What’s the correct answer for this?

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!!!

Answer:

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)

Step-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

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.

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%

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

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]

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.

Answer:

There is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

Step-by-step explanation:

Here we have our null hypothesis as H₀: σ² = s²

Our alternative hypothesis is then Hₐ: σ² ≠ s²

We therefore have a two tailed test

To test the hypothesis of difference in standard deviation which is the Chi squared test given as follows

[tex]\chi ^{2} = \dfrac{\left (n-1 \right )s^{2}}{\sigma ^{2}}[/tex]

Where:

n = Size of sample

s² = Variance of sample = 950²

σ² = Variance of population = 650²

Degrees of freedom = n - 1 = 71 - 1 = 70

α = Significance level = 0.1

Therefore, we use 1 - 0.1 = 0.9

From the Chi-square table, we have the critical value as

1 - α/2 = 51.739,  

α/2 = 90.531

Plugging the values in the above Chi squared test equation, we have;

[tex]\chi ^{2} = \dfrac{\left (23-1 \right )950^{2}}{650 ^{2}} = 49.994[/tex]

Therefore, since the test value within the critical region, we do not reject the null hypothesis, hence there is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

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

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°

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:

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

Answer:444+555=999 then(999)^3=9970029999.97*10^8

Step-by-step explanation:

Answer:

the anwser is c

Step-by-step explanation:

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

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

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]

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

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

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!!!

Answer:

-3

Step-by-step explanation:

Answer:

[tex](x-4)^2 + y^2= 100[/tex]

Step-by-step explanation:

edgenuity 2020

hope this helps!

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.

Answer:

idk

Step-by-step explanation:

Answer:

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:

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:

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]

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)

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]

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.

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]