Find the surface area of the prism

Length=6
Width=3
Height=12

The value of Milton Industries with leverage is $131.52 million.

Milton Industries expects free cash flows of $20 million each year.

Milton's corporate tax rate is 22%, and its unlevered cost of capital is 16%.

Milton also has outstanding debt of $26.48 million and it expects to maintain this level of debt permanently.

a. Value of Milton Industries without leverage: Formula to calculate the value of a firm without leverage is; VL = VU + (PV of Tax shield) Where, VL = Value of the firm with leverage VU = Value of the firm without leverage PV of Tax Shield = Present Value of Tax Shield Expected Free Cashflows of Milton Industries = FCF = $20 million

Corporate Tax rate = T = 22%Unlevered

Cost of Capital = Ku = 16%Debt of Milton Industries = D = $26.48 million

Weighted Average Cost of Capital = WACC = Ku (1 - T)PV of Tax Shield = D x T x (1 - T) = $6.52 million VL = VU + PV of Tax Shield VU = FCF / Ku = $125 million VL = $125 + $6.52 = $131.52 million

b. Value of Milton Industries with leverage: VL = VU + PV of Tax Shield PV of Tax Shield = D x T x (1 - T) = $6.52 million VL = VU + PV of Tax Shield VU = FCF / Ku = $125 million VL = VU + PV of Tax Shield = $125 + $6.52 = $131.52 million. Therefore, The value of Milton Industries without leverage is $125 million. The value of Milton Industries with leverage is $131.52 million.

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Answer:

Step-by-step explanation:

We know that:

Use the given to find the missing function:

Answer:

\({ \rm{f(x) = 4 - {x}^{2} }}\)

\({ \rm{(f - g)(x) = - {x}^{2} + x + 2}}\)

- From functions;

\({ \boxed{ \tt{(f - g)(x) = f(x) - g(x)}}} \\ \\ { \rm{ - {x}^{2} + x + 2 = (4 - {x}^{2} ) - g(x) }} \\ \\ { \rm{g(x) = (4 - {x}^{2}) + {x}^{2} - x - 2 }} \\ \\ { \boxed{ \rm{g(x) = 2 - x}}}\)

Answer:

Si x = 5, alors x + 3 = 5 + 3 = 8.

Si x = 3, alors 2x - 1 = 2(3) - 1 = 6 - 1 = 5.

Si x = -2, alors 3 + 5x = 3 + 5(-2) = 3 - 10 = -7.

Answer:

10971/20

Step-by-step explanation:

69 * 159/20

69/1 * 159/20

69 * 159 = 10971

1 * 20 = 20

So the answer is basically 10971/20.

Answer: 8

Step-by-step explanation:

let x = the number

(x + 2)*10 = 8x + 36

10x + 20 = 8x + 36

2x = 16

x = 8

Answer:

5

Step-by-step explanation:

3 squared + 4 squared = c squared

3 squared= 9   4 squared= 16

9+16=c squared

25=c squared

5= c

Answer:

102 beads will be used for each necklace.

Step-by-step explanation:

3,264/32=102

Value of the z-test statistic is 1.20.

To find the value of the z-test statistic, we need to calculate the sample proportion and the standard error of the proportion.

The sample proportion is:

p⁻ = 92/400 = 0.23

The standard error of the proportion is:

SE = √[(pq)/n] = √[(0.20.8)/400] = 0.025

where p = 0.2 and q = 0.8.

Now we can calculate the z-test statistic:

z = (p⁻ - p)/SE = (0.23 - 0.2)/0.025 = 1.2

Therefore, the value of the z-test statistic is 1.20.

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Answer:

A. 32 = 3x - 5

Step-by-step explanation:

2x-5

2x + x = 3x

3x - 5

32 - 5 = 27

27 divided by 3 = 9

This can be used to find the value of x.

Answer:

C) 32=6x-10

Step-by-step explanation:

As, a perimeter of a rectangle = 2 ( length + breath)

So, 32cm = 2 ( (2x - 5) + x) = 2(2x-5) + 2(x)

= 32cm = 4x - 10 + 2x = 6x - 10

= 32cn = 6x - 10

The standard deviation will stay the same as it is not affected by a change in a single measurement,

A standard deviation is a measure of how dispersed the data when compared to the mean.

In this case, the standard deviation will stay the same as it is not affected by a change in a single measurement. Therefore, the change will not affect the standard deviation of the set of student ages.

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Answer:

\(t=\frac{s-6}{n-x}\)

Step-by-step explanation:

\(nt+6-xt=s\)

\(\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\)

\(nt+6-xt-6=s-6\)

\(Simplify\)

\(nt-xt=s-6\)

\(nt-xt\)

\(=t\left(n-x\right)\)

\(t\left(n-x\right)=s-6\)

\(\frac{t\left(n-x\right)}{n-x}=\frac{s}{n-x}-\frac{6}{n-x};\quad \:x\ne \:n\)

\(t=\frac{s-6}{n-x}\)

Therefor the value of t after arrangement is t = (s-6)/(n-x)

What is Mathematical function ?

Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.

In other words the function represents the graph between x and y that is for each value of x there exist one value of y but here there is no restriction in values of y that is y can have infinity values.

Given equation is  nt+6-xt=s

Now solving for t by separately variables and constant :

 nt+6-xt=s

t(n-x) = s-6

t = (s-6)/(n-x)

Therefor the value of t after arrangement is t = (s-6)/(n-x)

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Anna uses 120 g of chocolate and 360 grams of margarine to needed to bake biscuits.

We have data as follows; To make 24 biscuits Anna uses following proportion of Ingredients;

80 g sugar

120 ml syrup

200 g oats

120 g margarine

40 g chocolate

Now We can analysis that anna uses 40 g chocolate to make 24 biscuits

So for 120 g of chocolate Anna can bake \( \frac{24(120)}{40}  \)

=  24 (3)

= 72 biscuits

∴ Anna can bake 72 biscuits if she uses 120 g of chocolate.

We want to find how many grams of margarine will she need to make 72 biscuits and this can be done as follows;

Ingredients for 24 biscuits require 120 g margarine

∴ For 72 biscuits anna require \( \frac{72(120)}{24}  \) g of margarine

= 3 (120)

= 360 g of margarine.

Hence 360 grams of margarine anna needed.

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Answer:

17 1/3 52/3

Step-by-step explanation:

3x+y=38

3x+2y=52

-y=14

y=-14

3x+-14=38

3x-14=38

3x=38+14

3x=52

3x/3=52/3

x=171\3

17 is a whole number then 1 divided by 3 . thus is x

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

Given that,

The function is f(x)= (x-5)³(x+2)²

We have to find at which root does the graph function touch the x-axis.

We know that,

Mathematical calculus' core component is functions. The unique forms of relationships are the functions. When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x.

Take the function

f(x) = (x-5)³(x+2)²

f(x) = 0 if a curve touches the x-axis.

⇒ (x - 5)³(x + 2)² = 0.

But if ab = 0

So, a=0 and b=0

⇒ (x - 5)³ = 0 and (x + 2)² = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x=5 and x=-2.

Therefore, The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.

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Answer: 492 miles

Step-by-step explanation:

The first thing to do in such a question is to find out the number of miles Violet can go on 1 gallon.

That figure is:

= 369 / 12

= 30.75 miles per gallon

With 16 gallons therefore, she can go:

= 16 * 30.75

= 492 miles

Answer:

Step-by-step explanation:

Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two. Notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). Dilations involve multiplication! Dilation with scale factor 2, multiply by 2

Answer:

Yea wut she said ._. above me...

Step-by-step explanation:

point B is located in quadrant II (option B)

Point A: (6, 3) = (x, y)

reflection of point A across the y axis:

The x coordinate will be negative and the y coordinate will remain the same

reflection of point A across the y axis = (-6, 3)

Attaching the graph showing the point after reflection:

Since point B is the reflection of point A.

Hence, point B is located in quadrant II (option B)

The correct answer is OD. Although the word "then" appears in the statement, it is not used as a logical connective. So the statement is not compound.

The statement "If Laura sells her quota, then Marie will be happy" is a single declarative sentence. It consists of a conditional clause ("If Laura sells her quota") and a consequent clause ("then Marie will be happy"). However, these two clauses are not independent statements that can stand alone. Instead, they are connected in a cause-and-effect relationship. The word "then" in this context is not functioning as a logical connective, but rather as an indicator of the consequent clause.

A compound statement is formed by combining two or more independent statements using logical connectives such as "and," "or," or "if...then." In the given statement, there is no logical connective joining two independent statements.

Therefore, the statement is not compound.

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Answer:

See below

Step-by-step explanation:

Mean: \(\frac{29+8+11+29+29+6+49}{7}=\frac{161}{7}=23\)

Median: \(6,8,11,\bold{29},29,29,49\)

Answer:

f(10) = 120

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = x² + 3x - 10

f(10) is x = 10

Step 2: Evaluate

Step-by-step explanation:

no calculator at hand ?

-1963 - x = -9512

-x = -9512 + 1963 = -7549

x = 7549

so, 7549 has to be subtracted.

Answer:

its c =0.48+12p..... i did the math on a piece of paper

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer: (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

The point estimate for the population proportion is 514 / 1012 = 0.507.

(b) Verify that the requirements for constructing a confidence interval about p are satisfied.

The sample is stated to be a simple random sample.

The value of n * p = 1012 * 0.507 = 514.7796 is greater than or equal to 10.

The value of n * (1 - p) = 1012 * (1 - 0.507) = 497.2204 is greater than or equal to 10.

The population proportion is less than or equal to 5% of the population size.

Therefore, the requirements for constructing a confidence interval are satisfied.

(c) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without.

The 95% confidence interval for the population proportion is 0.507 +/- 1.96 * sqrt((0.507 * (1 - 0.507)) / 1012) = 0.507 +/- 0.0245 = (0.4825, 0.5315).

We are 95% confident that the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.4825 and 0.5315.

(d) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?

It is possible that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval contains 60%. However, it is not likely because the confidence interval is relatively narrow and the point estimate is far from 60%.

(e) Use the results of part (c) to construct a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a necessity.

The 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is 1 - 0.5315 = 0.4685 to 1 - 0.4825 = 0.5175. Therefore, the 95% confidence interval for the population proportion of adults who believe that televisions are a necessity is (0.4685, 0.5175).

Step-by-step explanation:

Thus, the distance travelled  with one rotation of the tyre of bicycle is found as 31.4 in.

The circumference of a circle is its length. Either the circle's diameter or radius can be used to calculate the circumference. We refer to shapes consisting of straight lines as having a perimeter. The circumference of a circle is the designation given to its perimeter.

Given data:

diameter of bicycle d = 10 in.

radius r = 10/2 = 5 in

Distance in one rotation equals the circumference of circle say 'c'.;

c = 2πr

c = 2*3.14*5

c = 31.4 in

Thus, the distance travelled  with one rotation of the tyre of bicycle is found as 31.4 in.

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Answer:

The height of the tower is 310.6 ft

The height of the tower 310.6 ft if the angle of depression and elevation is given.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that  tower is located 327 feet from a building

A person from the second story measures an angle of elevation to the top of the tower as 32° and an angle of depression to the bottom of the tower as 18°.

We have to find the height of the tower.

By using angle of elevation we find the height.

327/sin 72 = x / sin18

343.8 = x/ sin 18

x=sin 18(343.8)

x= 106.25

Now 327/sin 58 = y/sin 32

385.59 = y/sin32

y=204.33

Height is 106.25+204.33 which is 310.6 ft.

Hence,  the height of the tower to the nearest tenth of a foot is 310.6 ft.

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Answer:

$234.25

Breakdown of calculations:

$256 × .15 (or 15%) = $38.40

$256 - $38.40 = $217.60 (cost of ticket after discount)

$217.60 × .0765 (or 7.65%) = $16.6464....round to $16.65

$217.60 + $16.65 = $234.25 final cost of train ticket including tax