What is the area of this quadrilateral?
4 ft
3 ft
10 ft
10 ft
31
4 ft

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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If Y is a subset of Z and Z is bounded in (X, d), then Y is bounded and the diameter of Y is less than the diameter of Z, and Assuming Y and Z are subsets of (X, d) and both are bounded, the diameter of the union of Y and Z, denoted as Y U Z, is less than the sum of the diameters of Y and Z. If Y is a subset of (X, d) and Y is bounded, the above statements still hold.

(a) If Y is a subset of Z and Z is bounded in (X, d), then Y is bounded and the diameter of Y is less than the diameter of Z.

To show that Y is bounded, we consider that Z is bounded, which means there exists a positive real number M such that for any two points z1 and z2 in Z, the distance between them, d(z1, z2), is less than or equal to M. Since Y is a subset of Z, every point in Y is also a point in Z. Therefore, the distance between any two points in Y, which is a subset of Z, is also less than or equal to M. Thus, Y is bounded.

Now, let's compare the diameters of Y and Z. The diameter of a set is defined as the supremum (least upper bound) of the distances between all pairs of points in the set. Since Y is a subset of Z, the distances between any two points in Y will also be distances between points in Z. Therefore, the diameter of Y cannot exceed the diameter of Z. In other words, diam Y < diam Z.

(b) Assuming Y and Z are subsets of (X, d) and both are bounded, we can show that the diameter of the union of Y and Z, denoted as Y U Z, is less than the sum of the diameters of Y and Z.

To prove this, let's consider two points p1 and p2 in Y U Z. These points can either both belong to Y or both belong to Z, or one point belongs to Y and the other belongs to Z. In any case, the distance between p1 and p2 will be either within Y or within Z, or it will be the sum of distances within Y and Z. In all scenarios, the distance between p1 and p2 will be less than or equal to the sum of the diameters of Y and Z.

Therefore, diam(Y U Z) < diam Y + diam Z.

(c) If Y is a subset of (X, d) and Y is bounded, the above statements still hold. The arguments presented in parts (a) and (b) remain valid regardless of the specific properties of Y as long as it is a subset of the metric space (X, d) and bounded.

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To prove that at any party of 31 people, there's always a person who knows an even number of others, we can use the pigeonhole principle.

The pigeonhole principle states that if we distribute more than "n" objects into "n" boxes, then at least one box must contain more than one object. In this case, the "objects" represent the people at the party, and the "boxes" represent the number of people each person knows.

Let's assume, for the sake of contradiction, that every person at the party knows an odd number of others. This means that each person has an odd number of acquaintances.

Now, let's consider the sum of the number of acquaintances for all 31 people. Since each person knows an odd number of others, the sum of odd numbers is also an odd number.

However, if we count the total number of acquaintances in a group, it must be even since each acquaintance involves two people. This creates a contradiction because we cannot have both an odd and an even sum for the total number of acquaintances.

Therefore, our assumption that every person knows an odd number of others must be false. Hence, there must be at least one person at the party who knows an even number of others.

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Answer:

1 is comutative 2 is distributive 3 is addition and 4 is multiplication

12 to 1

is the ratio :)

Answer:

Range: 75 Median: 58 1Q: 40 3Q: 75 Interquartile: 35

To show that the function Φ (Phi) is onto and one-to-one, we need to establish two properties:

Onto (Surjective):

For a function to be onto, every element in the range must have a preimage in the domain. In other words, for every y in the range, there must exist an x in the domain such that Φ(x) = y.

One-to-one (Injective):

For a function to be one-to-one, distinct elements in the domain must map to distinct elements in the range. In other words, if Φ(x₁) = Φ(x₂), then x₁ = x₂ Let's proceed to show both properties:

Onto (Surjective):

To show that Φ is onto, we need to demonstrate that for every y in the range of Φ, there exists an x in the domain such that Φ(x) = y.

Assuming that Φ(x) = y, we want to find the preimage x in the domain. However, you didn't provide the specific definition or context of the function Φ. Please provide the definition or specify the nature of the function Φ so that I can continue with the proof.

One-to-one (Injective):

To show that Φ is one-to-one, we need to prove that if Φ(x₁) = Φ(x₂), then x₁ = x₂ for any x₁ and x₂ in the domain.

Again, without the specific definition or context of the function Φ, I cannot proceed with the proof for the one-to-one property. Please provide the necessary information, and I'll be happy to help you further.

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Answer:

d = 1000 is the correct answer to that question

Answer:

d=4

Step-by-step explanation:

10^d=10000

Solve Exponent.

10d=10000

log(10d)=log(10000) (Take log of both sides)

d*(log(10))=log(10000)

d=

log(10000)

log(10)

d=4

Hope this helps :)

Answer:

C = 25.12

Step-by-step explanation:

C = 2πr

C = 2(3.14)(4)

C = 6.28(4)

C = 25.12

Answer: D.0

Step-by-step explanation:  i know am right, make me brainliest

Answer:

646.0 cm^3

Step-by-step explanation:

The volume of this cube with side length 8 cm is (8 cm)^3, or 512 cm^3.

The volume of the hemisphere (half sphere) is

V = (1/2)(4/3)(pi)(4 cm)^3                     (since half of the diameter, 8 cm,

V = (2/3)(3.14)(64 cm^3), or                   is the radius)

V = 133.86 cm^3, or approximately 133.9 cm^3.

The volume of the entire solid is (512 + 133.9) cm^3, or 646.0 cm^3

Answer:

It’s B

Step-by-step explanation:

I did this before and it’s B good luck

Answer: 62 hours per month

Step-by-step explanation:

Answer:

x = -1,3 I think

I put it into math day look it up

Answer:

The students rented 3 small cars and 6 large cars.

Step-by-step explanation:

Since a group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip, and each small car can hold 4 people and each large car can hold 6 people, and the students rented twice as many large cars as small cars, which altogether can hold 48 people, to determine the number of small cars rented, X, and the number of large cars rented, Y, the following calculation must be performed:

4X + 6Y = 48

4x4 + 6x8 = 16 + 48 = 64

4x3 + 6x6 = 12 + 36 = 48

Thus, the students rented 3 small cars and 6 large cars.

Answer:

C) 10

Step-by-step explanation:

lol

Answer:

I can't read it

Step-by-step explanation:

When asked to find the sum of two mixed numbers with different denominators, you should find a (C) common denominator before you add.

To add fractions with different denominators, it is necessary to find a common denominator for both fractions. Once the fractions have the same denominator, you can add or subtract the numerators while keeping the denominator unchanged. This allows for a meaningful addition of the fractions.

To find a common denominator, you need to determine the least common multiple (LCM) of the denominators. The LCM is the smallest multiple that both denominators can divide evenly into. Once you have the common denominator, you can convert each fraction to an equivalent fraction with that denominator and then perform the addition.

After finding the common denominator, you add the numerators of the fractions and keep the common denominator. This will give you the sum of the two mixed numbers with different denominators. The correct answer is C. find a common denominator.

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Answer:

x = 2

Step-by-step explanation:

The triangle is reflected across the circle meaning it should be the same on both sides.

Answer:

-3

Step-by-step explanation:

2·3-9

6-9 = -3

Total combinations = each item x each item:

3 breads x 5 cheese x 6 filling = 90 different combinations

The null hypothesis states that the average amount of coffee dispensed by the machine is equal to 7.8 ounces, while the alternative hypothesis states that the average amount is different from 7.8 ounces.

In this scenario, the null hypothesis (H0) is that the average amount of coffee dispensed by the machine is 7.8 ounces, while the alternative hypothesis (Ha) is that the average amount differs from 7.8 ounces. To test these hypotheses, the next step is to calculate the test statistic.

Using the given sample of 20 amounts, we can compute the mean of the sample, which is 7.816 ounces. The standard deviation of the sample is 0.044 ounces. With these values, we can calculate the t-test statistic.

The t-test statistic is calculated by subtracting the hypothesized value (7.8) from the sample mean (7.816) and dividing it by the standard deviation (0.044), multiplied by the square root of the sample size (20). The resulting t-value is approximately 1.818.

To determine the p-value associated with this t-value, we compare it to the t-distribution with n-1 degrees of freedom (19 degrees of freedom in this case). Using a statistical table or software, we find that the p-value is approximately 0.085.

Since the p-value (0.085) is greater than the significance level (α = 0.05), we fail to reject the null hypothesis. This means that there is insufficient evidence to conclude that the average amount of coffee dispensed by the machine is different from 7.8 ounces. Therefore, based on the p-value, the company cannot conclude that the average amount of coffee dispensed is significantly different from 7.8 ounces.

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Answer:

20.3%

Step-by-step explanation:

Hope that helps :)

Given:

The graph of a line segment.

The line segment AB translated by the following rule:

[tex](x,y)\to (x+4,y-3)[/tex]

To find:

The coordinates of the end points of the line segment A'B'.

Solution:

From the given figure, it is clear that the end points of the line segment AB are A(-2,-3) and B(4,-1).

We have,

[tex](x,y)\to (x+4,y-3)[/tex]

Using this rule, we get

[tex]A(-2,-3)\to A'(-2+4,-3-3)[/tex]

[tex]A(-2,-3)\to A'(2,-6)[/tex]

Similarly,

[tex]B(4,-1)\to B'(4+4,-1-3)[/tex]

[tex]B(4,-1)\to B'(8,-4)[/tex]

Therefore, the endpoint of the line segment A'B' are A'(2,-6) and B'(8,-4).

The given statement "When all the expected frequencies are equal the observed frequencies the calculated chi squared statistic equals zero." is true because chi-squared statistic will be zero in this case.

In a contingency table, the expected frequencies are calculated based on certain assumptions and can be different from the observed frequencies. The chi-squared statistic is used to determine whether there is a significant association between the variables in the contingency table.

When all the expected frequencies are equal to the observed frequencies, it means that there is a perfect match between the observed data and what would be expected under the assumption of independence.

In this case, the chi-squared statistic will be zero, indicating no discrepancy between the observed and expected frequencies.

This scenario is highly unlikely to occur in real-world data because observed frequencies typically deviate from the expected frequencies due to sampling variability or factors influencing the relationship between variables.

In most cases, the expected frequencies will differ from the observed frequencies, resulting in a non-zero chi-squared statistic, indicating a significant association or departure from independence between the variables.

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The Laplace transform is L{y(t)} = Y(s), [tex]L{e^t} = 1/(s-1), L{t*e^t} = -d/ds(1/(s-1))[/tex]

The inverse Laplace transform of [tex]1/(s^2+4)[/tex] is sin(2t)/2.

To solve the integral equation using convolution properties and Laplace transform, we can follow these steps:

Take the Laplace transform of both sides of the equation. Let Y(s) be the Laplace transform of y(t), and F(s) be the Laplace transform of f(t).

[tex]L{y(t)} = Y(s), L{e^t} = 1/(s-1), L{t*e^t} = -d/ds(1/(s-1))[/tex]

Apply the convolution property of Laplace transforms, which states that the Laplace transform of the convolution of two functions is equal to the product of their individual Laplace transforms.

Y(s) = F(s) * (1/(s-1)) - d/ds[F(s) * (1/(s-1))]

Substitute the given function [tex]F(s) = 1/(s^2+4)[/tex] into the equation.

[tex]Y(s) = (1/(s^2+4)) * (1/(s-1)) - d/ds[(1/(s^2+4)) * (1/(s-1))][/tex]

Simplify and find the inverse Laplace transform of Y(s) to obtain y(t).

Without the exact form of F(s), it is difficult to provide the specific calculations. However, based on the given answers, it seems that the correct answer is option B: [tex]y(t) = e^t - 1.[/tex]

For the second question, to find the inverse Laplace transform of [tex]1/(s^2+4)^2,[/tex] we can use the convolution theorem. The convolution theorem states that the inverse Laplace transform of the product of two Laplace transforms is equal to the convolution of their inverse Laplace transforms.

[tex]1/(s^2+4)^2 = L^{-1}{L{sin(2t)}/16 * L{2t*cos(2t)}/16}[/tex]

The inverse Laplace transform of [tex]1/(s^2+4) is sin(2t)/2.[/tex] The inverse Laplace transform of 1/s is 1.

Therefore, the inverse Laplace transform of [tex]1/(s^2+4)^2 is (1/16) * (sin(2t)/2 * 1) = sin(2t)/32.[/tex]

Based on the given answers, the correct answer is indeed option 3: sin(2t) - 2t*cos(2t)/16.

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Thus, h is not continuous on an uncountably infinite set.

(a) The function h(x) is defined as: h(x) = 1 if x is an element of the set C h(x) = 0 if x is not an element of the set C. The function h has discontinuities at each point of C and is continuous at every point of the complement of C.

Therefore, by the Lebesgue integrability criterion, h is integrable on (0, 1).

(b) Now we have to prove that h is integrable on (0,1). Let C be a countably infinite set, and let E = (0, 1) \ C be the complement of C in (0, 1). Since h is continuous on E, we know that h is integrable on E. Also, h is bounded on (0, 1), since it takes values in the closed interval [0, 1]. Therefore, by the Lebesgue integrability criterion, h is integrable on (0, 1)..The function h(x) is defined as: h(x) = 1 if x is an element of the set C h(x) = 0 if x is not an element of the set C. The function h has discontinuities at each point of C and is continuous at every point of the complement of C. Thus, h is not continuous on an uncountably infinite set.Since h is continuous on E, we know that h is integrable on E. Also, h is bounded on (0, 1), since it takes values in the closed interval [0, 1].

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Answer:

I guess we have the table:

x     f(x)

-4      7

-2      5

0       3

2       1

4      - 1

To find the slope of this, we need to select two different points (x1, y1) and (x2, y2) and use the relation:

slope = (y2 - y1)/(x2 - x1)

let´s use the first two:

(-4,7) and (-2, 5)

Slope = (5 - 7)/(-2 - (-4)) = -2/2 = -1

Now, if we want to be sure that this is a linear equation, we should do the same for other two pairs of points, now use the first and the third:

(-4, 7) and (0,3)

S = (3 - 7)/(0 -(-4)) = -4/4 = -1

Now, for the function g(x) we can see a constant line, that is parallel to the x-axis.

This means that the slope of this function is equal to zero.

This means that the slope of g(x) is bigger than the slope of f(x), because 0 > 1 i guess

Answer:

4w + 10

Step-by-step explanation:

If you have any questions feel free to ask

answer: 4w+10

explanation:: distribute;

= (4)(w)+(4)(3)+−2

= 4w+12+−2

combine like terms;

= 4w+12+−2

= (4w)+(12+−2)

= 4w+10