9514 1404 393
Answer:
(a) -29,884,416
(b) C(n,(n -k)/2) . . . where C(n,k) = n!/(k!(n-k)!) and k ∈ ℕ
Step-by-step explanation:
(a) The coefficient of the k-th term of the expansion is ...
C(20,k)(3x)^(20-k)(-2y)^k
For k=19, this is ...
19(3x)(-2y)^19 = -29,884,416xy^19
The coefficient of the term is -29,884,416.
__
(b) The p-th term of the expansion of (x +1/x)^n is ...
C(n,p)(x^(n-p)(1/x)^p = C(n,p)(x^(n-2p))
For some exponent k of x, the value of p will be ...
k = n -2p
p = (n -k)/2
Then the coefficient of x^k will be C(n, (n-k)/2), where C(n, x) = n!/(x!(n-x)!).
You will notice that there will only be a term x^k for k having the same parity as n.
Find the sale price of the item. Round to two decimal places if necessary.
Original price: $224.97
Markdown: 73%
The sale price is $
How do you do these questions?
I'll do the first problem to get you started.
Part (a)
We have a separable equation. Get the y term to the left side and then integrate to get
[tex]\frac{dy}{dt} = ky^{1+c}\\\\\frac{dy}{y^{1+c}} = kdt\\\\\displaystyle \int\frac{dy}{y^{1+c}} = \int kdt\\\\\displaystyle \int y^{-(1+c)}dy = \int kdt\\\\\displaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\[/tex]
I'm using D as the integration constant rather than C since lowercase letter c was already taken.
Let's use initial condition that [tex]y(0) = y_0[/tex]. This means we'll plug in t = 0 and [tex]y = y_0[/tex]. After doing so, solve for D
[tex]\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\\displaystyle -\frac{1}{c*(y_0)^{c}} = k*0+D\\\\\displaystyle D = -\frac{1}{c*(y_0)^{c}}\\\\[/tex]
Let's plug that in and isolate y
[tex]\diplaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\\\diplaystyle -\frac{1}{c}y^{-c} = kt-\frac{1}{c*(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = -ckt+\frac{1}{(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle \frac{1}{y^{c}} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle y^{c} = \frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\\\\\\\diplaystyle y = \left(\frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\right)^{1/c}\\\\\\\diplaystyle y = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\[/tex]
-------------------------
We end up with [tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\[/tex] as our final solution. There are likely other forms to express this equation.
========================================================
Part (b)
We want y(t) to approach positive infinity.
Based on the solution in part (a), this will happen when the denominator approaches 0 from the left.
So [tex]y(t) \to \infty[/tex] as [tex]1-c*(y_0)^{c}kt \to 0[/tex] in which we can effectively "solve" for t showing that [tex]t \to \frac{1}{c*(y_0)^{c}k}[/tex]
If we define [tex]T = \frac{1}{c*(y_0)^{c}k}[/tex] , then approaching T from the left side will have y(t) approach positive infinity.
This uppercase T value is doomsday. This the time value lowercase t approaches from the left when the population y(t) explodes to positive infinity.
Effectively t = T is the vertical asymptote.
========================================================
Part (c)
We're told that the initial condition is y(0) = 5 since at time 0, we have 5 rabbits. This means [tex]y_0 = 5[/tex]
Another fact we know is that y(3) = 35 because after three months, there are 35 rabbits.
Lastly, we know that c = 0.01 since the exponent of dy/dt = ky^(1.01) is 1.01; so we solve 1+c = 1.01 to get c = 0.01
We'll use y(3) = 35, c = 0.01 and [tex]y_0 = 5[/tex] to solve for k
Doing so leads to the following:
[tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\\displaystyle y(3) = \frac{5}{\left(1-0.01*(5)^{0.01}k*3\right)^{1/0.01}}\\\\\\\displaystyle 35 \approx \frac{5}{\left(1-0.0304867k\right)^{100}}\\\\\\\displaystyle 35\left(1-0.0304867k\right)^{100} \approx 5\\\\\\\displaystyle \left(1-0.0304867k\right)^{100} \approx \frac{1}{7}\\\\\\[/tex]
[tex]\displaystyle \left(1-0.0304867k\right)^{100} \approx 7^{-1}\\\\\\\displaystyle 1-0.0304867k \approx \left(7^{-1}\right)^{1/100}\\\\\\\displaystyle 1-0.0304867k \approx 7^{-0.01}\\\\\\\displaystyle k \approx \frac{7^{-0.01}-1}{-0.0304867}\\\\\\\displaystyle k \approx 0.63211155281122\\\\\\\displaystyle k \approx 0.632112\\\\\\[/tex]
We can now compute the doomsday time value
[tex]T = \frac{1}{c*(y_0)^c*k}\\\\\\T \approx \frac{1}{0.01*(5)^{0.01}*0.632112}\\\\\\T \approx \frac{1}{0.00642367758836}\\\\\\T \approx 155.674064621806\\\\\\T \approx 155.67\\\\\\[/tex]
The answer is approximately 155.67 months
18 ÷ x = -2
what is x PLEASE HELP FAST AS YOU CAN!!!!!!!!!!!!!!! I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST AND CORRECTLY 10 POINTS!!!!!!!!!
Answer: x=-9
Step-by-step explanation:
18/x=-2
multiply x
18=-2x
divide by -2
-9=x
x=-9
Answer:
[tex]18 \div x = - 2 \\ \frac{18}{x} = - 2 \\ x = \frac{18}{ (- 2)} \\ \boxed{x = - 9}[/tex]
-9 is the right answerA fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the variance to be 2.89. She thinks the mean is 5.6 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.11 at the 98% level of confidence?
Answer:
The minimum sample required = 1296.65
Step-by-step explanation:
Given that:
Variance [tex]\sigma^2 = 2.89[/tex]
Standard deviation [tex]\sigma = \sqrt{2.89}[/tex]
Standard deviation [tex]\sigma = 1.7[/tex]
Margin of error = 0.11
Confidence Interval = 98%
Level of significance = 1 - 0.98 = 0.02
The critical value = [tex]Z _{\alpha//2} = Z_{0.02/2} = Z_{0.01}[/tex]
= 2.33
Thus, the minimum sample size is given by the formula:
[tex]n = \bigg ( \dfrac{Z_{\alpha/2} \times \sigma }{E} \bigg)^2[/tex]
[tex]n = \bigg (\dfrac{2.33 \times 1.7 }{0.11} \bigg)^2[/tex]
n = 1296.65
Garrett reflects points A and B across the y-axis to make the images of the points A' and B'. If the distance between points A and B is 10 units, what is the distance between points A' and B'? Explain your answer.
Answer:
A'B' = AB = 10Step-by-step explanation:
Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units
Let the coordinates be:
A = (x1, y1) and B(x2, y2)Reflection:
A'= (-x1, y1) and B(-x2, y2) as per ruleLets compare distances:
AB = √(x2-x1)² + (y2 - y1)²and
A'B' = √(-x2 - (-x1))² + (y2 - y1)² = √(-(x2 - x1))² + (y2-y1)² = √(x2-x1)² + (y2 - y1)²As we see the results are same
Answer:
Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units
Step-by-step explanation:
producto de (10x+7)(10x-7)
Answer:
(10x−7)^2
Step-by-step explanation:
(10x+7)(10x-7)
i stead of making it a "100" since they are both the same but positive and negative () and bring it to the power of 2
A class has 48 minutes available to hear reports from 15 students. if the time is to be divided equally, how long may each student have?
Answer:
No, every student will have 3.2 minutes
Answer:
Each student has approximately 3 minutes and 12 seconds.
Step-by-step explanation:
You divide the total amount of minutes by the total amount of students. 48/15=3.2
After you get your answer, you convert to minutes. There are 3 minutes and the .2 converts to 12 seconds
2. Mr Alison fill ups his car at the gas station. He also gets a car wash at the station and visits with the manager, Then he drives to the next town on buisness
Which graph did you not choose for exercise 1 and 2?
Answer:
Hmm graph 3, i think.
Step-by-step explanation:
answer the geometry questions attached :) (you need to also find c)
Answer:
a = 18
b = 6√3
Step-by-step explanation:
WE can see in the diagram that there are two right angled triangles formed.
One with 45° angle as other interior angle and other with 60° interior angle.
So we will take the triangles one by one to find the required values.
As a is used in both triangles, first we will find the value of a using the left triangle.
In the triangle,
Hypotenuse = h = 18√2
θ = 45°
Using trigonometric ratio:
[tex]sin\ 45 =\frac{Perpendicular}{Hypotenuse}\\\frac{1}{\sqrt{2}}= \frac{a}{18\sqrt{2}}\\a = \frac{1}{\sqrt{2}} * 18\sqrt{2}\\a = 18[/tex]
Now in the right side triangle
θ1 = 60°
Perpendicular = a = 18
Base = b = ?
So,
[tex]tan\ 60 = \frac{perpendicular}{base}\\\sqrt{3} = \frac{\sqrt{18}}{b}\\b = \frac{18}{\sqrt{3}}\\b = \frac{6*3}{\sqrt{3}}\\b = \frac{6*\sqrt{3}*\sqrt{3}}{\sqrt{3}}\\b = 6\sqrt{3}[/tex]
Hence,
a = 18
b = 6√3
Find the area of this
Answer:
616
Step-by-step explanation:
What is the measure of M?
Answer:
<M = 50
Step-by-step explanation:
The sum of the angles of a triangle is 180
52+ 78+x = 180
Combine like terms
130 +x = 180
Subtract 130 from each side
130+x-130 =180-130
x = 50
Answer:
50°
Step-by-step explanation:
180 is the total of all the angles added together.
so if you subtract the 2 you already know from the total, you’ll have the size of the angle M.
180 - (52+78) = 180 - 130 = 50°
Solve for x in this equation: 3/4+|5-x| = 13/4
step 1: 3/4
step 2: -5/2
step 3: 5-x= 5/2
step 4: 5
step 5: 5/2
I just did the equation on edgeinuity 2020
Answer: X =5/2, 15/2 x=2.5, 7.5
Step-by-step explanation:
Please help with math
Are the two hearts congruent? How do you know?
Answer:
yes they are congruent
Step-by-step explanation:
they both the same shape and size
Express 45% as a ratio in its simplest form.
Answer:
4:5 is the ratio in it simplest form
Need help with this both please help me it due today at 11:59pm please will mark brainiest please
Answer:
c= -20
x= 38
Explanation:
Solve for x and c by simplifying both sides of the equation, then isolating the variable.
hope this helps!
Find the area of a right isosceles triangle with hypotenuse 10\sqrt{2}10
2 units
Answer:
A = 50 square units
Step-by-step explanation:
Right Triangles
A right triangle is identified because it has one internal angle of 90°.
The longest side is called hypotenuse and the other two sides are called legs. Being c the hypotenuse and a and b the legs, the Pythagora's theorem relates the with the equation:
[tex]c^2=a^2+b^2[/tex]
If the triangle is also isosceles, then both legs have the same measure or a=b:
[tex]c^2=a^2+a^2=2a^2[/tex]
Since we know the hypotenuse has a measure of 10\sqrt{2}:
[tex](10\sqrt{2})^2=2a^2[/tex]
Operating:
[tex]100*2=2a^2[/tex]
Dividing by 2:
[tex]a^2=100~~\Rightarrow a=\sqrt{100}[/tex]
a = 10 units
The area of the triangle is:
[tex]\displaystyle A=\frac{a.b}{2}[/tex]
[tex]\displaystyle A=\frac{10*10}{2}[/tex]
A = 50 square units
What is the cost of 2 bags of sugar if 3 bags cost $5.25 and the unit price for each bag is the same.
Answer:
$3.50
Step-by-step explanation:
5.25/3 = 1.75
1.75 x 2 = 3.5
If the temperature changes - 5/8 degrees per hour for 8 hours, what is the total change in temperature?
Answer:
I think it is 5.
Step-by-step explanation:
5/8 in decimal form is 0.625. 0.625 x 8 = 5. I hope this helps/ sorry if it didn't.
Brittany buys 2.55 pounds of turkey for $5.96 per pound and 3.7 pounds of
cheese for $3.35 per pound. She gave the clerk twenty dollars. How much
more money does Brittany need? Include your units.
Answer:
Brittany needs another $3.7405.
Step-by-step explanation:
Per pound Cost of turkey = $5.96 per pound
The amount Brittany buys the turkey = 2.55 pounds
Brittany's cost for turkey = 2.55 × $5.96 = $15.198
Per pound cost for cheese = $3.35 per pound
The amount Brittany buys the cheese = 3.7 pounds
Brittany's cost for cheese = 2.55 × $3.35 = $8.5425
So,
Brittany's total cost = Turkey cost + Cheese cost
= $15.198 + $8.5425
= $23.7405
As brittany gave the clerk 20 dollars.
So, the amount she further needs will be:
$23.7405 - $20 = $3.7405
Therefore, Brittany needs another $3.7405.
For the equation given below, evaluate y′ at the point (2,2).
xe^y−4y=3x−14+2e^2.
Answer:
[tex]y'\approx -0.41[/tex]
Step-by-step explanation:
Implicit Derivatives
When it's not possible to express one variable as an explicit function of the other, we use implicit derivatives and solve for y'.
Find y' in the equation given below:
xe^y - 4y = 3x - 14 + 2e^2
Taking derivatives with respect to x, recalling y'=dy/dx, and dx/dx=1:
(xe^y)' - (4y)' = (3x)' - (14 + 2e^2 )'
Using the product rule for the first derivative, and simple rules for the rest:
e^y + xe^yy' - 4y' = 3 - 0
Recall the derivative of a constant is zero.
Group terms with y' in the left side and the rest in the right side:
xe^yy' - 4y' = 3 - e^y
Factoring y':
y'(xe^y - 4) = 3 - e^y
Solving:
[tex]\displaystyle y'=\frac{3 - e^y}{xe^y - 4}[/tex]
Evaluating for x=2, y=2:
[tex]\displaystyle y'=\frac{3 - e^2}{2e^2 - 4}[/tex]
Calculating:
[tex]\mathbf{y'\approx -0.41}[/tex]
What percent is Rs15 of Rs 60?
Answer:
25%
Step-by-step explanation:
25% of 60 = 15
What is the product of = 4/9 and 1/11?
4/99
5/99
9/44
1/4
4/9 and 1/11
product means multiplying
4 times 1
4*1=4
9 times 11
9*11=99
answer: 4/99
(-3,6] to inequality
Answer:
-3 < x ≤ 6
Step-by-step explanation:
Left side is exclusive, right side is inclusive, hence the < and ≤, respectively.
5x−4 = 3x +8
i need the steps on how to find x
plz, i got a 0 the first time i did it
Answer:
5x − 4 = 3x + 8
5x - 4 + 4 = 3x + 8 + 4
5x = 3x + 12
5x - 3x = 3x + 12 - 3x
2x = 12
2x / 2 = 12 / 2
x = 6
Answer:
x=6
Step-by-step explanation:
Let's solve your equation step-by-step.
5x−4=3x+8
Step 1: Subtract 3x from both sides.
5x−4−3x=3x+8−3x
2x−4=8
Step 2: Add 4 to both sides.
2x−4+4=8+4
2x=12
Step 3: Divide both sides by 2.
2x/2=12/2
x=6
Answer:
x=6
There are 25 questions in a quiz, what is the minimum score you can get
Answer:
7/25
Step-by-step explanation:
From randomly guessing, it depends on how many you think you got right and how many you really don't know. You could get all 25 wrong, but more likely at random get 7 right.
Answer:
The minimum score you can get is 0.
Step-by-step explanation:
Use a standard inch ruler to answer this question
Carmen is an engineer making plans to run a rail line, represented by the transversal t, through a city. Parallel lines v and w are crossed by transversal t. Clockwise from top left, the angles formed with line v are 155 degrees, blank, blank, blank; with line w are 1, 2, 3, 4. Examine Carmen’s rail plans to identify the measure of ∠1. The streets represented by lines V and W are parallel. What is the mAngle1? 25° 35° 145° 155°
Answer:
155
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
I took the quiz
Easy Car Corp. is a grocery store located in the Southwest. It paid an annual dividend of $2.00 last year to its shareholders and plans to increase the dividend annually at the rate of 4.0%. It currently has 2,000,000 common shares outstanding. The shares currently sell for $13 each. Easy Car Corp. also has 30,000 semiannual bonds outstanding with a coupon rate of 10%, a maturity of 23 years, and a par value of $1,000. The bonds currently have a yield to maturity (YTM) of 8%. What is the weighted average cost of capital (WACC) for Easy Car Corp. if the corporate tax rate is 30%?
When answering this problem enter your answer using percentage notation but do not use the % symbol and use two decimals (rounding). For example, if your answer is 0.10469 then enter 10.47; if your answer is 10% then enter 10.00
Answer:_____
Answer:
Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.
Step-by-step explanation:
This can be calculated using the following steps:
Step 1: Calculation of the current bond price
Semiannual coupon amount = Bond face value * Semiannual coupon rate = $1000 * (10% / 2) = $50
Semiannual coupon discount factor = ((1 - (1 / (1 + r))^n) / r) .......... (1)
Where;
r = Semiannual yield to maturity (YTM) = 8% / 2 = 0.08 / 2 = 0.04
n = number of semiannuals = 23 years * 2 = 46
Substituting the values into equation (1), we have:
Semiannual coupon discount factor = ((1-(1/(1 + 0.04))^46) / 0.04) = 20.8846535613106
Present value of coupon = (Semiannual coupon amount * Semiannual coupon discount factor) = $50 * 20.8846535613106 = $1,044.23
Present value of the face value of the bond = Face value / (1 + r)^n = $1,000 / (1 + 0.04)^46 = $164.61
Therefore, we have:
Current bond price = Present value coupon + Present value of the face value of the bond = $1,044.23 + $164.61 = $1,208.84
Step 2: Calculation of weights of each finance source
Market value of common shares outstanding = Number common shares outstanding * Current price per share = 2,000,000 * $13 = $26,000,000.
Market value of bond = Number of bonds * Current bond price = 30,000 * $1,208.84 = $36,265,200
Total financing market value = Market value of common shares outstanding + Market value of bond = $26,000,000 + $36,265,200 = $62,265,200
Weight of Market value of common shares outstanding = Market value of common shares outstanding / Total financing market value = $26,000,000 / $62,265,200 = 0.42
Weight of Market value of bond = Market value of bond / Total financing market value = $36,265,200 / $62,265,200 = 0.58
Step 3: Calculation of return on equity
Current year dividend = Last year dividend * (1 + Dividend growth rate) = $2 * (1 + 4.0%) = $2.08
Next year dividend = Current year dividend * (1 + Dividend growth rate) = $2.08 * (1 + 4.0%) = $2.1632
The return on equity can now be calculated using the following formula:
Current share price = Next year dividend / (Return on equity – Dividend growth rate) ………………….. (2)
Where;
Current share price = $13
Next year dividend = $2.1632
Return on equity = ?
Dividend growth rate = 4.0%, or 0.04
Substituting the values into equation (2) and solve for return on equity, we have:
13 = 2.1632 / (Return on equity - 0.04)
13 * (Return on equity - 0.04) = 2.1632
(13 * Return on equity) – (13 * 0.04) = 2.1632
(13 * Return on equity) – 0.52 = 2.1632
13 * Return on equity = 2.1632 + 0.52
Return on equity = 2.6832 / 13
Return on equity = 0.21
Step 4: Calculation of Weighted average cost of capital
Weighted average cost of capital = (WS * CE) + (WD * CD * (1 – T)) ………………… (4)
Where;
WS = Weight of Market value of common shares outstanding = 0.42
WD = Weight of debt = Weight of Market value of bond = 0.58
CE = Cost of equity = Return on equity = 0.21
CD = Cost of debt = YTM = 8%, or 0.08
T = Tax rate = 30%, or 0.30
Substituting the values into equation (3), we have:
Weighted average cost of capital = (0.42 * 0.21) + (0.58 * 0.08 * (1 - 0.30)) = 0.12068, or 12.068%
Rounding to two decimal places, we have:
Weighted average cost of capital = 12.07%
Since the instruction in the question indicates that the % symbol should not be used, the weighted average cost of capital (WACC) for Easy Car Corp is therefore 12.07.
If line lis parallel to line m, find the value of x and y. (please help taking a test)
(7x + 12)
(12x - 28)
(9y - 77)"
O x = 10.3 and y = 17.9
O x = 8 and y = 21
O x = 7 and y = 12
x = 12 and y = 7
Answer:
x=8 and y=21
Step-by-step explanation:
12x-28=7x+12 (the 2 angles are equivalent)
12x-7x=12+28
5x=40
x=8
9y-77 + 12x-28 =180 (the sum of those 2 angles is a flat angle (180°))
9y-77+12*8-28=180
9y=180+28+77-96
9y=189
y=21