A set of composite numbers less than 12 .express it in listing and set builder methods​

Answers

Answer 1

Given:

A set of composite numbers less than 12.

To find:

The set by listing and set builder methods​.

Solution:

Composite number: A positive integer is called a composite number if it has at least one divisor other than 1 and itself.

Composite numbers less than 12 are 4, 6, 8, 9, 10.

By using the listing method , the given set can be expression as:

Set = {4, 6, 8, 9, 10}

The numbers 4, 6, 8, 9, 10 are greater than 1, less than 12 and non prime numbers.

By using set builder method, the given set can be expression as:

Set = [tex]\{x|x\neq P,1<x<12\}[/tex]

Therefore, the list and set builder notation of the given set are {4, 6, 8, 9, 10} and [tex]\{x|x\neq P,1<x<12\}[/tex] respectively.


Related Questions

what are important of mountain ?​

Answers

Answer:

hlw its jess

your answer is here

Mountains are particularly important for their biodiversity, water, clean air, research, cultural diversity, leisure, landscape and spiritual values.

Step-by-step explanation:

hope it may help you

mark as brainlist please

Put these numbers in order from least to greatest.

1 1/8, 0.7, and 1.4

Answers

Answer:

1.4, 1 1/8, 0.7

Step-by-step explanation:

1 1/8 is equal to 1.125 which it makes it less than 1.4 but more than 0.7.

Answer:

[tex]0.7, \frac{11}{8},1.4[/tex]

Step-by-step explanation:

In order to understand what numbers are greater and what numbers are smaller, we need to make them have the same common denominator. So firstly, we turn all of these numbers into fractions, and we get...

[tex]0.7 = \frac{7}{10}\\\\1.4 = \frac{14}{10}\\\\\frac{11}{8 }= \frac{11}{8 }[/tex]

Now we, need to find the least possible number divisible by 10 and 8, to find the least common denominator. And we get, that the least common denominator is 40, and knowing this, now we have to take each fraction and turn it into an equivalent fraction with the denominator of 40. So we do...

[tex]\frac{11}{8}= \frac{(11)(5)}{(8)(5)}= \frac{55}{40}\\\\\frac{7}{10} = \frac{(7)(4)}{(10)(4)} = \frac{28}{40} \\\\\frac{14}{10} = \frac{(14)(4)}{(10)(4)} = \frac{56}{40}[/tex]

Now we can put these fractions in order from least to greatest...

[tex]\frac{28}{40} < \frac{55}{40}<\frac{56}{40}[/tex]

Therefore, we know that...

[tex]0.7 < \frac{11}{8} < 1.4[/tex]


6. Find the slope of the line that passes through the following 2
points. Use the slope formula.
(-2, 4) (2, 4)

Answers

Answer:

You would do the change in y over the change in x.  

That means you subtract your y values and that's the numerator.  Subtract your x values and that is your denominator.  Then simplify.

(4 - 4)

______

(-2 - 2)

Step-by-step explanation:

Answer: y=4

Step-by-step explanation:

4 is the y-intercept. The slope is 0

Let A and B be two independent events. If p(A)=3/5 and p(B')=1/3 then the value of p(AUB)' is equal to?

Answers

Answer:

P(AUB)'=2/15

Step-by-step explanation:

According to the Question,

Given That, A and B be two independent events. If P(A)=3/5 and P(B')=1/3.

So, P(B)=1-P(B') ⇒ P(B)=1-(1/3) ⇔ P(B)=2/3

The Product Rule of Probability says For independent events P(A∩B)=P(A)×P(B)

P(A∩B)=3/5 × 2/3 ⇒ P(A∩B)=2/5

We know, P(AUB)=P(A)+P(B)-P(A∩B)

Thus, P(AUB)= 3/5 + 2/3 - 2/5

P(AUB)=1/5 + 2/3

P(AUB)=(3+10)/15 ⇔P(AUB)=13/15

Now, The Value Of P(AUB)'=1-P(AUB) ⇔ 1 - 13/15 ⇒ P(AUB)'=2/15

When an algebraic expression can be written as the product of two or more expressions, then each of these expressions is called a ____________of the given expression.​

Answers

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

=> Factor.

When an algebraic expression can be written as the product of two or more expressions, then each of these expressions is called a factor of the given expression.

[tex] \sf \: It's \: called \: a \: \boxed{\underline{\bf \: factor}}[/tex]

When an algebraic expression can be written as the product of two or more expressions, then each of these expressions is called a [tex]\boxed{\underline{\bf \: factor}}[/tex]of the given expression.

Does anyone know the answer ?!??!

Answers

Answer:

1/15

Step-by-step explanation:

Step 1 find probability of pulling 1 pink marble

Like stated previously probability = # of favorable outcomes / # of possible outcomes

The favorable outcomes is what we want to happen

We want to pull a pink marble and there are a total of 3 pink marbles

So # of favorable outcomes = 3

To find the # of possible outcomes we simply find the number of marbles. There are a total of ten marbles

So probability of pulling one pink marble = 3/10

Step 2 find the probability of pulling another pink marble ( IMPORTANT NOTE: It says to find the probability of pulling 2 pink marbles if the first one is NOT put back before the second pull. this meaning that we must subtract 1 from the total # of marbles and 1 from the total # of pink marbles )

3 - 1 = 2

10 - 1 = 9

So after the first pull there would be 2 pink marbles out of 9 total marbles

So the probability of pulling a pink marble on the second pull is 2/9

Finally we multiply the two probabilities together to find our answer

3/10 * 2/9 = 1/15

Given the equation f(x)=2x^2-14x+10, find g(x), the image of f(x) after a ry=x (reflection over the line y=x). Express your answer as a single fraction. ​

Answers

Given:

The function is:

[tex]f(x)=2x^2-14x+10[/tex]

The function g(x), the image of f(x) after a [tex]r_{y=x}[/tex] (reflection over the line y=x).

To find:

The function g(x).

Solution:

We have,

[tex]f(x)=2x^2-14x+10[/tex]

Substitute [tex]f(x)=y[/tex] in the given function.

[tex]y=2x^2-14x+10[/tex]

The function g(x), the image of f(x) after a [tex]r_{y=x}[/tex] (reflection over the line y=x). So, interchange x and y.

[tex]x=2y^2-14y+10[/tex]

Now, we need to find the value of y.

[tex]x=2(y^2-7y+5)[/tex]

[tex]\dfrac{x}{2}=y^2-7y+5[/tex]             [Divide both sides by 2]

[tex]\dfrac{x}{2}-5=y^2-7y[/tex]             [Subtract 5 from both sides]

Add both sides half of square of coefficient of y, i.e. [tex](\dfrac{-7}{2})^2[/tex], to make it perfect square.

[tex]\dfrac{x}{2}-5+(\dfrac{-7}{2})^2=y^2-7y+(\dfrac{-7}{2})^2[/tex]

[tex]\dfrac{x}{2}-5+\dfrac{49}{4}=y^2-7y+(\dfrac{7}{2})^2[/tex]

[tex]\dfrac{x}{2}-5+\dfrac{49}{4}=\left(y-\dfrac{7}{2}\right)^2[/tex]          [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]

[tex]\dfrac{x}{2}+\dfrac{49-20}{4}=\left(y-\dfrac{7}{2}\right)^2[/tex]

Taking square root on both sides, we get

[tex]\pm\sqrt{\dfrac{x}{2}+\dfrac{29}{4}}=y-\dfrac{7}{2}[/tex]

[tex]\dfrac{7}{2}\pm\sqrt{\dfrac{2x+29}{4}}=y[/tex]

[tex]\dfrac{7}{2}\pm\dfrac{\sqrt{2x+29}}{2}=y[/tex]

[tex]\dfrac{7\pm \sqrt{2x+29}}{2}=y[/tex]

Substituting [tex]y=g(x)[/tex], we get

[tex]\dfrac{7\pm \sqrt{2x+29}}{2}=g(x)[/tex]

Therefore, the required function is [tex]g(x)=\dfrac{7\pm \sqrt{2x+29}}{2}[/tex].

No files just type it in

Answers

Answer:

ok kdkdkddkkdkdkkfkffk

Answer:

37

Explanation:

3 + 3 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4

if my answer did help mark me as brainlist :D

(G-GPE.B.4) Prove or disprove the triangle with vertices R (−2, −2), S (1, 4), and T (4, -5) is an equilateral triangle.

Answers

Answer:

RST is not an equilateral

Step-by-step explanation:

Given

[tex]R = (-2,-2)[/tex]

[tex]S = (1,4)[/tex]

[tex]T = (4,5)[/tex]

Required

Prove or disprove the triangle is equilateral

To do this, we simply calculate the distance between each vertex using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]RS = \sqrt{(-2 - 1)^2 + (-2 - 4)^2}[/tex]

[tex]RS = \sqrt{45}[/tex]

[tex]ST = \sqrt{(1 - 4)^2 + (4 - 5)^2}[/tex]

[tex]ST = \sqrt{10}[/tex]

[tex]RS \ne ST[/tex] means the triangle is not an equilateral

What is the sum of the fractions? Use the number line to help find the answer.|
+
5

Answers

Answer:

-4/5

Step-by-step explanation:

If you use the number line, after adding 3/5 you can see that it still doesn't make it positive but brings it up to -4/5 (Hope this helps)

Answer:

You subtract them:

3/5-7/5 (the plus disappears when faced with a minus)

-4/5

Complete the function for this graph.

Answers

Answer:

y = |x - (-2)| -3

Step-by-step explanation:

Em 2016 o brasil vendeu para o exterior cerca de 3,5 milhoes de ingressos para espectadores estrangeiros sabendo total de ingressos vendidos é de 7,9 milhoes a quantia de ingressos vendida para a população brasileira foi de? a) 4.050.000 B) 4.400.000 C) 5.000.000 D) 5.500.000

Answers

Responder:

4.400.000

Explicação passo a passo:

A quantidade total de ingressos vendidos = 7,9 milhões = 7.900.000

Desse total, o valor vendido ao espectador estrangeiro = 3,5 milhões, = 3,5 milhões

O valor dos ingressos vendidos ao espectador brasileiro será a diferença entre o valor total do ingresso vendido e o total vendido ao espectador estrangeiro.

7.900.000 - 3.500.000 = 4.400.000

Simplify fully
(x²+3)² - (x²-1)²

Answers

Answer:

8x² + 8

Step-by-step explanation:

Given

(x² + 3)² - (x² - 1)² ← expand factors using FOIL

= [tex]x^{4}[/tex] + 6x² + 9 - ([tex]x^{4}[/tex] - 2x² + 1) ← distribute by - 1

= [tex]x^{4}[/tex] + 6x² + 9 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms

= 8x² + 8

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Answers

Answer:

x=57°

Step-by-step explanation:

the sum of the measures of the angles of a triangle add up to 180°.

it is given that there is a 33°, and a right angle which is 90°.

to find x:

x=180°-(90°+33°)

x=180°-123°

x=57°

Answer:

180° - 33° - 90° = 57°

x = 57°

HELP ASAPPPP
****
Liliana noted that the temperature was 45 degrees when she woke up. At noon she started recording the increase in
degrees from the morning temperature.
Vx
Temperature
30
Increase in Degrees
12 p.m. -
2 p.m. -
3:59 p.m.
4 p.m. - 6 p.m. -
5:59 p.m.
7:59 p.m.
Time of Day
8 p.m. -
9:59 p.m.
1:59 p.m.
10 p.m. -
11:59 p.m.
Which statement most reasonably explains the hours after the peak increase in temperature?

Answers

Answer:

C. The temperature increase went down because it became cooler as the sun went down for the night

Step-by-step explanation:

It is natural to have high temperatures when the sun is up, and as dusk begin to set, the temperature of a place drops. L

Going by the above stated fact, to explain the hours after the peak increase in temperature, it is plausible to conclude that as the sun went down, it became cooler for the night. That's why we have the lowest temperature displayed on the graph between 10 PM to 11:59 PM.

The function f(x) = 4x + 8 represents the distance traveled by a herd of elephants in miles. The function g(x) = x − 1 represents the time the herd traveled in hours. Solve f divided by g of 4, and interpret the answer.

Answers

Answer:

[tex](f/g)(4)=8[/tex]

Interpretation: 4 elephants traveled at a speed of 8 miles per hour

Step-by-step explanation:

Given

[tex]f(x) = 4x + 8[/tex]

[tex]g(x) = x -1[/tex]

Required

[tex](f/g)(4)[/tex]

This is calculated as:

[tex](f/g)(4)=\frac{f(4)}{g(4)}[/tex]

We have:

[tex]f(x) = 4x + 8[/tex]

[tex]f(4) = 4 * 4 + 8 =24[/tex]

[tex]g(x) = x -1[/tex]

[tex]g(4) = 4 - 1 = 3[/tex]

So:

[tex](f/g)(4)=\frac{f(4)}{g(4)}[/tex]

[tex](f/g)(4)=\frac{24}{3}[/tex]

[tex](f/g)(4)=8[/tex]

Answer:

Answer:C) 8; The elephants’ rate in miles per hour

Step-by-step explanation:

First write the question as an equation that can be solved to give you a numerical answer.

[f(4)=4(4)+8] / [g(4)=(4)-1]

Then solve the equation.

24/3=8

Finally use background information to give you the context.

Since the problem gives you the function for distance and the function for time then it can be concluded that the context will be the elephants’ rate in miles per hour

Step-by-step explanation:

solve the missing side in the right triangle below​

Answers

Answer: the root of 145 so b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Use the Pythagorean theorem:

a^2 + b^2 = c^2

9^2 + 8^2 = c^2

81 + 64 = c^2

144 = c^2

[tex]\sqrt{144}[/tex] = c

Remember, C is always the hypotenuse, or the longest side. A and B can be either base.


The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a
radioactive isotope, how much will be left after 6 half-lives?
Use the calculator provided and round your answer to the nearest gram.

Answers

Answer:

2 grams

Step-by-step explanation:

a = 145 * (1/2)⁶

a = 2.265625

Rounded

2 grams

120 to 150 find the percentage of increase

Answers

Answer:

25%

Step-by-step explanation:

increase by = 150 - 120

=30

increase percent = 30/120 * 100%

=3000/120

=25 %

Answer:

25%

Step-by-step explanation:

Percentage increase=(new value-original value)/(original value) x 100%

Percentage increase=(150-120)/120 x 100%

Percentage increase=30/120 x 100%

Percentage increase=1/4 x 100%

Percentage increase=25%

the length of rope P is three times the length of rope Q. After 10cm of rope is cut from rope P and rope Q respectively, the length of rope P is four times the length of Q. Calculate the original length, in cm, of rope P before it is cut.

Answers

Answer:

150 cm

Step-by-step explanation:

The information in the question includes;

The length of rope P = 3 × The length of rope Q

The length of rope P - 10 cm  = 4 × (The length of rope Q - 10 cm)

Let p represent the original length of rope P and let q represent the original length of rope Q, we have;

p = 3·q...(1)

p - 10 = 4·(q - 10)...(2)

Expanding equation (2) gives;

p - 10 = 4·q - 40

∴ p = 4·q - 40 + 10 = 4·q - 50

p = 4·q - 50...(3)

Equating the values of p in equation (1) and equation (3) gives;

p = 3·q, and p = 4·q - 50, therefore, by the substitution property of equality, we have;

3·q = 4·q - 50

50 = 4·q - 3·q = q

q = 50

p = 3·q

∴ p = 3 × 50 = 150

The original length of P before it was cut, p = 150 cm.

Is it polynomial? In case of a polynomial, write its degree: t^2-1/2t+root 5

Answers

Answer:

Step-by-step explanation:

An algebraic expression with non.zero coefficients and variables having non-negative integers as exponents is called a polynomial.

Yes, It is a polynomial. The highest power of the variable is the degree of the polynomial.

So, Degree = 2

U are a noob lol lol

A timer is started as a ball is dropped from a certain height and its velocity measured. After 0 seconds, the ball is falling at 0 feet per second. After 2 seconds, the ball is falling at 64 feet. After 3 seconds, the ball is traveling at 96 feet and after 4 second the ball is traveling 128. Is this a proportional relationship?

Answers

Answer:

yes

because the descent of the ball is 32m per second

Step-by-step explanation:

To determine if the relationship is proportional, determine the descent of the ball per second

after 2 seconds = 64 / 2 = 32

after3 seconds = 96/3 = 32

after 4 seconds = 128 / 4 = 32

the relationship is proportional

ETECSORI
ANICTUUOSO
ATOALNN
NIDLROA
ERNLVITA
T
IATRO
ULINOOTAPP
ASEMLP​

Answers

Answer:

what-

Step-by-step explanation:

4.2kg of oranges are £8.76. How much does 2kg cost

Answers

Answer:

x = 4.17

Step-by-step explanation:

We can use a ratio to solve

4.2 k                  2 k

---------------- = ---------------

8.76                     x

Using cross products

4.2 * x = 2 * 8.76

4.2x =17.52

Divide by 4.2

x=4.17

Answer:

2kg cost £4.18

Step-by-step explanation:

4.2 kg of oranges cost £8.76

:. 1 kg of orange cost £8.76/4.2 = £2.09

2kg cost 2 × £2.09 = £4.18

If 52%= 2600 then what would 100% be?
If you will spam don't even click on it

Answers

Answer:

5000

Step-by-step explanation:

100/52=?

?x2600=5000

Answer:

x=5000

Step-by-step explanation:

100%=5000

branliest

Find the value of x if 4(6x - 9.5) = 46. Show your work!

Answers

[tex] \huge \mathrm{ \underline{Ànswér : }}[/tex]

let's solve for " x "

[tex]➢ \: \: 4(6x - 9.5) = 46[/tex]

[tex]➢ \: \: 6x - 9.5 = \dfrac{46}{4} [/tex]

[tex]➢ \: \: 6x - 9.5 = 11.5[/tex]

[tex]➢ \: \: 6x = 11.5 + 9.5[/tex]

[tex]➢ \: \: 6x = 21[/tex]

[tex]➢ \: \: x = \dfrac{21}{6} [/tex]

[tex]➢ \: \: x = 3.5[/tex]

[tex] \mathrm{✌TeeNForeveR✌}[/tex]

in the equation above c is a constantly . if n =5 , what is the value of c ?

Answers

Answer:

D

Step-by-step explanation:

Given

5 - [tex]\sqrt{c+5}[/tex] = 1 ( subtract 5 from both sides )

- [tex]\sqrt{c+5}[/tex] = - 4 ( multiply both sides by - 1 )

[tex]\sqrt{c+5}[/tex] = 4 ( square both sides )

c + 5 = 4² = 16 ( subtract 5 from both sides )

c = 11

The value of c is 11 when n = 5.To find the value of c in the equation [tex]n - \sqrt(c + 5) = 1[/tex] when n = 5, you can simply substitute n with 5 and then solve for c.

Given equation: [tex]n - \sqrt(c + 5) = 1[/tex]

Now, replace n with 5:

[tex]5 - \sqrt(c + 5) = 1[/tex]

Next, isolate the square root term by moving the constant term to the other side:

[tex]sqrt(c + 5) = 5 - 1\\sqrt(c + 5) = 4\\[/tex]

Now, square both sides of the equation to eliminate the square root:

[tex](c + 5) = 4^2\\c + 5 = 16[/tex]

Finally, isolate c:

c = 16 - 5

c = 11

So, the value of c is 11 when n = 5.

To know more about equation:

https://brainly.com/question/10724260

#SPJ2

Help and explain pleaseeeeeeee!!!!!

Answers

Answer:

The choose (a)

2x+1

Step-by-step explanation:

f(g(x)) = 2(x-3)+7

=2x-6+7

=2x+1

Answer:

2x+1

Step-by-step explanation:

We know that g(x)= x-3

So f(g(x))= f(x-3)  

We put it in the equation :

f(x-3)= 2(x-3) +7 = 2x-6+7 = 2x +1

Which congruence theorem can be used to prove ABDA - ABDC?
С
B
D
А
OHL
O SSA
O AAS
O SSS

Answers

Answer:

SSS

Step-by-step explanation:

Same Sides Subtract

The congruence theorem that can be used to prove that ΔBDA ≅ ΔBDC is: D. SSS

What is the SSS Congruence Theorem?

The SSS Congruence Theorem is a theorem that proves that if one triangle has three sides that are congruent to the three corresponding sides of a another triangle, both triangles are congruent.

Thus, ΔBDA and ΔBDC both have three pairs of congruent corresponding sides, namely:

BD ≅ BD BA ≅ BCDC ≅ DA

Therefore, the congruence theorem that can be used to prove that ΔBDA ≅ ΔBDC is: D. SSS

Learn more about the SSS Congruence Theorem on:

https://brainly.com/question/25425647

please help me with this maths equation .

Answers

the answer is D. scalene

Answer:

2 words

Step-by-step explanation:

Scalene (D)

Obtuse-angled (E)

Other Questions
On January 1, 2018, Pomegranate Company acquired 90% of the voting stock of Starfruit Company for $91,700,000 in cash. The fair value of the noncontrolling interest in Starfruit at the date of acquisition was $6,300,000. Starfruits book value was $13,000,000 at the date of acquisition. Starfruits assets and liabilities were reported on its books at values approximating fair value, except its plant and equipment (10-year life, straight-line) was overvalued by $25,000,000. Starfruit Company had previously unreported intangible assets, with a market value of $40,000,000 and 5-year life, straight-line, which were capitalized following GAAP.Additional informationPomegranate uses the complete equity method to account for its investment in Starfruit on its own books. Goodwill recognized in this acquisition was impaired by a total of $2,000,000 in 2018 and 2019, and by $500,000 in 2020. It is now December 31, 2020, the accounting year-end. Here is Starfruit Companys trial balance at December 31, 2020: Dr (Cr)Current assets $28,200,000Plant & equipment, net 188,000,000Intangibles 2,000,000Liabilities (180,000,000)Capital stock (1,000,000)Retained earnings, January 1(29,500,000)Acumulated other comprehensive income, January 1(500,000)Dividends 400,000Sales revenue (24,000,000)Cost of goods sold 10,000,000Operating expenses 6,500,000Other comprehensive income (100,000)On the 2020 consolidated income statement, the noncontrolling interest in net income of Starfruit is:________.a. $150,000b. $175,000c. $200,000d. $750,000 state two problems children in a single-parent family may face? samantha recieved $500 as a graduation present and decided to invest it in an account that is compounded continuously. how much will be in the account at the end of 5 years if the interest rate is 3% I need to draw also no files just type it in and tell me what to draw What is the output? answer = "Hi mom print(answer.lower()) I The given equation has been solved in the table.StepStatement1fr 9 = -13RO2231et 9 + 9 = -13+ 9233 = -43 233 .(-4)2.3256in which step was the addition property of equality applied? Which of the following statements is more descriptive of active data warehouses in contrast with traditional data warehouses?A) strategic decisions whose impacts are hard to measure.B) detailed data available for strategic use only.C) large numbers of users, including operational staffs.D) restrictive reporting with daily and weekly data currency. PLWASE HELP PLEASE PLEASE Mi primo es ______ de mi abuela. a)nieta b) ta c)nieto d)to Count the number of breaths you take in a minute and compare it with the number of times a fish opens and closes its mouth. Which of the two is faster? What could be the reason? are you smart enough to do that task try it who is the first person made the light The four essentials of guest service include courtesy, efficiency, safety, and variety courtesy, efficiency, safety, and show diversity, efficiency, productivity, and show proficiency, safety, show, and warmth PLEASE ANSWER ASAPexpand and simplify the following:a) (6+3)(6-3) b)(5-2)(2+5) Here is some information about a holiday.7 night holiday$340 per person8% discount if you book before 31 MarchOn 15 February, Naseem books this holiday for 2 people.Calculate the total cost of his holiday. Reasons why South African post office taking private courier companies to court A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: kmgcos=mgsinma, where g=9.80meter/second2, a=3.60meter/second2, =27.0, and m is not given. Which of the following represents a simplified expression for k?A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: , where , , , and is not given. Which of the following represents a simplified expression for ?tan agTo avoid making mistakes, the expression should not be simplified until the numerical values are substituted.gsinagcosThe single equation has two unknowns and cannot be solved with the information given. why should we sleep????? I really need this question someone please help On January 1, the total market value of the Tysseland Company was $60 million. During the year, the company plans to raise and invest $30 million in new projects. The firm's present market value capital structure, shown below, is considered to be optimal. Assume that there is no short-term debt.Debt $30,000,000Common equity30,000,000Total capital $60,000,000New bonds will have an 10% coupon rate, and they will be sold at par. Common stock is currently selling at $30 a share. The stockholders' required rate of return is estimated to be 12%, consisting of a dividend yield of 4% and an expected constant growth rate of 8%. (The next expected dividend is $1.20, so $1.20/$30 = 4%). The marginal corporate tax rate is 30%. In order to maintain the present capital structure, how much of the new investment must be financed by common equity?Assuming there is sufficient cash flow such that Tysseland can maintain its target capital structure without issuing additional shares of equity, what is its WACC?Suppose now that there is not enough internal cash flow and the firm must issue new shares of stock. Qualitatively speaking, what will happen to the WACC?I. rs and the WACC will increase due to the flotation costs of new equity.II. rs and the WACC will decrease due to the flotation costs of new equity.III. rs will increase and the WACC will decrease due to the flotation costs of new equity.IV. rs will decrease and the WACC will increase due to the flotation costs of new equity.V. rs and the WACC will not be affected by flotation costs of new equity. are these correct? read this slowly