Answer:
Correct option is E. As the number of class absences increases, the final exam score tends to decrease.
Step-by-step explanation:
Based on the information given, we can conclude that option E is the most appropriate:
E. As the number of class absences increases, the final exam score tends to decrease.
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is -0.65.
A negative correlation coefficient indicates an inverse relationship between the variables.
Since the correlation coefficient is negative (-0.65), we can conclude that as the number of class absences increases, the final exam score tends to decrease.
However, it is important to note that the correlation coefficient does not provide information about causation or the exact magnitude of the effect.
Therefore, we cannot infer the exact amount by which the final exam score decreases with each additional absence (option A).
To know more about correlation coefficient refer here:
https://brainly.com/question/31958579
#SPJ11
Brad paid for a book that costs 13.40 with a $20 bill What is the least combination of coins and bills that can be used to make his change What are two other different combinations of coins and bills that can be used to make the change
The least combination of coins and bills that can be used to make the change of $6.60 is:
1 x $5 bill
1 x $1 bill
1 x 50-cent coin
1 x 10-cent coin
How to find the changeTo find the least combination of coins and bills that can be used to make the change, we need to subtract the cost of the book from the amount paid and determine the fewest number of bills and coins required.
Change = Amount paid - Cost of the book
Change = $20 - $13.40
Change = $6.60
To determine the least combination of coins and bills, we can start with the largest denominations and work our way down:
$5 bill
$1 bill
50-cent coin
10-cent coin
Using this approach, the least combination of coins and bills that can be used to make the change of $6.60 is:
1 x $5 bill
1 x $1 bill
1 x 50-cent coin
1 x 10-cent coin
Learn more about least combination of coins at
https://brainly.com/question/1210440
#SPJ1
Joe reaches into a gym bag for a pair of running shoes. If there are five different pairs of running shoes in the gym bag, how many ways can he choose two shoes that do not match (one after another)? Explain your method in a paragraph of English.
The final number of ways for Joe to choose two shoes that do not match is 40.
To determine the number of ways Joe can choose two shoes that do not match, we can use the concept of combinations. Since there are five different pairs of shoes, we have a total of 10 individual shoes in the gym bag. When Joe chooses the first shoe, he has 10 options. For the second shoe, he cannot choose the matching shoe from the first pair, so he has 8 options remaining.
The number of ways to choose two shoes that do not match can be calculated by multiplying the number of choices for the first shoe (10) by the number of choices for the second shoe (8). Therefore, the total number of ways is 10 * 8 = 80. However, we need to consider that the order of choosing the shoes does not matter, so we divide the total number of ways by 2 (since we counted each pair twice, once for the first shoe and once for the second shoe).
Thus, Joe has a total of 80 / 2 = 40 methods to select two pairs of unrelated shoes.
Learn more about combinations here:
https://brainly.com/question/29595163
#SPJ11
Use the method series solution to solve the following. - (a) (x² +1)y" (x) + xy'(x) − y(x) = 0. (b) x²y" (x) + xy' (x) + x² y(x) = 0.
The general solution to the differential equation (x² + 1)y''(x) + xy'(x) - y(x) = 0 using the method of series solution is y(x) = c₁ + c₂x - [tex]\frac{c_1x^3}{3}![/tex] - [tex]\frac{c_2x^4}{4}![/tex] + ..
To solve the differential equation (x² + 1)y''(x) + xy'(x) - y(x) = 0 using the method of series solution, we can assume a power series representation for the solution:
y(x) = Σ(aₙxⁿ)
where aₙ represents the coefficients of the power series.
Calculate the first and second derivatives of y(x):
y'(x) = Σ(naₙxⁿ⁻¹)
y''(x) = Σ(n(n-1)aₙxⁿ⁻²)
Substitute the series representation and its derivatives into the differential equation:
(x² + 1)Σ(n(n-1)aₙxⁿ⁻²) + xΣ(naₙxⁿ⁻¹) - Σ(aₙxⁿ) = 0
Simplify the equation and group terms by powers of x:
Σ((n(n-1)aₙxⁿ) + Σ((naₙxⁿ) + Σ(aₙxⁿ)) + Σ(aₙxⁿ) = 0
Equate the coefficients of each power of x to zero:
n(n-1)aₙ + naₙ - aₙ = 0
Simplifying the equation further, we have:
n(n-1)aₙ + naₙ - aₙ = 0
n(n-1) + n - 1 = 0
n² - 1 = 0
(n-1)(n+1) = 0
This gives us two possible values for n: n = 1 and n = -1.
Determine the recurrence relation for the coefficients:
For n = 1:
a₂ = 0
a₃ = 0
...
For n = -1:
a₀ = arbitrary constant (denoted as c₁)
a₁ = arbitrary constant (denoted as c₂)
a₃ = 0
a₄ = 0
...
Write the general solution by combining the terms:
y(x) = c₁ + c₂x - [tex]\frac{c_1x^3}{3}![/tex] - [tex]\frac{c_2x^4}{4}![/tex] + ..
To know more about power series, click here:
https://brainly.com/question/29896893
#SPJ11
(a) .2 Find the area of the region bounded by the curves y = x² (x ≥ 0), y = ½-½x² the line y = 2. (x ≥ 0) and [13 marks]
We need to find the area of the region which is bounded by the curves y = x² (x ≥ 0), y = ½ - ½x², the line y = 2 (x ≥ 0).For x ≥ 0, the curves y = x² and y = ½ - ½x² intersect when x² = ½ - ½x², so 3x² = 1, i.e. x = [math]\frac{1}{\sqrt{3}}[/math].
At this point, y = [math]\frac{1}{2}[/math] and so, the curve y = x² lies below the curve y = ½ - ½x² in the interval [0, [math]\frac{1}{\sqrt{3}}[/math]] and above y = 2 from 0 to some point a, where y = 2 and y = x² intersect. This gives a = [math]\sqrt{2}[/math].Now, we can find the required area as follows:
Area[tex][math][tex]= \int_0^{1/\sqrt3} \left(\frac{1}{2} - \frac{1}{2}x^2 - x^2 \right)dx + \int_{1/\sqrt3}^{\sqrt2} \left(2 - x^2 - x^2[/tex]\right)dx \\[/tex]=[tex]\left[\frac{1}{2}x - \frac{1}{6}x^3 - \frac{1}{3}x^3 \right]_0^{1/\sqrt3} + \left[2x - \frac{1}{3}x^3 - \frac{1}{3}x^3 \right]_{1/\sqrt3}^{\sqrt2}\\[/tex]= \[tex]left[\frac{1}{2\sqrt3} - \frac{1}{6(3)} - \frac{1}{3(3)} \right] + \left[2\sqrt2 - \frac{1}{3}(2\sqrt2)^3 - \frac{1}{3}(1/\sqrt3)^3 + \frac{1}{2\sqrt3} - \frac{1}{6(3)} - \frac{1}{3(3)} \right]\\[/tex] = [tex]\frac{\sqrt2}{3} + \frac{10\sqrt2}{3} - \frac{2}{9\sqrt3} - \frac{4}{9}\\ = \boxed{\frac{28\sqrt2}{9} - \frac{4}{9\sqrt3}}.[/tex]
To know more about curves visit:
https://brainly.com/question/29736815
#SPJ11
In January of 2002 , two students made worldwide headlines by spinning a Belgium euro 250 times and getting 140 heads (which is 56% ). This would make the 90% confidence interval (51%,61%). Which of the following conclusions are correct? Choose all that apply. We are 90% confident that spun Belgium euros will land heads between 51% and 61% of the time. We are 90% confident that in this experiment, this Belgium euro landed on heads between 51% and 61% of the time. Ninety percent of all spun euros will land heads between 51% and 61% of the time. If you spin a Belgium euro many times, you have a 90\% chance of getting between 51% and 61% heads. Between 51% and 61% of all Belgium euros are unfair.
In January of 2002, two students made worldwide headlines by spinning a Belgium euro 250 times and getting 140 heads (which is 56%). This would make the 90% confidence interval (51%, 61%). The correct conclusions are: We are 90% confident that spun Belgium euros will land heads between 51% and 61% of the time.
If you spin a Belgium euro many times, you have a 90% chance of getting between 51% and 61% heads. In this experiment, this Belgium euro landed on heads between 51% and 61% of the time. The other conclusions are not correct.
Ninety percent of all spun euros will not land heads between 51% and 61% of the time. Also, it is not correct to say that between 51% and 61% of all Belgium euros are unfair. This conclusion cannot be made based on the results of this experiment.
The correct conclusions can be made because of the 90% confidence interval. This interval provides a range of possible values for the population proportion (the proportion of all Belgium euros that will land on heads if spun many times) with 90% confidence. We can say that we are 90% confident that the population proportion falls between 51% and 61%.
This range only applies to the population proportion and not to individual coin tosses. So, if you spin a Belgium euro many times, you have a 90% chance of getting a sample proportion that falls between 51% and 61%.
Learn more about the 90% Confidence Interval:
https://brainly.com/question/29664127
#SPJ11
"A mortgage loan in the amount of $100,000 is made at 6 percent interest for 20 years. Payments are to be monthly in each part of this problem. Required: a. What will monthly payments be if (1) The loan is fully amortizing? (2) It is partially amortizing and a balloon payment of $50,000 is scheduled at the end of year 20 ? (3) It is a nonamortizing, or ""interest-only"" loan? (4) It is a negative amortizing loan and the loan balance will be $150,000 at the end of year 20 ? b. What will the loan balance be at the end of year 5 under parts a (1) through a (4)? c. What would be the interest portion of the payment scheduled for payment at the end of month 61 for each case (1) through (4) above? d. Assume that the lender-charges 3 points to close the loans in parts a (1) through a (4). What would be the APR for each? e. Assuming that 3 points are paid at closing and the 20 -year loan is prepaid at the end of year 5 , what will be the effective rate of interest for each loan in parts a (1) through a (4)? f. Assume the loan is fully amortizing except that payments will be ""interest only"" for the first three years (36 months). If the ioan is to fully amortize over the remaining 17 years. what must the monthly payments be from year 4 through year 20 ? g. If this is a negative amortizing loan and the borrower and lender agree that the loan balonce of $150.000 will be payable at the end of year 20 : (1) How much total interest will be paid from all payments? How much total principal will be paid? (2) What will be the loan balance at the end of year 3 ? (3) If the loan is repaid at the end of year 3 . What will be the effective rate of interest? (4) if the lender charges 4 points to make this loan, what will the effective rate of interest be if the loan is repaid at the end of year 3 ? Complete this question by entering your answers in the tabs below. What would be the interest portion of the payment scheduled for payment at the end of month 61 for each case (1) through (4) above? Note: Do not round intermediate calculations. Round your final answers to 2 decimal places. If this is a negative amortizing loan and the borrower and lender agree that the loan balance of $150,000 will be payable at the end of year 20: (1) How much total interest will be paid from all payments? How much total principal will be paid? Note: Round your final answer to 2 decimal places. (2) What will be the loan balance at the end of year 3 ? Note: Round your final answer to 2 decimal places. (3) If the loan is repaid at the end of year 3 , what will be the effective rate of interest? (4) If the lender charges 4 points to make this loan, what will the effective rate of interest be if the loan is repaid at the end of year 3 ? Note: Round your final answer to 2 decimal places."
To calculate the various scenarios described in the question, we will use the following information:
Loan amount: $100,000
Interest rate: 6% per annum
Loan term: 20 years
a) Monthly Payments:
(1) Fully Amortizing Loan:
To calculate the monthly payment for a fully amortizing loan, we can use the loan payment formula:
Payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-n))
where Monthly interest rate = Annual interest rate / 12
n = Total number of payments
Monthly interest rate = 6% / 12 = 0.005
n = 20 * 12 = 240
Using the formula, we can calculate the monthly payment for a fully amortizing loan:
Payment = ($100,000 * 0.005) / (1 - (1 + 0.005)^(-240))
(2) Partially Amortizing Loan with Balloon Payment:
For this scenario, we will have regular monthly payments, but a balloon payment of $50,000 at the end of year 20. The monthly payment will be calculated the same way as in the fully amortizing loan scenario.
Payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-n))
(3) Non-amortizing (Interest-only) Loan:
In an interest-only loan, the monthly payment consists only of the interest portion. The principal amount remains unchanged throughout the loan term.
Monthly Payment = Loan amount * Monthly interest rate
(4) Negative Amortizing Loan:
In a negative amortizing loan, the monthly payment is set lower than the interest due, resulting in an increase in the loan balance over time.
b) Loan Balance at the end of Year 5:
To calculate the loan balance at the end of year 5, we need to determine the remaining principal amount after 5 years of payments. This can be done by calculating the loan balance using the loan balance formula:
Loan Balance = Principal amount * (1 + Monthly interest rate)^(-n) + Monthly payment * ((1 + Monthly interest rate)^(-n) - 1) / Monthly interest rate
where Principal amount = Loan amount
Monthly interest rate = Annual interest rate / 12
n = Number of payments remaining
c) Interest Portion of Payment at the end of Month 61:
To calculate the interest portion of the payment at the end of month 61, we need to determine the interest amount based on the remaining loan balance and the interest rate.
Interest Portion = Loan balance * Monthly interest rate
d) APR Calculation:
The Annual Percentage Rate (APR) takes into account the lender charges and reflects the true cost of borrowing. The APR can be calculated using the following formula:
APR = ((Total Interest + Lender Charges) / Loan amount) * 100
e) Effective Rate of Interest:
To calculate the effective rate of interest, we need to consider the lender charges and the prepayment of the loan at the end of year 5. The effective rate can be calculated using the formula:
Effective Rate = (Total Interest + Lender Charges) / Loan amount
f) Monthly Payments from Year 4 to Year 20:
To calculate the monthly payments from year 4 to year 20, we need to determine the remaining principal amount and the remaining number of payments. We can then use the loan payment formula to calculate the new monthly payments.
g) Negative Amortizing Loan:
(1) Total Interest and Principal Paid:
To calculate the total interest and principal paid in a negative amortizing loan, we need to consider the monthly payments, interest rate, and loan balance at the end of year 20.
Total Interest Paid = (Monthly Payment - Monthly Interest) * Number of Payments
Total Principal Paid = Loan Amount - Loan Balance at the end of Year 20
(2) Loan Balance at the end of Year 3:
To calculate the loan balance at the end of year 3, we need to determine the remaining principal amount after 3 years of payments. This can be done using the loan balance formula.
Loan Balance = Principal amount * (1 + Monthly interest rate)^(-n) + Monthly payment * ((1 + Monthly interest rate)^(-n) - 1) / Monthly interest rate
(3) Effective Rate of Interest at the end of Year 3:
To calculate the effective rate of interest at the end of year 3, we need to consider the total interest paid and the loan balance at the end of year 3.
Effective Rate = (Total Interest Paid / Loan Balance at the end of Year 3) * 100
(4) Effective Rate of Interest with Lender Charges:
To calculate the effective rate of interest with lender charges, we need to include the lender charges in the calculation. The formula remains the same as (3), but with the inclusion of lender charges.
Effective Rate = ((Total Interest Paid + Lender Charges) / Loan Balance at the end of Year 3) * 100
To learn more about loan : brainly.com/question/11794123
#SPJ11
A customer service department receives on average 150 calls per day and the number of calls received is Poisson distributed. What is the standard deviation of the calls received per day?
The standard deviation of the calls received per day is 12.25.
The standard deviation of the calls received per day is 12.25. We know that the number of calls received follows a Poisson distribution and the average number of calls received per day is 150. The formula for the Poisson distribution is:P(x) = (e^(-λ) * λ^x) / x!Where:P(x) is the probability of x number of calls being received per day.λ is the average number of calls received per day.x is the number of calls received per day.We are given that the average number of calls received per day (λ) is 150.The formula for the standard deviation (σ) of a Poisson distribution is:σ = sqrt(λ)Therefore, substituting λ = 150, we get:σ = sqrt(150)σ = 12.25Therefore, the standard deviation of the calls received per day is 12.25.
Learn more about Standard deviation here,what does standard deviation mean?
https://brainly.com/question/475676
#SPJ11
Given the functions f and g below, find g(f(−1)). f(x)=−x−4
g(x)=−x 2
−3x−1
Do not include " g(f(−1))=" in your answer. Provide your answer below:
The value of the function g(f(−1)) using the substitution method by substituting the given functions f(x)=−x−4`, g(x)=−x 2−3x−1 is -1
Given the functions f and g below, to find g(f(−1)), we have to substitute -1 for x in the function f and then substitute the resulting value into the function g.
Here are the functions, f(x) = -x - 4, g(x) = -x^2 - 3x - 1
Firstly, we will determine f(-1) by substituting -1 for x in the function f, f(-1) = -(-1) - 4 = 1 - 4 = -3
Now that we know that f(-1) = -3, we will substitute this value for x in the function g.
g(f(-1)) = g(-3) = -(-3)^2 - 3(-3) - 1 = -9 + 9 - 1 = -1
Therefore, g(f(-1)) = -1.
To learn more about functions visit:
https://brainly.com/question/10439235
#SPJ11
Use identities to write this expression in terms of sine. \[ -2 \sin (3 \theta+2 \pi)-3 \cos \left(\frac{\pi}{2}-3 \theta\right) \]
The expression \(-2 \sin (3 \theta+2 \pi)-3 \cos \left(\frac{\pi}{2}-3 \theta\right)\) can be simplified to \(-5 \sin(3\theta)\) using trigonometric identities.
To write the given expression in terms of sine, we can use the following trigonometric identities:
1. $\cos(\frac{\pi}{2} - \alpha) = \sin(\alpha)$
2. $\sin(-\alpha) = -\sin(\alpha)$
Applying these identities, we can rewrite the expression as follows:
\[
-2 \sin(3\theta + 2\pi) - 3 \cos(\frac{\pi}{2} - 3\theta)
\]
Using identity 2, we can rewrite $\sin(3\theta + 2\pi)$ as $\sin(3\theta)$:
\[
-2 \sin(3\theta) - 3 \cos(\frac{\pi}{2} - 3\theta)
\]
Now, using identity 1, we can rewrite $\cos(\frac{\pi}{2} - 3\theta)$ as $\sin(3\theta)$:
\[
-2 \sin(3\theta) - 3 \sin(3\theta)
\]
Combining the terms:
\[
-5 \sin(3\theta)
\]
So, the expression \(-2 \sin (3 \theta+2 \pi)-3 \cos \left(\frac{\pi}{2}-3 \theta\right)\) can be written in terms of sine as \(-5 \sin(3\theta)\).
To learn more about sine Click Here: brainly.com/question/23556818
#SPJ11
What is the (standard
deviation of difference scores),
using the direct difference approach?
The standard deviation of difference scores using the direct difference approach can be calculated using the following steps:
Take the difference between each pair of corresponding values in the two sets.
Calculate the mean of the difference scores.
Subtract the mean from each difference score and square the result.
Calculate the mean of the squared differences.
Take the square root of the mean squared difference.
The formula for the standard deviation of difference scores using the direct difference approach is:
σ_diff = √[ Σ(x_i - y_i - M_diff)^2 / (n-1) ]
where x_i and y_i are the corresponding values in the two sets, M_diff is the mean of the difference scores, and n is the number of pairs of values.
By following these steps and using the provided data, the standard deviation of the difference scores can be calculated.
Please provide the actual values of the data or specify the two sets of values to proceed with the calculation.
To know more about corresponding, visit
https://brainly.com/question/12454508
#SPJ11
Convert the given unit of weight to the unit indicated. 620 mg to g
The given weight of 620 milligrams (mg) can be converted to grams (g) by dividing it by 1000. The result is 0.62 grams.
To convert milligrams to grams, we need to divide the given weight by 1000 since there are 1000 milligrams in a gram.
Given that the weight is 620 milligrams, we can perform the conversion as follows:
620 mg / 1000 = 0.62 g
Therefore, 620 milligrams is equal to 0.62 grams.
To learn more about grams: -brainly.com/question/30426054
#SPJ11
Using the given information, find the area of the sector of a circle of radius r formed by a central angle 0.
Radius, r
Central Angle, 0
36 meters
0=20°
The area of the sector is 72x square meters.
(Simplify your answer. Type an exact answer in terms of x.)
The area of the sector is approximately square meters. (Round to two decimal places as needed.)
Area of sector is given as (1/18) * π * r², where r represents radius. Exact value of area is 72x square meters,approximate value can be calculated by substituting specific value for π and given value of x into equation.
The problem provides information about a sector of a circle, including the radius (r) and the central angle (θ).
We need to find the area of the sector using the given information.
Recall that the formula for the area of a sector of a circle is (θ/360) * π * r².
Substitute the given values into the formula:
Area = (20/360) * π * r².
Simplify the expression:
Area = (1/18) * π * r².
The area of the sector is given as 72x square meters, so we can set up an equation:
72x = (1/18) * π * r².
Solve the equation for the radius squared (r²):
r² = (72x * 18) / π.
The area of the sector is expressed in terms of x, so we don't need to calculate the exact value.
If we are required to provide an approximate value, we can substitute a specific value for π and the given value of x into the equation.
For example, if we use π ≈ 3.14, we can calculate the approximate value of the area.
Substitute the values into the equation:
r² ≈ (72 * 18 * x) / 3.14.
Simplify the expression and calculate the approximate value of r².
Take the square root of r² to find the approximate value of the radius (r).
Finally, substitute the value of r into the formula for the area of the sector to find the approximate area.
In summary, the area of the sector is given as (1/18) * π * r², where r represents the radius. The exact value of the area is 72x square meters, and the approximate value can be calculated by substituting a specific value for π and the given value of x into the equation.
To learn more about Area of sector click here:
brainly.com/question/29055300
#SPJ11
Find the solution of the initial value problem. Write the answer in explicit form. y ′
= 1+2y
x
,y(−1)=0,
Given differential equation is `y' = 1 + 2y`.
Here, `dy/dx = 1 + 2y`. We need to find the solution of the initial value problem. Write the answer in explicit form.
y ′ = 1+2yx, y(−1) = 0. To solve the given problem we will use the concept of Separation of Variables: Solving the equation using separation of variables,
we get;`(dy/dx) = 1 + 2y`Dividing both sides by `1 + 2y`,
we get;`dy / (1 + 2y) = dx` Integrating both sides, we get;`
ln|1 + 2y| = x + C_1`Where `C_1` is the constant of integration. Rewriting the equation,
we get;`|1 + 2y| = e^(x + C_1)` Now, since `1 + 2y` is always positive or zero. We can write the above equation as;
`1 + 2y = e^(x + C_1)`or
`1 + 2y = -e^(x + C_1)` Now we will consider these two cases;
Case 1: 1 + 2y = e^(x + C_1) Here,
`y = (e^(x+C_1) - 1)/2`
Case 2: 1 + 2y = -e^(x + C_1)
Here, `y = (-e^(x+C_1) - 1)/2` Now, let's use the initial value to find the constant of integration;
When `x = -1` and
`y = 0`;
`y = (e^(x+C_1) - 1)/2`
`0 = (e^(-1+C_1) - 1)/2``
=> 0 = e^(-1+C_1) - 1``
=> e^(-1+C_1) = 1``
=> -1 + C_1 = 0`
`=> C_1 = 1` Therefore, the solution to the given differential equation is given by;
`y = (e^(x+1) - 1)/2`
To know more about value visit :
https://brainly.com/question/30035551
#SPJ11
Let x(t)=[ x 1
(t)
x 2
(t)
] be a solution to the system of differential equations: x 1
′
(t)=−12x 1
(t)+2x 2
(t)
x 2
′
(t)=−10x 1
(t)−3x 2
(t)
If x(0)=[ −2
4
], find x(t) Put the eigenvalues in ascending order when you enter x 1
(t),x 2
(t) below.
Given the differential equations are
x1(t)=−12x1(t)+2x2(t)x2′(t)=−10x1(t)−3x2(t)and x(0)=[−24].
We need to find x(t).
Solution:
Given the differential equations are
x1′(t)=−12x1(t)+2x2(t)x2′(t)=−10x1(t)−3x2(t)and x(0)=[−24].
We need to find x(t).
Let the characteristic equation be |A-λI|=0|A-λI| = (A - λI) = 0 ⇒ det(A - λI) = 0A=1210−3210=1−2λ1−3λ|A-λI|=0 ⇒ (1-λ)(-3-λ)+20 = 0 ⇒ λ²+2λ+17=0By using the quadratic formula,
we can find the roots as (-2±i√15) / 2.
Therefore the eigenvalues are
(-1+i√15) and (-1-i√15).x(t)=[(e-1+i√15t)[(-15+5i)/10]+(e-1-i√15t)[(-15-5i)/10]][-2/5i][(e-1+i√15t)[(-15+5i)/10]+(e-1-i√15t)[(-15-5i)/10]]+[4][(e-1+i√15t)[(-1+i√15)/10]+(e-1-i√15t)[(-1-i√15)/10]]
To know more about differential visit :
https://brainly.com/question/13958985
#SPJ11
You short $5,000 of Stock S and go long $5,000 of Stock L, as displayed in the chart. If the market rises by 10%, what is the expected dollar gain or loss for this trade. Ignore any margin requirements or interest. Write your answer as a dollar amount, without the $ sign. Use a negative sign to precede your answer if you lost money. It turns out that you made more or less than you calculated above. What is the best explanation: You used beta to predict the returns when you should only consider alpha You took on too much risk You did not account for the randomness of returns not included in beta Shorting a stock is risky and therefore expected return calculations do not apply
The expected dollar gain for this trade, if the market rises by 10%, is $500.
In this scenario, you shorted $5,000 of Stock S and went long $5,000 of Stock L. When you short a stock, you are essentially borrowing and selling shares with the expectation that their price will decrease. On the other hand, going long on a stock means buying shares with the anticipation that their price will rise.
Since you shorted Stock S, if the market rises by 10%, the value of Stock S is expected to decline by that amount. Therefore, you would make a gain on your short position. Conversely, if you went long on Stock L, you would benefit from the 10% increase in its value.
Considering the equal investment amounts of $5,000 for both stocks, your gain from the short position in Stock S would be -$500 (a loss), while your gain from the long position in Stock L would be +$500 (a profit). Therefore, the net expected gain from this trade would be $500, which is the difference between the two positions.
Learn more about Expected gains
brainly.com/question/24175866
#SPJ11
