Answer:
4
Step-by-step explanation:
Gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]
Gradient of line segment
[tex] = \frac{14 - 6}{10 - 8} \\ = \frac{8}{2} \\ =4[/tex]
Cotton On Ltd. currently has the following capital structure: Debt: $3,500,000 par value of outstanding bond that pays annually 10% coupon rate with an annual before-tax yield to maturity of 12%. The bond issue has face value of $1,000 and will mature in 20 years. Ordinary shares: $5,500,000 book value of outstanding ordinary shares. Nominal value of each share is $100. The firm plan just paid a $8.50 dividend per share. The firm is maintaining 4% annual growth rate in dividends, which is expected to continue indefinitely. Preferred shares: 45,000 outstanding preferred shares with face value of $100, paying fixed dividend rate of 12%. The firm's marginal tax rate is 30%. Required: a) Calculate the current price of the corporate bond? (4 marks) b) Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%? (3 marks) c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10% (3 marks)
Answer:
a) Calculate the current price of the corporate bond? (4 marks)
$818,18b) Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%? (3 marks)
$176.80c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10% (3 marks)
$120Step-by-step explanation:
total debt = $3,500,000 par value 10$ coupon with a YTM of 12%
YTM = [coupon + (F - P)/n] / [(F + P)/2]
0.12 = [100 + (1,000 - P)/20] / [(1,000 + P)/2]
0.12(500 + 0.5P) = 100 + 50 - 0.05P
60 + 0.06P = 150 - 0.05P
0.11P = 90
P = 90/0.11 = $818.18
total debt = $818.18 x 3,500
stock price:
Div₀ = $8.50
Div₁ = $8.50 x 104% = $8.84
g = 4%
rrr = 9%
using the perpetuity growth model:
stock price = $8.84 / (9% - 4%) = $8.84 / 5% = $176.80
preferred stock:
Div = $12
rrr = 10%
using the perpetuity formula:
preferred stock = $12 / 10% = $120
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. x - 3
Step-by-step explanation:
Set it up like this:
(3x - 2) - (2x + 1)
Combine like terms:
3x - 2 - 2x - 1
3x - 2x = x
-2 - 1 = -3
Put it together:
x - 3
A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x .] Simplify your formula as much as possible.
Answer:
Base Length of 84cmHeight of 42 cm.Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume, [tex]V=x^2h=296352[/tex]
[tex]h=\dfrac{296352}{x^2}[/tex]
Surface Area of the box = Base Area + Area of 4 sides
[tex]A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}[/tex]
Step 2: Find the derivative of A(x)
[tex]If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}[/tex]
Step 3: Set A'(x)=0 and solve for x
[tex]A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84[/tex]
Step 4: Verify that x=84 is a minimum value
We use the second derivative test
[tex]A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6[/tex]
Since the second derivative is positive at x=84, then it is a minimum point.
Recall:
[tex]h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42[/tex]
Therefore, the dimensions that minimizes the box surface area are:
Base Length of 84cmHeight of 42 cm.Urn has 5 white and 7 black balls. Urn has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn is selected, whereas if the outcome is tails, then a ball from urn is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?
Answer:
Suppose that a white ball is selected, the probability that the coin landed tails = (12/37) = 0.3243
Step-by-step explanation:
Complete Question
Urn A has 5 white and 7 black balls. Urn B has 3 white and 12 black balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected. What is the probability that the coin landed tails?
Solution
Let the probability of that a head turns up and urn A is selcted be P(A) = (1/2)
Probability that a tail turns up and urn B is selected = P(B) = (1/2)
Probability that a white ball is picked = P(W)
The probability that a white ball is picked given that the coin toss gives a head and urn A is selected = P(W|A) = (5/12)
The probability that a white ball is picked given that the coin toss gives a tail and urn B is selected = P(W|B) = (3/15) = (1/5)
We now require the probability that the coin lands on a tail and urn B is selected given that a white ball is picked, P(B|W)
Note that the conditional probability P(X|Y) is expressed mathematically as
P(X|Y) = P(X n Y) ÷ P(Y)
And P(X n Y) = P(X|Y) × P(Y)
Hence, the required probability
P(B|W) = P(B n W) ÷ P(W)
Although, we do not have the probabilities P(B n W) and P(W), we can calculate them
P(B n W) = P(W n B) = P(W|B) × P(B) = (1/5) × (1/2) = (1/10)
P(W) = P(W n A) + P(W n B) (Since the events A and B are mutually exclusive)
P(W n A) = P(W|A) × P(A) = (5/12) × (1/2) = (5/24)
P(W n B) = (1/10)
P(W) = (5/24) + (1/10) = (37/120)
P(B|W) = P(B n W) ÷ P(W) = (1/10) ÷ (37/120) = (12/37) = 0.3243
Hope this Helps!!!
Find the value of y.
Answer:
60°
Step-by-step explanation:
The value of y is half the measure of the arc the chord subtends:
y = 120°/2
y = 60°
In Seaton Park school, 60% of the boys play baseball and 24% of the boys play baseball and football. What percentage of those that play baseball also play football?
Answer:
[tex]0.4\%[/tex]
Step-by-step explanation:
Given: 60% of the boys play baseball and 24% of the boys play baseball and football in Seaton Park School
To find: percentage of those that play baseball also play football
Solution:
Let B denotes boys who play baseball and F denotes boys who play football.
[tex]P(B)=60\%[/tex]
[tex]P(F\cap B)=24\%[/tex]
Percentage of those that play baseball also play football = [tex]P\left ( F|B \right )=\frac{P(F\cap B)}{P(B)}=\frac{24}{60}=\frac{2}{5}=0.4\%[/tex]
If A={3,6,9,12 }and B={0,4,8,12}, then find A∩B. *
Answer:
idk
Step-by-step explanation:
Perform the indicated operation and write the answer in the form a + bi.
(1 + i)(-3 - 4i)
Answer:
[tex]1-7i[/tex]
Step-by-step explanation:
[tex]\left(1+i\right)\left(-3-4i\right)[/tex]
[tex]=\left(1\cdot \left(-3\right)-1\cdot \left(-4\right)\right)+\left(1\cdot \left(-4\right)+1\cdot \left(-3\right)\right)i[/tex]
[tex]1\cdot \left(-3\right)-1\cdot \left(-4\right)[/tex]
[tex]=-3+4[/tex]
[tex]=1[/tex]
[tex]1\cdot \left(-4\right)+1\cdot \left(-3\right)[/tex]
[tex]=-4-3[/tex]
[tex]=-7[/tex]
[tex]=1-7i[/tex]
A company estimates that 1% of their products will fall after the original warranty period but within 2 years of the
purchase, with a replacement cost of $480.
If they want to offer a 2 year extended warranty, what price should they charge so that they'll break even (in other words,
so the expected value will be 0)
(round to the nearest cent)
Answer:
They should charge a price of $4.85 so that they'll break even.
Step-by-step explanation:
The expected value will be the sum of the net values multiplied by it's probabilities.
1% of their products will fall after the original warranty period but within 2 years of the purchase, with a replacement cost of $480.
So in 1% = 0.01 of the cases, the company loses $480. That is, a net value of -480.
In 99% = 0.99 of the cases, the company makes x.
The expected value is 0.
We have to find x.
So
[tex]0.99x - 0.01*480 = 0[/tex]
[tex]0.99x = 0.01*480[/tex]
[tex]x = \frac{0.01*480}{0.99}[/tex]
[tex]x = 4.85[/tex]
They should charge a price of $4.85 so that they'll break even.
What is the value of a share of Henley Inc. to an investor who requires a 11 percent
rate of return if Henley is expected to pay a fixed dividend of $1.10 for the next 3 years and
then the dividends will grow at a constant rate of 5% indefinitely
Answer:
Value of Henley Inc.'s share is $16.76
Step-by-step explanation:
The present value of the dividends over for the three years and the terminal value of the dividends would give us a fair share price that an investor would pay
Year 1 PV of dividends=$1.10/(1+11%)^1=$0.99
Year 2 PV of dividends=$1.10/(1+11%)^2=$0.89
Year 3 PV of dividends=$1.10/(1+11%)^3=$0.80
The terminal value formula=dividend*(1+g)/(r-g)
g is the dividend growth rate of 5%
r is the investor's required rate of return which is 11%
terminal value=$1.10*(1+5%)/(11%-5%)=$19.25
The terminal is discounted to present value using the discount factor of year 3
PV of terminal value =$19.25 /(1+11%)^3=$ 14.08
Total present values=$0.99+$0.89+$0.80+$14.08 =$16.76
3. Compute the nominal annual rate of interest compounded semi-annually on a loan of $48000 repaid in installments of $4000 at the end of every 6 months in 10 years.
Answer:
Rate = 51.74%
Step-by-step explanation:
Principal amount= $48000
Amount paid is done 2 times in a year for ten years
= $4000*2*10
Amount paid= $80000
A= p(1+r/n)^nt
80000= 48000(1+r/20)^(20*10)
(80000/48000)= (1+r/20)^(200)
(200)√(1.6667)= 1+ r/20
1.025870255-1= r/20
0.025870255*20= r
0.5174= r
Rate in decimal= 0.5174
In percentage= 51.74%
Alan found 444 marbles to add to the 555 marbles in his collection. Then, he went to the store and tripled the number of marbles he had.
Answer:444+555=999 then(999)^3=9970029999.97*10^8
Step-by-step explanation:
Answer:
the anwser is c
Step-by-step explanation:
On the first day of the trip, he will drive one half of the total distance.On the second day of the trip, he will drive half of the remaining distance.On the third day, he will drive four times the distance of the fourth day.On the fourth day, he will drive 5 miles.How many miles is the total trip?
Answer:
Total distance traveled is 100 miles
Step-by-step explanation:
The man will drive half of the trip on the first day, therefore, distance that will be traveled on the first day = 0.5x
where x is the total distance of the trip.
On the second day, he will drive half of the remaining half of the distance, i.e he will drive 0.5 x 0.5x = 0.25x
This implies that the total distance that will be traveled traveled in the final two days of the journey will also be 0.5 x 0.5x = 0.25x.
0.5x + 0.25x + 0.25x = x, which is the total distance traveled.
on the third day he will drive 4 times the distance of the fourth day, therefore, distance that will be traveled on the third day = 4 x 5 = 20 miles
on the fourth day, he will drive 5 mile.
total of the last two days = 5 + 20 = 25 miles.
this 25 miles is equal to 0.25 of the whole trip. Equating these values, we have
0.25x = 25 miles
x = 25/0.25 = 100 miles
What’s the correct answer for this question?
Answer:
[tex]\frac{2}{13}[/tex]
Step-by-step explanation:
There are 4 suits in a standard deck of cards.
Each suit has a king and a queen.
Thus there are 4 kings and 4 queens
P(king) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
P(queen) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]
P( king) or P(queen) = [tex]\frac{1}{13}[/tex] + [tex]\frac{1}{13}[/tex] = [tex]\frac{2}{13}[/tex]
Question 1
Pogo sells shirts for $14.99 each. Baja Coast has a special deal: buy 2 and
get the third at 30% off the least expensive shirt. There are 3 shirts you want
to buy. At Baja Coast, the 3 shirts you want are $16.99, $15.99, and $15.50.
What is the least amount you can pay for all 3 shirts?
Note - Use the calculator above for help,
Answer:
the cheapest for the 3 shirts you can get is 43.83 (Baja Coast)
Step-by-step explanation:
For the three shirts at Pogo it costs $44.97. However, at the Baja Coast it costs $43.83. So the least amount you pay is $43.87.
What is the complete factorization of p(x)=32x5y−2xy5 over the integers?
Answer:
[tex]p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)[/tex]
Step-by-step explanation:
[tex]p(x)=32x^5y-2xy^5=2xy(16x^4-y^4)=2xy(4x^2-y^2)(4x^2+y^2)\\\\\boxed{p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)}[/tex]
__
The factoring of the difference of squares is applicable:
a^2 -b^2 = (a -b)(a +b)
What is 200÷30=??
Round your answer to the nearest tenths.
Answer: the answer will be 7
Step-by-step explanation:
when i round my answer to the nearest tenths I got 7.
My first answer is 6.66666666667
then I round my answer and got 7 because 6 is bigger than 5 so i can put it as a whole number.
Answer: the answer will be 7
Step-by-step explanation:
when i round my answer to the nearest tenths I got 7.
My first answer is 6.66666666667
then I round my answer and got 7 because 6 is bigger than 5 so i can put it as a whole number.
Brittany rents bicycles to tourists. She recorded the height (in cm) of each customer and the frame size (in cm) of the bicycle that customer rented. After plotting her results, Brittany noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting bicycle frame size from the height of the customer: y=x+ What is the residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame?
Answer: -1
Step-by-step explanation:
Here is the complete question:
Brittany rents bicycles to tourists. She recorded the height (in cm) of each customer and the frame size (in cm) of the bicycle that customer rented. After plotting her results, Brittany noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting bicycle frame size from the height of the customer: y'=1/3x + 1/3.
What is the residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame?
The regression equation is given as:
y'=(1/3)x + (1/3)
Since the height is given as 155cm, x=155 cm
The predicted frame size,
y'=(1/3)x + (1/3)
y'=(1/3) × 155+ (1/3)
= 51 2/3 + 1/3
= 52
The observed frame size,
y=51
Residual = Observed y- predicted y
=51-52
= -1
The residual of a customer with a height of 155 cm who rents a bike with a 51 cm frame is -1.
Answer:
-1
Step-by-step explanation:
Consider the transformation T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v
A. Computer the Jacobian:
\frac{\partial(x, y)}{\partial(u, v)} =
B. The transformation is linear, which implies that ittransforms lines into lines. Thus, it transforms the squareS:-65 \leq u \leq 65, -65 \leq v \leq 65 into a square T(S) with vertices:
T(65, 65) =
T(-65, 65) =
T(-65, -65) =
T(65, -65) =
C. Use the transformation T to evaluate the integral\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}
Answer:
Step-by-step explanation:
[tex]T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v[/tex]
A)
[tex]\frac{d(x,y)}{d(u,v)} =\left|\begin{array}{ccc}x_u&x_v\\y_u&y_v\end{array}\right|[/tex]
[tex]=(\frac{56}{65} )^2+(\frac{33}{65} )^2\\\\=\frac{(56)^2+(33)^2}{(65)^2} \\\\=\frac{4225}{4225} \\\\=1[/tex]
B )
[tex]S:-65 \leq u \leq 65, -65 \leq v \leq 65[/tex]
[tex]T(65,65)=(x=\frac{56}{65} (65)-\frac{33}{65} (65),\ \ y =\frac{33}{65} (65)+\frac{56}{65} (65)\\\\=(23,89)[/tex]
[tex]T(-65,65)=(-56-33,\ \ -33+56)\\\\=(-89,23)[/tex]
[tex]T(-65,-65) = (-56+33,-33-56)\\\\=(-23,-89)[/tex]
[tex]T(65,-65)=(56+33, 33-56)\\\\=(89,-23)[/tex]
C)
[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]
[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(x^2+y^2)(\frac{d(x,y)}{d(u,v)} du\ \ dv[/tex]
Now
[tex]x^2+y^2=(\frac{56}{65} u-\frac{33}{65} v)^2+(\frac{33}{65} u+\frac{56}{65} v)^2[/tex]
[tex][(\frac{56}{65} )^2+(\frac{33}{65}) ^2]u^2+[(\frac{33}{65} )^2+(\frac{56}{65}) ^2]v^2[/tex]
[tex]=\frac{(65)^2}{(65)^2} u^2+\frac{(65)^2}{(65)^2} v^2=u^2+v^2[/tex]
[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]
[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(u^2+v^2) du\ \ dv[/tex]
[tex]=\int\limits^{65}_{-65}\int\limits^{65}_{-65}u^2du \ \ dv+\int\limits^{65}_{-65}\int\limits^{65}_{-65}v^2du \ \ dv[/tex]
By symmetry of the region
[tex]=4\int\limits^{65}_0 \int\limits^{65}_0u^2 du \ \ dv + u\int\limits^{65}_0 \int\limits^{65}_0v^2 du \ \ dv[/tex]
[tex]= 4(\frac{u^3}{3} )^{65}_{0}(v)_0^{65}+(\frac{v^3}{3} )^{65}_{0}(u)_0^{65}\\\\=4[\frac{(65)^4}{3} +\frac{(65)^4}{3} ][/tex]
[tex]=\frac{8}{3} (65)^4[/tex]
Which of the following is NOT a from AGI deduction?
A. Standard deduction
B. Itemized deduction
C. Personal exemption
D. None of these.
All of these are from AGI deductions
The relationship requirement for qualifying relative requires the potential qualifying relative to have a family relationship with the taxpayer.
1. True
2. False
In year 1, the Bennetts' 25-year-old daughter, Jane, is a full-time student at an out-of-state university but she plans to return home after the school year ends. In previous years, Jane has never worked and her parents have always been able to claim her as a dependent. In year 1, a kind neighbor offers to pay for all of Jane's educational and living expenses. Which of the following statements is most accurate regarding whether Jane's parents would be allowed to claim an exemption for Jane in year 1 assuming the neighbor pays for all of Jane's support?
A. No, Jane must include her neighbor's gift as income and thus fails the gross income test for a qualifying relative.
B. Yes, because she is a full-time student and does not provide more than half of her own support, Jane is considered her parent's qualifying child.
C. No, Jane is too old to be considered a qualifying child and fails the support test of a qualifying relative.
D. Yes, because she is a student, her absence is considered as "temporary." Consequently she meets the residence test and is a considered a qualifying child of the Bennetts.
Answer:
1) D. None of these.
2) False
3) C. No, Jane is too old to be considered a qualifying child and fails the support test of a qualifying relative.
Step-by-step explanation:
1) AGI deductions are subtracted from the gross income to calculate the taxable income. Not all the individual's earnings are subject to taxation, therefore some expenses are deducted to calculate the Adjusted Gross Income, the one that will be taxed.
All of the three options listed ( Standard deduction, Itemized deduction, and personal exemption) are AGI deductions.
2) False
The potential qualifying relative does not have to be family/biologically related with the taxpayer. The IRS condition states that he/she is either family related or have lived in the taxpayer's abode for a whole year to be a qualified relative of the taxpayer. So far any of the two conditions are met, it is fine.
C. For a student to be regarded as a qualifying relative of her parents, she must not be up to 24 years at the end of the year according to IRS. Jane is already 25, she is too old and fails the test as a qualifying relative.
What is the range of the function f(x) = -2(64) + 3?
Answer:
Step-by-step explanation:
f(x) = -2(64) + 3 is not a function of x; it's a constant with the single value -125.
Ensure that you have copied down this problem correctly.
Answer: -2 multiply 64 add 3 equals -125
Step-by-step explanation:
-2 multiply 64 add 3
then multiply 2 and 64 which is 128
then add/subtract: -128 add 3 which is -125
Then final answer -2 multiply 64 add 3 equals -125
Suppose that the polynomial function is defined as follows. f(x) = 4(x -11) (x + 9) (x - 5)^3List each zero of according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None." Zero(s) of multiplicity one:_________Zero(s) of multiplicity two:_________ Zero(s) of multiplicity three:_________
Answer:
Zero(s) of multiplicity one: 11,-9
Zero(s) of multiplicity two: None
Zero(s) of multiplicity three: 5
Step-by-step explanation:
Suppose that we have a polynomial function in the following format:
[tex]f(x) = a*(x - x_{0})^{m_{0}}*(x - x_{1})^{m^{1}}*...*(x - x_{n})^{m^{n}}[/tex]
The zeros are [tex]x_{0}, x_{1}, ..., x_{n}[/tex].
The multiplicites are [tex]m_{0}, m_{1},..., m_{n}[/tex]
In this question:
f(x) = 4(x -11) (x + 9) (x - 5)^3
So
11 is a zero of multiplicity 1
-9 is a zero of multiplicity 1
5 is a zero of multiplicity 3.
So the answer is:
Zero(s) of multiplicity one: 11,-9
Zero(s) of multiplicity two: None
Zero(s) of multiplicity three: 5
A gym initially has 5000 members. Each year, the gym loses 10% of its current members and gains 100 new members. Which recursive rule represents the number an of members at the start of the n th year?
Answer:
An = A0 + 100 * n - (An-1) * 0.10
Step-by-step explanation:
Tenemos una regla recursiva para una secuencia es una fórmula que nos dice cómo avanzar de un término a otro en una secuencia. Por lo tanto debemos buscar a An.
Hay un valor inicial que es 5000, una ganancia y una perdida de clientes, que podemos representar así:
An = 5000 + Ganancia - Perdida
Inicial = A0 = 5000
Ganancia = 100, pero cómo sucede cada año, sería: 100 * n
Perdida = 10% de los miembros actuales, si al principio son 5000 por lo tanto A0 * 0.10, pero en este primer caso es que es A0, pero en general serían An-1
reemplazando:
An = A0 + 100 * n - (An-1) * 0.10
In converting 10 pounds to ounces, what unit (omit the number) would you
place in the numerator of your ratio? Use the plural form in your answer.
Remember that there are 16 ounces in 1 pound.
Answer:
pounds
Step-by-step explanation:
pounds : ounces
10 : [tex]x[/tex]
1 : 16
[tex]x=160[/tex]
The numerator would be pounds. [tex]\frac{10 pounds}{160 ounces}[/tex]
Find zw and StartFraction z Over w EndFraction . Leave your answers in polar form. z equals 4 (cosine 150 degrees plus i sine 150 degrees )w equals 2 (cosine 250 degrees plus i sine 250 degrees )
Answer:
a) zw = 8 (Cos 40° + i Sin 40°)
b) (z/w) = 2 (Cos 260° + i Sin 260°)
Step-by-step explanation:
z = 4(Cos 150° + i Sin 150°)
w = 2 (Cos 250° + i Sin 250°)
To first simplify,
Cos 150° = -0.8660
Sin 150° = 0.50
Cos 250° = -0.3420
Sin 250° = -0.9397
z = 4(Cos 150° + i Sin 150°)
z = 4 (-0.866 + 0.5i)
z = (-3.464 + 2i)
w = 2 (Cos 250° + i Sin 250°)
w = 2 (-0.342 -0.9397i)
w = (-0.684 - 1.8794i)
a) zw = (-3.464 + 2i) (-0.684 - 1.8794i)
zw = 2.369376 + 6.5102416i - 1.368i - 3.7588i²
Note that i² = -1
zw = 2.369376 + 5.1422416i + 3.7588
zw = (6.128176 + 5.1422416i)
A general complex number z = x + it has the Polar form = r (cos θ + i sin θ)
r = √(x² + y²)
θ = arctan (y/x)
zw = (6.128176 + 5.1422416i)
x = 6.128176
y = 5.1422416
r = √(6.128176² + 5.1422416²) = 7.99997 = 8
θ = arctan (5.1422416/6.128176) = 40°
zw = 8 (Cos 40° + i Sin 40°)
b) (z/w) = (-3.464 + 2i) / (-0.684 - 1.8794i)
To simplify This, we first rationalize, that is, multiply numerator and denominator by (-0.684 + 1.8794i)
(z/w) = [(-3.464 + 2i)×(-0.684 + 1.8794i)] ÷ [((-0.684 - 1.8794i)×((-0.684 + 1.8794i)
(z/w) = [2.369376 - 6.5102416i - 1.368i + 3.7588i²] ÷ [0.467856 - 3.53214436i²]
Note that i² = -1
(z/w) = [2.369376 - 3.7588 - 7.8782416i] ÷ [0.467856 + 3.53214436]
(z/w) = (-1.389424 - 7.8782416i)/4
(z/w) = (-0.347356 - 1.9695604i)
x = -0.347356
y = -1.9695604
r = √[(-0.347356)² + (-1.9695604)²] = 1.9997 = 2
θ = arctan (-1.9695604)/(-0.347356) = 80° on the first quadrant, but the signs on x and y indicates that this is the third quadrant, hence
θ = 180° + 80° = 260°
(z/w) = 2 (Cos 260° + i Sin 260°)
Hope this Helps!!!
Which equation represents a circle that contains the point (–2, 8) and has a center at (4, 0)?
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Answer:
-3
Step-by-step explanation:
Answer:
[tex](x-4)^2 + y^2= 100[/tex]
Step-by-step explanation:
edgenuity 2020
hope this helps!
Automobile policies are separated into two groups: low-risk and high-risk. Actuary Rahul examines low-risk policies, connuing unl a policy with a claim is found and then stopping. Actuary Toby follows the same procedure with high-risk policies. Each low-risk policy has a 10% probability of having a claim. Each high-risk policy has a 20% probability of having a claim. The claim statuses of polices are mutually independent. Calculate the probability that Actuary Rahul examines fewer policies than Actuary Toby.
Answer:
The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857
Step-by-step explanation:
It is said that Actuary Rahul examines a low risk policy
Probability of a low risk policy having a claim = 10% = 0.1
Actuary Toby examines high risk policy
Probability of a high risk policy having a claim = 20% = 0.2
Let the number of policies examined by actuary Rahul before he finds a claim and stop be n
Probability that actuary Rahul examines exactly n policies = [tex]0.9^{n-1} (0.1)[/tex]
Probability that Toby examines more than n policies = [tex]0.8^n[/tex]
Since the claim statuses of policies are mutually independent, the probability that both events happen simultaneously = [tex]0.9^{n-1} (0.1) (0.8)^n[/tex]
probability that both events happen simultaneously = [tex]\frac{0.1}{0.9} (0.72^{n})[/tex]
The probability that Actuary Rahul examines fewer policies that Actuary Toby = [tex]\sum\limits^ \infty_1 {\frac{0.1}{0.9} 0.72^{n} }[/tex] = [tex]\frac{1}{9}\sum\limits^ \infty_1 { 0.72^{n} } = \frac{1}{9} (\frac{0.72}{1-0.72} ) = \frac{1}{9} (\frac{0.72}{0.28} )[/tex]
The probability that Actuary Rahul examines fewer policies that Actuary Toby = 0.2857
1- A train is travelling at 125mph. How far will it travel in 2 hours?
Answer:
250 miles
Step-by-step explanation:
d= sxt
d= 125x2
125x2= 250
or
mph= miles per hour
there are two hours so 125 +125 =250
Answer=250 miles
Sides KM and FH in the triangles below will be placed together to form a quadrilateral.
Triangle M L K. Side M L has a length of 15 and side L K has a length of 35. Angle L is 110 degrees.Triangle F G H. Side F G has a length of 35 and side G H has a length of 15. Angle G is 110 degrees.
Answer:
Parallelogram (A)
Question:
Sides KM and FH in the triangles below will be placed together to form a quadrilateral.
Triangle M L K. Side M L has a length of 15 and side L K has a length of 35. Angle L is 110 degrees. Triangle F G H. Side F G has a length of 35 and side G H has a length of 15. Angle G is 110 degrees.
Which best describes the quadrilateral that will be formed?
parallelogram
rectangle
rhombus
trapezoid
Step-by-step explanation:
Given:
∆MLK:
Side ML = 15
Side LK = 35
Angle L = 110°
∆ FGH:
Side FG = 35
Side GH = 15
Angle G = 110°
Side MK and FH placed together to form a quadrilateral.
A quadrilateral is a polygon which has 4 sides.
See attachment for diagram
From the diagram and information given:
LK is parallel to FG
ML is parallel to GH
MK = FH
∠L = ∠G (opposite angles are congruent)
Since two pairs of opposite sides are parallel and opposite angles are congruent, it is a paralellogram.
A parallelogram is a quadrilateral which has pairs of opposite sides are parallel and equal.
Answer: Option A
(A) parallelogram
Step-by-step explanation:
I NEED HELP ASAP PLSSSSSSSS HELPPPPPP I BEG OF YOU
In 20 minutes, John can wrap____
small boxes and Hank can wrap____
small boxes. So, Hank can wrap_____
more small boxes in 20 minutes than John can.
