If today is August 4th, 2010, and your company uses the First-In-First-Out (FIFO) method for inventory management, the inventory purchased on June 15th, 2010, should be sold first. Option B.
FIFO follows the principle that the goods or inventory purchased first should be sold or used first. It means that the oldest inventory in stock should be sold before the more recently acquired inventory.
Comparing the given dates:
A. July 15th, 2010 - This inventory was purchased after June 15th, 2010, so it is more recent than the June 15th inventory. Therefore, it would not be sold first under the FIFO method.
B. June 15th, 2010 - This inventory was purchased first and is the oldest among the given options. According to FIFO, it should be sold first.
C. July 30th, 2010 - This inventory was purchased after June 15th, 2010, so it is more recent. Therefore, it would not be sold first under the FIFO method.
D. June 30th, 2010 - This inventory was purchased after June 15th, 2010, but before July 15th, 2010. However, since it is still more recent than the June 15th inventory, it would not be sold first under FIFO.
Therefore, based on the FIFO method, the inventory purchased on June 15th, 2010, should be sold first, followed by the subsequent inventory purchases in chronological order. So Option B is correct.
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What is the slope of (1,3/4) and (4,-3)
Answer:
=-0.75
Step-by-step explanation:
S=y2_y1/x2_x1
Where x1=1
Y1=3/4
X2=4
Y2=-3
Draw a rhombus with diagonals 4 and 6. What is the area of the rhombus?
first of all you have to draw a rhombus
area (d+d)/2
(4+6)/2
5
Re-write the following system of equations in matrix format and solve them by using Cramer's rule. z+5x= 24 3x+2z+3y=7 -x+2y=-9
The solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
The given system of equations is given as,z + 5x = 243x + 2z + 3y = 7-x + 2y = -9
To solve the given system of equations by using the Cramer's rule, we have to first represent the given system in matrix format.
Matrix format: ⎡1 0 5⎤ ⎡x⎤ ⎡24⎤ ⎢0 3 2⎥ ⎢y⎥=⎢7⎥ ⎣-1 2 0⎦ ⎣z⎦ ⎣-9⎦
Using the formula for Cramer's rule, we know that,
x = Dx / D, y = Dy / D, z = Dz / D, whereD is the determinant of the coefficient matrix, Dx is the determinant of the matrix obtained by replacing the x column with the constant matrix, Dy is the determinant of the matrix obtained by replacing the y column with the constant matrix, and Dz is the determinant of the matrix obtained by replacing the z column with the constant matrix.
Calculation of D: D = | A | = ⎡1 0 5⎤ ⎡0 3 2⎥ ⎣-1 2 0⎦
Applying the Laplace expansion along the first column, D = 1 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦| D = 6 Calculation of Dx: Dx = ⎡24 0 5⎤ ⎡3 2⎤ ⎢7 3 2⎥ ⎢-1 2⎥ ⎣-9 2 0⎦ ⎣2 0⎦
Applying the Laplace expansion along the first column, Dx = 24 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-9 2⎤| |⎣3 2⎦| |⎣3 2⎦| |⎣3 2⎦|
Dx = -18
Calculation of Dy: Dy = ⎡1 24 5⎤ ⎡0 2 2⎤ ⎢0 7 2⎥ ⎢-1 -1 0⎥ ⎣-1 -9 0⎦ ⎣2 0 0⎦
Applying the Laplace expansion along the second column, Dy = 0 |⎡1 5⎤| - 24 |⎡0 2⎤| + 5 |⎡0 2⎤| |⎣-1 0⎦| |⎣-1 0⎦| |⎣-1 0⎦|
Dy = 10
Calculation of Dz: Dz = ⎡1 0 24⎤ ⎡0 3 2⎥ ⎢0 3 7⎥ ⎢-1 2 -1⎥ ⎣-1 2 -9⎦ ⎣3 2 0⎦
Applying the Laplace expansion along the third column,
Dz = 24 |⎡3 2⎤| - 10 |⎡-1 2⎤| + 0 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦|
Dz = -24
Now we have the values of D, Dx, Dy and Dz.
Therefore, x = Dx / D, y = Dy / D, z = Dz / D,x = -18/6 = -3 y = 10/6 = 5/3 z = -24/6 = -4
Hence, the value of x, y, and z is (-3, 5/3, -4) respectively.
Therefore, the solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
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You randomly choose a number from thee set, replace it and then randomly choose another number.what is the probability of choosing a 2 first and a 3 second
Answer:
The probability of choosing a 2 first and a 3 second is 1/9
.
P(2 1st and 3 2nd) = P(2 1st ) * P(3 2nd)
= 1/3 * 1/3
= 1/9
.
What is the surface area of the three-dimensional figure formed by the net shown?
Answer:
336 cm²
Step-by-step explanation:
1 rectangle 24 cm by 12 cm
1 triangle with base 12 cm and height 8 cm (combining the two small triangles into 1 larger triangle)
SA = 24 cm * 12 cm + 12 cm * 8 cm / 2
SA = 288 cm² + 48 cm²
SA = 336 cm²
A population has parameters μ = 56.7 and σ = 75.9. You intend to draw a random sample of size n = 246. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
The mean of the distribution of sample means is 56.7, and the standard deviation of the distribution of sample means is approximately equal to 4.82.
To calculate the mean of the distribution of sample means, we use the fact that the mean of a sample is an unbiased estimate of the population mean, and therefore the mean of the distribution of sample means is equal to the population mean. Thus, the mean of the distribution of sample means is 56.7.
To calculate the standard deviation of the distribution of sample means, we use the formula for the standard error of the mean, which is the population standard deviation divided by the square root of the sample size. Thus, the standard deviation of the distribution of sample means is equal to 75.9 divided by the square root of 246, which is approximately equal to 4.83.
Therefore, the mean of the distribution of sample means is 56.7, and the standard deviation of the distribution of sample means is approximately 4.83
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Find X to this problem.
Point C is tangent to the circle and will be a right angle which is 90 degrees.
The three inside angles of a triangle need to equal 180.
X = 180-90-64 = 26
X = 26 degrees
The average of 5 numbers in a list is 35, and the average of the first two numbers is 26. What is the average of the last 3 numbers?
PLEASE HELP id appreciate help ASAP :)
The average of 5 numbers in a list is 35, and the average of the first two numbers is 26, then the average of the last 3 numbers is 41.
What is the average?
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words, it is the sum divided by the count.
Given that the average of 5 numbers is 35, their sum is = 5 * 35 = 175
Given that the average of the first two numbers is 26, their sum is 2 * 26 = 52.
So, the remaining two numbers add up to 175 - 52 = 123 and their average is = 123/3 = 41.
Therefore, the average of the last 3 numbers is 41.
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Errrrrrrrrrrrrrrrrr
Answer:
st and wx
Step-by-step explanation:
bc they are on oppostite sides
On a coordinate plane, triangle K J L is shown. Line segment G H goes from side J K to J L. Point K is at (0, 0), point G is at (e, f), point J is at (2 e, 2 f), point H is at (e + d, f), and point L is at (2 d, 0).
To prove part of the triangle midsegment theorem using the diagram, which statement must be shown?
The length of JK equals the length of JL.
The length of GH is half the length of KL.
The slope of JK equals the slope of JL.
The slope of GH is half the slope of KL.
Based on the triangle midpoint theorem, the statement which must be shown is that: B. the length of GH is half the length of KL.
What is triangle midpoint theorem?Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.
Based on the triangle midpoint theorem, we can infer and logically deduce that the statement which must be shown is that the length of GH is half the length of KL.
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Answer: B. The length of GH is half the length of KL.
Step-by-step explanation: TRUST ME! The answer is correct on Edge. :)
find the area of a circle with a diameter of 4 ft ( Take pi = 3.14 ) round your solution to two decimal places. pls and Hurryyyyy!!!!
Step-by-step explanation:
pi x r^2
3.14 x (2×2) = 12.56
Answer:
area of circle=πr^2= 3.14*4ft=12.56ft
in july of 2013, australians were asked if they thought unemployment would increase, and 47% thought that it would increase. in november of 2013, they were asked again. at that time 338 out of 800 said that they thought unemployment would increase. at the 8% level, is there enough evidence to show that the proportion of australians in november 2013 who believe unemployment would increase is lower than the proportion who felt it would increase in july 2013?
Since the p-value is less than the significance level of 0.08, we reject the null hypothesis and conclude that there is enough evidence to show that the proportion of Australians in November 2013 who believe unemployment would increase is lower than the proportion who felt it would increase in July 2013 at the 8% level of significance.
To determine if there is enough evidence to show that the proportion of Australians in November 2013 who believe unemployment would increase is lower than the proportion who felt it would increase in July 2013, we need to perform a hypothesis test.
Let p1 be the proportion who thought unemployment would increase in July 2013 and p2 be the proportion who thought unemployment would increase in November 2013.
The null hypothesis is that there is no difference between the two proportions: p1 = p2. The alternative hypothesis is that the proportion in November 2013 is lower than the proportion in July 2013: p2 < p1.
We can use a two-sample z-test to test this hypothesis, since we have two independent samples and the sample sizes are large enough.
The test statistic is calculated as:
z = (p1 - p2) / √(p * (1 - p) * (1/n1 + 1/n2))
where p = (x1 + x2) / (n1 + n2) is the pooled proportion, x1 and x2 are the number of people who thought unemployment would increase in July 2013 and November 2013, respectively, and n1 and n2 are the sample sizes.
Using the given data, we have:
p1 = 0.47
p2 = 338/800 = 0.4225
n1 = n2 = 800
p = (8000.47 + 8000.4225) / (800 + 800) = 0.44625
z = (0.47 - 0.4225) / √(0.44625 * (1 - 0.44625) * (1/800 + 1/800))
= 3.373
Using a standard normal distribution table or calculator, we find that the p-value for a one-tailed test with a z-score of 3.373 is less than 0.01.
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Solve the homogeneous recursive relation with constant coefficients of the following two. ao = 1 a1 == -2 a2 = -1 an= -3an-1-3an-2-an-3
The specific solution to the homogeneous recursive relation with the given initial conditions is: an = c1(r1)^n + c2(r2)^n + c3(r3)^n
To solve the homogeneous recursive relation:
an = -3an-1 - 3an-2 - an-3
We first need to find the characteristic equation by assuming a solution of the form:
an = r^n
Substituting this into the recursive relation gives:
r^n = -3r^(n-1) - 3r^(n-2) - r^(n-3)
Dividing both sides by r^(n-3) gives:
r^3 = -3r^2 - 3r - 1
This is the characteristic equation. To solve for the roots, we can use numerical methods or factoring. Factoring this cubic equation is not trivial, so we will use numerical methods.
Using a numerical solver, we find that the roots of the characteristic equation are approximately:
r1 = -0.5457
r2 = -1.8475 + 0.5088i
r3 = -1.8475 - 0.5088i
Therefore, the general solution to the homogeneous recursive relation is:
an = c1(r1)^n + c2(r2)^n + c3(r3)^n
where c1, c2, and c3 are constants determined by the initial conditions.
To find these constants, we use the given initial conditions a0 = 1, a1 = -2, and a2 = -1:
a0 = c1(r1)^0 + c2(r2)^0 + c3(r3)^0 = c1 + c2 + c3
a1 = c1(r1)^1 + c2(r2)^1 + c3(r3)^1 = c1(r1) + c2(r2) + c3(r3)
a2 = c1(r1)^2 + c2(r2)^2 + c3(r3)^2 = c1(r1)^2 + c2(r2)^2 + c3(r3)^2
We can write this system of equations in matrix form:
[ 1 1 1 ][ c1 ] [ a0 ]
[ r1 r2 r3][ c2 ] = [ a1 ]
[r1^2 r2^2 r3^2][ c3 ] [ a2 ]
Using Gaussian elimination or a similar method, we can solve for the constants c1, c2, and c3. The solution is:
c1 = (a0 - a1r2/(r2-r1) - a2(r3+r2)/(r3-r1))/(r1^2 - r2r1 - r3r1 + r2*r3)
c2 = (a0 - a1 - c1)/(r1-r2)
c3 = a0 - c1 - c2
Therefore, the specific solution to the homogeneous recursive relation with the given initial conditions is:
an = c1(r1)^n + c2(r2)^n + c3(r3)^n
where c1, c2, and c3 are determined by the above formulas.
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HELP ASAP
Ben travels by train 19 miles to work if ben travels 8 times a week how many miles does he travel
Answer: 152 miles
Step-by-step explanation:
19 x 8 = 152
You have created a 95% confidence interval for μ with the result 10≤ μ ≤15. What decision will you make if you test H0: μ =16 versus H1: μ s≠16 at α s=0.05?
based on the confidence interval and the hypothesis test, there is evidence to support the alternative hypothesis that μ is not equal to 16.
In hypothesis testing, the significance level (α) is the probability of rejecting the null hypothesis when it is actually true. In this case, the significance level is 0.05, which means that you are willing to accept a 5% chance of making a Type I error, which is rejecting the null hypothesis when it is true.
Since the 95% confidence interval for μ does not include the value of 16, and the null hypothesis assumes μ = 16, we can conclude that the null hypothesis is unlikely to be true. The confidence interval suggests that the true value of μ is between 10 and 15, which does not overlap with the value of 16. Therefore, we have evidence to reject the null hypothesis and accept the alternative hypothesis that μ is not equal to 16.
In conclusion, based on the 95% confidence interval and the hypothesis test, we would reject the null hypothesis H0: μ = 16 and conclude that there is evidence to support the alternative hypothesis H1: μ ≠ 16.
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what is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters? Write Your Answer In Terms Of pi.
Given the word problem, we can deduce the following information:
1. The diameter of the circle is 3 meters.
2. The side length of the square is 3 meters.
To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:
\(A_{circle}=\frac{\pi d^2}{4}\)where:
d=diameter
\(\text{A}_{square}=d^2\)where:
d=side length
The figures are shown below:
Based on this, the difference of areas would be:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ \end{gathered}\)Next, we plug in d=3:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ =(3)^2-\frac{\pi(3)^2}{4} \\ =9-\frac{9\pi}{4} \end{gathered}\)Therefore, the difference in areas is:
\(9-\frac{9\pi}{4}\)Write the equation of a line having slope 2 and y-intercept 6.
Answer:
Y= 2x + 6
Step-by-step explanation:
So, at first it would be y= mx + b
But now you need to fill it in with the numbers the y-intercept will replace B and 2 will replace m.
The circumference of a circular field is 166.42 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
Answer:
52.98
Step-by-step explanation:
See attached image to find radius
diamater = Radius * 2
26.49 Yards * 2 = 52.98
Volume of a cone rh, curved surface area of a cone = xr!] [Volume of a spheresurface area of a sphere 4ar']
The solid is formed from a hemisphere of radius rcm fixed to a cone of radius rcm and height hem. The volume of the hemisphere is one third of the volume of the solid.
(a) Find h in terms of r
(b) The slant height of the cone can be written as Vk cm, where k is an integer.
Find the value of k
(c) Find an expressionin terms of r and x, for the total surface area, in cm², of the solid
Answer:
Long solution
Step-by-step explanation:
(a) Let the height of the cone be h cm. The volume of the hemisphere is given by (1/2)(4/3)πr³ = (2/3)πr³. The volume of the solid is the sum of the volumes of the hemisphere and the cone, which is (2/3)πr³ + (1/3)πr²h. Since the volume of the hemisphere is one third of the volume of the solid, we have:
(2/3)πr³ = (1/3)πr²h
Simplifying, we get:
2r = h
Therefore, h is expressed in terms of r as h = 2r.
(b) The slant height of the cone can be found using the Pythagorean theorem. Let l be the slant height, then we have:
l² = r² + h²
Substituting h = 2r, we get:
l² = r² + (2r)² = 5r²
Taking the square root of both sides, we get:
l = r√5
Since k is an integer, we can write:
l = Vk cm, where k is an integer
Comparing the two expressions, we get:
Vk = r√5
Therefore, the value of k is k = ⌊r√5⌋, where ⌊x⌋ denotes the largest integer less than or equal to x.
(c) The total surface area of the solid is the sum of the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone. We have:
Curved surface area of the cone = πr l = πr(r√5) = πr²√5
Curved surface area of the hemisphere = 2πr²
Area of the circular base of the cone = πr²
Therefore, the total surface area of the solid, in cm², is given by:
πr²√5 + 2πr² + πr² = (πr²)(√5 + 3)
In Chapter, we examined a picture of winning time in men’s 500meter speed skating plotted across time. The data represented in the plot started in 1924 and went through 2010. A regression equation relating winning time and year for 1924 to 2006 iswinning time = 273.06 - (0.11865)(year)a. Would the correlation between winning time and year be positive or negative? Explain.b. In 2010, the actual winning time for the gold medal was 34.91 seconds. Use the regression equation to predict the winning time for 2010, and compare the prediction to what actually happened. Was the actual winning time higher or lower than the predicted time?c. Explain what the slope of -0.11865 indicates in terms of how winning times change from year to year.
a. The correlation between winning time and year would be negative because the regression equation has a negative slope (-0.11865).The slope of -0.11865, actual winning time in 2010 was 34.91 seconds.
b. Using the regression equation, we can predict the winning time for 2010 as follows:
winning time = \(273.06 - (0.11865)(2010)\)
winning time = \(273.06 - 239.2465\)
winning time = \(33.8135 seconds\)
The actual winning time in 2010 was 34.91 seconds, which is higher than the predicted time.
c. The slope of -0.11865 indicates that winning times decrease by an average of 0.11865 seconds per year. In other words, for each year that passes, the winning time decreases by approximately 0.12 seconds on average. This suggests that athletes are improving and getting faster over time, which is a common trend in many sports.
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Plz help me plz
I will give brainliest
Answer:
3 i think
Step-by-step explanation:
I divided 1/8 and four
Answer: 24/192. She would replace the water with 8 cups of salt
Step-by-step explanation:
write a fraction to show the value of each 9 in the decimal 0.999. how is the value of the 9 on the left related to the value of the 9 on the right? how is the value of the 9 on the rigth related to the value of the 9in the middle?
The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.
How to write decimal number in fractionTo write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method
The digit 9 in the tenths place represents 9/10 or 0.9.
The digit 9 in the hundredths place represents 9/100 or 0.09.
The digit 9 in the thousandths place represents 9/1000 or 0.009.
Thus, the fractions are
0.9 = 9/10
0.09 = 9/100
0.009 = 9/1000
The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.
The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.
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An airplane manufacturer intends to establish a component acceptance criterion that is based upon sound statistical methods. Preliminary tests on 61 acceptable components have determined that the mean load to psi. Based upon this information, provide (a) an estimate, with 99% confidence, of the value of the next (the 62nd) measured load to produce failure, (b) an estimate, with 99% confidence, of the true mean load to variance, Finally, the manufacturer wants to be 99% confidence, of the true if the batch sample meets the acceptance criterion. (d) Determine the range of sample standard deviation values (in psi) that the batch sample can have and still meet the test criterion.
(a) Estimate next load to failure using 99% confidence interval for mean load. (b) Estimate true mean load to variance with 99% confidence interval.(c) Check if batch meets acceptance criterion by comparing estimated mean load to criterion.
The estimate of the value of the next measured load to produce failure can be obtained by calculating the confidence interval for the mean load based on the sample data. With a 99% confidence level, we can use the t-distribution and the sample mean load of the acceptable components to estimate the next measured load.
To estimate the true mean load to variance, we can use the sample mean load and the sample variance of the acceptable components. With a 99% confidence level, we can construct a confidence interval for the true mean load to variance.
To determine if the batch sample meets the acceptance criterion, we need to compare the estimated true mean load to a specified criterion value. If the estimated true mean load falls within the confidence interval, we can be 99% confident that the batch sample meets the acceptance criterion.
The range of sample standard deviation values can be determined based on the acceptance criterion. If the batch sample meets the criterion, the sample standard deviation must be within a certain range. This range can be determined by considering the confidence interval for the sample standard deviation.
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A hot liquid is placed in a refrigerator to quickly cool down. The temperature of the liquid can be modeled with the exponential function T=a(b)^m where m is the number of minutes it has been cooling. Based on the graph below, which of the following is closest to the value b for this model?
1) b=0.65
2)b=0.84
3)b=1.28
4)b=2.17
Answer:
This is 3
Step-by-step explanation:
Safie can write a minimum of five questions per hour and a maximum of eleven questions per hour. What is the difference betwwen the last possible amount of hours and the greatest possible amount of hours Safie will need to write 275 questions?
A. 6
B. 16
C. 30
D. 800
Answer:
The difference is 30 hours
Step-by-step explanation:
Proportions
Safie can write a minimum of 5 questions per hour and a maximum of 11 questions per hour.
To write 275 she takes a maximum of 275/5=55 hours and a minimum of 275/11=25 hours.
The difference is 55 hours - 25 hours = 30 hours
How much is $1000 soles in dollars?
$1000 Soles would be equivalent to roughly $246.31 US dollars (1000 / 4.06 = 246.31).
The conversion rate may vary based on the time you are making the conversion because the value of the US dollar (USD) and the Peruvian sol (PEN) fluctuate over time. Around one US dollar is worth 4.06 soles as of February 20, 2023.
With this rate of exchange, $1000 Soles would be equivalent to roughly $246.31 US dollars (1000 / 4.06 = 246.31). Please be aware that this is a rough estimate and that the real exchange rate may vary depending on the conversion's particular conditions. The conversion rate may vary based on the time you are making the conversion because the value of the US dollar (USD) and the Peruvian sol (PEN) fluctuate over time. Around one US dollar is worth 4.06 soles as of February 20, 2023.
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The amplitude of the graphs of the sine and cosine functions is.
The amplitude of the graphs of the sine and cosine functions is the maximum value of the function.
In trigonometry, the amplitude of a sine or cosine function determines the maximum distance between the graph of the function and its central axis (usually the x-axis). It represents the magnitude of oscillation or the maximum displacement from the equilibrium position. The amplitude is always positive and can be identified by looking at the highest and lowest points of the graph. For both the sine and cosine functions, the amplitude is equal to the absolute value of the coefficient of the trigonometric term. For example, in the function y = Asin(x), the amplitude is A, and in the function y = Bcos(x), the amplitude is B. The larger the amplitude, the more stretched or compressed the graph becomes vertically.
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What is the amplitude of the graphs of the sine and cosine functions?
Danita and Juanita share $4500 in the ratio 2: 3. How much does Danita get and How much does Juanita get?
Answer: Danita gets 2×900 = 1800 and Juanita gets 2700
Step-by-step explanation: add ratios together. You get 2+3 = 5
Divide 4500 by 5 you get 900. Multiplying this by 2 and 3
sinx + cos2x + sin3x + 1 =0
Step-by-step explanation:
This is true statement.
have a great day
*what is the reward-to-variability (i.e., sharpe) ratio of the best feasible cal? group of answer choices .4221 .4511 .7639 .4315
The reward-to-variability ratio of the best feasible is 0.4221 that is option a.
The proportion of stocks invested in the optimal risky portfolio can be calculated with the use of following formula:
Portfolio Invested in the Stock = [(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 - (Expected Return of the Bond - Risk Free Rate)*Covariance between Bond and Stock]/[(Expected Return of the Stock - Risk Free Rate)*(Standard Deviation of Bond)^2 + (Expected Return of the Bond - Risk Free Rate)*(Standard Deviation of Stock)^2 - (Expected Return of Stock - Risk Free Rate + Expected Return of Bond - Risk Free Rate)]*Covariance between Bond and Stock
Portfolio Invested in Bond = 1 - Portfolio Invested in the Stock
Here, Risk Free Rate = 4 and Covariance = 32*24*.1250 = 96
Using these values and other information provided in the question, we get,
Portfolio Invested in the Stock = [(10 - 4)*(24)^2 - (7 - 4)*96]/(10 - 4)*(24)^2 + (7 - 4)*(32)^2 - [(10 - 4 + 7 - 4)]*96 = .5593
Portfolio Invested in Bond = 1-.5593 = .4407
Step 2: Calculate Expected Return and Standard Deviation of the Optimal Risky Portfolio
Expected Return = Portfolio Invested in Stock*Expected Return of Stock Portfolio Invested in Bond*Expected Return of Bond = .5593*10% + .4407*7% = 8.68%
Standard Deviation = [(Portfolio Invested in Stock)^2*(Standard Deviation of Stock)^2 + (Portfolio Invested in Bond)^2*(Standard Deviation of Bond)^2 + 2*(Portfolio Invested in Stock)*(Portfolio Invested in Bond)]^(1/2) = [(.5593)^2*(32)^2 + (.4407)^2*(24)^2 + 2*(.5593)*(.4407)*(96)]^(1/2) = 21.90%
Step 3: Calculate Reward-to-Volatility Ratio
The reward-to-volatility ratio can be calculated with the use of following formula:
Reward-to-Volatility Ratio = (Expected Return of the Portfolio - Risk Free Rate)/Standard Deviation of Portfolio = (8.68 - 4)/21.90 = .4221
To learn more about standard deviation check the link below:
https://brainly.com/question/475676
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