The log-linear demand function In(Q) = A - Bln(p) relates quantity demanded (Q) to price (p).
a. Q as a function of p:
Q = e^A / p^B
dp/dQ = -B * e^A / p^(B+1)
b. p as a function of Q:
p = e^(A/B) / Q^(1/B)
To solve this problem, let's start with the given demand function: In(Q) = A - Bln(p), where Q represents the quantity demanded, p is the price of the product, A and B are constants.
a. Express Q as a function of p:
To find the relationship between Q and p, we need to exponentiate both sides of the equation to remove the natural logarithm. By taking the exponential function, we get:
e^(In(Q)) = e^(A - Bln(p))
Using the property e^(A - Bln(p)) = e^A / e^(Bln(p)) = e^A / p^B, the equation becomes:
Q = e^A / p^B
Now, let's differentiate both sides of this equation with respect to p:
dQ/dp = d/dp(e^A / p^B)
To differentiate e^A / p^B, we can use the quotient rule:
dQ/dp = [e^A * (-B) * p^(B-1) - e^A * p^B * 0] / (p^B)^2
Simplifying this expression, we have:
dQ/dp = -B * e^A / p^(B+1)
b. Express "p" as a function of Q:
To find the relationship between p and Q, we can rearrange the equation Q = e^A / p^B:
p^B = e^A / Q
Now, taking the B-th root of both sides:
p = (e^A / Q)^(1/B)
Simplifying further:
p = e^(A/B) / Q^(1/B)
So, we have expressed "p" as a function of Q.
In summary, for the log-linear demand function In(Q) = A - Bln(p):
a. Q can be expressed as Q = e^A / p^B, and the derivative of Q with respect to p is dp/dQ = -B * e^A / p^(B+1).
b. p can be expressed as p = e^(A/B) / Q^(1/B).
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During a football game, a team lost 12 yards on the first play and then gained 5 yards on each of the next 3 plays. Wh
method finds the total yards at the end of the first four plays ?
O add-12 to 3 x 5
add 12 to 3 x 5
add-12, 5, and 3
O add 12, 5, and 3
Answer: Id go with the first answer if its multiple choice
Step-by-step explanation:
they had 3 more plays where they scored 5 points (3x5)
but they lost 3 in the beggining (-12)
Halfway through the season, the Florida State Seminoles football team had the highest average final score. What was the Florida State
Seminoles' average score if their final scores were 33, 41, 33, 45, and 43?
Help me plsss
(-3,24,-192,1536,...) find the next three terms
Answer:
-12288, 98304, -786532
Step-by-step explanation:
each number in the sequence is multiplied by -8
Is the function y =|x – 7| a one-to-one function? Justify your answer.
Answer:
Yes
Step-by-step explanation:
Whenever you have an absolute value function it will always be a one-to-one function unless the slop of the line is altered.
We need to determine whether the given function is one-to-one.
The given function is not one-to-one as explained below.
The given function is [tex]y=|x-7|[/tex]
In a one-to-one function each value of [tex]y[/tex] has only one value in [tex]x[/tex] and vice versa.
Let us use an example with the given equation.
[tex]x=4[/tex]
[tex]y=|4-7|=3[/tex]
[tex]x=10[/tex]
[tex]y=|10-7|=3[/tex]
So, for the same value of [tex]y[/tex] there are two values of [tex]x[/tex].
Hence, the given function is not one-to-one.
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do you ride horses??
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
i have a friesian horse named butters he is a male!
In a binomial distribution where n = 900 and p= 1/3, determine
the mean and standard deviation.
Select one:
a. 300, 14.14
b. 2,700, 200
c. 300, 200
d. 2,700, 14.14
The mean and standard deviation of a binomial distribution with n = 900 and p = 1/3 can be determined as follows:
Mean = n * p = 900 * (1/3) = 300
Standard Deviation = √(n * p * (1 - p)) = √(900 * (1/3) * (2/3)) ≈ 14.14
What are the formulas used to calculate the mean and standard deviation of a binomial distribution?In a binomial distribution, the mean (μ) represents the average number of successes that can be expected in a given number of trials. It is calculated by multiplying the number of trials (n) by the probability of success (p). In this case, with n = 900 and p = 1/3, the mean is obtained by multiplying 900 by 1/3, resulting in 300.
The standard deviation (σ) of a binomial distribution measures the amount of dispersion or variability in the distribution. It is calculated using the formula √(n * p * (1 - p)). By substituting the given values into the formula, we can compute the standard deviation as approximately 14.14.
Therefore, the mean and standard deviation of the binomial distribution with n = 900 and p = 1/3 are 300 and 14.14, respectively.
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Twice the smaller of two consecutive integers increased by the larger integer is at least 25. Model the problem with an inequality, and determine which of the given values 7, 8, an(d)/(o)r 9 are solutions.
Let the first of the two consecutive integers be n. Then the next consecutive integer is n+1.
From the given information, we can form an inequality, which is:2n + (n+1) ≥ 25
The above inequality is formed from the statement "Twice the smaller of two consecutive integers increased by the larger integer is at least 25". Now, let's solve this inequality and find the values of n that satisfy it.2n + (n+1) ≥ 25Simplifying the above inequality, we get:3n + 1 ≥ 25
Subtracting 1 from both sides, we get:3n ≥ 24
Dividing both sides by 3, we get:n ≥ 8
Hence, the first of the two consecutive integers is greater than or equal to 8.
Therefore, the two consecutive integers that satisfy the given information are 8 and 9.
Now, we need to check which of the given values, 7, 8, or 9, satisfy the above inequality. Let's check for
n=7.2n + (n+1) = 2(7) + (7+1) = 15 < 25
Therefore, n=7 is not a solution.
Let's check for n=8.2n + (n+1) = 2(8) + (8+1) = 25 ≥ 25
Therefore, n=8 is a solution. Let's check for n=9.2n + (n+1) = 2(9) + (9+1) = 28 ≥ 25
Therefore, n=9 is also a solution.
Thus, we have found that the solutions to the given problem are n=8 and n=9.
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Which expressions represent the amount of olive oil needed for 4 tablespoons of lemon juice? Write an expression to show the amount of olive oil in the recipe. Let j equal the number of
tablespoons of lemon juice.
To find out the amount of olive oil needed for 4 tablespoons of lemon juice, we have to express the amount of olive oil in terms of j, where j is the number of tablespoons of lemon juice used in the recipe.The recipe states that for every 4 tablespoons of lemon juice, we need 3/4 cups of olive oil.
That can be written as:3/4 cups of olive oil :
4 tablespoons of lemon juice To express the amount of olive oil in terms of j,
we can use ratios:3/4 cups of olive oil : 4 tablespoons of lemon juice = x cups of olive oil : j tablespoons of lemon juice
Cross-multiplying, we get:3/4 cups of olive oil * j tablespoons of lemon juice = 4 tablespoons of lemon juice * x cups of olive oil12 tablespoons of olive oil = 4x cups of olive oilx = 12/4x = 3
Therefore, the expression to show the amount of olive oil needed in the recipe is:
3/4 cups of olive oil : 4 tablespoons of lemon juice = 3 cups of olive oil : j tablespoons of lemon juice
Answer: The expression to show the amount of olive oil needed in the recipe is 3 cups of olive oil : j tablespoons of lemon juice.
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In a recent year, 19.8% of all registered doctors were female. If there were 41,900 female registered doctors that year, what was the total number of
registered doctors?
Round your answer to the nearest whole number.
what is the solution to this equation.
4(5x+3)=14x + 30
Answer:
= 3
Step-by-step explanation
I am sorry if I am wrong
please help will give brainliest and 50 points!!!
Answer:
see below
Step-by-step explanation:
The first had 2 dots
The second has 4 dots
The third has 8 dots
The number of dots is doubling each time
D(n) = 2^n
This is a geometric sequence, we are multiplying the number of dots by 2 each time we go to the next stage
The geometric formula is
xn = a r^(n-1) where n is the stage and a is the number in the first stage and r is the common ratio
Need help this is due in 20 minutes
Answer:
X=4 hope I help
Step-by-step explanation:
llllllllll
I need help plz help me
Answer:
$38.10
Step-by-step explanation:
because -46.90+86 is 38.1
ur welcome!
pls marbeanibrainliest!
Evelyn and her father collects rocks Evelyn’s father has 5 more rocks than four times Evelyn’s rock. How many rocks does Evelyn name when her father has 49 rocks?
Answer:
Evelyn has 11 rocks.
Step-by-step explanation:
I first made an equation for the father's rocks.
5 + 4x = 49
X is Evelyn's rocks. We subtract the 5 from each side to get,
4x = 44, dividing each side by 4, we get X = 11.
We can double-check our answer by multiplying 11 by 4 and adding 5 to it. We get 49 doing this, proving our answer.
Suppose an industry with four firms1) having the same constant marginal cost c, = C2 = C = C4 = 4;2) incurring no fixed cost of production; 3) producing a homogeneous good and choosing output simultaneously (i.e., being Cournot competitors); and 4) facing the linear inverse demand P = 10-Q with Q = q1 + q2 + q3 +q4
Q11) Determine the value for c such that the merger becomes profitable
Q12) Determine the value for c, such that the price decreases post-merger
The merger profitable is c ≤ 2.5. The value of c that makes the price decrease is c > 0.
1) Value for c such that the merger becomes profitable:
To calculate the value of c that makes the merger profitable, we must follow the following steps:
First, let's calculate the total output of the industry, which is:
Q = q1 + q2 + q3 + q4
Second, we must determine the total cost of production (TC) of each firm, which is:
TC = C*q,
where C is the marginal cost of each firm.
Third, we must determine the total cost of production of the industry, which is:
TC = C*(q1 + q2 + q3 + q4)
Fourth, we must determine the total revenue of the industry, which is:
TR = P*Q, where P = 10 - Q
Then, we can calculate the profit (Π) of each firm, which is given by:
Π = TR - TC
And, finally, we can calculate the total profit (Π) of the industry, which is given by:
Π = TR - TC * 4, where 4 is the number of firms in the industry.
Now, let's substitute the expressions we found for TR and TC into the equation for Π:
Π = (10 - Q)*Q - C*(q1 + q2 + q3 + q4) * 4
Π = (10 - (q1 + q2 + q3 + q4))*(q1 + q2 + q3 + q4) - C*(q1 + q2 + q3 + q4) * 4
Π = (10 - Q)*(Q) - C*Q * 4
Π = 10Q - Q² - 4CQ
Now, we must differentiate Π with respect to Q and equate it to zero to find the value of Q that maximizes profit:
Π' = 10 - 2Q - 4C = 0
Π' = 10 - 2(Q) - 4(C)
= 0Q
= 5 - 2C
The value of c that makes the merger profitable is c ≤ 2.5.
To verify that this is true, we can substitute this value of Q into the equation for Π and check if it is positive:
Π = 10Q - Q² - 4CQ
Π = 10(5 - 2C) - (5 - 2C)² - 4C(5 - 2C)
Π = 50 - 20C - (25 - 20C + 4C²) - 20C + 8C²
Π = 3C² - 30C + 25
Π = 3(C - 2.5)² - 3.75
Since Π is positive for c ≤ 2.5, the merger is profitable for c ≤ 2.5.2) Value for c such that the price decreases post-merger:
To calculate the value of c that makes the price decrease after the merger, we must follow the following steps:
First, let's calculate the output of each firm before the merger, which is given by:
q = (10 - C - q)/3, where q is the output of each firm.
Second, let's calculate the total output of the industry before the merger, which is given by:
Q = 4q
Third, let's calculate the price before the merger, which is given by:
P = 10 - Q
Substituting Q and q into this equation, we get:
P = 10 - 4q
Since the firms have the same marginal cost, their output levels are the same.
Thus, after the merger, the new output level of the merged firm is Q' = 4Q/2 = 2Q, and the price is given by:
P' = 10 - Q'
To find the value of c that makes the price decrease, we must compare P and P':
P = 10 - 4c/3
P' = 10 - 8c/3
To find the value of c that makes P' < P, we must solve the inequality:
P' < P
P' - P < 0-8c/3 + 4c/3 < 0-4c/3 < 0c > 0
Thus, the value of c that makes the price decrease is c > 0.
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.In the least-squares line y=5-2x,
a. what are the values of the slope and the intercept?
b. when x changes by 1 unit, how much does y change?
c. if two variables have a negative linear correlation, is the slope of the least-squares lines positive or negative?
a) In the least-squares line y = 5 - 2x, the slope is -2 and the y-intercept is 5. b) Since the slope of the line is -2, a change of 1 unit in x would cause a change of 2 units in y. c) When two variables have a negative linear correlation, the slope of the least-squares line is negative.
The least-squares line, also known as the linear regression line, is a straight line that shows the connection between two variables that are linearly related.
A straight line is used to connect two points, and the least-squares line is the line that connects the points with the smallest amount of error or the smallest amount of distance between the points and the line.
The formula for the least-squares line is given by y = mx + b,
where m is the slope of the line and b is the y-intercept.
In the least-squares line
y = 5 - 2x,
the slope is -2, and the y-intercept is 5.
The slope of the line tells us how much y changes when x changes by one unit. In this case, since the slope is -2, a change of 1 unit in x would cause a change of 2 units in y.
When two variables have a negative linear correlation, the slope of the least-squares line is negative.
A negative correlation means that when one variable increases, the other variable decreases.
For example, if we look at the correlation between temperature and snowfall, we would expect a negative correlation. As temperature increases, we would expect snowfall to decrease.
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A realtor has a budget of $4,180 to spend on their advertising. Each month, x, the realtor
spends $220 on different advertisements. The amount of money remaining in the budget can
be modeled by the function A(x) = -220x + 4180. Based on the graph on the linear function
A(x) and the context of the problem, what is the domain?
Answer:The domain of the function A(x) = -220x + 4180 represents the valid inputs or values of x in the context of the problem. In this case, the context is the monthly spending on advertisements for a realtor with a budget of $4,180.
Since the realtor's budget is fixed at $4,180, the domain of the function would be the range of valid values for x that represent the number of months the realtor can spend on advertisements.
In this situation, it would be reasonable to assume that the realtor cannot spend a negative number of months on advertisements. Additionally, the realtor cannot spend more months on advertisements than the total duration of their budget, which is determined by dividing the budget by the monthly spending.
To find the domain, we need to consider the restrictions mentioned above. Therefore, the domain would be:
x ≥ 0 and x ≤ 4180 / 220
Simplifying the inequality:
x ≥ 0 and x ≤ 19
So, the domain of the function A(x) would be the set of non-negative integers less than or equal to 19.
linear equations
a+2b=-1
2a+3b=23
Answer:
.2a + 4b = -2 2a + 3b = 23We subtract.. 0 + b = -25a + (2×-25) = -1a - 50 = -1a = -1+50a = 49.a = 49b = -25.Step-by-step explanation:
proving my answer.a + 2b = -149 + (2×-25) = -149 - 50 = -12a + 3b = 23(2×49) + (3×-25) = 2398 + (-75) = 2398 - 75 = 23A sphere has a volume of 80cm*3
Calculate the radius of the sphere.
[The volume, V, of a sphere with radius r is V =4/3 x 22/7 x r*3]
Answer:
Step-by-step explanation:
What value of x makes the equation true?
0.2x + 0.7 = 0.8 - 0.3x
Answer:
6
Step-by-step explanation:
Answer:
[tex]x = \frac{1}{5}[/tex] or [tex]0.2[/tex] (they're the same)
I hope this helps!
7x + 9 = 58
x/2 - 12 = -14
-3x + 33 = -12
8x + 16 = 8
2x - 2 = -18
Answer: a) 7 b) -4 c) 15 d) -1 e) -8
Step-by-step explanation:
7x + 9 = 58
-9 -9
7x = 49
÷7 ÷7
x = 7
x/2 - 12 = -14
+12 +12
x/2 = -2
×2 ×2
x = -4
-3x + 33 = -12
-33 -33
-3x = -45
÷-3 ÷-3
x = 15
8x + 16 = 8
-16 -16
8x = -8
÷8 ÷8
x = -1
2x - 2 = -18
+2 +2
2x = -16
÷2 ÷2
x = -8
2 1/6 − 11/15x=0.15
please solve for x asap
x=
44
------ <-------- fraction
201
=4.568
Step-by-step explanation:
8880 divided bye 10 to the power of 2
Answer:
444/5
Step-by-step explanation:
Answer:
88.8
Step-by-step explanation:
10^2 is 100, so dividing 8880 by 100 is equal to 88.8
| y-5) = 45
how you find y ?
Answer:
y=45+5
=50
Step-by-step explanation:
Answer:
Transpose -5 to the other side so it becomes 45 + 5 which is equal to 50. Therefore, the value of y is 50.
Use finite approximations to estimate the area under the graph of the function f(x) =8-x^2-2x between x = -4 and x = 2 for each of the following cases. a. Using a lower sum with two rectangles of equal width b. Using a lower sum with four rectangles of equal width c. Using an upper sum with two rectangles of equal width d. Using an upper sum with four rectangles of equal width
The estimated area under the graph of the given function between x = -4 and x = 2 for each of the given cases is as follows:
a) Using a lower sum with two rectangles of equal width = 60
b) Using a lower sum with four rectangles of equal width = 60
c) Using an upper sum with two rectangles of equal width = 40
d) Using an upper sum with four rectangles of equal width = 40
The given function is f(x) = 8 - x² - 2x. We are required to use finite approximations to estimate the area under the graph of the given function between x = -4 and x = 2 for each of the following cases:
Solution a) Using a lower sum with two rectangles of equal width:
Let us use two rectangles of equal width. Hence, the width of each rectangle is given by:$$\Delta x = \frac{b-a}{n} = \frac{2-(-4)}{2} = 3$$
The x-values for each rectangle can be determined as:$$x_1 = -4, x_2 = -4+3 = -1, x_3 = -1+3 = 2$$
Therefore, the area under the curve is given by:$$A = f(x_1)Δx + f(x_2)Δx = [8-(-4²)-2(-4)](3) + [8-(-1²)-2(-1)](3)$$$$= 60$$
Solution b)Using a lower sum with four rectangles of equal width :Let us use four rectangles of equal width. Hence, the width of each rectangle is given by:$$\Delta x = \frac{b-a}{n} = \frac{2-(-4)}{4} = 1.5$$
The x-values for each rectangle can be determined as:$$x_1 = -4, x_2 = -4+1.5 = -2.5, x_3 = -2.5+1.5 = -1, x_4 = -1+1.5 = 0.5, x_5 = 0.5+1.5 = 2$$
Therefore, the area under the curve is given by:$$A = f(x_1)Δx + f(x_2)Δx + f(x_3)Δx + f(x_4)Δx$$$$= [8-(-4²)-2(-4)](1.5) + [8-(-2.5²)-2(-2.5)](1.5) + [8-(-1²)-2(-1)](1.5) + [8-(0.5²)-2(0.5)](1.5)$$$$= 60$$
Solution c) Using an upper sum with two rectangles of equal width:
Let us use two rectangles of equal width. Hence, the width of each rectangle is given by:$$\Delta x = \frac{b-a}{n} = \frac{2-(-4)}{2} = 3$$
The x-values for each rectangle can be determined as:$$x_1 = -4+3 = -1, x_2 = 2$$
Therefore, the area under the curve is given by:$$A = f(x_1)Δx + f(x_2)Δx = [8-(-1²)-2(-1)](3) + [8-(2²)-2(2)](3)$$$$= 40$$
Solution d) Using an upper sum with four rectangles of equal width :Let us use four rectangles of equal width.
Hence, the width of each rectangle is given by:$$\Delta x = \frac{b-a}{n} = \frac{2-(-4)}{4} = 1.5$$
The x-values for each rectangle can be determined as:$$x_1 = -2.5, x_2 = -1, x_3 = 0.5, x_4 = 2$$
Therefore, the area under the curve is given by:$$A = f(x_1)Δx + f(x_2)Δx + f(x_3)Δx + f(x_4)Δx$$$$= [8-(-2.5²)-2(-2.5)](1.5) + [8-(-1²)-2(-1)](1.5) + [8-(0.5²)-2(0.5)](1.5) + [8-(2²)-2(2)](1.5)$$$$= 40$$
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The Mariana Trench is-35,840 feet deep. The Puerto Rico Trench is -28,374. What is the difference between the two depths?
Answer: -7,466 I would think.
Step-by-step explanation:
5
The points L, M and N are such that LMN is a straight line.
The coordinates of L are (-4, 3)
The coordinates of Mare (5, 8)
Given that LM: MN = 3:4,
find the coordinates of N.
The coordinates of point N are approximately (7.06, 10.74).
To find the coordinates of point N, we need to determine the position of N relative to points L and M. Since LMN is a straight line and the ratio of LM to MN is given as 3:4, we can use this information to find the coordinates of N.
Let's start by calculating the differences in the x-coordinates and y-coordinates between points L and M:
Δx = x-coordinate of M - x-coordinate of L = 5 - (-4) = 9
Δy = y-coordinate of M - y-coordinate of L = 8 - 3 = 5
Since the ratio of LM to MN is 3:4, we can express the differences in x-coordinates and y-coordinates as fractions:
Δx/LM = 3/7
Δy/LM = 4/7
To find the differences in x-coordinates and y-coordinates between points L and N, we can multiply the fractions by the length of MN:
Δx = (Δx/LM) * MN = (3/7) * MN
Δy = (Δy/LM) * MN = (4/7) * MN
Substituting the given values for Δx and Δy, we have:
9 = (3/7) * MN
5 = (4/7) * MN
To solve for MN, we can set up an equation using the two equations above:
9/(3/7) = 5/(4/7)
Simplifying, we have:
(9 * 7) / 3 = (5 * 7) / 4
21 = 35/4 * MN
Multiplying both sides by 4/35, we get:
MN = (21 * 4) / 35 = 84 / 35 = 24/5
Now that we know the length of MN, we can find its coordinates by adding the differences to the coordinates of point M:
x-coordinate of N = x-coordinate of M + Δx = 5 + (3/7) * (24/5) = 5 + 72/35 = 5 + 2.06 (rounded) ≈ 7.06
y-coordinate of N = y-coordinate of M + Δy = 8 + (4/7) * (24/5) = 8 + 96/35 = 8 + 2.74 (rounded) ≈ 10.74.
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What is the quotient in the expression
45
o?
Answer:
the quotient of 45 or o is 45/o. A quotient is the result of a division . For example 8/4=2 so, 2 is the quotient.
Can you help me plz on this
Answer: A
Step-by-step explanation: I think it's point A.
7. After consulting with his broker, Don Hochstetler purchases
2,000 shares of Fallon Energy stock at $20.10 per share. He
also purchased 1,500 shares of MacWord Scientific at $56.24
per share. The commission is 0.1% of the cost of the stock.
a. What was the cost of the Fallon Energy stock?
b. How much was the commission?
c. What is the total value of the stocks including the
commission?
a. The cost of the Fallon Energy stock was $40,200.
b. The commission was $96.34.
c. The total value of the stocks, including the commission, was $96,826.34.
a. To find the cost of the Fallon Energy stock, we multiply the number of shares (2,000) by the price per share ($20.10):
Cost of Fallon Energy stock = 2,000 shares * $20.10/share = $40,200.
Therefore, the cost of the Fallon Energy stock was $40,200.
b. The commission is calculated as 0.1% of the cost of the stock. To find the commission for the Fallon Energy stock, we multiply the cost of the stock ($40,200) by 0.1% (0.001):
Commission for Fallon Energy stock = $40,200 * 0.001 = $40.20.
Similarly, for the MacWord Scientific stock, we calculate the commission by multiplying the cost of the stock ($56.24/share) by 0.1% (0.001) and the number of shares (1,500):
Commission for MacWord Scientific stock = 1,500 shares * $56.24/share * 0.001 = $84.36.
Therefore, the total commission for both stocks is $40.20 + $84.36 = $124.56.
c. To calculate the total value of the stocks including the commission, we add the cost of the stocks and the commission:
Total value of the stocks including commission = Cost of Fallon Energy stock + Cost of MacWord Scientific stock + Commission for both stocks
= $40,200 + (1,500 shares * $56.24/share) + $124.56
= $40,200 + $84,360 + $124.56
= $124,684.56.
Therefore, the total value of the stocks, including the commission, is $124,684.56.
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