Suppose that 4 friends are given a vintage arcade game that they want to share. If they decide to divide their time, and they decide that they have 26 hours of available time to play in a week, what is each person's fair share of the playing time?

The relationship in the previous question involves the difference of squares pattern, which applies to polynomials of the form:

a^2 - b^2

where a and b are any real numbers.

If we replace a with x and b with 2, the equation would look like:

x^2 - 2^2 = (x + 2)(x - 2)

This means that any polynomial of the form x^2 - 4 can be factored using the difference of squares pattern.

As for creating our own replacement of a and b, let's say we replace a with y and b with 3. Then the equation would look like:

y^2 - 3^2 = (y + 3)(y - 3)

This means that any polynomial of the form y^2 - 9 can be factored using the difference of squares pattern.

The probability that a randomly selected person in the region is a woman in the 18-24 age range living alone is approximately 0.14 or 14%.

To find the probability that a randomly selected person in the region is a woman in the 18-24 age range living alone, we need to look at the intersection of the "Female" row and the "0-24" age column in the table.

The probability of selecting a woman in the 18-24 age range living alone is:

P(woman, 18-24, living alone) = (Number of women in the 18-24 age range living alone) / (Total number of people living alone)

From the table, we can see that the number of women in the 18-24 age range living alone is 20.9. The total number of people living alone is 153.6.

P(woman, 18-24, living alone) = 20.9 / 153.6

P(woman, 18-24, living alone) = 0.1362 or approximately 0.14

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The complete question:

The table shows the​ distribution, by age and​ gender, of the million people in a certain region who live alone. Use the data in the table to find the probability that a randomly selected person in the region is a woman in the 1824 age range living alone. Age |0-24|25-49|50+ |Total

Male|21.9|25.3 |28.6|75.8

Fem |20.9|26.1 |30.8|77.8

Tot |42.8|51.4 |59.4|153.6

Answer:

√(6 + 9 +12) = √27 = 3√3

√(-6 + 9 + 12) = √15 = √3√5

√(6 - 9 + 12) = √9 = 3

√(6 + 9 - 12) = √3

(1/4)(3√3)(√3√5)(3)(√3)

= (1/4)(27√3)(√5) = (27√15)/4 = 26.1

Answer:correct answer is 26.1

Step-by-step explanation:

Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:

A = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter, which is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, the side lengths are a = 6, b = 9, and c = 12. Therefore, the semiperimeter is:

s = (6 + 9 + 12) / 2 = 27 / 2

Using Heron's formula, we can now calculate the area of the triangle:

Answer:

The given equation is:

det [a 10 e b d 0] = [2 10 3 6 -1 0]

The determinant of a 3x3 matrix is calculated as follows:

|a b c|

|d e f| = a(ei - fh) - b(di - fg) + c(dh - eg)

Applying this formula to the given matrix, we get:

det [a 10 e b d 0] = a(d0 - b-1) - 10(ed - b0) + e(10*-1 - d*3)

= ab + 10b - 10ed - 3e

Substituting the given values, we get:

ab + 10b - 10ed - 3e = 2(6-0) - 10(3-(-1)) + 3(10-(-1))

ab + 10b - 10ed - 3e = 12 + 40 + 33

ab + 10b - 10ed - 3e = 85

We can simplify this equation by factoring out b and e:

b(a + 10) - e(10d + 3) = 85 - 10b

We can solve for a, d, and e by setting up a system of equations using the given values of the determinant:

ab + 10b - 10ed - 3e = 85

From this equation, we can solve for b:

b(a + 10) - e(10d + 3) = 85 - 10b

Substituting the value of b from the determinant equation, we get:

(a+10)(-1) - e(10d+3) = -8.5

Simplifying, we get:

-a - 10e - 3.3d = -8.5 ...(1)

Also, from the determinant equation, we have:

6a + 10d + 3e = 29

Solving for e in terms of a and d, we get:

e = (29 - 6a - 10d)/3 ...(2)

Substituting equation (2) into equation (1), we get:

-a - 10[(29 - 6a - 10d)/3] - 3.3d = -8.5

Simplifying and multiplying both sides by -3, we get:

3a + 20d - 29e = 25.5

Substituting equation (2) into this equation, we get:

3a + 20d - 29[(29 - 6a - 10d)/3] = 25.5

Simplifying, we get:

a + 6d - 29 = 1.5

a + 6d = 30.5

We have two equations in two variables:

-a - 10e - 3.3d = -8.5

a + 6d = 30.5

Solving for a and d using any method (substitution, elimination, etc.), we get:

a = 7

d = 4

Substituting these values into equation (2), we get:

e = (29 - 6a - 10d)/3 = (29 - 6(7) - 10(4))/3 = -3

Therefore, a = 7, d = 4, and e = -3.

Step-by-step explanation:

Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

Answer: - None of the above.

Step-by-step explanation:

The median is the middle value of the data set when arranged in order. In this case, we have an even number of values, so we need to take the average of the middle two values to find the median. The middle two values are 80 and 85. Therefore, the median student score is:  (80 + 85) / 2 = 82.5

The closest answer choice to this value is C. 85, but it is not the correct answer. Therefore, the correct answer is none of the above.

The graph shown corresponds to someone who makes: C. $20 an hour.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 20/1 = 40/2 = 60/3 = 80/4

Constant of proportionality, k = 20.

Therefore, the required linear equation or function is given by;

y = kx

y = 20x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The return on equity (ROE) for a project financed with 100% equity or 50% equity and 50% debt, given different levels of earnings before interest and taxes (EBIT) are 20.3%, -5.4%, 36.2% and  -20.3% respectively. So, the correct answers are A), B), A) and A). if Galaxy Corp. proceeds with a recapitalization then  Basic earning power (BEP), Return on assets (ROA), Net income are likely to increase. The correct option is A), B) and E).

ROE = EBIT*(1 - T)/Total Equity

Where T is the tax rate and Total Equity is the amount of equity used to finance the project.

If the EBIT is $145,000, then

ROE = $145,000*(1 - 0.30)/$500,000 = 20.3%

Therefore, the answer is 20.3%. So, the correct answer is A).

If the EBIT is -$45,000, then

ROE = -$45,000*(1 - 0.30)/$500,000 = -5.4%

Therefore, the answer is -5.4%. So, the correct answer is B).

If the project is financed with 50% equity and 50% debt at an interest rate of 11%, then the cost of equity can be calculated as follows

Cost of Equity = EBIT*(1 - T)/Total Equity

Cost of Debt = Interest Rate*(1 - T)

Weighted Average Cost of Capital (WACC) = Cost of Equity*(Equity/Total Capital) + Cost of Debt*(Debt/Total Capital)

ROE = EBIT*(1 - T)/Total Equity

ROE = [$145,000*(1 - 0.30)/($500,0000.50)] + [$145,000(1 - 0.30)0.50/($500,0000.50)*(1 - 0.11)]

ROE = 36.2%

Therefore, the answer is 36.2%. So, the correct answer is A).

If the project is financed with 50% equity and 50% debt at an interest rate of 11%, and the EBIT is -$45,000, then

ROE = -$45,000*(1 - 0.30)/($500,0000.50) + [-$45,000(1 - 0.30)0.50/($500,0000.50)*(1 - 0.11)]

ROE = -20.3%

Therefore, the answer is -20.3%. So, the correct answer is A).

If Galaxy Corp. proceeds with the recapitalization, the cost of debt is likely to increase since the firm is issuing new long-term debt. Therefore, the cost of debt (rdrd) will increase.

However, the basic earning power (BEP) and return on assets (ROA) are likely to increase since the firm will have a higher proportion of debt in its capital structure, which will increase the financial leverage of the firm.

As a result, the net income of the firm may also increase. The cost of equity (rsrs) may or may not change depending on how the market perceives the increased financial risk associated with the higher debt level.

Therefore, the items that are likely to increase are Basic earning power (BEP), Return on assets (ROA), Net income. The correct answer is A), B) and E).

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--The given question is incomplete, the complete question is given

" Universal Exports Inc. is considering a project that will require $500,000 in assets. The project will be financed with 100% equity. The company faces a tax rate of 30%. What will be the ROE (return on equity) for this project if it produces an EBIT (earnings before interest and taxes) of $145,000?

20.3%

22.3%

13.2%

14.2%

Determine what the project’s ROE will be if its EBIT is –$45,000. When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.

-7.6%

-5.4%

-6.3%

-5.7%

Universal Exports Inc. is also considering financing the project with 50% equity and 50% debt. The interest rate on the company’s debt will be 11%. What will be the project’s ROE if it produces an EBIT of $145,000?

36.2%

32.9%

24.7%

26.3%

What will be the project’s ROE if it produces an EBIT of –$45,000 and it finances 50% of the project with equity and 50% with debt? When calculating the tax effects, assume that Universal Exports Inc. as a whole will have a large, positive income this year.

-20.3%

-19.3%

-21.3%

-26.4%

Galaxy Corp. currently is financed with 10% debt and 90% equity. However, its CFO has proposed that the firm issue new long-term debt and repurchase some of the firm’s common stock. Its advisers believe that the long-term debt would require a before-tax yield of 10%, while the firm’s basic earning power is 14%. The firm’s operating income and total assets will not be affected. The CFO has told the rest of the management team that he believes this move will increase the firm’s stock price. If Galaxy Corp. proceeds with the recapitalization, which of the following items are also likely to increase? Check all that apply.

Basic earning power (BEP)

Return on assets (ROA)

Cost of debt (rdrd)

Cost of equity (rsrs)

Net income"--

Where the information relating to the circle and its diameter are given, the equation of the circle would be: "(x  5)²  + y2 = 81" (Option B)

The above is determined by the standard form equation of a circle which is:

(x- h) ² + (y - k)² = r²

Here,

(h, k)  is the center of the circle and r   is the radius

In this case, the center is (-5 , 0) and the diameter is 18, so the radius is half the diameter, whic is 18/ 2 = 9

So making the required substitutions, the expression becomes:

(x-(-5))² + (y-(0))² = 9²

Which becomes

(x  5)²  + y2 = 81

Thus, it is correct to state that Option B is the equation of the circle.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The center of a circle is at (-5, 0), and the diameter of the circle is 18. Which of the following is the equation of the circle?

A. (x  5)²  + y = 9

B. (x  5)²  + y2 = 81

C. (x  5)²  + y2 = 9

D. (x  5)²  + y2  81

17. 15 degrees

18. ABC

19. 5.88

20. 11.59

let me know if you'd like an explanation

By the principle of mathematical induction, the statement holds for all positive integers n.

Using mathematical induction:

Base case:

For n=1, results into:

2 = 2^2 + 1 - 2

which is true.

Inductive step:

For some positive integer k, we have:

2+4+8+...+2^k = 2^(k+1) + 1 - 2

This implies the statement for n=k+1, i.e.,

2+4+8+...+2^k+2^(k+1) = 2^(k+2) + 1 - 2

From the left-hand side of the equation, we can rewrite it as:

2+4+8+...+2^k+2^(k+1) = (2+4+8+...+2^k) + 2^(k+1)

Applying the induction hypothesis, substitute the expression for 2+4+8+...+2^k:

2+4+8+...+2^k+2^(k+1) = (2^(k+1) + 1 - 2) + 2^(k+1)

Simplify:

2+4+8+...+2^k+2^(k+1) = 2^(k+2) - 1

Using the formula for the sum of a geometric series to simplify the right-hand side of the original statement:

2^(k+2) + 1 - 2 = 2^(k+2) - 1

Thus, the statement holds for n=k+1, supposing it holds for n=k. By the principle of mathematical induction, the statement holds for all positive integers n.

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Answer:

The equation Qd = 50 - 4Px + 0.5I + 10Py - 2Pz represents the demand function for a certain good X, where Qd is the quantity demanded, Px is the price of X, I is the consumer's income, Py is the price of another good Y, and Pz is the price of another good Z.

To solve for the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied. However, without information on the supply function or market conditions, we cannot find the equilibrium price and quantity.

We can use the demand equation to determine the effect of changes in the independent variables on the quantity demanded for the good. For example, an increase in the price of X (Px) would lead to a decrease in the quantity demanded (Qd), while an increase in the price of Y (Py) or a decrease in the price of Z (Pz) would lead to an increase in the quantity demanded (Qd). An increase in income (I) would also lead to an increase in the quantity demanded (Qd).

Note that it is important to understand the context and assumptions underlying the demand function in order to make accurate economic predictions or decisions based on it.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Select the smaller fraction. 1/10 or 1/2

1/10 = 1 : 10 = 0.1

1/2 = 1 : 2 = 0.5

so your answer is 1/10

As per the given details, the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

To rewrite the equation y+5=5(x-4) in Ax+By=C form, we need to simplify and rearrange the equation to isolate y on one side:

y + 5 = 5(x - 4)

y + 5 = 5x - 20 (Distribute 5 on the right side)

y = 5x - 20 - 5 (Subtract 5 from both sides)

y = 5x - 25

Now the equation is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. To rewrite it in Ax + By = C form, we need to rearrange the terms to get the x and y terms on the left side and a constant on the right side:

y = 5x - 25

-5x + y = -25

So the equation in Ax + By = C form is -5x + y = -25, where A = -5, B = 1, and C = -25.

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The equation with the following y-intercepts are matched

a) c ⁢ x + b ⁢ y = a: (0, a/b)

b) c ⁢ x + a ⁢ y = b: (0, b/a)

c) b ⁢ x + a ⁢ y = c: (0, c/a)

d) a ⁢ x + b ⁢ y = c: (0, c/b)

Given data ,

Let the set of equations be represented by

c ⁢ x + b ⁢ y = a

c ⁢ x + a ⁢ y = b

b ⁢ x + a ⁢ y = c

a ⁢ x + b ⁢ y = c

Now , the y-intercept of the equation is when the value of x = 0

So , when x = 0

The y intercepts of the equation are

c ⁢ x + b ⁢ y = a: (0, a/b)

c ⁢ x + a ⁢ y = b: (0, b/a)

b ⁢ x + a ⁢ y = c: (0, c/a)

a ⁢ x + b ⁢ y = c: (0, c/b)

Hence , the equations are solved

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Answer: 9

Step-by-step explanation: volume is l x w x h, so 9 x 9 x height = 729

9 x 9 = 81, so 81 x height = 729

by dividing 729 / 81, you get 9

Answer: The answer is H=9.

The reason of this is because the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

Hence,

We can see that thats the answer because volume is l x w x h, so 9 x 9 x height = 7299 x 9 = 81, so 81 x height = 729by divide 729 / 81, you get 9

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Step-by-step explanation: Please give Brainliest.

Hope this helps!!!!

I can answer more questions if you want.

The breadth and error margin of the confidence interval will rise when the confidence level is raised from 95% to 98%.

We are more certain that the genuine population mean falls inside the interval if the confidence level is larger. The range of feasible values for the population means will be broader since we need to widen the interval in order to reach this higher degree of confidence.

Since the margin of error equals half of the interval's breadth, it is directly proportional to the interval's width. The margin of error will therefore expand as the confidence level does as well.

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_5(x-7)=2\implies 5^{\log_5(x-7)}=5^2\implies x-7=5^2 \\\\\\ x-7=25\implies x=32[/tex]

Answer:

This statement means that subgroups divide a larger group into smaller groups, and each of these smaller groups has the same number of things in it. For example, if there are 12 people in a group, and they form subgroups of 3 people each in a group, there will be 4 groups total, and each individual subgroup will have 3 people in it.

The essay, "I, Pencil," illustrates that production of an ordinary wood pencil used for writing d. involves the cooperative efforts of millions of people, whose actions are directed through markets.

I, Pencil, an essay by Leonard Read portrays that the manufacture of a common wood pencil utilized for writing necessitates the collective efforts of millions of human beings whose activities are strictly regulated through markets.

The paper conveys that though an ordinary pencil looks like such a straightforward item, it is actually created from a complex system of people, procedures, and materials from far and wide. From timber harvesters who procure the wood, to the miners who take graphite out from the ground, to the employees in manufacturing plants who produce the finished article, the lead holder necessitates the orderly collaboration of multiple individuals and enterprises.

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The function that can be used to determine the amount of money is f(x) = 40 * (1.05)^x

From the question, we have the following parameters that can be used in our computation:

Principal = 40

Rate = 5% annually

Time = x

The function that can be used to determine the amount of money is represented as

f(x) = P * (1 + r)^x

Substitute the known values in the above equation, so, we have the following representation

f(x) = 40 * (1 + 5%)^x

Evaluate

f(x) = 40 * (1.05)^x

Hence, the function is f(x) = 40 * (1.05)^x

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The division of the given algebraic expression is:  (x + 4)/2x

The division algorithm for polynomials says, if p(x) and g(x) are the two polynomials, where g(x) ≠ 0, we can write the division of polynomials as: p(x) = q(x) × g(x) + r(x).

Where:

p(x) is the dividend.

q(x) is the quotient.

We want to solve:

[(x + 4)/x²] ÷ 2/x

Thus, we can simplify to:

[(x + 4)/x²]  * x/2

= (x + 4)/2x

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Answer: 54

Step-by-step explanation:

Start from the middle of the equation and work your way out.

First find g(3) :

g(3) = 3+7 = 10

Then plug g(3) into the f equation:

f(g(3)) = 5(10) + 4 = 54