Suppose x’s represent solutions and y’s represent problems. S(x, y) means "x is a solution for
problem y". Explain, in English, what each of these statements is saying.

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 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:

its 1 4/5  or 19/15

they are both the same

Step-by-step explanation:

so first you need to find the same common factor

A-10/15=9/15

then add 10/15 and 9/15 to find a

19/15-10/15=9/15

or

1 4/15-2/3=3/5

yw :)

12 to 1

is the ratio :)

Answer:

Look below.

Step-by-step explanation:

45. B

46. D

47. B

Answer:

45.A   46. Bike A    47.C

Step-by-step explanation:

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:

20.3%

Step-by-step explanation:

Hope that helps :)

Answer:

(A) seems to have the least amount of slope with a slope of -6, compred to all, its the least one.

Step-by-step explanation:

Follow slope formula

(y2-y1) / (x2-x1)

Or calculate using rise over run method

Answer:

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

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

The probability of P(X ≤ 2) is  0.0135

We have the information available from the question:

Binomial variable is X

the value of n = 5

and, the value of p = 0.4

We are given to compute the probability P(X [tex]\leq[/tex] 2) and round the answer to five decimal places.

The binomial distribution formula is given by:

[tex]P(X)=nCx(p)^x(1-q)^n^-^x[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)!x!}[/tex]

We have to find the probability:

P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)

P(X = 1) = [tex]5C1(0.4)^1(1-0.4)^5^-^1[/tex] = 0.0026

P(X= 2) =[tex]5C2(0.4)^2(1-0.4)^5^-^2[/tex] = 0.0109

P(X [tex]\leq[/tex] 2) = P(X=1) + P(X=2)

P(X [tex]\leq[/tex] 2) = 0.0026 + 0.0109

P(X [tex]\leq[/tex] 2) =  0.0135

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This question seems extremely odd to me. I don't really even understand what's being asked.

As far as exponential functions go, it's missing an exponent for one. The dependent variable is missing. This essentially saying f(x) = -4 or y = -4. Which is fine, but is definitely not an exponential function and in a very odd and incomplete form to begin with.

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:

400 inches

Step-by-step explanation:

Area of all sides and add them

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:

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

Answer:

infinity

Step-by-step explanation:

Answer:

C = 25.12

Step-by-step explanation:

C = 2πr

C = 2(3.14)(4)

C = 6.28(4)

C = 25.12

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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Answer : 6 fence posts. The best way to demonstrate the answer to students is to use the formula

Explanation: To install a 15-metre long fence, the posts are 3 metres apart, how many fence posts will you need?                         The best way to demonstrate the answer to students is to use the formula:                                                                                        Total number of posts = (Length of fence ÷ Distance between posts) + 1

Where;Length of the fence = 15 metres, Distance between posts = 3 metres

Total number of posts = (15 ÷ 3) + 1                                                                                                                                             Total number of posts = 5 + 1 = 6                                                                                                                                                                        Therefore, you will need 6 fence posts.

The best way to demonstrate the answer to students is to use the formula:      Total number of posts = (Length of fence ÷ Distance between posts) + 1

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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).

Answer: x = 13

angel bge and angle agf are vertical meaning they’re equivalent

77 + 90 + x = 180 (180 because all of them added together are supplementary)

167 + x = 180

x = 13

Answer:

Step-by-step explanation:

X=13

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:

x = 2

Step-by-step explanation:

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

Answer:

its not that i got it wrong

Step-by-step explanation:

Answer:

C) 10

Step-by-step explanation:

lol

Answer:

postitive

Step-by-step explanation:

|-a| = a, a>0

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: 70

Step-by-step explanation: if you look at it hard enough they both look the same, this is called a vertical angle, I'm down for more questions lol. you keep on getting on my fyp