
The number of times interest is compounded n = 52 weeks
The formula for compound interest becomes -
P = W[1 - {1 + (r/n)}^(-nt)] / (r/n)
Substitute the values into the equation -
30000 = 150[1 - {1 + (0.031/52)}^(-52)t] / (0.031/52)
Divide both sides with 150 and simplify -
200 = [1 - ({1 + 0.00059}^(-52)t)]/0.00059
200 = [1 - (1.00059)^(-52)t)]/0.00059
Multiply both sides with 0.00059 -
0.118 = 1 - (1.00059)^(-52)t
(1.00059)^(-52)t = 1 - 0.118
(1.00059)^(-52)t = 0.882
Using one to one property, and power property -
-52t log 1.00059 = log 0.882
t = (log 0.882/log 1.00059) / -52
t = (-0.0545/0.000256) / -52
t = -212.890625/ -52
t = 4.09 ≈ 4
Therefore, the time value is obtained as 4 years.
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A program began at 6:30 P.M. and ended at 7:00 P.M. There were two 4.5-minute commercial breaks. How long was the program itself?
Answer:
The total length of the commercial breaks is 4.5 minutes x 2 = 9 minutes.
So the length of the program itself is 7:00 P.M. - 6:30 P.M. - 9 minutes = 30 minutes - 9 minutes = 21 minutes.
Answer:
21 minutes
Step-by-step explanation:
30-9-21 minutes of program
Please help with this:(
Answer:
Step-by-step explanation:
a.0.002
Modeling with Composite Functions
A store is offering a 10% discount on all items. In addition, employees get a 25% discount.
a. Write a composite function to model taking the 10% discount.
b. Write a composite function to model taking the 25% discount first.
c. If you were an employee, which would you prefer or does it matter?
a. A function to model taking the 10% discount will be 0.9x.
b. A function to model taking the 25% discount first will be 0.75x.
c. If I was an employee, I'll prefer the 25% discount.
How to illustrate the functionFrom the information given, the store is offering a 10% discount on all items and in addition, employees get a 25% discount.
Let the price of the goods be given as x.
A function to model taking the 10% discount will be:
= x - (10% × x)
= x - 0.1x
= 0.9x
A function to model taking the 25% discount first will be:
x - (25% × x)
= x - 0.25x
= 0.75x
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Let the random variables x and y have joint pdf as follows: f(x,y) = 1/5(11x^2 + 4y^2), 0 < x < 1,0 < y < 1 Find Cov(x,y) (round off to third decimal place). Find E(Y) (round off to third decimal place).Find E(XY) (write up to third decimal place).
Let the random variables x and y have joint pdf as follows: f(x,y) = 1/5(11x^2 + 4y^2) so Cov(x,y) (round off to third decimal place) is 0.241.
The covariance formula in statistics is used to evaluate the relationship between two variables. In essence, it serves as a gauge for the variation between two variables. Covariance is calculated by multiplying the units of the two variables, and it is expressed in units. Any positive or negative value might be the variance.
E[(X−EX)(Y−EY)]
=E[XY−X(EY)−(EX)Y+(EX)(EY)]
=E[XY]−(EX)(EY)−(EX)(EY)+(EX)(EY)
=E[XY]−(EX)(EY).
E(Y) = ∫ 1/x dx = ∫ 11/5 = ln 11/5 = 0.788
E(XY) = E[X 1/X]= 1
It is feasible to get the correlation coefficient formula from the covariance using the aforementioned formula, and vice versa. Units of covariance are calculated by multiplying the units of the two provided variables.
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Use the data on the table to determine the solution
Answer:
Step-by-step explanation:
21.7 IS ALSO EQUAL TO 50% . SO IT WOULD BE =20
